mechanical and microstructural study of silicon …

MECHANICAL AND MICROSTRUCTURAL STUDY OF

SILICON CARBIDE AND PYROLYTIC CARBON

COATINGS IN TRISO FUEL PARTICLES

A thesis submitted to The University of Manchester for the degree of

Doctor of Philosophy

In the Faculty of Engineering and Physical Science

2012

Huixing Zhang

Material Science Centre School of Materials

List of Contents

2

List of Contents

List of Contents 2

Abstract 6

Declaration 7

Copyright Statement 8

Acknowledgement 9

List of Figures 10

List of Tables 17

CHAPTER 1 Introduction 19

11 TRI-Isotropic (TRISO) fuel particles 19

12 Failure mechanism 21

121 Traditional pressure vessel failure mode 21

122 Stress concentration mode 22

13 Goals of dissertation 24

14 References 26

CHAPTER 2 Literature Review 28

21 Introduction 28

22 Microstructure of silicon carbide 29

221 Atomic structure 29

222 Defects in SiC 31

2221 Stacking faults and dislocations 31

2222 Non-stoichiometric and point defects 36

23 Properties of silicon carbide 41

231 Youngrsquos modulus 41

232 Hardness 45

233 Fracture toughness 52

234 Fracture strength 55

235 Effect of thermal treatment on SiC 59

24 Microstructure and properties of pyrolytic carbon 60

241 Microstructure of pyrolytic carbon 61

242 Mechanical properties of pyrolytic carbon 65

List of Contents

3

2421 Youngrsquos modulus and hardness 65

2422 Deformation mechanism 67

2423 Effect of thermal treatment on properties of PyC 70

25 Summary 70

26 References 72

CHAPTER 3 Hardness and Youngrsquos Modulus of SiC Coatings Measured by

Indentation 83

31 Introduction 83

32 Experimental details 85

33 Results 88

331 Hardness and Youngrsquos modulus 88

332 Microstructure of low temperature FBCVD SiC 91

333 Deformation behaviour under the indentation 97

34 Discussion 100

341 Influence of porosity on Youngrsquos modulus 101

342 Mechanism for High hardness 102

343 Deformation mechanism under nano-indentation 104

35 Conclusions 105

36 References 107

CHAPTER 4 Vickers Indentation Fracture Toughness of SiC Coatings 112

41 Introduction 112


43 Results and discussion 117

431 VIF fracture toughness study 117

432 Influence of non-stoichiometries on the VIF fracture toughness 121

433 Microstructural analysis of fracture behaviour under the indenter 122

44 Conclusions 126

45 References 127

CHAPTER 5 Influence of Interfacial Roughness on Fracture Strength of SiC

Coatings 131

51 Introduction 131


List of Contents

4

521 Materials 132

522 Test method and analysis 133

523 Characterisation methods 135

53 Results and discussions 136

531 Fracture strength and dimensional effect 136

532 Observe and qualify the effect of interfacial roughness on fracture strength

140

533 Characterise and quantify the interfacial roughness 143

5331 Self-affine theory introduction and experimental setup 143

5332 Results of self-affine theory 144

534 Quantify the influence of interface roughness on fracture strength 146

54 Conclusions 149

55 References 150

CHAPTER 6 Effect of Thermal Treatment on Microstructure and Fracture

Strength of SiC Coatings 154

61 Introduction 154


63 Results 156

631 Fracture strength of SiC coatings 156

632 Change in morphologies 160

633 Evolution in microstructure 163

64 Discussion 167

641 Influence of interfacial roughness and pores on fracture strength 167

642 Mechanism of microstructural change 169

65 Conclusions 171

66 References 172

CHAPTER 7 Microstructure and Mechanical Properties of Pyrolytic Carbon

Coatings 175

71 Introduction 175


73 Results 178

731 Microstructure of PyC coatings 178

7311 Raman spectroscopy 178

7312 Domain sizes 181

List of Contents

5

7313 Evolution of crystallinity 182

732 Mechanical properties of PyC coatings 185

7321 Force-displacement curve 185

7322 Youngrsquos modulus and the mean pressure 187

74 Discussions 188

741 Disorders and their changes after thermal treatment 189

742 Hysteresis after indentation 191

743 Mechanical property of low density PyC coatings 192

744 Mechanical Property of high density PyC coatings 193

74 Conclusions 195

75 References 197

CHAPTER 8 Conclusions and Future Works 201

81 Conclusions 201

82 Suggestions for future work 203

Abstract

6

Abstract

Mechanical and Microstructural Study of Silicon carbide and Pyrolytic Carbon

Coatings in TRISO Fuel Particles

The University of Manchester

Huixing Zhang

Doctor of Philosophy in Materials Science

TRISO fuel particles have been developed as nuclear fuels used for a generation IV

nuclear reactor high temperature reactor Such particle consists of a fuel kernel

pyrolytic carbon (PyC) and silicon carbide (SiC) coatings This study has been carried

out to establish a relationship between mechanical properties and microstructures of

SiC coating and PyC coatings produced by fluidized bed chemical vapour deposition

Indentations were used to measure hardness Youngrsquos modulus and fracture behaviour

of SiC and PyC coatings Fracture strength of SiC coatings was measured by crush

test Microstructure of SiC and PyC was mainly characterised by transmission

scanning electron microscopy and Raman spectroscopy

For SiC coatings produced at 1300 ordmC Youngrsquos modulus is an exponential function of

relative density Hardness of SiC coatings is higher than the bulk SiC produced by

CVD and it is attributed to the high density of dislocations and their interactions The

deformation mechanism of SiC coatings under indentation is explained by presence of

defects such as grain boundaries and nano-pores The fracture of these coatings

beneath the Vickers indentation is the Palmqvist cracks and indentation fracture

toughness was in the range of 35-49 MPa m12

The stress-induced micro-cracks are

assumed to be the mechanism for the high indentation fracture toughness Different

hardness and fracture toughness in these SiC coatings are attributed to influences of

defects and grain morphology

Measurement of fracture strength was carried out on SiC coatings deposited at

1300-1500 ordmC Weibull modulus and fracture strength of the full shell are dominated

by the ratio of radius to thickness of coatings and decrease linearly with the increase

of this ratio The influence of SiCPyC interfacial roughness on fracture strength of

the SiC was quantified by self-affine theory The fracture strength decreases linearly

with the increase of the roughness ratio which is the long-wavelength roughness

characteristic After thermal treatment at 2000 ordmC fracture strength decreased in SiC

coatings due to the formation of pores which are results of diffusion of native defects

in as-deposited SiC coatings and the change of Weibull modulus is related to the size

and distribution of pores

For low density PyC coatings Youngrsquos modulus and the mean pressure increase with

the increase of the density however for high density PyC coatings they are

determined by interstitial defects The hysteresis deformation behaviour under

nano-indenation has been found be affected by density variation and thermal

treatment which is proposed to be due to the disorder structure in PyC coatings

Declaration

7

Declaration

No Portion of the work referred to in the thesis has been submitted in support of an

application for another degree or qualification of this or any other university or other

institute of learning

Copyright Statment

8

Copyright Statement

i The author of this thesis (including any appendices andor schedules to this thesis)

owns any copyright in it (the lsquolsquoCopyrightrsquorsquo) and she has given the University of

Manchester certain rights to use such Copyright including for administrative

purposes

ii Copies of this thesis either in full or in extracts and whether in hard or electronic

copy may be made only in accordance with the Copyright Desings and Patents Act

1988 (as amended) and regulations issued under it or where appropriate in

accordance with licensing agreements which the University has from time to time

This page must form part of any such copies made

iii The ownership of certain Copyright patens designs trade marks and other

intellectual property (the lsquolsquoIntellectual Property Rightsrsquorsquo) and any reproductions of

copyright works in the thesis for example graphs and tables (lsquolsquoReproductionsrsquorsquo)

which may be described in this thesis may not be owned by the author and may be

owned by third parties Such intellectual Properties Rights and Reproductions cannot

and must not be made available for use without the prior written permission of the

owner(s) of the relevant Intellectual Property Rights andor Reproductions

iv Further information on the conditions under which disclosure publication and

commercialization of this thesis the Copyright and any Intellectual Property andor

Reproductions described in it may take place is available in the University IP policy

(see httpwwwcampusmanchesteracukmedialibrarypoliciesintellectual-property

Pdf) in any relevant Thesis restriction declarations deposited in the University

Library The University Libraryrsquos regulations (see

httpwwwmanchesteracuklibraryaboutusregulations) and in the Universityrsquos

policy on presentation of Thesis

Acknowledgement

9

Acknowledgement

I will always be appreciative to Professor Ping Xiao for his support and guidance

during this project period and his enthusiasm for work and positive attitude towards

life inspired me I am thankful for what he shared about his own experience doing

research which impressed me and motivated me to make improvement

I would like to thank in particular Dr Eddie Loacutepez-Honorato for his patient guidance

on my experiments and valuable advices on my project His caution on preparing

delicate specimen infected me and helped me through my project He was always

there listening my ideas and discussing with me and he has set an example for being

a good researcher

I give my thanks to all the members in ceramic coating group old and new and I

treasure and appreciate this chance working with you

I would like to give my great gratitude to Dr Alan Harvey for his kind help on

transmission electron microscopy Mr Andrew Forest and Mr Kenneth Gyves on

nano- and micro-indentation Mr Andrew Zadoroshnyj on Raman spectroscopy Dr

Ali Gholinia and Dr Ferridon Azough on TEM sample preparation Dr Judith

Shackleton and Mr Gary Harrison on X-ray diffraction Mr Christopher Wilkins and

Mr Michael Faulkner on scanning electron microscopy and Mr Stuart Mouse on

tensile tests

I am grateful to my dear friends Yola David and Dean and you make my life more

colourful and interesting I would like to thank my beloved parents and brother for

your love care and support and you are great examples of hard work and kindness

My thanks also go to the ORS scheme the CSC grant and the F-BRIDGE for their

financial support during my PhD studies

List of Figures

10

List of Figures

CHAPTER 1 Introduction

Fig 11 Fuel pellet with TRISO coated fuel particles embedded in a graphite block

matrix [5]

Fig 12 Behaviour of coated layers in fuel a particle [10]

Fig 13 A failed case of TRISO-coating observed from post-irradiation examination

[10]

CHAPTER 2 Literature Review

Fig 21 (a) Examples of the crystal structure of SiC polytypes 3C 4H 6H and 15R

[17] (b) calculated XRD patterns for perfect SiC polycrystalline structures redrawn

from Ref [18]

Fig 22 Stacking sequences for an ideal fcc structure (left panel) fcc with inner

stacking fault (middle panel) and fcc with external stacking fault (right panel) [24]

Fig 23 TEM images of the typical stacking faults of the SiC a) extrinsic stacking

faults in the (111) planes viewed along the [110] direction indicated by the arrows b)

and c) represent the difference in stacking fault width [34]

Fig 24 XRD pattern of SiC produced by fluidized bed chemical vapour deposition at

different deposition temperatures (the β represents stacking faults) [8]

Fig 25 Schematic images of dislocations and stacking faults in SiC (a) Showing a

perfect dislocation split into Shockley partials is still able to glide on the same glide

plane the stacking fault just moves along (b) Schematic of perfect dislocation

dissociated into two partial dislocations forming a stacking fault (c) Shockley partial

dislocation (stacking fault is indicated in the dashed rectangle the other partial

dislocation is on the left with b=a6[2-11]) ([101] projection) and (d) Frank partial

dislocations (lt110gt projection stacking faults (inserted extra layer) are indicated by

the dashed rectangle) [38]

Fig 26 The TEM images a) HRTEM image showing a Si crystallite embedded in a

matrix phase composed of SiC crystallites b) HRTEM image showing a

homogeneous distribution of the 3C-SiC crystallites c) HRTEM image of the diffuse

interphase region between the 3C-SiC and Si crystallites [35]

List of Figures

11

Fig 27 TEM images of SiC a) is a dark field TEM image showing a crystal SiC b)

is a dark field image showing Si crystallites as bright points in a dark background

[48]

Fig 28 Raman spectroscopy of the Carborundum fibre (a) average spectra of this

carbon and (b) carbon rich fibre (about 04 of extra carbon) [49]

Fig 29 Schematic image of the possible representational surface for Youngrsquos

modulus in SiC crystal with Z gt 1 [3]

Fig 210 The effect of porosity on elastic modulus of SiC (Redrawn from Ref [1])

Fig 211 HRSEM image of indentation impression on single SiC crystal [70]

Fig 212 (a) force-loading curve of polycrystalline CVD SiC with micro meters grain

size of 5-10 microm and (b) deformation behaviour under nano-indentation[62]

Fig 213 Deformation mechanism of nanocrystalline SiC (competition between

crystallization and disordering with grain sizes (5-15 nm)) White atoms ordered in

the entire range up to critical point (yield of crystalline phase within the grains)

yellow atoms disordered in the entire range blue atoms changed from disordered to

ordered brown atoms changed from ordered to disordered [72]

Fig 214 (a) A typical load-displacement curve and (b) the deformation pattern of an

elastic-plastic sample during and after indentation [65]

Fig 215 A general scheme of a plastic indentation and system of cracks formed

under an indenter [81]

Fig 216 Schematic of different fracture strength tests (a) hemisphere bending of

inner surface of SiC shell [10] (b) inner pressurization and (c) cush test (diametrical

loading) [89]

Fig 217 (a) schematic and (b) TEM image showing the polyhedral growth features

in high density PyC (b) schematic and (d) TEM image showing the globular growth

features in low density PyC [15]

Fig 218 Schematic drawing of a crystallite (turbostratic carbon) with curved

graphene layers (a) [101] less ordered turbostratic carbon (b) [102]

Fig 219 HRTEM image showing half Frank loops and kink bands(a) and the

selected area electron diffraction pattern from the same sample (b) [103] the HRTEM

image showing low texture of pyrolytic carbon and highly distorted lattice planes(c)

and arc shape selected area electron diffraction pattern of pyrolytic carbon (d) [15]

List of Figures

12

Fig 220 Schematic representation of the change of Raman spectra on PyC with

changes in nanostructure (a-c) D signal produced by domain boundaries (c-e) D

signal dominated by the presence of five-member rings in the PyC structure [15]

Fig 221 First order Raman spectra of one of the various pyrocarbons [106]

Fig 222 The schematic figures showed the typical force-displacement curve under

indentation of carbon materials [110]

Fig 223 Loading of an irregular graphite grain in the stress field below a spherical

indenter [110]

Fig 224 Schematic of (a) incipient kink band comprised of two walls of dislocations

of opposite polarity (b) Same as (a) but after the formation of a pair of mobile

dislocation walls (c) Formation of two IKBrsquos under the indenter [105]

CHAPTER 3 Hardness and Youngrsquos Modulus of SiC coatings Measured by

Indentation

Fig 31 (a) SEM micrographs showing the polished cross-section (x-y plane) and (b)

polished external surface section (x-z plane) of TRISO fuel particles (c) Composition

of nearly stoichiometric FBCVD SiC coatings detected by Raman spectroscopy the

inset is the Raman result of bulk CVD SiC (Rohm amp Haas Ltd UK) (d) XRD results

of three SiC coatings

Fig 32 (a) Typical nanoindentation load-displacement curve for SiC coating at the

maximum indentation depth of 500 nm under a Berkovich indenter inserted is the

hardness curve (b) and (c) are the hardness and Youngrsquos modulus of three types of

coating samples and bulk CVD SiC (Rohm amp Haas Ltd UK) respectively

Fig 33 SEM images showing the microstructure for (a) and (b) etched S1 (SiC)

coating (c) and (d) etched S2 (SiC+C) SiC coating (e) and (f) etched S3 (SiC+Si)

SiC coating White arrows indicate the coating growth direction

Fig 34 Bright field TEM image of the S2 (SiC+C) coating shows the grain

interaction with each other and the arrow indicates grain growth direction

Fig 35 Bright field TEM images of three SiC based coatings (a) the S1 (SiC) with

stacking faults perpendicular to the growth direction (b) the S2 (SiC + C) showing the

laminar nanoporous layer (as indicated by the black overlaid line) (c) the S3 (SiC + Si)

with a wrinkled like defects layer (indicated by the black overlaid line)

Fig 36 An example of the crystal misorientation formed during SiC deposition (a)

List of Figures

13

BF-TEM and (b) DF-TEM

Fig 37 High resolution TEM images for three FBCVD SiC coatings (a) S1 (SiC) (b)

S2 (SiC+C) and (c) S3 (SiC+Si)

Fig 38 TEM Images showing the defects in S1 (SiC) coating (a) HRTEM image

with [110] zone axis (diffraction patter after FFT) (b) inverse FFT image shows high

density of Frank partial dislocations (b-vector of a3lt111gt) observed from the lt110gt

projection

Fig 39 Bright field TEM images of the deformed zone under a nano-indentation of a

S1 (SiC) coating (a) an overview of the deformation zone higher magnification

images of the zone marked as BCD in Fig 39 (a) are shown in (b) (c) and (d)

respectively Inset in (c) shows the micro cracks in the dashed square Left bottom

inset in (d) shows a high magnification of a shear crack while right upper inset in (d)

shows a high magnification of the dashed circle under the indenter tip

Fig 310 TEM bright field images show the mechanical reaction underneath the

indentation (a) and (b) S3 (SiC+Si) SiC coating (c) and (d) S2 (SiC+C) SiC coating

CHAPTER 4 Vickers Indentation Fracture Toughness of SiC coatings

Fig 41 Cross-section view (y-z plane) of Vickers indentation (indented on x-z plane)

(a) half-penny crack systems and a crossed-cracks would be seen on the top view of

the dashed line (b) Palmqvist crack (or radial) system redrawn according to

reference

Fig 42 Crack propagation mode under the Vickers diamond indenter on the polished

external surface of a SiC coating (a) indentation before polishing (b) image after

removal of indentation impression (c) image after removal of the plastic deformation

zone

Fig 43 Optical micrographs showing different crack lengths along the radial and

tangential directions for extra-Si SiC coatings

Fig 44 Bright field TEM images of the deformed zone under the indentation of the

S1 SiC coating (a) an overview of the deformation zone (similar as in Fig 39(a)) (b)

(c) and (d) are higher magnification images of the median crack initiation zone (circle

B) the median crack (circle C) and the median crack tip (circle D) respectively

Fig 45 Cross-sectional SEM image of stoichiometric SiC coating showing the grain

boundary (dark arrow) and laminar structure (while arrow)

List of Figures

14

Fig 46 Bright TEM images showing the grain morphology of SiC coatings (a)

extra-C SiC (b) extra-Si SiC


Coatings

Fig 51 Schematic of the modified crush test system for SiC half shell [5]

Fig 52 The calculated local fracture strength of SiC shells in the form of Weibull

distribution

Fig 53 The relationship between the modulus (y) derived from local fracture

strength and the ratio of outer radius to SiC thickness (x) circle is experiment dashed

line represents linear fit data with fitted equation y=945-022x

Fig 54 Weibull distribution of fracture strength for a full spherical shell for all the

SiC coatings

Fig 55 The relationship between the fracture strength for a full spherical shell (y)

and the ratio of outer radius to SiC thickness (x) circle is from experiment dashed

line is linear fit data with fitted equation y=1144-286x

Fig 56 SEM image of IPyC top surface on the top of which SiC was coated (a)

TEM image of an IPyCSiC coating interface (b) the inset is a higher magnification

TEM image showing the spherical shape of IPyC surface

Fig 57 Comparison of scanned and digitalized IPyCSiC interfacial roughness

profile (the measured flaw sizes are randomly given in the profile of each interface as

seen the information in blue) with the calculated critical flaw size according to the Eq

(1)

Fig 58 Log-log representation of the height-height correlation function ∆h

computed along the x axis for three representative samples The solid line represents

the linear regression of slops of three samples and the dashed short lines represent

saturation roughness

Fig 59 Roughness ratio (x) influence on local fracture strength (y) circle is from

experiment dashed line is linear fitted data with the equation y=2265-1396x

Fig 510 Influence of roughness ratio (x) on fracture strength for a full spherical shell

(y) circle is from experiment dashed line is linear fitted data with the equation

y=1351-1150x

List of Figures

15


Strength of SiC coatings

Fig 61 Weibull plots of local fracture strength (L

f ) before (black triangle) and after

(red circle) thermal treatment at 2000 ordmC Linear fitted Weibull modulus were given

black and red lines are before and after thermal treatment

Fig 62 Weibull modulus plots of fracture strength of the whole shell (F

f ) before

(black triangle) and after (red circle) thermal treatment

Fig 63 SEM images showing the change in microstructure after thermal treatment at

2000 ordmC for 1 hr (a) and (b) SiC1 before and after thermal treatment (c) and (d) SiC2

before and after thermal treatment (e) and (f) SiC3 before and after thermal treatment

(g) and (h) SiC4 before and after thermal treatment Dashed and solid arrows indicate

growth direction and pores respectively

Fig 64 The IPyCSiC interfacial morphology of coating SiC1 (a) SiC2 (b) SiC3 (c)

and SiC4 (d) as deposited (left in each figure) and thermal treated at 2000 degC (right in

each figure) The white arrow points towards to the interface irregularities (except for

thermal treated SiC4 coating (d)) black circle represents the pores in SiC coatings

Fig 65 XRD results of as-deposited SiC coatings and coatings after thermal treated

at 2000 degC in argon atmosphere (a) is SiC3 and could represent SiC1 and SiC2 inset

shows the peak shift of as-deposited (dash line) and after thermal treatment (solid

line) (b) is SiC4 and inset is the high angle diffraction peak after thermal treatment

showing splitting while it is a single peak in as-deposited coating

Fig 66 HRTEM showing the microstructure of SiC4 after thermal treatment arrows

indicate stacking faults and micro twins

Fig 67 Change of SiC before and after thermal treatment measured by Raman

spectroscopy carried out at the polished cross section of the coatings (a-d) are

specimen SiC1 SiC2 SiC3 and SiC4 coatings

Fig 68 (a) SEM image and (b) Raman spectroscopy show precipitates

microstructure on the out surface of SiC3 coating The Raman spectroscopy of out-off

surface precipitates are taken from site A and B shown in (a)

CHAPTER 7 Microstructure and Mechanical Properties of PyC Coatings

List of Figures

16

Fig 71 Raman spectroscopy of as-deposited high density PyC coating (C5 200

gcm3) was fitted into 4 bands (band positions of I and Drdquo were kept constant during

fitting to limit the uncertainty in spectral parameters) The green line represents the

difference between the calculated curve and the experimental curve

Fig 72 High density PyC sample C5 (200 gcm3) thermally treated at a range of

temperatures

Fig 73 Raman spectroscopies from low density PyC coatings (a) C7 (174 gcm3) (b)

C10 (141 gcm3) before and after thermal treatment at 1800 ordmC

Fig 74 Dark field TEM images of sample C5 (200 gcm3) (a) before and (b) after

thermal treatment at 1800 ordmC (c) is the bright field TEM image of the conical

structure after thermal treatment insets are the SAED images with aperture diameter

of 200 nm

Fig 75 HRTEM images of high density sample C1 (212 gcm3) (a) before and (b)

after thermal treatment at 1800 ordmC

Fig 76 Bright field TEM and HRTEM images from a low density PyC coating (C7

174 gcm3) (a) and (b) are as-deposited sample (c) and (d) are samples after thermal

treatment at 1800 ordmC the inset in (c) is the SAED result after thermal treatment

Fig 77 Force-displacement curves for PyC coatings of different density with the

maximum load of 60 mN and 100 mN the red curve is from sample C3 after thermal

treatment at 1800 ordmC The contact depth of hc derived from the power law function of

the unloading curve [24]

Fig 78 (a) Youngrsquos modulus and (b) the mean pressure of as-deposited PyC coatings

as functions of density

List of Tables

17

List of Tables


Table 21 The formation energy of stacking faults in SiC investigated by different

methods

Table 22 Calculated formation energies for native point defects in SiC (calculated in

stoichiometric cubic SiC) [23]

Table 23 Elastic tensors of 3C-SiC at room-temperature

Table 24 Vickers and nano-indentation hardness of polycrystalline CVD SiC

Table 25 Fracture strength of SiC in TRISO fuel particles measured by different

methods

Table 26 Summary of the hardness and Youngrsquos modulus for pyrolytic carbon

measured by different methods

CHAPTER 3 Hardness and Youngrsquos Modulus of SiC Measured by Indentation

Table 31 Deposition conditions of the low temperature FBCVD SiC coatings


Table 41 Indentation parameters from S3 SiC and calibrated geometrical constantχv

along the radial and tangential directions

Table 42 VIF fracture toughness of SiC coatings deposited under different

conditions


Coatings

Table 51 Shows the deposition conditions and dimensions of SiC coatings produced

by fluidized bed chemical vapour deposition

Table 52 Summary of measured and calculated parameters for all the coatings

List of Tables

18

Table 53 Numerical characteristic parameters of the IPyCSiC interfacial roughness

self-affine exponent ( ) saturation roughness (σ0) and correlation length (ξ)

Table 54 Results and variations influences on fracture strength for SiC coating


Strength of SiC Coatings

Table 61 Deposition conditions of SiC coatings

Table 62 Summary of the modulus derived from the local fracture strength mean

local fracture strength and fracture strength of the whole shell before and after thermal

treatment

Table 63 Summary of microstructural changes of SiC coatings before and after

thermal treatment


Table 71 PyC coatings deposition conditions and physical properties

Table 72 Domain size (XRD) of as-deposited and thermal treated PyC coatings

Table 73 Changes of mechanical properties after thermal treatment of PyC coatings

Table 74 The parameters used to explain different mechanical properties of high

density PyC

Table 75 Interstitial defects peak intensity measured by Raman spectroscopy of

sample C5 (200 gcm3)


19


11 TRI-Isotropic (TRISO) fuel particles

A fission reaction is about that a large atomic nucleus (such as Uranium-235) is hit by

a neutron and absorbs the neutron forming a larger unstable nucleus The unstable

larger atomic nuclear breaks into two small nuclei and releases a high amount of

energy more neutrons beta and alpha particles and gamma The energy release is

much greater than for traditional fuels eg 1 g Uranium nuclear fuel releases the

same amount of energy as approximately 3 tonne of coal [1] The energy can be

transferred through the cooling system and used to boil the water to make steam to

drive a turbine and electrical generator in a nuclear power station

The high-temperature gas cooled reactor is one of the most promising candidates for

the production of nuclear energy according to its unique features For example it has

high coolant outlet temperature (850-1000 degC) which provides more efficient

electricity production due to the increased difference of the hot and cold coolant

temperatures [2] Furthermore it has the safety advantages due to the enclosure of the

fuel kernel (such as UO2 UC) within few layers of ceramic coatings Currently the

most common technique to fabricate fuels for operating the next generation

high-temperature gas cooled reactors is the TRISO fuel particles coating system [3]

The TRISO system was designed not only to retain all fission products during neutron

irradiation but also to withstand the thermo-mechanical stresses generated during

service [4]


20


matrix [5]

Figure 11 is the schematic of TRISO fuel particles embedded in a graphite matrix A

TRISO fuel particle consists of a fuel kernel and coating layers of porous pyrolytic

carbon (PyC) called buffer layer inner dense PyC (IPyC) silicon carbide (SiC) and an

outer dense PyC (OPyC) [5] and these layers were designed to have different

purposes The buffer layer absorbs metallic fission products recoils from kernel and

provides a space for fission product gases It also takes the volume change caused by

the kernel swelling without transmitting forces to outer layers The dense and

isotropic IPyC layer stops the chlorine from reacting with the kernel during deposition

of SiC and provides a firm substrate for the SiC layer Furthermore it protects the

SiC layer from most of the fission products and carbon monoxide during operation

The OPyC layer protects SiC layer during the remainder of the fabrication process

and provides structural stability to the particle during irradiation [3] The high

mechanical properties of SiC are needed to contain the high pressure generated in the

kernel and withstand the stress developed by the dimensional change of IPyC [3]


21

12 Failure mechanism

The radiation effects on the performance of the fuel particles such as fundamental

performance characteristics and fission product relsease mechanisms have been well

understood Different testing conditions (eg temperature up to 1300 degC and the does

of neutron) reflected the senariors encountered real applications [6-8]

During irradiation a number of potential failure mechanisms were revealed according

to several tests of coated fuel particles conducted in material test reactors and in

real-time operating HTR reactors [6-8] Chemically the corrosion of SiC by the

fission product palladium has been observed in almost all kinds of fuel compositions

and is considered as one of the key factors influencing the fuel performance However

this could be avoided by limiting the fuel temperature irradiation time or increase the

thickness of SiC layer [9] Mechanically the built up of the internal gas pressure (eg

CO) of irradiated particle and the neutron induced embrittlement of PyC coatings

could promote the failutre of the TRISO fuel particle The primary mechanisms which

may result in mechanical failure of TRISO fuel particles and lead ultimately to fission

product release depends significantly on the magnitude of the de-bonding strength

between IPyC and SiC layers [3 9]

121 Traditional pressure vessel failure mode

In this mode the failure was assumed to occur due to simple overload of the SiC layer

due to internal pressure build-up from fission gas [10] Both IPyC and OPyC layers

shrink during operation because of the irradiation exposure [11] This causes

compression stress in the SiC layer and tensile stress in the PyC layers Failure of the

SiC layer can only occur if the internal gas pressure is high enough to overcome the

compressive stress and critical stress of the SiC layer itself


22


Figure 12 shows the basic behaviour modelled in a three layers standard model [10]

It shows that both IPyC and OPyC layers shrink and creep during irradiation but the

SiC layer exhibits only elastic deformation A portion of gas pressure is transmitted

through the IPyC layer to the SiC The pressure continually increases as irradiation of

the particle goes However if the PyC layer could remain in tension the failure by

fracture of SiC layer would be less likely to happen in this mode When the failure of

the PyC layer occurs a tensile hoop stress in the SiC layer is generated This leads to

the development of the stress concentration mode provided by the fracture of the inner

PyC layer

122 Stress concentration mode

In this mode it is been proposed that there is a point at which the fracture strength of

the IPyC would be exceeded during exposure When this occurs a radial crack will

form in the IPyC layer The crack could either penetrate through the SiC layer or

partially de-bonding the IPyCSiC interface This would lead to severe stress

concentration near the crack tip and it could reach the maximum of 440 MPa

according to previous simulation work [10] Once de-bonding goes through the whole

interface the source of stress in the SiC layer would be fission product gas build-up


23

and this case has similar failure mechanism of traditional pressure vessel failure mode

Although this process could decrease the probability of failure compared with the

stress concentration case the probability of failure may be higher than the traditional

failure mode Because the stress generated in the SiC layer after de-bonding would

increase [3]


[10]

All these behaviours make it easier for the SiC layer to reach its fracture strength and

lead to the radial crack and failure of the SiC results in an instantaneous release of

elastic energy that should be sufficient to cause simultaneous failure of the

pyrocarbon layer Shown in Fig 13 is a photomicrograph illustrating the failure of a

TRISO coating According to the above discussion all the carbon layers are partially

designed to support or protect the SiC layer The SiC layer serves as the main

containment barrier for gas and metallic fission products [3] and high mechanical

properties of the SiC layer are needed However without appropriate microstructure

and mechanical properties of the PyC layer the stresses or structural changes

introduced in this layer during the irradiation process could result in the failure of the

whole particle [9 12] Furthermore mechanical properties such as the hardness (It is


24

the resistance to plasticpermanent deformation of materials under constant load from

a sharp object) Youngrsquos modulus (It reflects the resistance to reversible deformation

of a material) fracture toughness (It describes the ability of a material containing a

crack to resist fracture) and fracture strength (It is the maximum stress at which a

specimen fails via fracture) of SiC and PyC coatings are also important factors for the

safety design and evaluation of the TRISO coating system [10]

13 Goals of dissertation

Due to the importance of mechanical properties of SiC and PyC layers in keeping the

integrity of TRISO fuel particles and providing adequate information for modelling

the probability of failure of particles a good understanding of the elastic plastic and

fracture properties and their relation with microstructure is necessary Therefore all

the work carried out in this project is aimed at studying the relationship between

microstructure and mechanical properties of these two layers aiming to provide a

fundamental understanding about the deformation mechanism and solve the practical

issues

Due to small scale of SiC and PyC coatings two main techniques used to measure

mechanical properties are micronano-indenation and crush test Furthermore to study

the effect of microstructures on mechanical properties characterization techniques

such as transmissionscanning electron microscope and Raman spectroscopy are

widely used in the current work

In this thesis Chapter 2 reviews the recent progress in microstructural characterisation

and mechanical properties of SiC and PyC related materials which provides basic

information with regard to future study about hardness Youngrsquos modulus

deformation mechanism and fracture behaviour in these

Chapter 3 studies the influences of microstructure on hardness and Youngrsquos modulus


25

of SiC coatings and focuses on understanding the deformation mechanism of SiC

under nano-indentation The fracture toughness of these SiC coatings is measured by

Vickers-indentation and the importance of crack modes is discussed in Chapter 4

In Chapter 5 the fracture strength of SiC coatings in TRISO fuel particles is measured

and influence of the IPyCSiC interface on fracture strength is discussed Effect of

thermal treatment on fracture strength and microstructure of SiC coatings deposited at

different conditions are introduced in Chapter 6

Chapter 7 investigates the microstructure and mechanical properties of PyC coatings

with focus on deformation mechanism under indentation and the effect of density and

disorders on mechanical properties before and after thermal treatment

At last the main results and conclusions together with suggestions on future work are

given in Chapter 8


26

14 References

[1] httpnuclearinfonetNuclearpowerTheScienceOfNuclearPower

[2] J J Powers Fuel performance modelling of high burnup transuranic TRISO fuels

Disertation of Master University of California Berkeley 2009

[3] L L Snead T Nozawa Y Katoh T S Byun S Kondo D A Petti Handbook

of SiC properties for fuel performance modelling J Nucl Mater 371 (2007)

329-77

[4] D L Hanson J J Saurwein D W McEachern A S Shoeny Development plan

for advanced high temperature coated-particle fuels Report Nopc000513

[5] httpwwwmpafrprocessphp

[6] W Burck H Nabielek A Christ H Ragos AW Mehner HTR coated particle

fuel irradiation behaviour and performance prediction Specialists meeting on

gas-cooled reactor fuel development and spent fuel treatment IWGGCR-8 1983

174-88

[7] H Nickel H Nabielek G Pott A W Mehner Long-time experience with the

development of HTR fuel elements in Germany Nucl Eng Des 217 (2002)

141-51

[8] H Nabielek W Kuhnlein W Schenk W Heit A Christ and H Ragoss

Development of advanced HTR fuel elements Nucl Eng Des 121 (1990)

199-210

[9] K G Miller D A Petti J Varacalle T Maki Consideration of the effects on

fuel particle behaviour from shrinkage cracks in the inner pyrocarbon layer J

Nucl Mater 295 (2001) 205-12

[10] A C Kadak R G Ballinger M JDriscoll et al Modular pebble bed reactor

project university research consortium Annual report INEELEXT-2000-01034

MIT-ANP-PR-075

[11] J D Hunn G E Jellison Jr R A Lowden Increase in pyrolytic carbon optical

anisotropy and density during processing of coated particle fuel due to heat


27

treatment J Nucl Mater 374 (2008) 445-52

[12] E Loacutepez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry

microstructure and mechanical properties in SiC coatings produced by fluidized

bed chemical vapour deposition J Mater Res 23 (2008) 1785-96


28


21 Introduction

To model the probability of failure of fuel particles a number of key mechanical

properties of silicon carbide (SiC) are needed such as Youngrsquos modulus hardness

fracture toughness and fracture strength [1 2] These properties could be affected by

the microstructure of SiC coatings such as orientation porosities grain size and

defects [1-5] The small dimensions of the SiC coating limits the techniques available

to measure its mechanical properties However the development of the

nano-indentation has provided an important tool for probing the mechanical properties

of small volumes of material From the load ndash displacement data many mechanical

properties such as hardness Youngrsquos modulus and even fracture behaviour can be

determined [6] When an indentation system is used in conjunction with a focused ion

beam system and a transmission electron microscope images of deformation under

the nano-indentation can be obtained and the 3-D crack morphology can even be

reconstructed [7] Since there is a need to explain the high mechanical properties of

SiC deposited at temperature of 1300 ordmC by fluidized-bed chemical vapour deposition

[8] this combination of techniques could provide fundamental understanding of the

deformation mechanisms during indentation Another important parameter is fracture

strength and there have always been efforts to establish one method to characterise

fracture strength of SiC for example by brittle-ring test [9] whole particle crush test

[10] and modified crush test [5] Furthermore the high temperature application of SiC

and the compact of fuel pellet could affect the microstructure of SiC [2] which would

lead to the changes of mechanical properties


29

The pyrolytic carbon (PyC) has been introduced by previous studies [11-14] and is

important in helping the SiC act as the main loading bearing layer The high

mechanical properties such as Youngrsquos modulus and anelasticity of PyC are necessary

to protect from damage caused by internal stresses and by external mechanical

interactions [12] However cracking and debonding between the SiC and inner PyC

layers could increase the probability of failure of TRISO fuel particles [13 14] It was

shown that without appropriate microstructure and mechanical properties of PyC the

structural or stress changes introduced in the coating during irradiation process could

result in total failure of the particle [11 13] The microstructure of PyC varied under

different deposition conditions [15] and it dominates the mechanical properties of

PyC coatings Therefore in this Chapter we review both the microstructure of SiC

and PyC including atomic structure morphology and defects and their mechanical

properties eg hardness Youngrsquos modulus deformation behaviour etc

22 Microstructure of silicon carbide

221 Atomic structure

The basic structural unit in SiC is a covalently bonded tetrahedron a carbon atom is at

the centre of four silicon atoms (C-Si4) and vice versa (Si-C4) The length of each

bond and the local atomic environment are nearly identical while the stacking

sequence of the tetrahedral bonded Si-C bilayers could be different The different

stacking sequences give SiC more than 250 polytypes [16] of which the 3C 4H 6H

and 15R are the most common The leading number of polytypes shows the repetition

of the SindashC pair and the letter C H and R represents the cubic hexagonal and

rhombohedral crystals respectively The 3C is the only cubic polytype in which the

stacking sequence of the planar unit of Si and C in tetrahedral coordination is depicted

as ABCABC in the lt111gt direction The cubic SiC crystal is called β-SiC and all

the other polytypes are α-SiC The crystal structures of 3C- 4H- 6H- and 15R-SiC

are schematically illustrated in Fig 21(a) [17] and corresponding XRD images were


30

shown in Fig 21(b) [18]



from Ref [18]

Although the transformation of SiC polytypes is primarily dependent on temperature

it could be affected by purity of the pre-existing phase pressure andor stacking faults

[19-22] The cubic form of SiC (β -SiC) is believed to be more stable than the

hexagonal structure (α-SiC eg 6H-SiC) below 2100 ordmC [19] However the polytype

of 2H-SiC which has the simplest stacking sequence is rarely observed at higher

temperature Krishna et al [20] reported that single crystals of 2H-SiC can be easily

transformed to 3C-SiC on annealing in argon at temperatures above 1400 ordmC It was


31

found that the pre-existence of α-SiC (except 2H-SiC) could promote β-SiC

transformation to α-SiC while the transformation from α-SiC (6H-SiC) back to β-SiC

(3C-SiC) needs high temperature and pressure [21]

It has also been shown that the phase transformation could be closely related to

pre-existing defects such as stacking faults and their distribution [18] of which the

concentration is high even in single crystal SiC [22] Furthermore due to their low

formation energy the other intrinsic defects such as vacancies interstitials and

antisites were found to be common in SiC [23] These defects could affect mechanical

properties of SiC [8] so it is important to review their structure and properties

222 Defects in SiC

2221 Stacking faults and dislocations

A stacking fault is a disordered part of the ordered sequence in fcc crystal and the

most common stacking faults in cubic SiC are intrinsic and extrinsic stacking faults

(ISF and ESF) [24] For ISF the resulting stacking sequence is ABCACABC

if a double layer B is removed (condensation of vacancies) as for instance shown in

Fig 22[24] The ESF could be thought of as adding a double layer to the stacking

sequence (condensation of interstitials) resulting stacking sequence of

ABCACBCABChellip




32

Another interpretation of the stacking faults is related to a twist of the three equivalent

bonds between two bilayers by 180deg [24] There may be an intrinsic shear stress

which could promote the glide of partial dislocations and thereby result in a faulted

crystal containing an error in stacking sequence so itrsquos reasonable to interpret

stacking faults in this way [25] Compared with dislocations and vacancies no bonds

are broken by stacking faults leading to a small energy difference between faulty and

perfect structures [26]


methods

[27] [28] [24] [29] [30] [31] [32]

ESF (mJ m-1

) -15 -- -28 -6 -61 -154 -323

ISF (mJ m-1

) 12 34 -34 14 138 111 -71

Table 21 lists the formation energy of stacking faults in SiC and it shows that

extrinsic stacking faults have much lower formation energy than intrinsic stacking

faults in fact the values become negative The negative formation energy of stacking

faults in 3C-SiC means they can be formed very easily even more easily than perfect

3C-SiC As a result the stacking faults in 3C-SiC are spontaneously formed and most

likely in the form of extrinsic faults in the lt111gt direction Furthermore due to the

low energy of formation the length of a stacking fault can only be limited by the size

of the crystal or the presence of other defects that act as obstacles [33]


33




The morphology of stacking faults in SiC observed by TEM is given in Fig 23 It

shows that the stacking faults could form a small domain (around 1 nm thick in Fig

23(a)) with different distances between small domains When a large concentration of

stacking faults exists in SiC it has been claimed that a conversion of cubic SiC to

hexagonal SiC on the nano-scale could happen by twinning [35] Furthermore the

stacking sequence of the faulted 3C-SiC was previously treated as random mixing of

α-type unit structures such as 6H and 4H in the 3C structure [36] Therefore it is

important to identify the properties and the microstructure of stacking faults of SiC

layers in TRISO fuel particles because the presence of α-SiC could result in reduction

of strength under irradiation which was due to enhanced possibility of anisotropic

swelling of α-SiC under irradiation compared to β-SiC [37]

(a) (b)

(c)


34



Figure 24 gives the XRD images of SiC in TRISO fuel particle deposited by fluidized

bed chemical vapour deposition showing the extra peak at 2θ~335ordm a high

background intensity at the peak at 2θ~353ordm and the broadening of the 3C peaks [8]

This is different from the perfect atomic structure of 3C-SiC as shown in Fig 21(b)

According to a previous simulation study [18] this kind of XRD diffraction pattern

could be caused by the existence of a high density of stacking faults and twins in the

regular cubic sequences It was demonstrated that it was unlikely to be due to the

presence of 2H-SiC or other polytypes [18] and two possible explanations were given

First two types of crystalline 3C-SiC with different populations of faults and twins

and second one type of crystal having clusters of faulted regions In SiC single

crystals although the concentration of stacking faults and twins is high the density of

dislocations is low (102-10

5cm

2) compared with metallic materials [22]

Figure 25 shows schematic images of the dislocations in face centred cubic (fcc)

crystals (β-SiC) The perfect dislocation is the (111) lt110gt system with burgers

vector of b=a2[110] (0308 nm) in SiC as shown in Fig 25(a) The perfect

dislocation could be easily dissociated into two partial dislocations of a6[121] and a6


35

[21-1] as shown in Fig5 (a) and (b) because this reduces the total energy As a result

of this split a stacking fault must also be produced between the two partial

dislocations [38] Figure 25 (c) and (d) are lt110gt projections showing the Shockley

and Frank partial dislocations and their formation all related to the formation of

stacking faults







(a)

(b)

(c) (d)


36



By comparing with previous studies [39-41] it is found that the relationship between

dislocation and stacking faults is complex The stacking faults have influences on the

mechanical properties for example enhancing the mobility of dislocations [39]

Different roles of stacking faults in II-VI heterostructures and devices have been

observed and results indicate that the stacking faults serve as the sources of misfit

dislocations [40] It is necessary to study the propagation of stacking faults or the

formation of stacking faults under stress and their influence on the properties of SiC

For example generation of stacking faults is shown to have occurred during the

fracture process together with the corresponding partial dislocation Furthermore

Agarwal et al [41] observed the growth of stacking faults from certain basal plane

dislocation within the base layer of the SiC

2222 Non-stoichiometric and point defects

Another common class of defects in SiC are non-stoichiometric (excess silicon or

carbon) and point defects [23 41 42] The purity of SiC may have effect on the

crystal structure strength corrosion resistance thermal conductivity diffusion

coefficient and other coating properties depending on its amount [43] The purity

could also affect defects in SiC eg if the stoichiometry deviates (even less than 1)

the concentrations of point defects in cubic SiC were found to be elevated [23]

Although the effect of point defects on general behaviour of nuclear fuel during

application process is not clear but their effect on microstructure evolution during

thermal treatment could be significant [44]

Silicon in SiC Stoichiometric 3C-SiC has generally been obtained at temperatures

between 1500 and 1600 [45] with carbon and silicon codeposited above and below

this temperature range By adding propylene as another carbon source the deposition

temperature of stoichiometric SiC could be reduced to about 1300 [8] The extra-Si


37

SiC is less commonly investigated compared with the extra-C SiC because it has

been found that during the irradiation process the extra-Si plays a negative role in

material properties due to its low melting point [1] It has been found that the effect of

excess-Si on the Youngrsquos modulus and hardness it is more likely depending on its

amount and location [8 46]

Raman spectroscopy is an effective way to identify free Si both in amorphous and

crystalline phases eg it detected excess-Si when the XRD result showed the SiC was

stoichiometric [8] If the extra-Si is high (could be detected by XRD) TEM could be

used to detect its location and characterise the Si lattice contrast For example TEM

was carried out using both high resolution [35 47] and dark field imaging modes [48]

The HRTEM images in Fig 26 show the 3C-SiC crystallite with Si inclusions in

which nano-crystalline 3C-SiC and Si are separated by a weakly crystallized

interphase



(a)

(b) (c)

β-SiC

β-SiC

β-SiC

β-SiC

Si

Si

025 nm

025 nm

025 nm

0 312 nm

0312 nm


38



Figure 27 shows bright-field and dark-field images of extra-Si SiC It shows the

crystalline Si as bright points in the dark background located at the grain boundaries

[48] The above observations were carried out in SiC with more than 1 at excess Si

(by comparing the intensity of Si Raman peak) as such observations are difficult

when the amount of excess Si is low Since the Youngrsquos modulus in SiC with low

amount of excess Si was comparable to that of stoichiometric SiC[8 46] it may have

unique properties that are worth further exploitation



[48]

Carbon in SiC Excess C can also be identified by Raman spectroscopy but it is more

difficult to quantify its content and observe where this extra carbon exists due to its

small atomic number A comparative method was used to measure the content of

excess carbon by combining Raman spectroscopy auger electron spectroscopy

electron probe microanalysisand X-ray photoelectron spectroscopy [49] Once the

carbon concentration was measured (by above methods) the ratio of free excess to

SiC peak intensity (I796I1600) of Raman spectroscopy could be obtained as shown in

Fig 28 and the excess carbon concentration in the nearly stoichiometric SiC could

(a) (b)


39

be estimated [49]



There are few reports regarding the location of excess C in SiC The research carried

out by KKaneko et al [50] in carbon-doped hot pressed szlig-SiC showed that grain

boundaries were found to be free of any second phase by HRTEM although excess C

is found to form the second graphite phase Mykhaylyk and Gadzira revealed that

extra-C atoms are located as planar defects [51] The C atoms in the β-SiC structure

were supposed to arrange either as diamond-like carbon interlayers or as

non-correlated point defects after sintering of the as-synthesized powder at high

pressures and high temperature Since it showed that the presence of excess C atoms

in SiC crystal structure changes the local atomic environment [52] they may exist

within the SiC crystal and be correlated with other defects

The above discussion about the excess Si and C indicates that their influences on

properties of SiC depend on their content and that they could be discussed together

with the other point defects when their amount is low (less than 1 at ) [23]

Point defects in SiC SiC has eight kinds of point defects which keep the tetrahedral

symmetry of the perfect SiC crystal [23] They are carbon vacancies (Vc) silicon

vacancies (VSi ) carbon antisites (CSi) silicon antisite (Sic) a tetrahedral interstitial

silicon atom surrounded by four Si atoms (SiTSi) a tetrahedral interstitial silicon atom


40

surrounded by four C atoms (SiTC) a tetrahedral interstitial carbon atom surrounded

by four Si atoms (CTSi) and a tetrahedral interstitial carbon atom surrounded by four

C atoms (CTC) [23] The formation energies for these defects are listed in Table 22

Due to their low formation energies the individual antisites and vacancies

particularly CSi were expected to appear even in as-deposited coatings [53 54]



Vc VSi Sic CSi SiTSi SiTC CTSi CTC

Ef (eV) 59 68 73 11 150 147 86 110

The importance of point defects for different applications of SiC was studied and

these properties were studied in the relation to the properties of the point defects

including their formation annealing and interaction with each other [53] According

to Raulsrsquos study [54] the actual results of diffusion of CSi are more likely to be the

formation of CSi clusters which could be promoted by the diffusion of vacancies For

the coexistence of self-interstitials and vacancies (eg in irradiated material) it has

been found that the annealing temperature for VSi and Vc by recombination in β-SiC

were about 500 ordmC and 750 ordmC respectively [55] For as-deposited β-SiC without

interstitials the annealing process was only dominated by the out-diffusion of

vacancies the disappearances of VSi and Vc were found at temperature of 1400 ordmC and

1600 ordmC respectively [54] It is also been found that the migration of silicon vacancies

is easier than carbon vacancies due to its lower migration energy barrier Furthermore

in the case of excess carbon inside SiC the carbon clusters may form in SiC after

annealing and the size of the cluster depends on the content of interstitial carbon [56]

The general atomic-scale microstructure of SiC was reviewed above which showed

high degree of defects such as stacking faults dislocations vacancies and antisites


41

The kind and concentration of these defects could affect the mechanical properties

such as hardness Youngrsquos modulus and fracture behaviour of SiC Since variation of

mechanical properties could also be due to other microstructural factors such as grain

size and density the relationship between microstructure and mechanical properties

are further reviewed in the following session

23 Properties of silicon carbide

231 Youngrsquos modulus

Youngrsquos modulus is physically related to the atomic spacing atomic bond strength

and bond density It is accepted that high-purity SiC material eg CVD SiC exhibits

the highest elastic modulus and that a porous microstructure with a high

concentration of impurities could decrease the elastic modulus [1 57] In contrast

neither grain size nor polytype was recognized as having a significant effect on the

elastic modulus of SiC in coated fuel [1 58]


C11 (GPa) C12 (GPa) C44 (GPa) Z Ref

3C-SiC a 3523 1404 2329 18196 [59]

3C-SiC b 511 128 191 10026 [1]

3C-SiC c 390 142 256 -- [60]

3C-SiC a 420 126 287 19503 [61]

a Theoretical calculations

b Sonic resonance measurement

c Raman Spectroscopy

According to the definition of Youngrsquos modulus an important factor which could

affect its value for SiC material is the texture which is the degree of anisotropy (lack

of randomness with regard to the orientation) of SiC crystals The Youngrsquos modulus is

different by a combining of elastic tensors for deformation of the crystal in different


42

orientation The elastic tensors or the stiffness tensors reflect the linear stress-strain

relation of a material There are 81 elastic tensors because the stresses and strains

have 9 components each However due to the symmetries of the SiC the tensors were

reduced to 3 unknown values They could be measured by sonic resonant method [1]

and Raman spectroscopy [60] based on vibrational theory of the crystal lattice They

are defined for SiC in Table 23 and will cause the variation of Youngrsquos modulus for

anisotropic materials The elastic tensors for 3C-SiC identified by previous theoretical

and experimental results [59-61] are substantially different from the current updates

of sonic resonance data The difference could be caused by the difference of the size

of SiC mateirals which could introduce the influences of defects such as grain

boundaries and stacking faults It was proposed to be more reasonable estimation for

SiC in TRISO fuel particle [1]

A measurement of the anisotropy in β-SiC (faced centre cubic crystals) is the ratio of

the two shear moduli [3] 100 shear modulus and 110 shear modulus μ0 and μ1

respectively which is

0 44

1 11 12

2CZ

C C

(1)

the parameter Z is known as the Zener ratio or elastic anisotropy factor (given for

different elastic tensor Table 23) When Zgt1 the Youngrsquos modulus is minimum

along lt100gt and a maximum along lt111gt and the representational surfaces for

Youngrsquos modulus in cubic crystals is shown in Fig 29 For the case when Z=1 the

cubic crystal would also be isotropic and the representation surface would be

spherical


43



If the samples were random polycrystals which means samples are isotropic the

theoretical Youngrsquos modulus can be unambiguously given by [3]

3

[1 ( 3 )]E

B

(2)

While bulk modulus and shear modulus are

11 122

3

C CB

(3)

1

0 1

1 0

52( 6 )

(4)

where 0 44C 1 11 12( ) 2C C and

01

0 0

3( 2 )

5 (3 4 )

B

B

(5)

The theoretical value can be gained when the elastic constants are known Using the

Eqs (2-5) the theoretical Youngrsquos modulus E was calculated to be 496 GPa for

isotropic SiC materials when the elastic tensor obtained by Lambrecht et al was used

The calculated value is close to the Youngrsquos modulus measured by nano-indentation

(about 527 GPa) of isotropic bulk CVD SiC [62] But this value is higher than the

Youngrsquos modulus measured by nano-indentation of SiC in TRISO fuel particle which

is about 450 GPa [8 46]

By using the elastic tensors measured by sonic resonance in Snead et alrsquos study [1]


44

the calculated Z (10026) is very close to 1 and it means the Youngrsquos modulus in

TRISO coated fuel particle may show no orientation effect According to Eqs (2-5)

the calculated Youngrsquos modulus is about 459 GPa under the elastic tensors given in

Ref [1] This value is close to the Youngrsquos modulus measured by nano-indentation in

TRISO fuel particle regardless of the orientation effect [1 8 46] Therefore for

TRISO fuel particle the recommended elastic tensors measured by sonic resonances

were supposed to be appreciable due to the scale and the microstructure similarities of

SiC materials [1]

Another significant factor which affects the Youngrsquos modulus is the density The

elastic modulus E at room temperature can be empirically expressed in an exponential

function of porosity pV as [63]

0 exp( )pE E CV (6)

where 0E is the elastic modulus and C is a constant of 357 for a pore-free bulk CVD

SiC pV is the ratio of the relative density difference to the theoretical density of SiC

(322 gcm3)

The relationship between density and Youngrsquos modulus of different kinds of SiC

materials measured by different methods were summarised in a previous study [1] as

shown in Fig 210 It has been found that the standard deviation of elastic modulus of

SiC is about plusmn 10 when the density is higher than 99 and increased to plusmn 15 for

porosity higher than 1


45


232 Hardness

In a brittle material indentation hardness is defined as the mean pressure the material

will support under load and it is a complex property which could involve crack

initiation and propagation and the development of new surfaces during the

indentation process [1] Furthermore the value of hardness measured by indentation

also depends on external factors Due to the difference in dimensions of materials

such as the bulk small scale and thin film materials indentation on the nano- micro-

and even macro-scale have been used to measure the hardness [64] The hardness of

β-SiC related material has mainly been investigated by Vickers and nano-indentation

techniques (introduced in the later part of this session according to Ref [65]) as

summarized in Table 24 Reviews have found that the nano-hardness is generally

higher than Vickers hardness [1] which was attributed to the indentation size effect

Although few hardness values of β-SiC are available to be compared (given in Table

24) it shows the difference of hardness within a given sample Regardless of external

influences on the measurement of hardness generally it can be affected by grain size

or grain morphology [46] density composition and defects [1 8 66] To identify the


46

controlling factor for hardness it is necessary to understand the deformation

mechanism of SiC under indentation

Table 24 Vickers and nano-indentation hardness of β-SiC related materials

Deformation mechanism Research into the deformation mechanism of SiC have

shown the availability of dislocation related plasticity [70] phase transformation

(cubic phase to amorphous) [71 72] fracture mechanisms [73] and also the

combination of any two or three [62 73]


First the dislocation related plastic deformation was found in single crystal 6H-SiC

[70] and the propagation morphology of dislocations was observed after indentation

as shown in Fig 211 This observation confirmes that the dislocation slip is a

Materials Vickers hardness (GPa) Nano-hardness (GPa) Ref

Single β-SiC (001) 28 -- [67]

CVD β-SiC 207-32 325-406 [466668]

FBCVD β-SiC -- 36-42 [8]

Sintered β-SiC 211-239 -- [69]

500 nm


47

mechanism of plastic deformation from nucleation of a few dislocation loops (at or

near the theoretical strength) to extensive dislocation plasticity

Furthermore the dislocation related plastic deformation in polycrystalline CVD β-SiC

(with micro meters grain size) was first observed by Zhao et al [62] It was found that

the initiation of the plastic deformation was reflected by the burst (pop-in) of the

force-displacement curve which is similar as the initiation of plastic deformation in

metallic materials as shown in Fig 212(a)

According to the Hertzian contact theory [74] the burst was attributed to initiation of

the dislocation glide by comparing the shear stress generated under the indentation at

that load with the theoretical shear stress in β-SiC [62] During the whole indentation

process it was shown that shear slip is the predominant deformation mechanism and

that cracks were associated with the shear faults Figure 212(b) is one of the TEM

images showing the microstructure under indentation and it shows the dislocation

induced shear bands at one side of indent [62] which depend on the orientation of

grains


size of 5-10 microm and (b) deformation behaviour under nano-indentation [62]

Second following the observations of phase transformation under indentation in

silicon [75] and the formation of SiC amorphous phase during high speed machining

(a) (b)


48

process [71] the investigation of phase transformation under indentation was carried

out in SiC [7274] It has been demonstrated thermodynamically that the direct

amorphization is less likely to happen under nano-indentation [76] The

amorphization observed in single crystal SiC was attributed to the formation

propagation and accumulation of dislocations which formed the disordered phase at

the maximum stress region under a punch indentation [71] In SiC with nanometers

grain size the molecular dynamic study indicated thedominated deformation under

nano-indenation is a crossover of the indentation-induced crystallization to

disordering leading to amorphization [72] as shown in Fig 213






Further studies demonstrated that the phase transformation from β-SiC to α-SiC is not

possible under nano-indentation because a pressure of nearly 100 GPa is needed [76]

even when assisted by high dislocation density shear stress and temperature This

simulation work concluded that the primary response of β-SiC to nano-indentation is

dislocation nucleation and propagation which has been confirmed by experimental

observations [62]

Third the plastic deformation of β-SiC under indentation was divided into two parts


49

which are primary dislocation initiation and propagation and the formation of micro

cracks [73] The former contributes to 13 of plastic deformation under indentation

while the later provides 23 of total deformation The hardness related plastic

deformation could be explained well by this mechanism which included above two

process as discussed in previous studies [1 46 62] Moreover considering the effect

of micro cracks the deformation mechanism under indentation could be related to

other factors which could contribute to the formation of micro cracks such as

porosity grain boundaries and stacking faults in SiC [3]

Youngrsquos modulus and hardness of coatings in TRISO fuel particle can be measured by

nanoindentation due to the limitation of small dimension A typical

load-displacement curve and the deformation pattern under nanoindentation of an

elastic-plastic sample during and after indentation are shown in Fig 214 in which the

hc is contact indentation depth and hs is the displacement of the surface at the perimeter

of the contact [65] The peak load and displacement are Pmax and hmax respectively

and the diameter of the contact circle is 2a During unloading process the elastic

displacements are recovered and when the indenter is fully withdrawn the final depth

of the residual hardness impression is hf [65]

Nanoindentation hardness is the ratio of the load to the projected contact area of the

indentation The mean pressure that the material can support under indentation is

defined as the hardness From the loadndashdisplacement curve as in Fig 214(a) hardness

can be gain when the load is at the maximum value

A

PH max (7)

where A is the projected contact area


50



The elastic modulus of the indented sample can be inferred from the initial unloading

contact stiffness S=dPdh ie the slope of the initial portion of the unloading curve A

geometry-independent relation involving contact stiffness contact area and elastic

modulus can be derived as follows

2A

S E

(8)

where szlig is a constant that depends on the geometry of the indenter (szlig=1034 for a

Berkovich indenter) [65] and Er is the reduced elastic modulus which accounts for the

fact that elastic deformation occurs in both the sample and the indenter Er is given by


51

22 11 1 i

r i

vv

E E E

(9)

where E and υ are the elastic modulus and Poissonrsquos ratio for the sample respectively

and Ei and υi are the same quantities for the indenter For diamond Ei=1141 GPa and

υi=007[65]

For an indenter with a known geometry the projected contact area is a function of the

contact depth The area function for a perfect Berkovich indenter is given

by 2245 cA h Indenters used in practical nanoindentation testing are not ideally sharp

Therefore tip geometry calibration or area function calibration is needed A series of

indentations is made on fused quartz at depths of interest A plot of A versus hc can be

curve fit according to the following functional form

11 12 1 1282 4

1 2 3 8245 c c c c cA h C h C h C h C h (10)

where C1 through C8 are constants In some cases only the first three constants were

considered

The contact depth can be estimated from the load-displacement data using

maxmaxc

Ph h

S (11)

Where ε is a constant that depends on the indenter geometry (ε=075 for a Berkovich

indenter)

It is worth noting that high Youngrsquos modulus and hardness does not gurantee the

suitability of ceramic material to an engineering application because of the

importance of other mechanical properties such as fracture toughness and fracture

strength


52

233 Fracture toughness

The definition of fracture toughness from Munz and Fett is [77] if a component or a

test specimen with a crack is loaded the stress intensity K1 increases with increasing

load until unstable crack propagation occurs at a critical value of K1 This critical

value is the fracture toughness (KIC) Therefore the measurement of fracture

toughness should be made on sample with a pre-crack however due to the small size

of SiC coating methods could be used are limited Although the most recently

developed micro-beam bending test could measure the fracture toughness of SiC in

TRISO fuel particles [78] this process is costly and time consuming because it

involves the preparation of micro-beams and notched cantilevers by focused ion beam

milling which limites the application of this technique

Indentation is now one of the most commonly used techniques to evaluate the fracture

toughness of ceramics and coating systems because it is easy to perform does not

need special samples and causes only negligible surface damage However some

researchers have declared that the indentation method is not suitable for the

measurement of fracture toughness [79 80] They concluded that the indentation

method does appear to represent some form of a complex crack arrest phenomenon

but that this occurrs in the presence of a multiple-crack path and a highly complex

residual stress field

Despite of these considerations the indentation method is an effective way to

compare the fracture behaviour of materials [80] particularly for small size specimens

and it provides information about the crack initiation and propagation Figure 215 is

the most typical characterization of the crack system generated by Vickers indentation

[81] This crack system is termed as median-radial cracking and consists of

approximately semi-circular cracks


53



The mode of crack initiation and propagation under an indenter proposed by Chiang

et al explains many of the features observed in indentation crack patterns and is the

most recent advance [82] It was found that radial cracks are the first to initiate

trigged by a combination of the highly tensile surface stress field and the availability

of surface flaws [74 82] These cracks grow on unloading and can either propagate

into the plastic zone (half penny cracks) or terminate in the elastic zone (Palmqvist

cracks) [83] depending on the microstructure of the material

For different types of crack modes such as half-penny and Palmqvist cracks different

equations were developed based on theoretical analysis of stress field and empirically

calibrations to calculate the fracture toughness under indentation For example in the

half penny crack model the Vickers indentation fracture toughness was most

frequently determined using the relationship proposed by Anstis et al [84] This

equation was first inferred based on isotropic materials and it is suitable for general

application to well-developed cracks [84]

1 2

3 2( )IC

E PK

H c (12)

Where P is the indentation load c is the radial crack length from indentation centre to

crack tip E and H are the Youngrsquos Modulus and hardness of the materialand χ

denoted as the geometrical constant which is independent of the materials The Eq


54

(12) was developed on the basis of half penny cracking in homogeneous brittle

materials under high load for example in glasses [84]

The above information shows that it is possible to compare fracture toughness under

indentation in SiC coatings with different microstructures The fracture toughness of

SiC could depend on a large number of factors such as grain size porosity micro

cracks and inclusions which could dissipate the fracture energy from the main crack

[3] According to a previous review [1] fracture toughness of SiC peaks at the grain

size range of 1-5 microm So fracture toughness of SiC in TRISO fuel particle is likely to

be influenced by the grain size due to the similar range of grain size Although micro

cracks and pores could improve fracture toughness they would decrease the strength

[3] which is detrimental for the safe design of fuel particles Over several decades

studies have worked to improve the fracture toughness by introducing a

heterogeneous microstructure such as weak grain boundary phases [85] In the

heterogeneous phase toughening mechanism the cracks could initiate in or be

reflected into weak defects and thereby dissipate the fracture energy for the main

crack propagation Furthermore the distribution of grain boundary character (the

crystallagraphic type and frequency of grain boundaries) and morphology could

influence the fracture toughness [85 86] Different grain boundary orientations and

their frequency were found to affect the fracture toughness by controlling the

intergranular fracture of materials [86] Different grain morphologies such as

elongated grains could increase the fracture toughness by crack bridging or by

generating micro cracks along grain boundaries or triple junctions [85] No

heterogeneous phase is supposed to exist in SiC in TRISO fuel particles so the

fracture toughness is most likely to be affected by grain morphologies or as-deposited

defects

According to the Griffth fracture theory once the size of the critical flaw is the same

the fracture toughness is propotional to the fracture strength which is another


55

parameter used in modelling of the probability of the failure of fuel particle

234 Fracture strength

For brittle materials the fracture strength is best considered as a distribution rather

than a fixed value as the flaws (such as surface cracks pores and inclusions) from

which fracture initiates vary in size and type (result in different frature strength value)

between nominally identical samples [3] The Weibull approach is a commonly used

empirical method to characterise the strength of a brittle material It assumes a simple

power-law stress function (eg in Eqs (18-20)) for the survival of the elements

which is integrated over the body volumesurface area (as shown in Eqs (19) and

(21)) In many cases this function gives results in the form of Weibull modulus (m in

Eq (19)) and characterstic strength which describe the width and magnitude of the

strength distribution [3] The Weibull modulus is the slope of Log-Log distribution

function of the survival of elements and strength (Eq (19)) For engineering

application the high Weibull modulus represents the small variation of the fracture

strengthes for a given material

Higher Weibull modulus reflects lower variability of the strength and it is typically in

the range of 5-20 [3] The commonly used strength test methods for bulk ceramics are

uniaxial tension three- and four-point bending However the small dimensions of

TRISO fuel particles make it difficult to measure the strength by those conventional

methods As a consequence some specific methods were developed in the last few

decades such as O-ring test [87 88] C-ring test [88] hemisphere bending [10]

internal pressurization [89] and crush test [5 89 90] The schematic of easily

repetitive fracture strength test geometries are given in Fig 216 and the obtained

fracture strength by different methods was shown in Table 25


56


methods

Methods L

f (MPa) Weibull Modulus F

f (MPa) Ref

O-ring compression 596-1412 41-66 -- 87


C-ring Compression 980-2200 40-90 -- 88

Semi-spherical bend 720-1350 70-80 340-620 10

Inner pressurization -- 43-62 222-448 89

Crush test -- 58-75 356-427 89

Crush test 770-1324 40-73 330-647 5

Crush test 1484-1721 135-183 1045-1091 90

L

f Local fracture strength F

f Fracture strength of the full particle

The local fracture strength is in the range of 596-2200 MPa and the fracture strength

of the whole particle varies from 222 MPa to 1091 MPa Such significant variation is

tought to be caused by the differences in specimen size and loading mode which were

related to the nature of the Weibull distribution [1 3] It has been demonstrated that

specimens with larger volumesurface area (under the same loading mode) have lower

strength because there is an increased probability that a larger flaw exists in a larger

body Similarly when there is no volume difference the loading mode which stresses

larger area has lower local fracture strength [3] These discussions show the

importance of regulating the fracture strength test method and producing specimens

with regular shape and size


57



loading) [89]

The modified crush test developed by Byun et al [5] is recommended for the fracture

strength measurement of SiC in TRISO fuel particles because it considered the effect

of contacting area between SiC shell and plunger which reduced the variation and

uncertainty of the stress distribution under tensile stress

Modified crush test When a partial spherical shell is diametrically loaded by an

external load F concentrated on a small circular contact area of radius 0 the

maximum membrane stress and bending stress are given by [91]

2

1 2

1membrane

FC

t

(13)


58

2 2

1bending

FC

t

(14)

where ν is the Poisson ratio t is the thickness of shell and C1 and C2 were defined as

2

1 0115004022050 C (15)

)27031exp(204412 C (16)

2 2 2 1 4

0[12(1 ) ( )]r R t (17)

max membrane bending (18)

where max (L

f ) is the fracture strength for locally loaded specimens R is the outer

diameter of shell t is the thickness of the SiC shell The distribution of local fracture

strength is analysed by the Weibull distribution function which presents the

cumulative probability of failure P as [5]

mL

f

E

m

s

F

fSdAP

00

exp1exp1

(19)

where L

f m 0 and ES are the local fracture strength the Weibull modulus the

characteristic sterngth and the size effect factor respectively The size effect factor is

dAS

m

s L

f

F

f

E

Byun et al [5] used the probability estimator as follows

1

N

iPi (20)

where iP is the probability of failure for the i th-ranked strength and N is the


59

sample size The increased probability that the full SiC shell has more critical flaws

compared with the stress-weighted surface is corrected by the size effect and the

fracture strength of the full shell (F

f ) is given

L

f

m

L

f

m

F

E

L

EF

ftR

r

S

S

1

2

2

0

1

)(4

(21)

After adjusting the size effect the fracture strength of the full particl of different SiC

coatings could be compared In a previou study [87] the difference of the fracture

strength was attributed to the microstructural variations which were determined by

deposition conditions [87] More detailed analysis [510] showed that the variation of

fracture strength was due to factors such as porosity roughness of the IPyCSiC

interface and grain size For example Evans et al [10] observed that the surface

roughness influenced the failure of the particle withstrength improved by reducing

the inner surface roughness According to above discussion the variation of Weibull

modulus could be attributed to the different test methods flaw distribution and sample

size [3 5]

Micostructure and mechanical properties of as-deposited SiC are reviewed above

which may change after high temperature treatment and the degree of evolution could

be different due to variational deposition conditions of SiC coatings As summarized

in a previous study [92] one of the critical properties for SiC layers in TRISO fuel

particle is that the microstructure remains unchanged after thermal treatment at 2000

ordmC for 1 hour in an inert atmosphere as determined by electron microscopy and X-ray

diffraction

235 Effect of thermal treatment on SiC

The SiC with perfect crystal structure tends to have good high temperature thermal

stability however due to the concentration and type of imperfections generated


60

during deposoition process its thermal stability could be affected Defects such as

stacking faults vacancies and interstitials in as-deposited SiC coatings affect the

microstructural change after thermal treatment [93-96] For example the phase

transformation from β- to α-SiC generally happened at temperatures above 2100 ordmC

[19] but it could take place at lower temperature (gt 1700 ordmC) in special cases (eg

CVD β-SiC deposited on Si substrate with high amount of stacking faults) [93]

During high temperature thermal treatment (about 2000 ordmC) of CVD β-SiC one

significant microstructural change would be the annihilation of stacking faults [94

95] A thermodynamics study [94] has shown that the mechanism of reduction of the

stacking faults was due to the diffusion of Si or C atoms and it also demonstrated that

the migration energy of Si atoms was smaller than C atoms Considering the

abundance of intrinsic defects (section 222) there has been little investigation of

their effects on microstructure change of β-SiC after thermal treatment Furthermore

the effects of high temperature thermal treatment on mechanical properties such as

the hardness Youngrsquos modulus [97] and strength [98] have been carried out Their

results showed that mechanical properties showed little change when the treatment

temperature was lower than 2000 ordmC while there was decrease in the strength after

thermal treatment at 2100 ordmC

24 Microstructure and properties of pyrolytic carbon

In this part the microstructure of carbon related material is reviewed first which is

followed by the measurement of Youngrsquos modulus and hardness Furthermore to

know the controlling factor on mechanical properties of PyC coatings different

deformation mechanisms under indentation are introduced A brief review about effect

of thermal treatment on properties of PyC coatings is given


61

241 Microstructure of pyrolytic carbon




The graphite structure consists of graphene sheets having localized in-plane σ (sp2)

hybrids bonds and delocalized out of plane π (pz) orbital bonds connecting graphene

sheets The out-of-plane bond is a van der Waals interaction which is much weaker

than sp2 and sp

3 hybrids Pyrolytic carbon is a material with some covalent bonding

between its graphene layers as a result of imperfections (defects) in its structure [99]

Figure 217 gives schematics and TEM images showing different microstructures of

PyC with different densities The growth features are polyhedral or conical shape in

high density pyrolytic carbon (Fig 217 (ab)) but are globular in low density

pyrolytic carbon (Fig 217(cd)) [15] It shows that the microstructure of pyrolytic

carbon consists of growth features between 200 nm- 1000 nm in size (Fig 217 (b)

and (d)) [15] Pores were formed at the boundaries or triple junctions between growth

(a) (b)

(c) (d)


62

features

According to previous studies [15101] individual growth features contain crystallites

(domains) as shown schematically in Fig 218(a) They are composed of a series of

curved graphene layers randomly rotated with respect to each other along the c-axis

[101] The dimensions of the crystal were described by La (diameter of crystal along

the χ direction) and Lc (height of the crystal perpendicular to χy plane) as shown in

Fig 218(a) Regarding the definition of the PyC there are defects within the growth

features together with crystallites A local atomic structure of less ordered graphene

layers is shown in Fig 218(b) which could reflect the plane defects in graphene

layers [102]



A high density of defects such as dislocation loops and kink bands were observed in

ball milled graphite by HRTEM as shown in Fig 219(a) The distorted

microstructure of graphite was also inferred from the striped diffraction points in

selected area electron diffraction image (Fig 219(b)) [103] since the diffraction

pattern gives information on orientation of crystal planes Compared with ball milled

graphite the HRTEM image of pyrolytic carbon has higher amount of defects as

shown in Fig 19(c) which is reflected from the highly distorted lattice planes and low

texture The selected area electron diffraction image of pyrolytic carbon (Fig 219(d)

with eperture diameter of 200 nm) showed arc shaped diffraction patterns [15 104]

The arc represents the overlap of diffraction patterns from different graphite domains


63

with different orientations and this indicats that the microstructure is more distorted

eg smaller domain size and increased random orientation of domains In heavily

disordered PyC it is not possible to observe the individual dislocations or other

defects which is thought to be due to the numerous defects such as tilt boundaries

which obscure individual defects as described in Ref [105]





Raman spectroscopy is one of the most effective techniques to characterise the defects

in carbon materials and has previously been used to characterise the microstructure of

PyC [15 106] These spectra can identify even quantify the microstructure such as

crystallite boundaries and size disorders (5-memebered rings) and chemical bonding

type Figure 220 shows the evolution of the Raman spectra with the change of the


64

in-plane defect types The carbon spectra of Fig 220(a-c) showed increased and

broadened D signal and the main in-plane defects observed in these structures were

supposed to be domain boundaries [15] In Fig 220(d-e) the D signal became shaper

which was attributed to the formation of five-member rings [15]




The high density of disorders such as in-plane domain boundaries makes the Raman

bands become broder and overlapped with each other as shown in Fig 220(c) which

inferred the structure of turbostratic or high density PyC [10 15] According to

previous studies [106 107] the broadened Raman bonds could be deconvoluted into a

number of peaks which correspond to different types of disordered structure in

carbon materials Figure 221 is an example of a first order Raman spectra fitted with

Lorentzian and Gaussian functions and it includs I (~1170 cm-1

) D (~1330 cm-1

) Drdquo

(~1500 cm-1

) G (~1580 cm-1

) and Drsquo(~1618 cm-1

) bands [106] The Drdquo peak was


65

attributed to amorphous carbon with a certain amount of sp3 carbon [106108] which

could reflect the interstitial defects coupling to the graphene layers or adjacent

domains [109]


242 Mechanical properties of pyrolytic carbon

The different deformation mechanism of carbon materials compared to ceramic

materials results in distinct force-displacement curves which show the complete

recovery of the unloading curve [110 111] Therefore we describe the mechanical

properties of PyC coatings and deformation mechanism of carbon materials

2421 Youngrsquos modulus and hardness

Due to the importance of PyC in the nuclear industry mechanical properties were

measured by three-point bending [102 112] and nano-indentation [113-115] Table

26 gives the Youngrsquos modulus and hardness of PyC measured by different methods

In three-point bending tests the mechanical properties were functions of density

orientation angle and domain size No individual factor could clearly explain the

variation in Youngrsquos modulus strength or fracture toughness [112116] In previous

nano-indentation tests the low density PyC was found to have low hardness and

Youngrsquos modulus [114] whereas the influence on mechanical properties was


66

uncertain which could be due to lack of investigation about the deformation

mechanisms

Table 26 Summary of the hardness and Youngrsquos modulus for PyC measured by

different methods

Methods Density range

(gcm3)

Youngrsquos modulus

(GPa)

Hardness

(GPa)

Ref

3-point-bending 150-212 310-427 -- 112

137-206 165-281 -- 116

Nano-indentation 185-190 255 + 2 -- 114

165-203 235-270 30-44 115

155-187 70-150 05-18 115

135-212 125-346 15-48 113

Youngrsquos modulus was changed from PSI to GPa

Figure 222 is a schematic of the typical force-displacement curve of different kinds

of materials under indentation [65110111] The curve of carbon materials shows a

completely recovery and no net displacement after unloading as shown in Fig

222(a) In carbon materials the force-displacement curve formed a closed loop and

this phenomenon was called anelastic deformation behaviour [14 117] This was

related to the internal friction of materials but there is controversy regarding the

sources of the internal friction [14105111] Since the force-displacement curve gives

information about the energy change during indentation the deformation behaviour of

carbon material can be analysed by the energy method

The energy distribution under indentation is shown in Fig 222 which includs the

hysteresis energy (Uh) and unloading energy (Uunloading) and the total energy (loading

energy Uloading) is the sum of the above two energies [110] As shown in Fig 222 the

ratio of the hysteresis energy to total loading energy could be different for different

microstructure of carbon materials [118] The ratio could be used to estimate the


67

flexibility of elasticityductility [110119] For example a low ratio corresponds to

higher elasticity whist a high ratio meants higher ductility



The different force-displacement curve of carbon materials was compared with the

irreversible deformation behaviour of materials with linear elasticity such as SiC as

shown in Fig 214(a) [65] In linear elastic deformation the final displacement of hf

was left after complete unloading and the unloading curve nearly followed the linear

relationship Furthermore the area between the loading and unloading curves

represents the energy consumed by the plastic deformation which could be due to the

movement of dislocations and formation of micro cracks [1 62]

2422 Deformation mechanism

Reversible slip and sliding friction theory In this theory the complete recovery of

strain was due to the reversible slip of graphene planes and the energy loss was

attributed to the friction during the slip which was caused by a compressive stress on

the graphene layers [110111] The theory was obtained by considering an arbitrary

grain located at some position in a radially declining hydrostatic stress field below a

spherical indenter as shown in Fig 223 [110111] The force was resolved into


68

compressive stress perpendicular to and shear stress parallel to the slip plane By

using the equation proposed by Kelly [120] the shear component (τ τ0 shear stress

with and without friction respectively) may be expressed as τ= τ0 +μσ where μ is a

friction coefficient and σ is normal stress component To initiate slip between

graphene layers the shear stress needs to exceed some critical value Therefore the

inter-layer slip with friction was supposed to be the mechanism of anelastic

deformation The authors [110111] also concluded that the hysteresis during

unloading appeared to be a natural result of friction between the graphene layers but

additional mechanisms were supposed to be operating in the different forms of

graphitic materials Furthermore the study did not give a clear explanation about how

the reversibility of the basal plane slip was realized


indenter [110]

Dislocation pileup theory This idea was derived from isotropic carbon after thermal

treatment at the temperature range of 880-2600 ordmC by using micro indentation [121]

The authors attributed the unique unloadingreloading behaviour of the

well-graphitized carbons to the slip of dislocation networks on graphitic basal planes

which is partially or fully reversible It is supposed that the dislocations could pile up

at grain boundaries as in metals The stress at grain boundaries due to dislocation pile

ups could reverse the dislocation movement during indentation unloading but it did


69

not explain why deformation behaviour of PyC is unlike that of metals This is also

the reason that other researches [105] doubt this theory because it fails to explain the

nature of the reversible behaviour [121]

Kink band theory It was suggested that the origin of the loops obtained in single

polycrystalline and porous carbons is the formation of incipient kink band and kink

bands [105] The kink band model was proposed by Frank and Stroh [122] as

shown in Fig 224 which showed pairs of dislocations of opposite sign nucleate and

grow at the tip of a thin elliptical kink (not clear about the nature) The stability of

kink bands depended on a shear stress [122]




In this theory since the dislocations were confined to the basal plane the hysteresis

process was attributed to the reversible movement of the dislocation along a long

distance The same mechanism was used to explain the deformation behaviour of the

bulk polycrystalline graphite The microstructural change under indentation should

first be related to the kink band initiation and then further microstructure change

could be reflected in the accumulation of other chemical bonds which could resist

dislocation glide


70

2423 Effect of thermal treatment on properties of PyC

The effect of thermal treatment on the microstructure of carbon materials has been

widely studied [112 123 124] The change of the microstructure of carbon materials

during thermal treatment mainly involves the growth of the domain size (in-plane

crystal size along a axis) La and (along c axis crystal size) Lc with the increase of

temperature For different kinds of carbon materials these evolutions started at

different temperatures For example the crystal growth in-plane happened at 400-600

ordmC for graphitisable carbon and could continue up to high temperature the

coalescence of crystallites along the c-axis started above 1000-1200 ordmC the

coalescence of crystallites along ab direction occurred at temperature above 1400 ordmC

[124] For carbons with strong cross-linking (non-graphitisable) the coalescence of

domains usually happened at temperatures higher than 2400 ordmC [124] Although the

increase in anisotropy and density during processing of coated particle fuel was

reported by Hunn et al [11] no change in texture was identified on PyC due to the

post deposition of SiC shown in Lopeacutez-Honorato et alrsquos study [125] Furthermore no

significant change of mechanical properties was obtained after thermal treatment at

temperatures in the range 1000-1980 ordmC in PyC coatings with density of about 19

gcm3 [97] however a decrease of Youngrsquos modulus was observed in high density

(above 2 gcm3) PyC coatings [125] It was assumed that certain microstructures of

PyC would be less affected by thermal treatment

25 Summary

The microstructure and mechanical properties of SiC and PyC were reviewed in this

Chapter and the information obtained is summarized below

(1) It is common for SiC to have defects such as stacking fautls and dislocations

non-stoichiometry and point defects due to their low formation energy

particularly in SiC deposited by chemical vapour deposition


71

(2) Defects interact with each other Stacking faults could be the result of gliding

of partial dislocations Vacancies promoted diffusion of antisites forming

antisite clusters

(3) The Youngrsquos modulus of SiC coatings in TRISO fuel particle is affected

mainly by texture and porosity

(4) Hardness related plastic deformation in single and polycrystalline (nano-meter

or micro-meter grain size) SiC is related to dislocation propagation fracture

of crystallites or phase transformation

(5) A combination of indentation together with electron microscopy is an

effective way to study the fracture behaviour of SiC coatings in TRISO fuel

particle

(6) Fracture strength of SiC coating in TRISO fuel particle varies significantly in

different measurements and the modified crush test is recommended The

interface roughness and porosity are found to be main factors controlling

fracture strength of SiC coatings

(7) The typical change of microstructure after thermal treatment in SiC is the

annihilation of stacking faults through the diffusion of vacancies

(8) The disorder in PyC coatings could be significant such as domain boundaries

and 5-membered rings Raman spectroscopy together with transmission

electron microscopy are important techniques to characterize these disorders

(9) Carbon related materials show hysteretic deformation behaviour under

indentation Different deformation mechanisms are proposed which all relate

to the slip of graphene layers


72

26 References


of SiC properties for fuel performance modeling J Nucl Mater 371 (2007)

329-77

[2] DT Goodin Accident condition performance of fuels for high-temperature gas

-cooled reactors J Am Ceram Soc 65 (1982) 238-42

[3] D J Green An Introduction to the mechanical properties of ceramics 1st ed

Cambridge Solid State Science Series Cambridge the University Press 1998

[4] K H Park T Hinoki A Kohyama Influence of irradiation-induced defects on

fracture behavior in highly pure SiC J Nucl Mater 367 (2007) 703-07

[5] T S Byun J D Hunn J H Miller L L Snead J W Kim Evaluation of

Fracture Stress for the SiC Layer of TRISO-Coated Fuel Particles Using a

Modified Crush Test Method Int J Appl Ceram Tec 7 (2010) 327-37

[6] X Li B Bhushan A review of nanoindentation continuous stiffness

measurement technique and its applications Mater Charact 48 (2002) 11-36

[7] A Grabulov U Ziese HW Zandbergen TEMSEM investigation of

microstructural changes within the white etching area under rolling contact

fatigue and 3-D crack reconstruction by focused ion beam Scripta Matterialia 57

(2007) 635-38



bed chemical vapor deposition J Mater Res 23 (2008) 1785-96

[9] T Lin A G Evans R O Ritchie A Statistical-Model of Brittle-Fracture by

Transgranular Cleavage J Mech Phys Solids 34 (1986) 477-97

[10] A G Evans C Padgett R W Davidge Strength of Pyrolytic Sic Coatings of

Fuel Particles for High-Temperature Gas-Cooled Reactors J Am Ceram Soc

56 (1973) 36-41


73


anisotropy and density during processing of coated fuel due to heat treatment J

Nucl Mater 374 (2008) 445-52

[12] D G Martin Considerations pertaining to the achievement of high burn-ups in

HTR fuel Nucl Eng Des 213 (2002) 241-58

[13] G K Miller D A Petti D J Varacalle J T Maki Consideration of the effects

on fuel particle behaviour from shrinkage cracks in the inner pyrocarbon layer J

Nucl Mater 295 (2001) 205-12

[14] G K Miller D A Petti J T Maki Consideration of the effects of partial

debonding of the IPyC and particle asphericity on TRISO-coated fuel behaviour

J Nucl Mater 334 (2004) 79-89

[15] E Loacutepez-Honorato P J Meadows P Xiao Fluidized bed chemical vapour

deposition of pyrolytic carbon - I Effect of deposition conditions on

microstructure Carbon 47 (2009) 396-410

[16] R Cheung Silicon carbide microelectromechnical systems for harsh

environments Imperial College Press 2006 p 3

[17] M Iwami Silicon carbide fundamentals Nuclear instruments and methods in

physics research section A accelerators spectrometers detectors and associated

equipment 466 (2001) 406-11

[18] V V Pujar J D Cawley Effect of stacking faults on the X-ray diffraction

profiles of β-SiC powders J Am Ceram Soc 78 (1995) 774-82

[19] W F Knippenberg Growth phenomena in silicon carbide Philips Res Report

18 (1963) 161-274

[20] P Krishna RC Marshall CE Ryan The discovery of a 2H-3C solid state

transformation in silicon carbide single crystals J Crys Grow 8 (1971) 129-31

[21] S Sugiyama M Togaya Phase relationship between 3C- and 6H-silicon carbide

at high pressure and high temperature J AmCeramSoc 84 (2001) 3013-16

[22] R Stevens Defects in silicon carbide J Mater Sci 7 (1972) 517-21


74

[23] C Wang J Bernholc Formation energies abundances and the electronic

structure of native defects in cubic SiC Phys Rev B 38 (1988) 12752-56

[24] P Kaumlckell JFurthmuumlller FBechstedt Stacking faults in group-IV crystals an ab

initio study Phys Rev B 58 (1998) 1326-30

[25] U Lindefelt H Iwata S Oumlberg P R Briddon Stacking faults in 3C- 4H and

6H-SiC polytypes investigated by an ab initio supercell method Phys Rev B 67

(2003) 155204-15

[26] P T B Shaffer A review of the structure of silicon carbide Acta Crystal Sec B

25 (1969) 477-88

[27] P J H Denteneer W v Haeringen Stacking-fault energies in semiconductors

from first principle calculations J Phys C Solid State Phys 20 (1987) 883-87

[28] X G Ning H Q Ye Experimental determination of the intrinsic stackingfault

energy of SiC crystals J Phy Condens Matter 2 (1990) 10223-25

[29] P J H Denteneer W v Haeringen Ground-state properties of wurtzite silicon

carbide Solid State Commun 65 (1988) 115-19

[30] P J H Denteneer Stacking-fault energies in silicon diamond and silicon

carbide Mater Res Soc 141 (1988) 343-48

[31] K Karch G Wellenhofer P Pavone U Roumlssler D Strauch Proceedings of the

22nd international conference on the physics of semiconductors 1995 p 401

[32] C Cheng V Heine and R J Needs Atomic relaxation in silicon carbide

polytypes J Phys Condensed Matter 2 (1990) 5115-34

[33] M Marinova A Mantzari E K Polychroniadis Some recent results on the

3C-SiC structural defects Solid State Phenom 159 (2010) 39-48

[34] VV Pujar JD Cawley Computer simulations of diffraction effects due to

stacking faults in β-SiC II Experimental verification J Am Ceram Soc 84

(2001) 2645-51

[35] B Reznik DGerthsen W Zhang K J Huumlttinger Microstructure of SiC

deposited from methyltrichlorosilane J Eur Ceram Soc 23 (2003) 1499ndash508


75

[36] T Mitani S Nakashima H Okumura et al Raman Scattering Analyses of

Stacking Faults in 3C-SiC Crystals Mater Sci Forum 527-29 (2006) 343-46

[37] G Newsome LL Snead T Hinoki et al Evaluation of neutron irradiated

silicon carbide and silicon carbide composites J Nucl Mater 371 (2007) 76-89

[38] httpwwwtfuni-kieldematwisamatdef_enkap_5backboner5_4_2html

[39] P Pirouz J W Yang Polytypic transformations in SiC the role of TEM

Ultramicroscopy 51 (1993)189-214

[40] S Guha J M DePuydt J Qiu Role of stacking faults as misfit dislocation

sources and nonradioactive recombination centres in II-VI heterostructures and

devices Appl Phys Lett 63 (1993) 3023-25

[41] AK Agarwal SKrishnaswami JRichmond et al Influence of basal plane

dislocation induced stacking faults on the current gain in SiC BJTs Mater Sci

Forum 527-29 (2006) 1409-12

[42] N W Mueggenburg H M Jaeger S R Nagel Stress transmission through

three-dimensional ordered granular arrays Phys Rev E 66 (2002) 031304

[43] S Somiya Y Inomata Silicon carbide ceramics-2 ceramic research and

development in Japan p1-18

[44] A Gali N T Son E Janzeacuten Electrical characterization of metastable carbon

clusters in SiC A theoretical study Phys Rev B 73 (2006) 033204-08

[45] C Chu Y Luand M Hon Growth characteristics of β-SiC by chemical vapour

deposition J Mater Sci 27 (1992) 3883-88

[46] J Tan Mechanical properties of SiC in TRISO fuel particle PhD Thesis

University of Manchester 2010

[47] Z R Huang B Liang DL Jiang S H Tan Preparation of nanocrystal SiC

powder by chemical vapour deposition J Mater Sci 31 (1996) 4327-32

[48] R A Shatwell K L Dyos C P Rentice Y Ward R J Young

Microstructural analysis of silicon carbide monofilaments J Microscopy 201

(2001) 179-88


76

[49] S M Dong G Chollon C Labrugere M Lahaye A Guette J L Bruneel M

Couzi R Naslain D L Jiang Characterization of nearly stoichiometric SiC

ceramic fibres J Mater Sci 36 (2001) 2371-81

[50] K Kaneko M Kawasaki T Nagano et al Determination of the chemical width

of grain boundaries of boron- and carbon-doped hot-pressed β-SiC by HAADF

imaging and ELNES line-profile Acta Materialia 48 (2000) 903-10

[51] O O Mykhaylyk M P Gadzira Superhard materials based on the solid solution

SiC-C J Mater Chem 11 (2001) 217-22

[52] O O Mykhaylyk YZ Khimyak JP Attfield Phase Segregation in Silicon

Carbide-Carbon Solid Solutions from XRD and NMR Studies Chem Mater 14

(2002) 1348-35

[53] E Janzeacuten N T Son N Magnusson A Ellison Intrinsic defects in high-purity

SiC Microelectronic Eng 83 (2006) 130-34

[54] E Rauls Th Frauenheim A Gali PDeaacutek Theoretical study of vacancy

diffusion and vacancy-assisted clustering of antisites in SiC Phys Rev B 68

(2003) 155208-09

[55] N T Son P N Hai E Janzeacuten Carbon vacancy-related defect in 4H and 6H SiC

Phys Rev B 63 (2001) 201201-04

[56] X Shen M P Oxley Y Puzyrev B R Tuttle G Duscher S T Pantelides

Excess carbon in silicon carbide J Appl Phys 108 (2010) 123705-10

[57] J M Grow R A Levy Micromechanical characterization of chemically vapor

deposited ceramic films J Mater Res 9 (1994) 2072-78

[58] T D Guldn H Nickel Coated particle fuels Nucl Technol 35 (1977) 206-35

[59] KB Tolpygo Optical elastic and piezoelectric properties of ionic and valence

crystals with ZnS type lattice Sov Phys Solid State 2 (1961) 2367

[60] D W Feldman J H Parker Jr J W Choyke L Patrick Phonon dispersion

curves by Raman scattering in SiC polytypes 3C 4H 6H 15R and 21R Phys

Rev 173 (1968) 787-93


77

[61] W R L Lambrecht B Segall M Methfessel M van Schilfgaarde Calculated

elastic constants and deformation potentials of cubic SiC Phys Rev B 44

(1991) 3685-94

[62] X Zhao R M Langford I P Shapiro P Xiao Onset plastic deformation and

cracking behaviour of silicon carbide under contact load at room temperature J

Am Ceram Soc 94 (2011) 3509-14

[63] R W Rice Mechanical properties of ceramics and composites 1st ed New

York Marcel Dekker 2000 p 457-534

[64] O Grabco O Shikimaka E Harea Translation-rotation plasticity as basic

mechanism of plastic deformation in macro-micro- and nanoindentation

processes J PhyD Appl Phys 41 (2008) 074016-24

[65]W C Oliver GMPharr An improved technique for determining hardness and

elastic-modulus using load and displacement sensing indentation experiments J

Mater Res 7(1992)1564-83

[66] MC Osborne JC Hay LL Snead Mechanical- and physical-property changes

of neutron-irradiated chemical-vapour-deposited silicon carbide J Am Ceram

Soc 82 (1999) 2490-96

[67] D M Teter Computational alchemy the search for new superhard materials

MRS Bull 23 (1995) 22-27

[68] S Nagappa M Zupan CA Zorman Mechanical characterization of

chemical-vapor-deposited polycrystalline 3C silicon carbide thin films Scripta

Materialia 59 (2008) 995 -98

[69] M J Slavin G D Quinn Mechanical property evaluation at elevated

temperature of sintered β-silicon carbide Inter J High Tech Ceram 2 (1986)

47-63

[70] T F Page L Rester S V Hainsworth The plasticity response of 6H-SiC and

related isostructural materials to nanoindentation Slip vs densification Mater

Res Soc Symp P 522 (1998) 113-18


78

[71] I Szlufarska R K Kalia A Nakano P Vashishta Atomistic mechanisms of

amorphization during nanoindentation of SiC A molecular dynamics study Phys

Rev B 71 (2005) 174113-23

[72] I Szlufarska A Nakano P Vashishta A crossover in the mechanical response of

nanocrystalline ceramics Science 309 (2005) 911-14

[73] S J Zhou X Y Zhou Y S Zhao Study of hardness and deformation of brittle

materials with a density functional theory J Appl Phys 104 (2008) 053508-16

[74] A C Fischer-Cripps Introduction to Contact Mechanics Mechanical

Engineering Series 1st ed New York Springer 2000

[75] I Zarudi J Zou L C Zhang Microstructures of phases in indented silicon A

high resolution characterization Appl Phys Lett 82 (2003) 874

[76] M Mishra I Szlufarska Possibility of high-pressure transformation during

nanoindentation of SiC Acta Mater 57 (2009) 6256-6165

[77] D Munz T Fett Ceramics Mechcanical properties failure properties failure

behavior and materials selection Springer Verlag NewYork 1999 p 20

[78] X Zhao RM Langford J Tan P Xiao Mechanical properties of SiC coatings

on spherical particles measured using the micro-beam method Scripta Mater 59

(2008) 39ndash42

[79] G D Quinn RC Bradt On the Vickers indentation fracture toughness test J

Am Ceram Soc 90 (2007) 673-80

[80] R Morrell Fracture toughness testing for advanced technical ceramics

internationally agreed good practice Adv Appl Ceram 105 (2006)1-11

[81] R E Cook G M Pharr Direct observation and analysis of indentation cracking

in glasses and ceramics J Am Ceram Soc 73 (1990) 787 - 817

[82] S S Chiang D B Marshall AG Evans The response of solids to elasticplastic

indentation I stresses and residual stresses J Appl Phys 53 (1982) 298-311

[83] M T Laugier Palmqvist toughness in Wc-Co composites viewed as a ductile

brittle transition J Mater Sci Lett 6 (1987) 768-70


79

[84] G R Anstis P Chantikul B R Lawn D B Marshall A critical-evaluation of

indentation techniques for measuring fracture-toughness 1 Direct Crack

Measurements J Am CeramSoc 64 (1981) 533-38

[85] X F Zhang Q Yang L C D Jonghe Microstructure development in

hot-pressed silicon carbide effects of aluminium boron and carbon additives

Acta Mater 51 (2003) 3849-60

[86] T Watanabe The impact of grain boundary character distribution on fracture in

polycrystals Mater Sci Eng A 176 (1994) 39-49

[87] S J Xu J G Zhou B Yang B Z Zhang Effect of deposition temperature on

the properties of pyrolytic SiC 224 (1995) 12-16

[88] K Bongartz E Gyarmati H Schuster K Tauber Brittle ring test ndash method for

measuring strength and Youngs modulus on coatings of HTR fuel particles J

Nucl Mater 62 (1976) 123-37

[89] S G Hong T S Byun R A Lowden L L Snead Y Katoh Evaluation of the

fracture strength for silicon carbide layers in the Tri-Isotropic-Coated fuel particle

J Am Ceram Soc 90 (2007) 184-91

[90] J W Kim TSByun YKatoh Optimization of fracture strength tests for the SiC

layer of coated fuel particles by finite element analysis

[91] Roark Young Wc Formulas for stress and strain Mc Graw-Hill New York

1974

[92] SDKurbakov TAMireev Deposition of high-density silicon carbide coatings

by fluidized-bed pyrolysis of chlorinated silane derivatives Solid Fuel Chem 43

(2009) 113-23

[93] M Hundhausen R Puumlsche J Roumlhrl L Ley Characterization of defects in

silicon carbide by Raman spectroscopy Phys Stat Sol 245 (2008) 1356-68

[94] N Shirahata K Kijima A Nakahira and K Tanaka Thermal stability of

stacking faults in beta-SiC Sci Eng Ceram Ii 2 (1999) 623-26


80

[95] W S Seo C H Pai K Koumoto H Yanagida Microstructure development and

stacking fault annihilation in β-SiC powder compact Ceram Soc Jap 99 (1991)

443-47

[96] Z G Cambaz G N Yushin Y Gogotsi K L Vyshnyakova L N

Pereselentseva Formation of carbide-derived carbon on beta-silicon carbide

whiskers J Am Ceram Soc 89 (2006) 509-14

[97] I J V Rooyen J H Neethling J Mahlangu Influence of temperature on the

micro-and nanostructures of experimental PBMR TRISO coated particles A

comparative study Proceedings of the 4th international topical meeting on high

temperature reactor technology HTR 2008 September 28-October 1 2008

Washington DC USA HTR 2008-58189

[98] I J v Rooyen J H Neethling P M v Rooyen The influence of annealing

temperature on the strength of TRISO coated particles J Nucl Mater 402 (2010)

136-46

[99] httpenwikipediaorgwikiPyrolytic_carbon

[100]J L Kaae Microstructures of isotropic pyrolytic carbons Carbon 13 (1975)

55-62

[101]Z Q Li C J Lu Z P Xia Y Zhou Z Luo X-ray diffraction patterns of

graphite and turbostratic carbon Carbon 45 (2007) 1686-95

[102]W P Hoffman W C Hurley P M Liu T W Owens The surface topography

of non-shear treated pitch and PAN carbon fibers as viewed by the STM J

Mater Res 6 (1991) 1685-94

[103]J Y Huang HRTEM and EELS studies of defects structure and amorphous-like

graphite induced by ball-milling Acta Mater 47 (1999) 1801-08

[104]P J Meadows E Loacutepez-Honorato P Xiao Fluidized bed chemical vapour

deposition of pyrolytic carbon-II Effect of deposition conditions on anisotropy

Carbon 47 (2009) 251-62


81

[105]M W Barsoum A Murugaiah S R Kalidindi T Zhen YGogotsi Kink bands

nonlinear elasticity and nanoindentations in graphite Carbon 42 (2004) 1435-45

[106]J M Vallerot X Bourrat A Mouchon G Chollon Quantitative structural and

textural assessment of laminar pyrocarbons through Raman spectroscopy

electron diffraction and few other techniques Carbon 44 (2006) 1833-44

[107]A Sadezky H Muckenhuber H Grothe R Nissner U Poschl Raman

microspectroscopy of soot and related carbonaceous materials spectral analysis

and structural information Carbon 43 (2005) 1731-42

[108]A C Ferrari Raman spectroscopy of graphene and graphite Disorder

electron-phonon coupling doping and nonadiabatic defects Solid State

Communic 143 (2007) 47-57

[109]J N Rouzaud A Oberlin Carbon films Structure and microtexture (optical and

electron microscopy Raman spectroscopy) Thin Solid Films 105 (1983) 75-96

[110]N Iwashita Elasto-plastic deformation of glass-like carbons heat-treated at

different temperatures Carbon 39 (2001) 1525-32

[111]N Iwashita J S Field M V Swain Indentation hysteresis of glassy carbon

materials Philosophical Magazine A 82 (2002) 1873-81

[112]J C Bokros R J Price Deformation and fracture of pyrolytic carbons

deposited in a fluidized bed Carbon 3 (1966) 503-19

[113]E Loacutepez-Honorato P J Meadows P Xiao G Marsh T J Abram Structure

and mechanical properties of pyrolytic carbon produced by fluidized bed

chemical vapour deposition Nucl Eng Des 238 (2008) 3121-28

[114]C Bellan J Dhers Evaluation of Youngrsquos modulus of CVD coatings by

different techniques Thin solid films 469-70 (2004) 214-20

[115]G Hofmann M Wiedenmeier M Freund A Beavan J Hay G M Pharr An

investigation of the relationship between position within coater and pyrolytic

carbon characteristic using nanoindentation Carbon 38 (2000) 645-53


82

[116]J L Kaae Relations between the structure and the mechanical properties of

fluidized-bed pyrolytic carbons Carbon 9 (1971) 291-99

[117]L M Brown In H Libelt R Talreja Fatigue and creep of composites

materials Riskilde Denmark Riso National Laboratory 1982 p 1-18

[118]M Skai The Meyer hardness A measure for plasticity J Mater Res 14 (1999)

3630-39

[119]M Sakai R Nowak In Bannister MJ editor Austceram 92 Ceramics ndash adding

the value Vol 2 Melbourne The Australian Ceramic Society 1992 p 922-31

[120]B T Kelly The physics of graphite Applied Science Publications London

1981

[121]M Sakai Y Nkano S Shimizu Elastoplastic indentation on heat-treated

carbons J Am Ceram Soc 85 (2002) 1522-28

[122]F C Frank A N Stroh On the theory of kinking Proc Phys Soc 65 (1952)

811-21

[123]R F Franklin Royal Society London A London 1951 209 196

[124]F G Emmerich Evolution with heat treatment of crystallinity in carbons

Carbon 33 (1995) 1709-15

[125]E Loacutepez-Honorato P J Meadows R A Shatwell P Xiao Characterization

of the anisotropy of pyrolytic carbon by Raman spectroscopy Carbon 48 (2010)

881-90

CHAPTER 3 Hardness amp Youngrsquos modulus of SiC coatings measured by indentation

83

CHAPTER 3 Hardness and Youngrsquos Modulus of SiC

Coatings Measured by Indentation

31 Introduction

The silicon carbide (SiC) coating is the most important component for structural

integrity of Tri-isotropic (TRISO) fuel particles as it sustains most of the internal

pressure produced by the fission gases produced in the kernel [1-3] Youngrsquos modulus

and hardness are mechanical properties used in modeling to estimate the failure

probability of TRISO fuel particles [4] The values at room temperature are used due

to the fact that the Youngrsquos modulus slightly decreased at elevated temperature in SiC

material and the higher value could be kept until the temperature reached 2000 degC [1]

It was also found that SiC material with higher hardness at room temperature

maintains higher hardness values at temperatures up to 1600 degC [1] To achieve a

reliable fuel design a better understanding of the mechanical properties of the SiC

layer at room temperature needs to be established

It is difficult to use traditional methods to measure hardness and Youngrsquos modulus

due to the small dimension of the TRISO fuel particles (~1 mm) Nano-indentation

has made it possible to measure the hardness and Youngrsquos modulus accurately [5 6]

for a coating of such a small dimension Furthermore this method also offers the

ability to study the deformation behaviour under the indentation [7-12] as the

indentation stress field is of a localized character

Loacutepez-Honorato et alrsquos [5] study of SiC deposited at 1300 degC by fluidized bed


84

chemical vapour deposition (FBCVD) showed that the SiC coatings produced under

those conditions had high hardness (gt 42 GPa) and Youngrsquos modulus (~455 GPa)

They found that even samples with the composition of SiC+C or SiC+Si showed high

mechanical properties It was shown that the coatings had sub-micrometer (lt1 μm

diameter) grain size but due to the complex microstructure the mechanism controlling

the hardness and Youngrsquos modulus was unknown Researchers [10 11 13-16] have

made efforts to study the deformation mechanism under indentation in SiC single

crystals and polycrystals (with a grain size lt 100 nm or grain size gt 1μm) Szlufarska

et al [15] suggested a crossover mechanism from indentation-induced crystallization

to deformation-dominated amorphization in nano-crystalline SiC

From the work reported [11 16 17] it is clear that dislocation initiation and

propagation is the primary response for the plastic deformation under an indentation

in single crystal and polycrystalline (gt 1μm) SiC Further it has also been found

while studying the microstructure [11 16 17] that defects such as stacking faults and

dislocations were present in these polycrystalline (gt 1 μm) SiC materials

(nano-indentation hardness less than 36 GPa) However the amount of defects were

lower compared to the low temperature (ie 1300 o

C vs 1500 o

C) FBCVD SiC [5]

The discrepancies in the microstructure and mechanical properties still demand

further explanation on the deformation mechanism of low temperature FBCVD SiC

This chapter focus on the fundamental study on the mechanical properties of SiC we

have investigated the Youngrsquos modulus and hardness of three sub-micrometer FBCVD

SiC coatings using the indentation method The microstructure and mechanical

properties are explained on the basis of defects observed with a transmission electron

microscope (TEM) The deformation behaviour underneath a nano-indentation is

discussed


85

32 Experimental details

Silicon carbide (SiC) coatings were produced on top of highly-dense pyrolytic carbon

coatings using fluidized-bed chemical vapour deposition (FBCVD) method The SiC

coatings with varied stoichiometry and deposited at low temperature of 1300 oC by

Loacutepez-Honorato et alrsquos [5] were chosen and studied in this Chapter Table 1 gives the

deposition conditions of these coatings which were found and demonstrated to give

superberb mechanical properties in prevous studies [5] Figure 31(a) and (b) show the

polished cross-section (x-y plane) and (b) polished external surface section (x-z plane)

of TRISO fuel particles (defining the directions used in the later part of this Chapter)

Densities were measured by the Archimedes method in ethanol (density is the mean

value of three tests the weight of SiC shells is 01-03 g) Composition was measured

by Raman spectroscopy (Renishaw 1000 Raman system with a 514 nm argon laser

source) with a single spot measurements of around 1 microm diameter through an times50

objective lens as shown in Fig 31 (c) Two peaks at around 794 and 970 cm-1

are for

SiC and the asymmetric peaks around 200-500 cm-1

and 1500 cm-1

are acoustic SiC

and second order SiC respectively (S1 coating) [5] Carbon peaks are around 1360

and 1600 cm-1

(S2 coating) and the peak at 520 cm-1

represents silicon (S3 coating)

[5] It was estimated that the excess C amount is less than 1 at in S2 by measuring

the intensity ratios of I1600I794 and compared to previous study [18] where Raman

spectroscopy and elemental analysis (EPMA AES and XPS) were used

The phase and composition were also analysed using X-ray diffraction (XRD PW

1830 Philips Eindhoven The Netherlands) with Cu Kα1 radiation Figure 31(d)

shows the XRD spectra of the three types of SiC coatings All three coatings exhibit

the β-SiC phase A very small shoulder peak around 2θ=345deg was also obtained from

the coatings which indicated the presence of stacking faults No evidence of a Si or C

peak was found in the XRD result This was probably due to the fact that the

additional levels of Si and C were very small (le 1at ) and it would be difficult to


86

identify these traces using XRD [5 19]


Codes H2MTCS (volvol) Additives Temperature Density (gcm3)

S1 (SiC) 10 01vol Propylene 1300 o

C 3173 + 0029

S2 (SiC+C) 10 10 vol Propylene 1300 o

C 3135 + 0034

S3 (SiC+Si) 10 -- 1300 o

C 3188 + 0002

SiC+C or SiC+Si means that nearly stoichiometric SiC with low excess C or Si less than 1 at

Productions of samples are contributed by Dr Eddie Loacutepez-Honorato

SiC coated fuel particles were hot mounted in copper-loaded conductive resin To

reduce the influence of the surface roughness the FBCVD SiC coatings were first

ground down to obtain a flat surface where the nano-indentation could be carried out

The flat surface was further polished using increasingly finer diamond suspensions

until frac14 μm and finally polished using a 003 μm colloidal silica suspension The

thickness of the coating after final polishing was estimated to be around 60 μm A

final surface roughness of lt 5 nm was detected by atomic force microscopy (AFM)

Youngrsquos modulus and hardness were measured using a nano-indenterTM

XP (MTS

System Corp USA) and a micro-indenter (CSM Instruments Switzerland)

Nano-indentation was made using a Berkovich indenter calibrated with a standard

silica specimen Before the measurement the initial contact of the indenter with the

specimen surface was checked and the compliance of the loading column was

corrected Arrays of indentations were performed on each specimen with an interval

of 20 times the indentation depth between each indentation The penetration depth for

the measurement of Youngrsquos modulus and hardness was 500 nm All data were

analysed using the Oliver and Pharr method [7] Micro-indentation was made using a

Vickers indenter at a maximum load of 3 N and the interval between each indentation


87

was also kept to 20 times the indentation depth of ~26 μm



(c)

(d)


88




Moreover a high purity (gt999995) and fully dense polycrystalline 3C-SiC bulk

(diameter 3 cm thickness 15 cm) sample fabricated by static CVD (Rohm amp Haas

Ltd UK) was used as a reference sample in order to confirm the accurate mechanical

property measurements for FBCVD SiC coatings The Raman spectroscopy of bulk

CVD SiC was the inset in Fig 31(b) and no excess C or Si was found in it

To observe the grain morphology more clearly the finely polished (no scratch could

be seen under optical microscopes times50) cross-section (Fig 1(a)) of the coatings were

chemically etched using Murakamirsquos solution (10 g sodium hydroxide and 10 g

potassium ferricyanide in 100 ml of boiling water) The surface morphology of

coatings was characterized using scanning electron microscopy (Field emission gun

Philips XL30 FEG-SEM) A transmission electron microscope TEM (FEG-TEM

Tecnai TM

G2 F30 U-TWIN 300KV) was used to study the microstructure of the

coating layer before and after indentation For cross-sectional analysis of indentations

TEM samples were made from thin plates which are parallel to one edge and through

the center of Berkovich indentation using a focused ion beam (FIB FEI Nova 600

Dual Beam system) milling For high resolution TEM (HRTEM) the samples were

prepared using an ion beam milling method

33 Results

331 Hardness and Youngrsquos modulus

Figure 32 shows the typicl load-displacement curve of SiC coatings and the hardness

(H) and Youngrsquos modulus (E) as a function of composition of the three types of

coatings The load-displacment curve (Fig 32(a)) shows a smooth character of the

deformation process during nanoindentation There is multiple mini lsquopop-inrsquo events


89

reflected on the hardness curve which started at the beginning from the low

indentation load These mini lsquopop-inrsquo can not provide enough consumption of the

internal stresses induced by indenter as it was needed for the initiation and

propagation of dislocations so no well-pronounced lsquopop-inrsquo effect was observed from

the load-displacement curve





Measurements were made on the x-z plane of SiC coatings (Fig 31(b)) and static

bulk CVD SiC for both micro- and nano-indentation to give reliable comparison with

previous studies [20-23] In the reference material the nano-hardness (36 GPa) and

Youngrsquos modulus (496 GPa) of bulk CVD SiC are nearly the same as in a previous

(c) (b)

(a)


90

study [20] namely 36 GPa and 503 GPa respectively From Fig 32(b) it can be seen

that S1 has a higher hardness compared with S2 and S3 Further the values of

hardness obtained by nano-indentation (Fig 32(b)) are higher than by

micro-indentation for all samples

For low temperature FBCVD coatings the nano-hardness varies in the range 39 GPa

to 44 GPa whereas the micro-hardness varies between 36 GPa - 42 GPa These values

are at least 8 higher than the bulk static CVD SiC which has a nano-hardness ~36

GPa and a micro-hardness ~32 GPa (see Fig 32(b)) Moreover the low temperature

FBCVD SiC coatings have higher hardness as compared to a previous study of CVD

SiC for which the hardness values varied in the range of 25-39 GPa as measured by

nano-indentation under the similar experimental conditions [20-23]

In FBCVD SiC coatings Youngrsquos modulus of all three coatings is lower than the bulk

CVD SiC (see Fig 32(c)) which is an average Youngrsquos modulus (438 GPa) of

polycrystalline CVD SiC reported by Roy et al[24] The difference in hardness and

Youngrsquos modulus data could not be simply explained by the existence of C or Si due

to their low concentration (lt 1 at ) and location in the coatings which has been

addressed in detail in previous study [25] Therefore the difference of hardness and

modulus could be related to other microstructure such as pores which could vary

from atomic scale to micrometres which is discussed in the following session

Both nano- and micro-hardness results (Fig 32(b)) are higher than the available data

for polycrystalline CVD SiC [20-23] as discussed above and the correct measurement

of SiC coatings with small dimensions was ensured by comparing with the bulk CVD

SiC As mentioned the hardness and Youngrsquos modulus measured by

micro-indentation are slightly lower than the values measured by nano-indentation

because cracks were formed under micro-indentation due to the higher indentation

load


91

332 Microstructure of low temperature FBCVD SiC




Figure 33 shows SEM images of the three etched FBCVD SiC coatings In all three

coatings the width and length of columnar grains were found to be approximately 200

nm and 1-2 μm respectively These are found to be much smaller than the SiC coating


92

produced at a temperature of 1500 degC which had width ~1μm and length ~4-5 μm

[17] They are also smaller than the SiC showing dislocation movement under the

indentation deformation zone which was produced at temperature of 1500-1600 degC

by FBCVD and 1500 degC by static CVD with grain size of 1-5 μm and 5-10 μm

respectively [11 16]

Although the grain size is in a similar range for three coatings (as mentioned above)

due to different deposition conditions the grain morphologies of three coatings vary

First a less laminar structure was observed in the S1 coating (see Fig 33 (a)) as

compared to the coatings with excess C or Si (Fig 33 (c) and (e)) Fig 33 (b) shows

the existence of triple junctions (dashed circle) that could resist the movement of

grain boundaries and dislocation slip [12] Pores were also observed along the laminar

structure after etching In the S2 coating it has a large amount of a laminar structure

running through a single grain (laminar structure parallel to growh direction) as

illustrated in Fig3 (d) The information of grain morphology in S2 was mostly a

laminar structure perpendicular to the growth direction after etching (Fig 33(d))



To get more information about the grains morphology in S2 coating a TEM image

05 μm


93

was taken and shown in Fig 34 Figure 34 shows that grains in S2 coating interact

(branch-like grain growth pattern on the lower-left part of Fig 34) with each other

which is similar as in sample S1 (Fig 33(b)) and grains form branch like structures

In the S3 coating (as can be seen in Fig 33 (f)) a parallel growth of grains with less

interaction among grains was observed





According to a previous study [25] about definition of grain boundary the grain

boundary in the S3 coating is smooth while in the S1 and S2 coating the grain

(c)


94

boundaries are rough which could result in branch-like grain growth pattern It could

be attributed to the different CSi ratio in reaction gas which produce SiC with

different morphologies on the (111) crystal plane which may have three different

morphologies rough smooth and pyramidal defect [26] Grains with differently

finished surfaces could lead to different grain growth morphologies because of

different surface energy For example in rough grain boundaries of S1 and S2

coatings branch like crystals were found as in Fig 33(b) and Fig 34

Figure 35 shows bright field TEM images of the S1 coating S2 and S3 coatings The

columnar grains were observed to grow perpendicular to the coating surface which

was consistent with the SEM results Further nano porous layers normal to the

coating growth direction are observed in the S2 coating (see Fig5 (b)) The formation

of porosity in thin films could be due to differences in diffusion of growth species the

incident molecule direction and deposition of secondary phases such as excess Si or C

[27]



At low deposition temperatures the probability of a precursor reaching the edge of the

nucleus is considerably lower compared with that of arriving on the top due to a low

surface diffusion As these nuclei grow the areas immediately around them will suffer


95

from a shadowing effect blocking the arrival of new molecules and the formation of

new nuclei Since the diffusivity of atoms is low and no new nuclei are formed in

those regions gaps will be formed among grains A wrinkled like defect layer was

seen in the S3 coating (Fig 35 (c)) which could be attributed to the interruption of

the SiC crystallization growth during the deposition process such as crystal lattice

misorientation as seen in Fig 36



No obvious laminar defect was observed in the S1 coating by TEM this could be due

5 nm

(a) (b)

5 nm

5 nm

(c)


96

to less interruption during deposition process According to above observation it was

proposed that the laminar structure observed in SEM images indicates some

instability during the fabrication process resulting in the deposition of the nano- and

micro-pores and misorientation This was attributed the variations in circulation and

deposition occurring close to the nozzle or at the hot zone [5]

Stacking faults were observed for all three types of samples as shown in Fig 35 with

a higher density than for the SiC deposited at a temperature of 1500 C [11 16 17]

These stacking faults could cause an intrinsic residual stress due to the coexistence of

the partial dislocations This was supported by the high resolution TEM images

(shown in Fig 37) exhibiting wave pattern fringes and they could only be observed

in one direction which is determined by the intrinsic stress




projection

Since the dislocation mobility under nano-indentation deformation has not been fully

understood in hard ceramic materials therefore it is significant to study this

behaviour in FBCVD SiC coatings with a sub-micrometer grain size However it is

difficult to observe the dislocations under the two-beam or weak beam dark field

2 nm

(a)

(111)

[110]

(111)

Sessile

dislocations

(b)


97

conditions due to the high density of defects In the present study the reversed fast

Fourier transform (FFT) images of the corresponding high resolution TEM images

was used to obtain information about the dislocations This method has been used in

many cases for dislocation observations [28]

Figure 38(a) shows a high resolution TEM image of a S1 coating which was taken as

a representative image to compare the atomic structure of all three coatings Figure

38(b) is the reverse FFT image using the marked inset diffraction pattern of Fig

37(a) in which sessile and glide dislocations can be observed The dislocation

density was calculated from the total number of glide dislocations divided by the area

in the image [29 30] From the analysis of images shown in Fig 38 the dislocation

density in S1 coatings was found to be 1013

cm2 The same magnitude of dislocations

density was found in the S2 and S3 coatings as shown in Fig 37 (three HRTEM

images were analysed for each coating)

333 Deformation behaviour under the indentation

The deformation zone under the indentation was investigated through the images of

FIB milled TEM samples in order to study the deformation mechanism of the low

temperature FBCVD SiC coatings Figure 39 shows the bright field TEM images

showing the mechanical behaviour of a S1 coating under nano-indentation on the x-z

plane (Fig 31(b)) at a maximum indentation depth of 500 nm

Figure 39(a) is an overview of the deformation area under an indentation A median

crack has formed just underneath the surface and has a direction aligned with the

indenter tip impression A higher magnification image around the elastic and plastic

interface is shown in Fig 39(b) It can be seen that a large amount of inter-granular

and trans-granular micro cracks were produced around the median crack initiation

zone This is substantially different from the dislocation-related plastic deformation

behaviour [10 11 16 31] which usually has a severe plastically deformed region


98

with few or no cracks Moreover the micro cracks were also observed in the C and D

zones under the indentation







Figure 39(c) shows that micro cracks that are formed along the grain boundaries

which tend to follow the shear band direction with the formation of a few

trans-granular cracks In Fig 39(d) it can be seen that shear band micro cracks were

formed in one single grain (see inset in the left bottom corner of Fig 39(d)) This

single grain has a large amount of defects which are supposed to be the as-deposited


99

defects as shown in Fig 35(a) Shear band cracks were also observed just underneath

the indenter tip (right top inset in Fig 39(d)) As a result a shear band dominated

deformation zone can be seen in Fig 39(c d) under the indentation in a S1 coating



The S2 and S3 coatings only show a micro crack pattern which is different from S1

coating Figure 310 gives the TEM images of the S2 and S3 coatings showing the

mechanical reaction underneath the indentation It can be seen from Fig 310(a) and

Fig 310(c) that the median cracks are not always produced under the indentation for

S2 and S3 coatings However some irregular cracks in S3 coatings and lateral cracks

in S2 were produced In particular in the S3 coating (Fig 310(b)) more micro cracks

either intragrain or transgrain were found than in the S1 and S2 coatings This is due

to the fact that the most micro cracks propagate along the grain boundaries in S1 and


100

S2 coatings (Fig 39(b) and Fig 310(d)) A careful analysis of the TEM images

shows that only micro cracks were found under the indentation and no

dislocation-induced shear band was observed This is different from previous studies

on the deformation behaviour of polycrystalline SiC [11 16 31] For example in bulk

polycrystalline CVD SiC [11] it was found that it has more dislocation slip bands

rather than micro cracks either in grains or along grain boundaries even though the

indentation load is higher than the load used in the FBCVD SiC based materials The

possible reason of this discrepancy is discussed later Moreover no amorphous phase

and α-SiC phase was formed under the indentation observed by diffraction and bright

field TEM images which is consistent with the work of Mishra and Szlufarska [32]

34 Discussion

High hardness and Youngrsquos modulus were obtained in the sub-micrometer grain size

coatings produced at a low temperature by FBCVD In the S1 coatings the

nano-hardness is ~22 higher while the micro-hardness is ~31 higher compared to

a commercial CVD SiC The higher hardness was also obtained in S2 and S3 coatings

All the coatings retained a higher Youngrsquos modulus than those SiC materials having

high hardness in previous study (equal or higher than 40 GPa nano-hardness) [33]

making these coatings unique among polycrystalline phase brittle ceramic material

Under nano-indentation only micro cracks were found in the deformation zone The

results seem to be consistent with the conventional view of the failure mechanism of

brittle ceramics at room temperature [34] The lack of dislocation and the high Peierls

force are reasons for fracture to occur in brittle materials However

dislocation-related plastic deformation routinely occurred in hardness testing because

the indentation stress field offers conditions of stress conductive to plastic

deformation [11 13 16 34] Molecular dynamic simulations even demonstrate that

13 of the hardness-related deformation is from dislocation-related plastic deformation


101

while 23 comes from fracture in SiC [31] It is rare to see a deformation zone

dominated by micro cracks in polycrystalline SiC such as in FBCVD SiC coatings

(Fig9 and Fig10 and see for example Ref [11 16 31]) With the above questions

we first estimated the factors controlling Youngrsquos modulus in FBCVD SiC coatings

followed by a study of the mechanism of superior hardness and deformation under an

indentation which influence the hardness in the three coatings

341 Influence of porosity on Youngrsquos modulus

Youngrsquos modulus presents a material constant for uniaxial tensile deformation which

is physically related to the atomic spacing inter atomic bond strength and bond

density In a low temperature FBCVD SiC coating it was shown from XRD

measurements that a shoulder peak was observed in addition to the β-SiC (111)

diffraction peak which corresponded to a crystal plane spacing of ~0266 nm (Fig

31(c)) Moreover we found that the XRD peak shifted to a lower diffraction angle

compared with the bulk CVD SiC According to the XRD pattern in Fig 31(c) the

crystal lattice constants of about 04366 04368 and 04368 nm for S1 S2 and S3

coatings were obtained respectively However the crystal lattice constant for bulk

CVD SiC is ~04359 nm (XRD pattern obtained by the same condition was shown in

Ref 25)

Further crystal orientation impurities and porosity may affect the Youngrsquos modulus

As the Youngrsquos modulus on the x-z plane (Fig 31(b)) was similar to the value

obtained along the cross-section (Fig 31(a)) [5 25] which meant that the orientation

has no effect on Youngrsquos modulus Moreover as discussed before the effect of C or Si

in S2 was found to have no effect on the difference of hardness and Youngrsquos modulus

Excluding these two factors (orientation and impurities) the effect of porosity on

variation of the elastic properties in three coatings was investigated The presence of

nano-pores in S2 coating as in Fig 35(b) results in a lower density Although no


102

pores were directly observed by TEM in the S1 and S3 coatings their density is lower

than the theoretical density of SiC Thus the elastic modulus E at room temperature

can be expressed in an exponential function of porosity pV [35] as

0 exp( )pE E CV (1)

where 0E = 496 GPa is the elastic modulus and C = 357 is a constant for a pore-free

bulk CVD SiC pV is the ratio of the relative density difference to the theoretical

density of SiC (322 gcm3)

The calculated Youngrsquos modulus for S1 S2 and S3 coatings is 465 plusmn 15 446 plusmn 17 and

473 plusmn 1 GPa respectively which follows a trend similar to the experimental data

presented in Fig 32 It was concluded that the different Youngrsquos modulus in the three

low temperature FBCVD SiC coatings is attributed to porosity although the

experimental Youngrsquos modulus data of FBCVD SiC coatings is slightly lower than the

values calculated using the Eq(1) The difference between calculated and measured

value of FBCVD SiC coatings is due to the fact that the 0E from pore-free bulk

CVD SiC instead of pore-free FBCVD SiC coatings (not available) FBCVD SiC

coatings have larger crystal lattice constant (~0437 nm) than bulk CVD SiC (~04359

nm) as discussed above Since the expanded lattice constant leads to a decrease of the

Youngrsquos modulus according to a previous study [20] the 0E of pore-free FBCVD SiC

coating is expected to be lower than bulk CVD SiC

342 Mechanism for High hardness

From previous studies [10 11 16 31] dislocation nucleation and glide is the primary

response of SiC under nano-indentation Formation of shear bands due to dislocations

has also been reported [11] which were found under the plastic deformation zone


103

when indentations were made on a particular grain in polycrystalline SiC and at the

grain boundaries Moreover dislocation nucleation is also correlated with the discrete

pop-ins observed in the force-displacement curve [32] No pop-ins was found due to

the presence of a large amount of dislocations in the present study Dislocation

mobility can be estimated similar to the case of a metallic material having intrinsic

dislocations Mishra and Szlufarska [32] worked on the dislocation mobility in

3C-SiC using large-scale molecular dynamics simulations The results indicated that

dislocation mobility decreased by dislocation interaction as its density reached a

saturation value This is similar to the work hardening effect in a metallic material [34]

We estimated the stress ( ) needed for dislocation to move using Taylorrsquos work

hardening equation [34] given by

1 2

0 Gb (2)

where 0 is the shear stress for a dislocation to move without any obstacle and the

value of 0 taken was 75 GPa [13] is a numerical constant depending on the

locking strength of a nod The value of taken was 8 [36] b is Burgers vector

where b = 0178 nm for a Shockley partial dislocation in SiC initiated and gliding on a

close packed (111) plane and is the density of glide dislocations G is the shear

modulus which can be written as

2(1 )

EG

(3)

where is the Poissonrsquos ratio and E is the Youngrsquos modulus The dislocation density

was ~03times1012

cm2 The calculated shear stress according to Eq (2) was ~52 GPa and

this value is much higher than the theoretical shear stress which is in the range of

295-4312 GPa obtained from previous reports [37-39] The theoretical shear stress is

the maximum stress provided for the dislocation nucleation and propagation in SiC


104

crystals Therefore the dislocation-related yield behaviour could not occur under the

plastic deformation zone in sub-micrometer FBCVD SiC coatings

The superior hardness value in FBCVD SiC coatings is attributed to the immobility of

the dislocations In the case of the SiC-C solid solution [40] the occurrence of a high

density of dislocations causes a strain-hardening effect Furthermore given that

dislocations could be motivated by the shear stress a phase transformation from a

crystalline phase to an amorphous could occur [32] However no amorphous phase

was observed under the nano-indentation (Fig 37 and 8) nor was dislocation

movement band observed in this study This suggests that the dislocation-related

phase transformation did not occur under the indentation

343 Deformation mechanism under nano-indentation

The hardness-related plastic deformation which occurs due to the nucleation and

propagation of micro cracks in FBCVD SiC coatings can be explained as follows

(i) The onset of plastic deformation under the indentation occurs as the maximum

shear stress approaches the yield stress [41] According to 15H Y (Y is the yield

stress H is the hardness) the yield stress in FBCVD SiC coatings is around 26 GPa

The yield stress is lower than the stress needed for the movement of dislocations and

the theoretical shear stress [37-39] This indicates that the hardness-related plastic

deformation first occurred by the nucleation of defect-induced cracks which

propagated to the indented surface (see inset (top right) in Fig 39(d)) The

deformation impression was accommodated by the densification of defects such as

the pores dislocation pile ups and grain boundaries as in Fig 33(b)

(ii) The shear stress was used to promote the movement of dislocations under the

indentation and form slip bands in previous studies [10 11 42] The highest amount

of micro cracks were observed in FBCVD SiC coatings contrary to plastic


105

deformation under the indentation found in previous studies [10 11 42] The micro

cracks formed in the hardness-related plastic deformation zone is the Mode-II crack)

[43] as shown in Fig 39(c) and (d) Unlike Mode-I which is dominated by the tensile

stress a Mode-II crack is the consequence of a confined shear stress [34] At the

interface of the elasticplastic deformation branch-like micro cracks were observed

as in Fig 39(b) The above discussions distinguish the hardness-related plastic

deformation mechanism in FBCVD from previous studies on ceramics which showed

dislocations are the main deformation mechanism underneath the indentation [31 44]

A unique hardness-related plastic deformation mechanism was used to explain the

difference in hardness of all three types of FBCVD SiC coatings According to Qian

et al [45] the hardness could reach an asymptotic value with the saturation of the

micro cracks growth population In three FBCVD SiC coatings studied here different

amounts of micro cracks were found (Fig 39(b) and Fig 310(b d)) and micro cracks

nucleated at stress concentration zones such as the grain boundaries or defects within

the grains Thus the difference in hardness was attributed to the grain morphologies

as shown in Fig 33 which gives different degree of resistance to the initiation and

propagation of micro cracks In the S1 coating triple junctions hamper grain

boundary shear by forming interlocks [12] which could resist and deflect the initiation

and propagation of micro cracks In the S2 coating elongated grains interact with the

surrounding small grains which could also provide interlocks (Fig 33(d) and Fig

34) The slightly lower hardness of the S2 coating as compared to the S1 coating is

due to the nano pores as seen in Fig 35(b) A lack of triple junctions and grain

interactions could be the reason for the lower hardness in the S3 coating as it has a

parallel crystalline morphology which has less constraint towards the initiation and

propagation of cracks

35 Conclusions


106

The microstructure and mechanical properties of three types of FBCVD SiC coatings

(SiC SiC+C and SiC+Si) were studied FBCVD SiC coatings with a sub-micrometer

grain size were deposited on simulated TRISO fuel particles by FBCVD at a low

temperature (1300 oC) The mechanical properties were studied using micro and

nano-indention The microstructures were studied using SEM and TEM It was

found that the Youngrsquos modulus of all three coatings differ which was attributed due

to the presence of nano-pores The high hardness of FBCVD SiC coatings was due to

the large amount of defects particularly the high density of dislocations It is found

that the interactions between dislocations reduced their mobility and make

dislocation-related plastic deformation unavailable We suggest that the work

hardening effect is the reason for the high hardness in the sub-micrometer grain size

FBCVD SiC coatings A hardness related-deformation mechanism was attributed to

the initiation and propagation of micro cracks The nano-indentation indent volume is

most likely be accommodated by the densification of defects such as the pores As a

result the hardness difference in FBCVD SiC coatings is due to the different grain

morphologies producing different amounts of micro cracks


107

36 References



329-77

[2] G K Miller D A Petti D J Varacalle J T Maki Statistical approach and

benchmarking for modeling of multi-dimensional behavior in TRISO-coated fuel

particles J Nucl Mater 317 (2003) 69-82

[3] D A Petti J Buongiorno J T Maki R R Hobbins G K Miller Key

differences in the fabrication irradiation and high temperature accident testing of

US and German TRISO-coated particle fuel and their implications on fuel

performance Nucl Eng Des 222 (2003) 281-97

[4] A C Kadak R Gnallinger M J Driscoll S Yip D G Wilson H C No J

Wang H Maclean T Galen C Wang J Lebenhaft T Zhai D A Petti W K

Terry H D Gougar A M Ougouag C H Oh R L Morre G K Miller J T

Maki G R Smolik D J Varacalle Modular pebble bed reactor Modular pebble

bed reactor project University research consortium annual report Beijing 2000

[5] E Lopez-Honorato P J Meadows J Tan P Xiao Control of stoichiometry



[6] J Tan P J Meadows D Zhang X Chen E Lopez-Honorato X Zhao F Yang

T Abram P Xiao Youngs modulus measurements of SiC coatings on spherical

particles by using nanoindentation J Nucl Mater 393 (2009) 22-29

[7] W C Oliver G M Pharr An improved technique for determining hardness and


Mater Res 7 (1992) 1564-83

[8] C H Chien S R Jian C T Wang J Y Juang J C Huang Y S Lai

Cross-sectional transmission electron microscopy observations on the Berkovich

indentation-induced deformation microstructures in GaN thin films J Phys D


108

Appl Phys 40 (2007) 3985-90

[9] T C Tan C A Merrill J B Orton A K Cheetham Anisotropic mechanical

properties of polymorphic hybrid inorganic-organic framework materials with

different dimensionalities Acta Mater 57 (2009) 3481-96



Res Soc Symp P 522 (1998) 113-18

[11] X Zhao X R M Langford I P Shapiro P Xiao Onset plastic deformation and

cracking behaviour of 3C-SiC upon indentation at room temperature J Am

Ceram Soc 94 (2011) 3509-14

[12] D Grabco O Shikimaka E Harea Translation-rotation plasticity as basic

mechanism of plastic deformation in macro- micro- and nanoindentation

processes J Phys D Appl Phys 41 (2008) 074016-24

[13] H P Chen R K Kalia A Nakano P Vashishta I Szlufarska

Multimillion-atom nanoindentation simulation of crystalline silicon carbide

Orientation dependence and anisotropic pileup J Appl Phys 102 (2007)

063514-22



Rev B 71 (2005) 174113-23



[16] G Chollon J M Vallerot D Helary S Jouannigot Structural and textural

changes of CVD-SiC to indentation high temperature creep and irradiation J Eu

Ceram Soc 27 (2007) 1503-11

[17] D Heacutelary X Bourrat ODugne G Maveyraud M Peacuterez O Guillermier

Microstructures of silicon carbide and pyrocarbon coatings for fuel particles for

high temperature reactors 2nd international topical meeting on high temperature


109

reactor technology Beijing China 2004




[19] T Fukuzaki K Tanaka K Nishimoto Y Mur K Nishio and R Tamura

Magnetic property and microstructure of Nd-Fe-B-M (M=Si C) bulk

pnanocomposite magnets prepared by spark plasma sintering method - art no

012015 J Phys Conf Ser 106 (2008) 12015-124

[20] M C Osborne J C Hay L L Snead D Steiner Mechanical- and

physical-property changes of neutron-irradiated chemical-vapor-deposited silicon

carbide J Am Ceram Soc 82 (1999) 2490-96

[21] K H Park S Kondo Y Katoh A Kohyama Mechanical properties of beta-SiC

after Si- and dual Si plus He-ion irradiation at various temperatures Fusion Sci

Technol 44 (2003) 455-59

[22] S Nagappa M Zupan C A Zorman Mechanical characterization of


Mater 59 (2008) 995-98

[23] C Bellan J Dhers Evaluation of young modulus of CVD coatings by different

techniques Thin Solid Films 469-70 (2004) 214-20

[24] S Roy C Zorman M Mehregany R Deanna C Deeb The mechanical

properties of polycrystalline 3C-SiC films grown on polysilicon substrates by

atmospheric pressure chemical-vapor deposition J Appl Phys 99 (2006)

044108-20

[25] J Tan Mechanical properties of SiC in TRISO fuel particle Thesis University of

Manchester 2010

[26] M J Hernandez G Ferro T Chassagne J Dazord Y Monteil Study of surface

defects on 3C-SiC films grown on Si (111) by CVD J Cryst Growth 253 (2003)

95-101


110

[27] E S Machlin Materials science in microelectronics I The relationships between

thin film processing and structure 2nd

ed Oxford Elsevier Science 2005

p206-47

[28] A Nakamura T Yamamoto Y Ikuhara Direct observation of basal dislocation

in sapphire by HRTEM Acta Mater 50 (2002) 101-08

[29] H Y Shin S K Kwon Y I Chang M J Cho K H Park Reducing

dislocation density in GaN films using a cone-shaped patterned sapphire substrate

J Cryst Growth 311 (2009) 4167-70

[30] W D Callister Materials science and engineering An introduction 7th ed

Australia John Wiley amp Sons Australia Limited 2006 p191-99





[33] A R Beaber L J Qi J Hafiz P H Mcmurry J V R Heberlein W W

Gerberich S L Girshick Nanostructured SiC by chemical vapor deposition and

nanoparticle impaction Surf Coat Tech 202 (2007) 871-75



p162-91


York Marcel Dekker 2000 p457-534

[36] U Messerschmidt Dislocation dynamics during plastic deformation Part 2

Ceramic Single Crystals Springer Series in Materials Science On line 2010

p264

[37] S Ogata J Li N Hirosaki Y Shibutani S Yip Ideal shear strain of metals and

ceramics Phys Rev B 70 (2004) 104104-10

[38] Y Umeno Y Kinoshita T Kitamura Ab initio DFT study of ideal shear


111

strength of polytypes of silicon carbide Strength Mater 40 (2008) 2-6

[39] Y Umeno M Cerny Effect of normal stress on the ideal shear strength in

covalent crystals Phys Rev B 77 (2008) 100101-04




Engineering Series 1st ed New York Springer 2000 p139-77



[43] A A Wereszczak K E Johanns O M Jadaan Hertzian Ring Crack Initiation

in Hot-Pressed Silicon Carbides J Am Ceram Soc 92 (2009) 1788-95

[44] S L Lloyd A Castellero F Giuliani Y Long K K Mclaughlin J M

Molina-Aldareguia N A Stelmashenko L J Vandeperre W J Clegg

Observations of nanoindents via cross-sectional transmission electron microscopy

a survey of deformation mechanisms P Roy Soc a-Math Phy 461 (2005)

2521-43

[45] J Qian L L Daemen Y Zhao Hardness and fracture toughness of moissanite

Diam Relat Mater 14 (2005) 1669-72

CHAPTER 4 Vickers indentation fracture toughness of SiC coatings

112

CHAPTER 4 Vickers Indentation Fracture Toughness of

SiC Coatings

41 Introduction

Silicon carbide (SiC) layer is considered to be the most important component for

structural integrity as during the operation of a nuclear reactor it has the ability to

sustain most of the internal pressure caused by gaseous fission products produced in

the kernel and retain most of the fission products [1-4] Previous work was focused on

the investigation of mechanical properties (Youngrsquos modulus and fracture strength) of

SiC coatings on TRISO particles using different techniques such as a ring test [5 6]

a crush test [7 8] a micro-cantilever test [9] and indentation [10 11] However few

reports exist on the measurement of the fracture toughness of SiC coatings even

though it is a property used in modeling to estimate the failure probability of TRISO

fuel particles [12] For example Kadak et al [12] used a fracture toughness value of

33 plusmn 053 MPa m12

This value was obtained from bulk SiC produced by a static

CVD method The fracture toughness value may well differ for SiC coatings produced

by fluidized bed chemical vapour deposition (FBCVD) on TRISO fuel particles [10]

Because microstructure of SiC produced by static CVD and FBCVD methods could

vary significantly For example the static CVD SiC usually has larger grain size and

high density while FBCVD SiC with large grain size is usually accompanied with

porosity [13] Different grain size range and porosity fraction can lead to variation of

fracture toughness [1 2] Therefore the fracture toughness value of bulk SiC may not

be truly representative of SiC coatings used in nuclear fuel applications To our

knowledge the only available data on the fracture toughness of a SiC layer on TRISO


113

fuel particle is reported by Zhao et al[9] where the fracture toughness was measured

by the micro-beam method However this method is time consuming and expensive

restricting its implementation as a standard characterization technique where

repetitive measurements are required to confirm the reproducibility of experimental

data

In this Chapter micro-indentation is used to investigate the fracture behaviour of

different SiC coatings produced (on TRISO fuel particles) by FBCVD due to its

capacity to measure the mechanical properties in a small area and produce visible

cracks [14-16] The fracture behaviour under an indenter is also studied using a

transmission electron microscope (TEM) in order to give better understanding of the

fracture mechanism The characteristics of the SiC microstructures are then correlated

with their fracture behaviour


The SiC coatings used are the same as the ones in Chapter 3 and the deposition

conditions were shown in Table 31 Chapter 3

For the micro-indentation study SiC coated fuel particles were hot mounted in

copper-loaded conductive resin (to get better SEM images) and then ground to a

cross-section (as shown in Fig 31(a)) or polished a flat external surface (as shown in

Fig 31(b)) In this Chapter the y direction is called radial direction x is called

tangential direction according to Fig 31(a) and (b) The samples were then polished

using increasingly fine diamond suspensions to 14 μm Indentation fracture

toughness measurements were performed using a Vickers diamond indenter (CSM

Instruments Switzerland) Due to the through-thickness (in the radial direction)

failure behaviour of a SiC coating in a TRISO fuel particle under tensile stresses

generated from gases due to nuclear reactions similar tensile stresses could be


114

generated from indentation of polished external surface of TRISO particles which

could generate cracks along the radial direction (y direction in Fig 31(b)) of the

TRISO particles as well The indentations were carried out under a maximum load of

3 N (corresponding to a maximum indentation depth of ～26 μm) To avoid PyC

influence the thickness of SiC coatings (in the section as shown in Fig 31(b)) were

kept to ～60 μm after polishing which is more than 20 times the indentation depth

In this case the elastic zone has not expanded to the substrate according to the

criterion that indentation depth is less than 10 of coating thickness [17] For each

sample six indents were made on the polished external surface of SiC perpendicular

to the radial direction with a separation of 70 μm between each indent




reference [25]

The calculation of the VIF fracture toughness must account for the crack profile under

the indenter whether the cracks are of the Palmqvist mode or half-penny mode which

are illustrated in Fig 41 The halfpenny crack system is formed by the joining of

radial cracks as shown in Fig 41(a) while the Palmqvist crack system is always

shallow as shown in Fig 41(b)

To observe the crack impression under the indenter on the polished external surface

an indentation (as in Fig 42(a)) with a final indentation depth of 26 μm was

sequentially polished with 6 μm diamond suspensions The surface was polished until

the plastic deformation zone was exposed together with the radial cracks (as shown in


115

Fig 42(b) Afterwards polishing continued until the removal of the plastic

deformation zone (as shown in Fig 42(c)) The surface showed no cross-over

cracking present as illustrated in Fig 41(a) and this confirms the presence of the

Palmqvist mode cracks on the polished external surface of SiC coatings under the

Vickers indenter The three polished samples showed the same crack propagation

mode and this is consistent with previous reports [18 19] where a Palmqvist crack

system has been observed in SiC at low loads (lt 10 N)

The Palmqvist crack mode allows the VIF fracture toughness to be calculated using

the equation proposed by Laugier [15 16] given as

1 2 23

3 2( ) ( )IC v

a E PK

l H c

(1)

In Eq (1) the geometrical constant v is a calibrated value using the already known

fracture toughness due to the variation in use of the Vickers hardness or the

nano-hardness [14 16 20 21] The 2a and l are the lengthes of diagonal and radial

crack length of Vickers indentation (as shown later in Fig 43) respectively c=a+l

the E and H are Youngrsquos modulus and hardness measured by nano-indentation P is

the load of Vickers indentation Therefore this geometrical constant was calibrated

before it was used to calculate the VIF fracture toughness of SiC coatings


116




zone


117

The only already known fracture toughness was measured on the cross-section of

extra-Si SiC coatings using a micro-beam bending method [9] so the calibration of

v was carried out on the cross section (as in Fig 31(a)) of the same coating

According to Eq(1) the hardness (H ) and Youngrsquos modulus (E) are nano-hardness

and Youngrsquos modulus as measured in a previous study [22] P is the load a is the

impression half diagonal l is the crack length and c is the half diagonal crack length

(see later in Fig 43) To get the load and dimensional values of indentations a total

of 8 indentations at different loads (3 35 and 4 N) were applied on the cross-section

of the extra-Si SiC coating

The crack lengths were measured using a scanning electron microscope (Philips XL30

FEG-SEM) FEG-TEM (Tecnai TM

G2 F30 U-TWIN 300KV) which was used to

study the fracture behaviour under the indenter For the TEM study the cross

sectional specimens for the indents were prepared using focused ion beam milling

(FIB FEI Nova 600 Dual Beam system) Note that due to the large deformation zone

(gt10 μm diameter) and radial crack length (gt15 μm) observed from micro-indent

impression it was not possible to produce a sufficiently large TEM sample by the FIB

technique This limitation restricted us to study the fracture behaviour under a sharper

indenter (Berkovich) with lower load

43 Results and discussion

431 VIF fracture toughness study

Figure 43 is the crack morphology observed in S3 (SiC + Si) coating cross-section It

shows that the fracture resistance is different in the tangential and radial directions of

the cross-section which is consistent with the previous measurements along these

directions measured by the micro beam method [9] Different crack lengths along the

tangential and radial directions observed from 8 indentations are illustrated in Table

41 Correspondingly fracture toughness values of 347 MPa m12

and 672 MPa m12


118

taken from Ref [9] were used as the standard values for the tangential and radial

directions of the SiC coating respectively According to Eq (1) taking into account

observed and measured parameters (KIC a c l H and E) the geometric constant

value v was calculated in each indentation for each direction (Table 41)


tangential directions for S3 SiC coatings

Table 41 illustrates the indentation parameters and the calibrated geometrical

constant v for the Palmqvist crack mode According to the results shown in Table

41 the calibrated mean value of v is 002008plusmn000273 and this value is within

the range of the geometrical constant value (0014-0023) from previous theoretical

studies [14 23] By using nano-indentation hardness and Youngrsquos modulus v was

taken as 002 for the calculation of the VIF fracture toughness in SiC layers in this

study which is the upper limit of 0016plusmn0004 used for previous studies of bulk

CVD SiC using the HE from micro-indentation [14 24-27]


119

Table 41 Indentation parameters from S3 SiC and calibrated geometrical constantχ

v along the radial and tangential directions

Load Radial direction

Tangential direction

a (μm) c (μm) l (μm) χv a (μm) c (μm) l (μm) χv

3 N 6650 13125 6475 0020368 6685 18285 11600 0023088

6900 13090 6190 0019473 6995 15470 8475 0015013

6675 11895 5220 0015749 6120 16615 10495 0019880

6695 13130 6435 0020249 6555 15935 9380 0017057

6790 12610 5820 0017997 6425 18275 11850 0023783

35 N 7195 14970 7775 0022404 7235 20790 13555 0024930

6670 14080 7410 0020721 6715 18160 11445 0019412

4 N 7770 15855 8085 0020967 7390 20240 12850 0020187

χv 002008 plusmn 000273

Note The geometrical constantsχv presented in Table 41 were calculated using Eq(1) The fracture

toughness along the radial (672 MPa m12

) and tangential directions (347 MPa m12

) were taken from

Ref 9

Although the Vickers indentation method for fracture toughness measurement has

been discredited as a mean to obtain true fracture toughness [28] and always gives a

lower fracture toughness value than that obtained using the standard methods (such as

single edge V-norched bending)[1] the values obtained can be compared with each

other This is particular important for small samples and thin coatings since Vickers

indentation provides a method to quantify fracture behaviour when it is not feasible to

obtain true fracture toughness However to get reasonable comparison of Vickers

indentation fracture toughness in SiC coatings the following conditions should be

met

(1) SiC materials produced four regular radial cracks along the corners of the

Vickers indenter For indentation at the polished external surface of SiC


120

coatings deposited by FBCVD similar fracture resistance along different

orientation at the surface should be obtained

(2) The calibration of the geometrical constant should be made v was obtained

as 002 based on previous experimental results (see above)


conditions

Sample Grain size range (μm) Vickers toughness (MPa m12

)

S1 (SiC) 02-2 351plusmn042

S2 (SiC + C) 02-2 403plusmn043

S3 (SiC + Si) 02-2 493plusmn016

Table 42 presents the measured VIF fracture toughness on the polished external

surface using equation (1) for the SiC coatings in which the deposition conditions and

grain size were given It can be seen that the SiC coating with excess Si (S3) has

highest indentation fracture toughness followed by SiC with excess carbon (S2) and

stoichiometric SiC coatings (S1)

Vickers indentation fracture toughness values obtained in this study are slightly higher

than that of commercial CVD β-SiC which has been reported to vary from 24 to 33

MPa m12

measured by the same method [24 26 27] The VIF fracture toughness of

49 MPa m12

for extra-Si SiC measured on a polished external surface is between

347 and 672 MPa m12

when measured on a cross section by micro-beam method [9]

This is consistent with the observation of radial crack length differences ndash the crack

length on the polished external surface is between those in the tangential and radial

direction on the cross-section It is suggested that Vickers indentation is an effective

method for the characterization of fracture behaviour of FBCVD SiC coatings

Moreover the high hardness and Youngrsquos modulus of these three coatings [22] do not


121

cause a decrease in fracture toughness which is explained in the later part of this

paper

432 Influence of non-stoichiometries on the VIF fracture toughness

The VIF fracture toughness in S2 SiC coating is ～14 higher than the value for S1

SiC coatings and this can not be attributed to heterogeneous toughening due to the

excess carbon being at the grain boundaries Due to the low content of excess C it is

difficult to identify such an excess at the grain boundaries [29] Previous work

reported in Ref[30] showed that there was no presence of carbon at the grain

boundaries for a concentration up to 1 wt excess C In our case a similar situation

was found in S3 SiC coating where excess Si has not been found along the grain

boundaries Previous studies had [31 32] shown that excess Si in SiC was observed in

grains or near the grain boundaries by TEM only when the amount of excess Si is

high enough (such that it could be detected by XRD or a much higher Raman

spectroscopic intensity)Thus it is assumed that the excess Si could not be considered

as giving heterogeneous toughening which caused a ~43 higher VIF fracture

toughness in the S3 SiC than the S1 SiC coatings As a result the small amount of

excess carbon or silicon in SiC coatings does not seem to have influence on the VIF

fracture toughness through serving as the heterogeneous phase along the grain

boundary

The excess Si or C could be related to different grain morphologies according to

previous study [33] where it was observed that different SiC ratios in the reaction

gas produced rough smooth and irregular pyramid-like grain surfaces This further

affects the growth morphology and cohesion stress between grains For example the

smooth grain surface favours the parallel grain growth The weak grain boundary

cohesion could be the micro crack initiation zone while the strong grain boundary

could transfer the stress to stress concentration zone Here the role of grain

morphology is studied later in terms of stress concentration zone under indentation


122

433 Microstructural analysis of fracture behaviour under the indenter

SiC coating under nano-indentation on the polished external surface at a maximum

indentation load of 160 mN It can be seen that the median crack propagation root

deflected slightly and changed from intergranular to transgranular fracture as shown

in Fig 44(a) It is worth noticing that the median crack observed under

nano-indentation was not found under indentation because the indentation cracking

mode depends on the condition of the indenter tip [34] Higher magnification images

(Fig 44(b)) show that a large number of micro cracks were produced at the

elasticplastic interface






123

Both intergranular and transgranular cracks were observed near the median crack

initiation zone These cracks are under a tensile stress dominated by Mode I cracks as

the elastic-plastic stress field gives the highest tensile stress around this interface

according to a previous report (see Ref [35]) Moreover micro-cracks were observed

surrounding the median crack and also at the median crack tip as shown in Fig 44(c)

and Fig 44(d) respectively Figure 44(c) illustrates that the micro-cracks are along

the grain boundaries while the micro-cracks around the crack tip were found to both

pass through the grains and along grain boundaries (Fig 44(d))

Non-stoichiometric SiC coatings (S2 and S3) show quite different crack morphologies

under the indenter from that in the stoichiometric SiC (S1) coating as shown in Fig

310 in chapter 3 It can be seen that the propagation root of median cracks in S3 SiC

and S2 SiC coatings were affected by the microstructures as in Fig 310(a) and (c) in

chapter 3 Moreover a lateral crack was found in the S2 SiC coating The irregular

median crack propagation route in non-stoichiometric SiC coatings seems to be

related to the laminar structure

Fig 45 Cross-sectional SEM image of the S1 SiC coating showing the grain


Figure 45 shows the cross section of S1 SiC coating and the laminar structure (as

indicated by the dashed lines) is perpendicular to the grain growth direction It was


124

discussed in chapter 3 that the laminar structure is due to either nano-pores or a high

concentration of stacking faults and it is much less evident in the stoichiometric SiC

coating as compared to the coatings with impurities [22] In the S3 SiC coating (Fig

310(b) in chapter 3) a larger amount of micro cracks either intergranular or

transgranular were found under the indenter than in the S1 and S2 SiC coatings

The fracture mechanism of materials is influenced by their microstructure and the

fracture toughness could be enhanced by changing it For example ceramics

containing micro-cracks during fabrication could be associated with good fracture

behaviour but low strength and hardness since the micro-cracks usually serve as the

failure origins A better solution is to fabricate materials with microstructures that can

form stress induced micro-cracks under an external force [36] In FBCVD SiC a

number of micro cracks were observed under the indenter (Fig 44(b) Fig 310(b)

and (d) in chapter 3) from where the main cracks initiated and propagated away from

this zone According to a previous study although the tip of the main crack leaves the

micro-cracked zone under the indenter the wake region can provide stress shielding

against some further crack extension [37]

Thus the micro-cracks under the indentation (Fig 44(b) Fig 310(a) and (c) in

chapter 3) seem to be a mechanism for the toughening behaviour of FBCVD SiC by

dissipating the fracture energy for brittle fracture Micro-cracks were also found near

the main crack tip and surrounding the main crack for example in the stoichiometric

SiC coating (Fig 44(c) and (d)) This further confirms the toughening behaviour

through micro-cracking In CVD SiC which has a slightly lower fracture toughness

(around 33 MPa m12

) only a few micro-cracks were observed under the indentation

[38] which could be caused by indentation-induced slip bands As a result the

micro-cracks formed under the indentation near the main crack seem to be the reason

for the high VIF fracture toughness in SiC coatings when a high hardness is obtained


125

Fig 46 Bright TEM images showing the grain morphology of SiC coatings (a) S2

SiC (b) S3 SiC

Stress concentration zones are known to facilitate the nucleation of micro-cracks so a

large amount of micro-faults (eg pores) and weak grain boundaries (inducing the

micro-cracks under an external stress) could increase the VIF fracture toughness A

higher VIF fracture toughness in the extra-C SiC than in stoichiometric SiC coatings

may be due to the presence of the nano-pores (as shown in Fig 35(b) in chapter 3)

The S3 SiC has an even higher VIF fracture toughness than the S2 SiC coating and

this may correspond to a larger number of micro-cracks under the indentation We

assume this difference is due to their varied grain boundary morphologies as shown

in Fig 46 For example we observed different length of cracks on the cross section

(Fig 43) with cracks parallel to the grain growth direction shorter than cracks

perpendicular to the grain growth direction This is because along grain growth

direction itrsquos more likely to produce micro-cracks along the grain boundary As we see

in Fig 46 grains interact with each other in extra-C SiC (Fig 46(a)) forming branch

grains while in S3 SiC grains grow parallel (Fig 46(b)) According to a previous

study it is easier for parallel grains to form a transgranular fracture when the grain

boundaries are along the loading axis [39] This can explain the larger number of

transgranular micro-cracks under the indentation in the extra-Si SiC compared to the

extra-C coatings (Fig 310(b) in chapter 3) which caused different VIF fracture


126

toughness This different grain morphology could be caused by the

non-stoichiometries and further work needs to be done to study how excess C or Si

affects the microstructure of the SiC

44 Conclusions

In summary micro-indentation on the polished external surface of the SiC coating in

TRISO particles has been successfully applied to measure the VIF fracture toughness

of the silicon carbide (SiC) Three different types of SiC coatings (stoichiometric SiC

SiC with excess silicon and SiC with excess carbon) produced on spherical particles

by FBCVD were analysed The VIF fracture toughness (measured on the polished

external surface) in these three coatings investigated in this study was observed to

vary between 35 and 49 MPa m12

The results have shown that the VIF fracture

toughness is influenced by the microstructure and non-stoichiometry of SiC coatings

For FBCVD SiC coatings a high VIF fracture toughness accompanied with superior

hardness was attributed to the formation of micro-cracks The difference in VIF

fracture toughness was proposed to be dominated by the laminar defects and grain

morphologies in the SiC coatings


127

45 References

[1] L L Snead T Nozawa Y Katoh T S Byun S Kondo and D A Petti

Handbook of SiC properties for fuel performance modeling J Nucl Mater 371

(2007) 329-77

[2] N Swaminathan P J Kamenski D Morgan and I Szlufarska Effects of grain

size and grain boundaries on defect production in nanocrystalline 3C-SiC Acta

Mater 58 (2010) 2843-53

[3] G K Miller D A Petti D J Varacalle and J T Maki Statistical approach and



[4] D A Petti J Buongiorno J T Maki R R Hobbins and G K Miller Key




[5] K Bongartz E Gyarmati H Schuster and K Tauber Brittle Ring Test - Method

for Measuring Strength and Youngs Modulus on Coatings of Htr Fuel Particles J

Nucl Mater 62 (1976) 123-37

[6] K Bongartz E Gyarmati H Nickel H Schuster and W Winter Measurement of

Youngs Modulus and Fracture Stress on Htr Particle Coatings by Brittle Ring Test

J Nucl Mater 45 (1972) 261-64

[7] M W Kim J H Kim H K Lee J Y Park W J Kim and D K Kim Strength

of chemical vapor deposited silicon carbide films using an internal pressurization

test J Ceram Process Res 10 (2009) 373-77

[8] T S Byun J D Hunn J H Miller L L Snead and J W Kim Evaluation of



[9] X Zhao R M Langford J Tan and P Xiao Mechanical properties of SiC

coatings on spherical particles measured using the micro-beam method Scripta


128

Mater 59 (2008) 39-42

[10] E Lopez-Honorato P J Meadows J Tan and P Xiao Control of stoichiometry




T Abram and P Xiao Youngs modulus measurements of SiC coatings on

spherical particles by using nanoindentation J Nucl Mater 393 (2009) 22-29

[12] ACKadak RGNallinger MJDriscoll SYip DGWilson HCNo JWang

HMaclean TGalen and CWang et al Modular Pebble Bed Reactor Project

University Research Consortium Annual Report Beijing 2000

[13] J I Federer Parametric Study of Silicon-Carbide Coatings Deposited in a

Fluidized-Bed Thin Solid Films 40 (1977) 89-96

[14] G R Anstis P Chantikul B R Lawn and D B Marshall A Critical-Evaluation

of Indentation Techniques for Measuring Fracture-Toughness 1 Direct Crack


[15] M T Laugier Palmqvist Toughness in Wc-Co Composites Viewed as a Ductile

Brittle Transition J Mater Sci Lett 6 (1987) 768-70

[16] M T Laugier Palmqvist Indentation Toughness in Wc-Co Composites J Mater

Sci Lett 6 (1987) 897-900

[17] W D Nix and R Saha Effects of the substrate on the determination of thin film

mechanical properties by nanoindentation Acta Mater 50 (2002) 23-38

[18] J Lankford and D L Davidson Crack-Initiation Threshold in Ceramic Materials

Subject to Elastic-Plastic Indentation J Mater Sci 14 (1979) 1662-68

[19] Z Li A Ghosh A S Kobayashi and R C Bradt Indentation

Fracture-Toughness of Sintered Silicon-Carbide in the Palmqvist Crack Regime J

Am CeramSoc 72 (1989) 904-11

[20] H Hatta M Zoguchi M Koyama Y Furukawa and T Sugibayashi

Micro-indentation method for evaluation of fracture toughness and thermal


129

residual stresses of SiC coating on carboncarbon composite Adv Compos Mater

12 (2003) 155

[21] C B Ponton and R D Rawlings Vickers Indentation Fracture-Toughness Test 1

Review of Literature and Formulation of Standardized Indentation Toughness

Equations Mater Sci Tech Ser 5 (1989) 865-72

[22] H Zhang E Lopez-Honorato A Javed X Zhao and P Xiao Study of the

microstructure and mechanical properties of SiC coatings on spherical particles J

Eur Ceram Soc In Press (2011)

[23] A Leonardi F Furgiuele S Syngellakis and R J K Wood Analytical

Approaches to Stress Intensity Factor Evaluation for Indentation Cracks J Am

Ceram Soc 92 (2009) 1093-97

[24] M C Osborne J C Hay L L Snead and D Steiner Mechanical- and



[25] R D Dukino and M V Swain Comparative Measurement of Indentation

Fracture-Toughness with Berkovich and Vickers Indenters J Am CeramSoc 75

(1992) 3299-304

[26] K H Park S Kondo Y Katoh and A Kohyama Mechanical properties of

beta-SiC after Si- and dual Si plus He-ion irradiation at various temperatures

Fusion Sci Technol 44 (2003) 455-59

[27] S Nogami S Ohtsuka M B Toloczko A Hasegawa and K Abe Deformation

during surface modification of silicon carbide using rare-gas ion-beam irradiation

Pricm 4 Forth Pacific Rim International Conference on Advanced Materials and

Processing Vols I and Ii 1367-70 3028 (2001)

[28] G D Quinn and R C Bradt On the Vickers indentation fracture toughness test J

Am Ceram Soc 90 (2007) 673-80

[29] J Tan Mechanical properties of SiC in TRISO fuel particle PhDThesis

University of Manchester Manchester 2010


130

[30] K Kaneko M Kawasaki T Nagano N Tamari and S Tsurekawa

Determination of the chemical width of grain boundaries of boron- and

carbon-doped hot-pressed beta-SiC by HAADF imaging and ELNES line-profile

Acta Mater 48 (2000) 903-10

[31] B Reznik D Gerthsen W G Zhang and K J Huttinger Microstructure of SiC

deposited from methyltrichlorosilane J Eur Ceram Soc 23 (2003) 1499-508

[32] R A Shatwell K L Dyos C Prentice Y Ward and R J Young Microstructural

analysis of silicon carbide monofilaments J Microsc-Oxford 201 (2001) 179-88

[33] M J Hernandez G Ferro T Chassagne J Dazord and Y Monteil Study of

surface defects on 3C-SiC films grown on Si(111) by CVD J Cryst Growth 253

(2003) 95-101

[34] D S Harding W C Oliver and G M Pharr Cracking during nanoindentation

and its use in the measurement of fracture toughness Thin Films Stresses and

Mechanical Properties V 356 (1995) 663-68

[35] ACFischer-Cripps Introduction to contact mechanics Springer New York

2000

[36] DJGreen An introduction to the mechanical properties of ceramics Cambridge

University Press Cambridge 1998

[37] S B Biner A Numerical-analysis of crack-growth in microcracking brittle solids

Acta Metall Mater 42 (1994) 3643-51

[38] K H Park T Hinoki and A Kohyama Influence of irradiation-induced defects

on fracture behavior in highly pure SiC J Nucl Mater 367 (2007) 703-07

[39] H Horii and S Nematnasser Brittle failure in compression - splitting faulting

and brittle-ductile transition Philos T Roy Soc A 319 (1986) 337-74

CHAPTER 5 Influence of Interfacial Irregularities on Fracture Strength of SiC

131

CHAPTER 5 Influence of Interfacial Roughness on Fracture


51 Introduction

During the irradiation process of TRI-Isotropic (TRISO) fuel particles the high

tensile stress could be accumulated at crack tips These tips were due to direct

penetration of the cracks formed in the PyC layer or the high stress concentration as a

result of the debonding of IPyCSiC interface [1 2] When the tensile stress inside of

the particle exceeded the critical fracture stress of the SiC coating it caused the

failure of the whole particle [3] Furthermore the fracture strength is a main

parameter used in modeling the probability of failure of fuel particles so it is

important to measure the fracture strength of SiC to determine their performance

which is determined from the maximum tensile stress

Different methods such as hemi-spherical bending [4] crush test [5 6] and inner

pressure [6] were introduced to measure the fracture strength of SiC coating in

TRISO fuel particle The fracture strength was in a range and could be characterised

by the Weibull distribution function [4-6] The common vague conclusion derived

from previous results is the significant effect of the IPyCSiC interface on the fracture

strength [4-6] The interface was also found to affect the primary failure mechanism

by determining if the load can transmit through the SiC [6] Previous analyses are

consistent with the well-known prescription that the fracture strength of ceramic

materials varies largely and it is dependent on the size and surface condition of the

specimen [7-9] Among these methods the latest modified crush test proposed by

Byun et al[510] showed a well controlled scatter of the fracture strength in a given


132

sample

Although the importance of the interface has been noticed the lack of an accurate and

scientific description of the interface has limited the further study about its

relationship with the fracture strength Roughness is a commonly used terminology to

describe the interface and it could be measured by atomic force microscope and

characterised by the standard deviation of the vertical features [11 12] However

roughness is not enough to describe the interface and to relate it to fracture strength

[13] Due to the importance of the statistical analysis for ceramic materials the

self-affine theory was used to characterise the complex interface numerically

according to previous studies [14-17] A self-affine interface is characterised by a

correlation length the saturation roughness and the roughness exponent [18] A

similarly straightforward approach was applied to demonstrate the importance of the

interfacial roughness on the mechanical properties [19] showing that interfaces with

big and sharp irregularity fail first

In this work the modified crush test was used to measure the fracture strength of a

SiC layer deposited at different temperatures The IPyCSiC interface was well

described by self-affine theory Therefore the effect of the IPyCSiC interface and

dimension of particles together with other possible influences such as porosity and

grain size on the fracture strength were discussed The improvement of this work is

being able to do statistical analysis on the interfacial roughness


521 Materials

In this Chapter the buffer pyrolytic carbon and dense pyrolytic carbon coatings were

deposited on the top of ZrO2 kernel (~ Φ500 μm) by fluidized bed chemical vapour

deposition Thirteen SiC coatings were deposited at different temperature flow rate


133

MTS concentration and added gas as shown in Table 51 The deposition conditions

were chosen according to previous studies to get different microstructures and more

deposition mechanisms of SiC coating can be found in Ref [20] For fracture strength

measurement the SiC particles were mounted with thermoplastic resin and ground to

about 55 portion of the sphere and polished using increasingly fine diamond

suspensions until frac14 μm SiC shells were released from surrounded PyC layers by

oxidizing at 700 ordmC for 8 hours and further washed in an ultrasonic bath with acetone

for 5 minutes



Sample Temperature

(ordmC)

MTS

(vol )

Added gas concentration Flow rate

(LMin)

Radius

Thickness (~)

S1 1300 91 05vol C3H

6 600 72

S2 1300 91 01vol C3H

6 600 76

S3 1280 91 01vol C3H

6 600 83

S4 1300 91 -- 600 85

S5 1400 19 57vol Ar 778 87

S6 1500 22 82vol Ar 700 90

S7 1500 19 89vol Ar 778 101

S8 1500 22 79vol Ar 700 112

S9 1400 19 57vol Ar 777 117

S10 1300 19 57vol Ar 778 129

S11 1500 19 89vol Ar 777 151

S12 1500 22 76vol Ar 700 158

S13 1500 19 57vol Ar 778 190

The difference between sample S5 and S9 S7 and S11 is the thickness of the PyC layer MTS

methyltrichlorosilane Lmin the flow rate measured in liter per minute To produce SiC coatings with

particular microstructures and compositions different deposition conditions were chosen which were

contributed to Dr Eddie Lopez-Honorator

522 Test method and analysis

The crush test taking the contact area into consideration was used in this study [2 5

21] and the loading profile of the crush system is shown in Fig 51 When a partial

spherical shell (Radius R thickness t) was diametrically loaded by an external load F


134

concentrated on a small circular area (radius 0 ) the maximum membrane stress and

bending stress could be calculated by the equations developed by Roark and Young

[21] The combination of the maximum bending and membrane stress (Local fracture

strengthL

f ) in the inner side of the shell was the maximum fracture strength for

partially loaded shell (around 55 of the sphere)

The fracture strength of brittle SiC coating is best considered as a distribution rather

than a fixed number and the most widely used expression for characterisation is the

cumulative distribution functionmdashWeibull distribution function [7 22] In the current

study the distribution of local fracture strength and fracture strength for a full

spherical shell were characterised by the Weibull distribution The Weibull modulus m

is derived from the local fracture strength (Eq 14 in Chapter 2) The calculation of the

fracture strength for the full spherical shell (F

f ) is based on the size effect (scaling

factor mtRr 122

0 ))(4( R radius of the particle t thickness of SiC shell 0

radius of residual impression after loading) which is equal to the partial strength

divided by the scaling factor [5 7] More details about fracture strength calculation

are available in Ref [5]


According to a previous study [5] one reason for the difference of local fracture

10 ordm

t


135

strength in a given batch of coating is due to different sizes of residual impression

( 0 ) under which the distribution of defects could be different To reduce the

influence of the 0 the radius (R) at the edge of the residual impression was kept at

an angle of around 10ordm (as shown in Fig 51) from the loading axis by inserting

different kind of soft metal It varied slightly (the ratio of standard deviation to mean

value is around 10) in each batch of SiC

The crush test was carried out in a universal tensile machine INSTRON 5569

(INSTRON High Wycombe Bucks) with a 100 N maximum load cell For each batch

of SiC shell (except for S13) at least 30 specimens were tested at room temperature

with a crosshead speed of 0005 mms The failure load recorded by the tensile

machine was used as the fracture load The individual impression left on the soft

metal (Nickel alloy cold worked copper or brass) was marked under corresponding

load and its diameter was measured by optical microscope (times100 ZESIS Company

German)

523 Characterisation methods

A Philips XL30 FEG-SEM (Philips Eindhoven Netherlands) was used to characterise

IPyCSiC interfacial roughness grain size and porosity from the finely polished cross

section of SiC coatings Characterisation of the IPyCSiC interfacial roughness was

realized by editing the SEM images (in the magnification of times1600) with the Image J

software and extracted it as a line from the background SEM image The interfacial

roughness could be described by a series of pairs of x (distance tangential to the

interface) and y (distance normal to the interface) coordinates assuming the interface

is flat at a scale of 70 microm

Porosity was measured by controlling the threshold of SEM images (times1600 TIF) at a

gray level and adjusted to distinguish pores from grains with the Image J software


136

Pore fraction was defined as the ratio of the pores and the total area of the SEM image

Grain size of FBCVD SiC coatings varied in a range and in a columnar shape It was

characterised by measuring mean width and length of single crystals from SEM

images (times6400) and the grain size of the coatings is represented by the mean width

timeing the length of grains A FEG-TEM (TecnaiTM G2

F30 U-TWIN) was used to

observe the IPyCSiC interfacial roughness and TEM samples were prepared by

focused ion beam milling The linear regression method was used to analyze and

quantify the influences of parameters on the fracture strength and Weibull modulus

53 Results and discussions

531 Fracture strength and dimensional effect

Table 52 gives the summary of the measured and calculated parameters for all the

coatings It includes the diameter of impression (mean value 2 0 ) force (mean value

F) Weibull modulus (derived from local fracture strength m) local fracture strength

(L

fmean value) and fracture strength for the full spherical shell (

F

fmean value)


Sample 2 0 μm F N L

f MPa Modulus (m) Scaling Factor

For Size Effect

F

f MPa

S 1 15239 2235 1784 7397 185 963

S 2 15043 1999 1599 7687 183 872

S 3 14898 1540 1446 7459 187 774

S 4 16052 2042 1620 8261 178 908

S 5 17018 2573 1810 7927 178 1018

S 6 16220 1885 1648 6953 193 855

S 7 14662 1691 1974 7755 190 1019

S 8 14905 1336 1717 7102 198 868

S 9 13040 1088 1825 6495 223 820

S10 16410 1215 1472 6801 204 722

S11 16165 1006 1430 6104 219 652

S12 14677 903 1512 6616 205 737

S13 11586 489 1762 4912 300 587


137

As given in Table 52 a significant difference (49-257 N) of the load among SiC

coatings was obtained According to a previous study [5] the variation is mainly

caused by different thicknesses (varied from 30 μm to 60 μm) of SiC coatings

because the relatively thin coating tends to reach higher strength concentration at

fracture


distribution

The Weibull modulus derived from the local fracture strength (as given in Fig 52) is

in the range of 49-86 (as shown in Table 52) and it falls into the category of moduli

for ceramics materials (from 5 to 30) This range of Weibull modulus is similar to the

values obtained from the brittle ring tests which also gave a similar range of the local

fracture strength [23 24] In different batches of SiC coatings it was found that the

Weibull modulus decreases linearly with the increase of the ratio of outer radius (R) to

the thickness of SiC coatings ( tR ) as shown in Fig 53 The ratio of Rt accounts

for up to 778 (2R from linear regression) of differences of the modulus This is

because the tR ratio is a critical dimension value for the strength distribution of the


138

SiC shell and it represents the relative thickness of SiC coating The higher the ratio

is the thinner the SiC coating So it corresponds to the larger inner surface area

resulting in larger scattering sizes of the critical flaws This observation is consistent

with the previous finite element modeling results showing that the Weibull modulus is

related to the sample dimension [10]




As given in Table 52 the scaling factor (effective area-parameter based on the local

fracture strength) between the local fracture strength and the fracture strength of the

full shell are in the range of 18-30 The results are consistent with Byun et alrsquos study

(19-31) [5] and it indicated the importance of the size effect on the fracture strength

of the full shell

The fracture strength for the full spherical shell of thirteen SiC coatings were given in

the form of Weibull plots as shown in Fig 54 The mean fracture strength for the full

spherical shell was in the range of 587-1019 MPa (as given in Table 52) which is

higher than the range of 330-650 MPa obtained by Byun et al [5] This is because the


139

Rt ratio (above 11) in Ref [5] falls into the higher value categary in current work as

shown in Fig 53


SiC coatings

Because the Weibull modulus is dominated by the tR ratio (Fig 53) its influence on

fracture strength for a full spherical shell could also be from this ratio as shown in

Fig 55 It shows that the fracture strength for the full shell decreases nearly linearly

with the increase of the tR ratio which produces a difference of 6528 (2R derived

from linear curve fit which represents fair agreement) of differences In this work the

similar range of Rt ratio (above 11) corresponds to the fracture strength lower than

850 MPa (as shown in Fig 55) which reduced the difference from previous results

[5] Furthermore the fracture strength of about 1000 MPa was obtained when the Rt

was about 8 [25] and it is similar as the result given in Fig 55 This again

demonstrated the importance of the geometry on the fracture strength of SiC coating

Therefore it is important to eliminate the external influence and study the influences

of microstructures such as interfacial roughness porosity and grain size on fracture


140

strength which are discussed in the following parts





According to Griffith fracture theory the fracture strength (L

f ) is a function of the

critical flaw size (C) and the fracture toughness ( ICK ) as shown in the following

equation [26]

12( )

L ICf

K Z

Yc (1)

Y is a loading geometrical parameter Z is the flaw size parameter The magnitude of

the critical flaw size could be related to the IPyCSiC interfacial irregularities

The interfacial flaw shape of SiC coatings is modeled from the surface morphology of

PyC coating during deposition process as shown in Fig 56(a) The crack was taken

as a semi-circular surface crack as given in Fig 56(b) where Y is 2 and Z is 16 (Y


141

Z are geometrical constants introduced in Eq (1) [26] The fracture toughness of SiC

coatings in TRISO fuel particle was taken to be 33 MPamiddotm12

according to previous

report [27] Taking the result of the local fracture strength from individual SiC coating

into Eq (1) the magnitude of the critical flaw size C could be obtained




Figure 46 shows the redraws of the IPyCSiC interfacial roughness from SEM images

and the calculated critical flaw sizes according to Eq (1) (range and mean values) for

all specimens are given in the right columns If the fracture initiated at the IPyCSiC

interface as proposed in previous studies [4-6] the calculated critical flaw size range

of each type of SiC coating was expected to match the size range of the interfacial

irregularities


142




(1)

In Fig 57 most of the calculated critical flaw sizes according to Eq (1) are in the

same magnitude as the flaw size observed directly from the interfacial profile images

and this indicates that the dominant effect of the surface roughness on the local

fracture strength For example the direct observation of the biggest flaw size from the

profile is about 43 μm and 26 μm in sample S9 and S13 respectively and they are in

the range of the calculated defect sizes of 09-65 μm and 17-47 μm for S9 and S13

respectively However exceptions were found such as specimens S1 and S2 which

show slightly higher calculated surface flaw size than the observation from SEM

images Furthermore it is difficult to accurately characterise the difference of the

interfacial roughness by observing the converted images and give specific

information (such as shape) of single profile (shown in Fig 57) The estimation of

the shape of surface irregularities to be half-circular could also result in the error on

the critical flaw size calculation [7] To give a direct estimation about the influence of

interfacial roughness on local fracture strength the scaling behavior of IPyCSiC

interface need to be characterised by a statisticalnumerical method


143

533 Characterise and quantify the interfacial roughness

Self-affine theory has become a standard tool in the study of various rough interfaces

[18 28 29] Here it was the first time being proposed to describe the IPyCSiC

interfacial roughness accurately and scientifically and then was used to quantify the

relationship between interfacial roughness and local (intrinsic) fracture strength and

fracture strength of the full shell

5331 Self-affine theory introduction and experimental setup

In order to describe the IPyCSiC interfacial roughness with specific parameters an

easy way is using a height-height function [29 30]

2 1 2( ) ( ( ) ( )) xh x h x x h x x (2)

where the x axis is along the IPyCSiC interface and ( )h x is the surface height profile

The amplitude of the roughness ( )h x is correlated with the length scale x and

lt gt denotes the spatial average over ( )h x in a planar reference surface If the

interfacial roughness of IPyCSiC were self-affine the correlation of x and

h should follow the power law relationship (Eq (2)) and it could be obtained by the

log-log plot of x and h The (for self-affine surface 0lt lt1) is the roughness

exponent and it describes the degree of surface roughness at short length scales [31]

This short length scale is shorter than correlation length ξ which is another parameter

used to describe the self-affine surface (besides the surface roughness h and

roughness exponent ) It is the average distance between the features in the surface

profiles within which the surface variations are correlated [28] Therefore the small

(close to 0) characterises extremely jagged or irregular interfaces while large

value characterise interface with smooth hills and valleys [32]

For all the samples the scaling properties of IPyCSiC interface (as shown in Fig 57)

are characterised by their one-dimensional height-height correlation function Eq (2)


144

The characteristic parameters of the digitalized IPyCSiC interfacial roughness are as

follows The resolution between two points along x axis is 020833 μm and x

changes by timing the resolution with integer (1 2 3hellip15) According to previous

self-affine theory study [16] the number of recorded points along the x axis was

taken in the range of 250-400 in this work corresponding to the length of 50-70 μm

for different IPyCSiC interfaces

5332 Results of self-affine theory

Figure 58 is a log-log plot showing the variation of h as a function of the distance

x for three SiC coatings The h varied as a power law of x (solid line ) when

x ltξ while remained nearly constant ˗ saturation roughness (σ0 dashed parallel

lines) for x gtξThese results indicated that these three IPyCSiC interfacial

roughness were self-affine with the roughness exponent of around 063-067 For the

rest of the samples the same scaling characterisation method was used Theξ σ0 and

are given in Table 53

Fig 58 Log-log representation of the height-height correlation function h




ξ3 ξ12 ξ6


145



Sample σ0 (μm) ζ ξ(μm) σ0ξ

S 1 02378 05903 06250 03804

S 2 04142 06950 08333 04971

S 3 06701 06673 16666 04021

S 4 06825 05244 14583 04680

S 5 05271 06308 14581 03615

S 6 08500 06343 20833 04080

S 7 04293 05162 14583 02944

S 8 07452 05107 14583 05110

S 9 05453 06099 12500 04362

S10 06953 05490 13044 05330

S11 05806 04949 10417 05574

S12 07584 06899 16666 04550

S13 05522 02971 18750 02945

The roughness exponent values for the 93 of IPyCSiC interface were in the range

of 05-07 (as shown in Table 53) This indicated the self-affine measurement is

reliable according to Schmittbuhl and Vilottersquos review [14] which showed that this

range of roughness exponents could have the minimum characterisation errors

Furthermore these roughness exponents are comparable except specimen S13 and it

was consistent with the observation of the interfacial roughness (Fig 57) in which

only specimen S13 showed the high degree of high frequency and short wavelength

irregularities (the dark pits in S13 profile) According to previous study [31] the

concentration of the roughness exponent values could be attributed to the same

original mechanism of the IPyCSiC interface which was produced by the FBCVD

under different conditions As a result the different roughness exponent value could

not describe the difference of the IPyCSiC interface

As shown in Table 53 the saturation roughness (σ0) and correlation length (ξ) are in

the range of 024-085 μm 063-208 μm respectively (Table 53) According to

previous studies [16 17 30] the σ0 and ξ couldnrsquot represent the interfacial


146

irregularities correlated with the critical flaw size Because the σ0 value range was

nearly one magnitude lower than the calculated critical flow size (mean value range of

2-4 μm) and the dimension of ξ was perpendicular to the calculated critical flaw size

direction Furthermore it was found that σ0 and ξ values were correlated to the sample

size (recorded points) [16] With the increase of the sample size for the same profile

both the ξ and the σ0 values increased and indicated these two parameters may not be

intrinsic properties of the samples However the roughness ratio σ0ξ is constant

which was found in both the current work and previous study [16]

As a result of above discussions the roughness ratio of σ0ξ was proposed to

characterise the interfacial roughness which could represent the sharpness of the

interfacial irregularities according to Ref [30] For example the low ξ value

corresponded to narrow surface irregularity when the σ0 and values were the same

With the increase of the σ0 value the surface irregularity became deep and narrow

which was hazard to the mechanical properties according to previous simulation work

on the fracture strength of SiC coatings [22] The above observations and analysis

results are supported by previous study [31] when length scale x gt ξ (shown in

Fig 58) the roughness ratio σ0ξ describes mainly the long-wavelength roughness

characteristics which could be statistically equal to the effect of the critical flaw size

on fracture strength

534 Quantify the influence of interface roughness on fracture strength

Figure 59 gives the influence of roughness ratio on the local fracture strength and it

contributes to nearly 50 (R2 from linear regression) of variation of the local fracture

strength It shows that the local fracture strength decrease linearly with the increase of

the roughness ratio This result approves previous findings about the importance of

the interfacial roughness [4-6] and is correlated with the Griffth fracture theory (Eq

(1)) about the importance of the shape and dimension of critical flaws Furthermore

the relation between interfacial roughness has been characterised quantitatively and a


147

linear relationship between roughness ratio and local fracture strength is proposed



Except for the interfacial roughness the local fracture strength could also be affected

by the fracture toughness as shown in Eq (1) Although Vickers-indentation fracture

behavior of SiC coatings was different due to the laminar defects and grain

morphology [33] the fracture toughness of SiC was found to be insensitive to the

microstructure of materials [34] This could be attributed to the fact that

Vickers-indentation provided a static propagation of the crack while the real fracture

toughness was measured dynamically In this work the fast fracture process could

overtake the effect of microstructure on the different static fracture behaviour [5 25]

Since porosity and grain size were main microstructural variations in SiC coatings [1]

their effects on fracture strength were estimated

The characterisation and quantification of grain size and porosity were shown in Table

54 The grain size was found to have no effect on fracture strength according to

previous studies [5] which was also indicated from the regress analysis (R2 is close to

0) No influence was found by regressing the local fracture strength on pores

Therefore the dominant influence on the local fracture strength is from the roughness


148

ratio


Specimen S 1 S 2 S 3 S 4 S 5 S 6 S 7 S 8 S 9 S10 S11 S12 S13

Grain size

(μm2)

04 06 06 08 20 20 20 28 20 08 20 28 25

Porosity

(Area )

0 0 0 0 05 04 12 09 03 0 08 21 20



y=1351-1150x

Because the fracture strength for a full spherical shell is a function of the Weibull

modulus and local fracture strength [5] it was affected by factors such as the

dimension ratio of thickness to radius of the coating (as shown in Fig 55) the

roughness ratio (as shown in Fig 510) Figure 510 shows the influence of roughness

ratio on fracture strength of the full shell The linear relationship was found in 12

samples as indicated by the dashed line in Fig 510 and it could explain about 68

(2R from linear regression) of difference in fracture strength of the full particle The

high roughness ratio would decrease the fracture strength of the full shell linearly The

deviated point of sample S13 could be due to its largest Rt ratio (as shown in Fig

55) which may have over taken the effect of the roughness ratio (Work about the size


149

effect on the fracture strength has being carried out)

54 Conclusions

The fracture strength of SiC coatings deposited under different conditions were

measured by the modified crush test and analyzed by the statistical analysis (Weibull

function and Self-affine theory) The influences on fracture strength were studied

such as the IPyCSiC interfacial roughness specimen size and porosities Following

results were obtained

(1) Weibull modulus and fracture strength of the full shell were significantly affected

by the ratio of radius to thickness of SiC coating and both of them decrease

linearly with the increase of the ratio

(2) The dominant effect of the IPyCSiC interfacial roughness on intrinsic fracture

strength was found by matching the SEM images with the calculated critical flaw

size based on the Griffith fracture theory

(3) The interfacial roughness were successfully characterised by a

numericalstatistical method and the roughness ratio representing the shape of the

irregularities was proposed to be a unique parameter among different coatings

(4) The difference of the local fracture strength was dominated by the roughness ratio

and it decreased linearly with the increase of the roughness ratio It is been the

first time that the interfacial roughness was numerically related to the fracture

strength

(5) Microstructures such as grain boundaries and porosity were found to have

neglectable influence on fracture strength


150

55 References





fracture strength for silicon carbide layers in the tri-isotropic-coated fuel particle J

Am Ceram Soc 90 (2007) 184-91

[3] T Nozawa L L Snead Y Katoh J H Miller E Lara-Curzio Determining the

shear properties of the PyCSiC interface for a model TRISO fuel J Nucl Mater

350 (2006) 182-94


Fuel Particles for High-Temperature Gas-Cooled Reactors J Am Ceram Soc 56

(1973) 36-41




[6] S G Hong T S Byun RA Lowden L L Snead Y Katoh Evaluation of the

fracture strength for silicon carbide layers in the TRI-Isotropic-coated fuel particle

J Am Ceram Soc 90 (2007) 184-91

[7] D J Green An introduction to the mechanical properties of ceramics Cambridge

solid state science series Cambridge Cambridge University press 1998

[8] R Danzer Some notes on the correlation between fracture and defect statistics

Are Weibull statistics valid for very small specimens J Eur Ceram Soc 26

(2006) 3043-49



[10] J W Kim T S Byun Y Katoh Optimization of fracture strength tests for the

TRISO layers of coated fuel particles by finite element analysis 33rd international

conference on advanced ceramics and composites Daytona Beach FL2009


151

[11] W N W Chen X Nie A A Wereszczak D W Templeton Effect of Loading

Rate and Surface Conditions on the Flexural Strength of Borosilicate Glass J Am

Ceram Soc 92 (2009) 1287-95

[12] R T Wu X Wang A Atkinson On the interfacial degradation mechanisms of

thermal barrier coating systems Effects of bond coat composition Acta Mater 58

(2010) 5578-85

[13] X Nie W N W Chen A A Wereszczak D W Templeton Effect of Loading


Ceram Soc 92 (2009) 1287-95

[14] J Schmittbuhl J P Vilotte S Roux Reliability of Self-Affine Measurements

Phys Rev E 51 (1995) 131-47

[15] J T M De Hosson G Palasantzas Roughness effect on the measurement of

interface stress Acta Mater 48 (2000) 3641-45

[16] L Ponson H Auradou M Pessel V Lazarus J P Hulin Failure mechanisms

and surface roughness statistics of fractured Fontainebleau sandstone Phys Rev

E 76 (2007) 036108-14

[17] L Ponson H Auradou P Vie J P Hulin Low self-affine exponents of

fractured glass ceramics surfaces Phys Rev Lett 97 (2006) 125501-4

[18] F Spaepen Interfaces and stresses in thin films Acta Mater 48 (2000) 31-42

[19] W G Sloof T S Hille T J Nijdam A S J Suiker S Turteltaub Damage

growth triggered by interface irregularities in thermal barrier coatings Acta Mater

57 (2009) 2624-30





1974

[22] G K Miller D A Petti J T Maki D L Knudson An evaluation of the effects


152

of SiC layer thinning on failure of TRISO-coated fuel particles J Nucl Mater

355 (2006) 150-62

[23] K Bongartz E Gyarmati H Schuster KTauber The brittle ring test A method

for measuring strength and Youngrsquos modulus on coatings of HTR fuel particles J

Nucl Mater 62 (1976) 123-37

[24] K Minato K Fukuda K Ikawa Strength of silicon-carbide coating layers of

fuel Pparticles for high-temperature gas-cooled reactors J Nucl Sci Tech 19

(1982) 69-77

[25] J W Kim T S Byun Y T Katoh Optimization of fracture tests for the SiC

layer of coated fuel particles by finite element analysis Ceram Nucl Appl DOI

1010029780470584002 ch13 2010

[26] S Gonzalez B Ferrari R Moreno C Baudin Strength analysis of

self-supported films produced by aqueous electrophoretic deposition J Am

Ceram Soc 88 (2005) 2645-48

[27] J J Bellante H Kahn R Ballarini C A Zorman M Mehregany A H Heuer

Fracture toughness of polycrystalline silicon carbide thin films Apply Phys Lett

86 (2005) 071920-22

[28] B N Dev A Roy K Bhattacharjee H P Lenka D P Mahapatra Ge growth

on self-affine fractal Si surfaces influence of surface roughness J Phys D Appl

Phys 42 (2009) 145303-10

[29] J Feder Fractals Plenum New York 1988

[30] J T M De Hosson R Van Tijum Effects of self-affine surface roughness on the

adhesion of metal-polymer interfaces J Mater Sci 40 (2005) 3503-08

[31] G Palasantzas Roughness spectrum and surface width of self-affine fractal

surfaces via the K-correlation model Phys Rev B 48 (1993) 14472-78

[32] P Meakin Fractals scaling and growth far from equilibrium Cambridge

Cambridge University Press 1998

[33] H Zhang E Loacutepez-Honorato A Javed I Shapiro and P Xiao A study of the


153

microstructure and indentation fracture toughness of silicon carbide (SiC) coatings

on TRISO fuel particles J Am Ceram Soc 95 (2012) 1086-92

[34] J J Bellante H Kahn R Ballarini C A Zorman M Mehregany and A H

Heuer Fracture toughness of polycrystalline silicon carbide thin films Apply

Phys Lett 86 (2005) 071920-22

CHAPTER 6 Microstructure amp Fracture strength of SiC after Thermal Treatment

154

CHAPTER 6 Effect of Thermal Treatment on

Microstructure and Fracture Strength of SiC Coatings

61 Introduction

The mechanical properties of the as-deposited SiC coatings have been widely studied

eg Youngrsquos modulus and hardness [1-3] fracture toughness [4] and fracture strength

[5] etc However after it experiences the high temperature the composition and the

microstructure of the SiC coating may change which consequently influences the

mechanical properties It has been found that mechanical properties of SiC such as

Youngrsquos modulus and hardness are less affected when experiencing the current fuel

operation temperature (less than 1600 ordmC) [1 6] even after thermal treatment

temperatures of 1980 ordmC [7] To enhance the operational temperature of the high

temperature reactor in the future design it would be necessary to understand the

evolution of microstructure and mechanical properties of SiC coatings at even higher

temperature Some research [8-10] has been carried out to study the effect of high

temperature (more than 2000 ordmC) thermal treatment on the density and microstructure

of the fuel particle Itrsquos concluded that fuel failure and fission product release

dependent on SiC thermal stability at high temperature [9] Rooyen et al[11]

measured the annealing temperature effect on the fracture strength of SiC coatings It

is found that the fracture strength increases after thermal treatment at temperature up

to 2000 ordmC decreases in strength after thermal treatment at 2100 ordmC However no

clear explanation was given on this result

Due to the importance of the SiC on the safety of this fuel it is necessary to study the

thermal stability of SiC and characterise any change in microstructure and mechanical


155

properties It has been previously found that SiC deposited at 1300 ordmC with the

addition of propylene and methyltrichlorosilane as gas precursors not only have good

mechanical properties such as hardness and Youngrsquos modulus [3] fracture toughness

[4] but also have high silver and palladium diffusion resistance [12 13] Therefore in

this Chapter we thermally treated SiC coatings deposited at a range of temperature

(1300-1500 ordmC) at 2000 ordmC for 1 hour in argon atmosphere The change of fracture

strength and thermal stability of SiC coating were studied in terms of composition and

microstructural change of the coatings after thermal treatment


Four batches of SiC coatings (with nearly stoichiometry) deposited by Fluidized bed

chemical vapour deposition at different tempearure were chosen to study the thermal

treatment effect on the evolution of the microstructure and fracture strength Table 61

gives the deposition conditions of coatings studied and symbols used to describe each

sample The stoichiometry was measured by the Raman spectroscopy (Renishaw 1000

Raman microprobe system with 514 nm Argon laser) The laser beam was focused on

the surface of the cross section through a times50 objective lens


Sample Temperature

(oC)

MTS concentration

(vol)

Added gas

concentration

Stoichiometry

SiC1 1280 91 01vol C3H6 SiC

SiC2 1300 91 01vol C3H6 SiC+C

SiC3 1400 19 57vol Ar SiC

SiC4 1500 22 79vol Ar SiC+C

The inner side of the coating is stoichiometric (23 of the thickness) while outside of the coating is

SiC with excess C The microstructure characterization was done in the inner side coating while the

fracture strength measurement is related to the full coating SiC+C means that the C peak around

1300-1500 cm-1

was observed in SiC coating Chosen of deposition conditions was contributed to Dr


156

Eddie Lopez-Honorato

The sample preparation for fracture strengths measurement is the same as described in

Chapter 5 As introduced before thermal treatment was carried out at 2000 ordmC for 1

hour in argon protected atmosphere on SiC half shells The same fracture strength test

and equipment settings as described in Chapter 5 were used in this Chapter

In addition to Raman spectroscopy the microstructure of SiC coatings before and

after thermal treatment was also characterised using X-ray diffraction (PW 1830

Philips) with a Cu Kα1 radiation source The XRD samples were the SiC segments

(fractured SiC shells without external residual stress) Scanning electron microscopy

(Philips XL30 FEG-SEM) was used to characterise the change in morphologies of

SiC coatings Porosity was measured by setting a threshold of the SEM images

(times1600 TIF) at a gray level and adjusted to distinguish pores from grains with Image

J software Three SEM images were measured for each SiC coating Average pore size

(diameter nm) and the pore fraction (area ratio of pores to the total area as observed

by SEM) were obtained For transmission electron microscopy (TEM) the specimens

were prepared by crushing the SiC shell and dispersing the fragments on a carbon

holy film copper grid and crystal structures were characterised using an FEG-TEM

(TecnaiTM G2

F30 U-TWIN)

63 Results

631 Fracture strength of SiC coatings

Figure 61 shows the Weibull distribution of the local fracture strength ( L

f ) in SiC

coatings before and after thermal treatment at 2000 ordmC It gives a direct observation on

the decrease of the local fracture strength in coating SiC2 SiC3 and SiC4 after

thermal treatment while the local fracture strength of coating SiC1 is nearly

overlapped with the as-deposited coating The magnitude of the mean local fracture


157

strength (as summarised in Table 62) could represent the decrease trend of the full

batch of the coating in current study

Fig 61 Weibull plots of local fracture strength ( L




The Weibull modulus (m) was obtained by linearly fitting the curves shown in Fig 61

It shows that the Weibull modulus decreased by 14 07 and 21 in coating SiC1 SiC3

and SiC4 respectively however it increased slightly (by 12) in SiC2 after heat

treatment As shown in Fig 61 the Weibull modulus derived from linear fitting is

affected by the deviation of few points from the linear distribution of the local fracture

strength (as shown in Fig 61) For example in sample SiC3 the slightly decrease

could be attributed to the deviation of the lowest points According to previous study

[14] the slight decrease (07) of Weibull modulus in SiC3 could be neglected since


158

the deviated points could be caused by different failure mechanisms involved in the

fracture process [14]

Fig 62 Weibull modulus plots of fracture strength of the full shell ( F

f ) before


Figure 62 shows the Weibull plots of fracture strength of the full shell ( F

f ) before

and after thermal treatment at 2000 degC In the same batch of coatings (the same size

effect) the fracture strength of the full shell increase with the increase of the Weibull

modulus and local fracture strength according to previous study [5] Therefore the

decrease of local fracture strength and increase of the modulus in SiC2 could explain

the slight change (decreased 25 MPa obtained from Table 62) of the fracture strength

of the full shell after thermal treatment In the other three samples the fracture

strength of the full shell decreased significantly (more than 110 MPa obtained from

Table 62) after thermal treatment due to the decrease of local fracture strength and


159

unchanged modulus)

Table 62 summarized the results of the fracture strength measured before and after

thermal treatment at 2000 degC including the Weibull modulus (m) derived from the

distribution of the local fracture strength ( L

f ) the mean local fracture strength and

fracture strength of the full shell ( F

f ) After thermal treatment the mean local

fracture strength of coatings decreased significantly except SiC1 coating which

retained the same level as in as-deposited coating The mean fracture strength of the

full shell was reduced after thermal treatment in a different degree but the change of

Weibull modulus is more complex which shows both decreased and increased values


local fracture strength and fracture strength of the full shell before and after thermal

treatment

Sample m (from

L

f )

as deposited 2000degC

L

f MPa


F

f MPa


SiC1 75 61 1445 1421 774 660

SiC2 77 89 1599 1395 872 847

SiC3 65 58 1824 1333 820 548

SiC4 74 53 1717 1443 858 587

As concluded from Fig 61 Fig 62 and Table 62 the fracture strength decreases

less in coatings deposited at lower temperature (about 1300 degC) than those deposited

at higher temperature (1400-1500 degC) This is consistent with previous study about

high properties of SiC coatings deposited at low temperature such as the hardness

Youngrsquos modulus and resistance to the fission products [12 13 15]


160

632 Change in morphologies


2000 ordmC for 1 hr (a) and (b) SiC1 before and after (c) and (d) SiC2 before and after

(e) and (f) SiC3 before and after (g) and (h) SiC4 before and after thermal treatment

Dashed and solid arrows indicate growth direction and pores respectively


161

Figure 63 gives the SEM images showing the microstructure of SiC coatings before

and after thermal treatment at 2000 ordmC Before thermal treatment no pores were found

in SiC1 and SiC2 coatings (Fig 63(a) and (c)) while nano-pores were found in SiC3

coating (Fig 63(e)) and even bigger (micrometres) pores were occasionally found in

SiC4 coating (Fig 63(g)) Among four as-deposited coatings SiC4 has highest area

fraction of pores (~09) followed by SiC3 (~03) coating (Fig 63 (a) (c) (e) and

(g) summarized in Table 63)

After thermal treatment at 2000 ordmC pores with different size and area fraction were

observed in all the coatings even though as-deposited SiC1 and SiC2 were free of

pores as shown in Fig 63(b) (d) (f) and (h) The amount of pores formed in treated

SiC1 coating (area fraction of ~05 ) is lower than the other three coatings which

have similar area fraction of pores (~14 ~13 and ~15 for SiC2 SiC3 and

SiC4 respectively given in Table 63) Similar to the content of the pores the pore

size (mean size of ~50 nm) in SiC1 is smaller than in the other coatings (gt 100 nm)

Among coatings SiC2 SiC3 and SiC4 much larger pores (micro-meter sized as in

Fig 63(f) and (h)) were produced in SiC3 and SiC4 coatings after thermal treatment

compared with nano-sized pores in SiC2 Furthermore it is found that most of pores

in coatings SiC2 SiC3 and SiC4 were formed along the grain boundaries and triple

junctions as we can see from Fig 63(d) (f) and (h)

The pores are uniformly distributed through the coatings and no area free of pores or

area with highly concentrated pores is observed However there are connections of

pores (2 or 3 pores formed closely) in SiC2 SiC3 and SiC4 as indicated by solid

arrows in Fig 63(d) (f) and (h) and the diameter of the porous connection zone

(black circle in Fig 63(d) (f) and (h)) could be in the magnitude of few micrometres

The connection of pores could easily become larger pores of few micrometres

diameter under external tensile strength due to the high strength concentration [14]


162

Fig 64 The IPyCSiC interfacial roughness of coating SiC1 (a) SiC2 (b) SiC3 (c)

and SiC4 (d) as deposited (left in each figure) and thermally treated at 2000 degC (right

in each figure) The white arrow points towards to the interface irregularities (except

for thermally treated SiC4 coating (d)) black circle represents the pores in SiC

coatings

Figure 64 gives the evolution of interfacial roughness in different coatings after

thermal treatment at 2000 ordmC to study their influence on the change of fracture

strength Compared with the as-deposited coating the changes of the interfacial

roughness in SiC1 are similar to SiC3 which show the smoother interface with

interval of irregularities were observed Fig 64(a) and (c) However different from

as-deposited coatings with defects mainly at the interface defects (pores) are also

observed through the coating after thermal treatment (as seen in Fig 61(b) (f) and

Fig 64(a) (c)) Furthermore the size of pores is in the same magnitude as their


163

interfacial roughness (shown in Fig 64(a) and (c))

The change of the interfacial roughness in SiC2 is more significant than SiC1 and

SiC3 since pores formed as part of the interface (indicated by arrows in Fig 64(b))

and they are larger than the pores formed in the coating (circle in Fig 64(b))

Different from others three coatings the IPyCSiC interface of SiC4 becomes

smoother (Fig 64(e)) after thermal treatment compared with as-deposited coating so

the defects (pores) within the coating are bigger than surface irregularities

633 Evolution in microstructure

Fig 65 XRD results of as-deposited SiC coatings and coatings after thermally

treated at 2000 degC in argon atmosphere (a) is SiC3 and could represent SiC1 and

SiC2 inset shows the peak shift of as-deposited (dash line) and after thermal

treatment (solid line) (b) is SiC4 and inset is the high angle diffraction peak after

thermal treatment showing splitting while it is a single peak in as-deposited coating

Figure 65 gives XRD results of the as-deposited and thermally treated samples

which show the presence of the β-SiC in coatings The peak presents at 2θ~335ordm is

from the crystallographic errors which could either be due to the stacking faults or

the disordered α-SiC according to previous descriptions [16 17] It is found that the

intensity ratio of the 2θ~335ordm peak to the (111) plane peak (2θ~356ordm) decreased after

thermal treatment in all the coatings The coating SiC4 also shows the split of high

angle diffraction peaks (inset of the Fig 65(b) 2θ~613ordm and 713ordm) which is


164

attributed to the X-ray double diffraction and this implies the high crystallites after

thermal treatment

Figure 66 is the HRTEM image of sample SiC4 after thermal treatment in which the

stacking faults and micro twins could still be seen The stacking sequence of

ABCACBACBACB was observed as shown in the dashed square zone in Fig 66

According to study about crystal structure [18] this stacking sequence is supposed to

be the micro twins compared with the rest 3C stacking sequence rather than the

6H-SiC domain Furthermore the (111) peak shifted to the high angle after thermal

treatment in all the coatings as shown in the inset of Fig 65(a) which corresponded

to the decrease of the crystal constant



Figure 67 gives the Raman spectroscopic results of SiC coatings before and after

thermal treatment The carbon peak at 1300-1600 cm-1

was found in the as-deposited

SiC2 and SiC4 coatings According to previous studies [4 19] the intensity ratio of

I1600I796 indicated that the estimated amount of excess C was less than 05 at in

this study The peak between TO and LO peaks (around 882 cm-1

) was attributed to

the stacking faults or highly disordered stacking faults cluster [3 15 20-22]


165

After thermal treatment the weak carbon related peaks appeared at around 1395 cm-1

and 1600 cm-1

(G band) in sample SiC1 SiC2 and SiC4 The peak around 1395 cm-1

could represent the methyl group and amorphous carbon structures and G band is due

to the stretching mode of all pairs of sp2 atoms in chains and rings [23] The arising of

the 2D peak (also called G peak 2715 cm-1

) after thermal treatment was observed in

sample SiC2 SiC3 and SiC4 which is the second order of zone-boundary phonons

[24]Considering the amount of excess carbon in SiC coatings the symmetry of the

2D peak indicates that the carbon after treatment is more likely to be graphene rather

than graphite [24] which means the concentration of excess C is low in SiC coatings

It is also found that the intensity ratio of the disordered stacking faults (around 882

cm-1

) to the TO peak decreases in all samples after thermal treatment (shown in Fig

67)



specimen SiC1 SiC2 SiC3 and SiC4 coatings The lower line is before thermal


166

treatment and the upper line is after thermal treatment at 2000 degC in individual

sample


thermal treatment

Sample Porosity ()

As 2000degC

Stoichiometry

As 2000degC

Critical Defects

As 2000degC

SiC1 0 05 0 C clusters Inter Inter+ Pore

SiC2 0 14 C clusters Ordered C Inter Inter

SiC3 03 13 0 Ordered C Inter Inter+ Pore

SiC4 09 15 C cluster Ordered C Inter Pore

First order Raman spectroscopy (1200-1600 cm-1

) Represents the carbon structure related to the

methyl group or amorphous carbon structures (contains SP2 and SP

3) [23] Second order (2700 cm

-1)

single layer grapheme related carbon materials [24]

Represents the interface irregularities




Furthermore the narrowing of the TO peak was found (the inset in Fig 67 (b)) in the

Raman spectroscopy Although it could be an overlap of two peaks at around 796 cm-1

and 789 cm-1

in coatings before and after thermal treatment the peak at 789 cm-1

corresponding to the stacking sequence of ABCACBhellip [25] is more likely to be

micro-twins in current study(as shown in Fig 66) Table 63 summarized the main


167

morphological and microstructural change of SiC coatings before and after thermal

treatment

Particularly for sample SiC3 except for the appearance of weak 2D peak after thermal

treatment without visible first order carbon peaks in the sample SiC3 the precipitates

were also observed from both inner and outside of the shell These precipitates were

demonstrated to be the single 3C-SiC crystal by Raman spectroscopy as shown in Fig

68 Raman spectra of precipitates represents the incident direction of the laser is

perpendicular to the SiC single crystal (111) plane which the LO mode at around 970

cm-1

is forbidden when Raman spectra were obtained in a backscattering geometry

[22] (The appearance of the forbidden LO band might be due to to finite collecting

angle of the spectrometer)

64 Discussion

641 Influence of interfacial roughness and pores on fracture strength

To evaluate the critical flaw size we used the equation 1

2( )

L ICf

K Z

Yc for tensile

strength (local fracture strength) and the case for the semi-circular surface crack

(Y=125 [26]) of radius c and inside holes (Y= π12

[14]) of diameter 2a When the

fracture toughness ( ICK ) of the SiC coating was taken as 33 MPa m-12

[27] the

critical surface defect radius and the diameter of the inside pores were calculated to be

in the range of 15 ndash 78 microm obtained from all the coatings The mean critical flaw

size is in the range of 30 ndash 40 microm after thermal treatment The calculated critical

flaw sizes are in the same magnitude as the defects observed at the IPyCSiC interface

and the pores in the SiC coatings after thermal treatment (see in Fig 63 and Fig 64)

Therefore the decrease of the local fracture strength after thermal treatment could be

related to the formation of these defects in SiC coatings Accordingly the sources of

critical defects were summarized in Table 63 for coatings before and after thermal


168

treatment The interfacial roughness and pores within the coating compete to be the

critical flaws Once the size of interfacial irregularities is lower than critical flaw size

and rarely distributed their effect on fracture strength could be decreased or even

excluded according to previous study [14] Therefore the pores inside the coating

with the diameter of 2a would be considered as the main failure origins [14] These

could explain the decrease of local fracture strength in coatings SiC2 SiC3 and SiC4

which have micrometer pores formed within the coatings andor at the interface while

the local fracture strength is less affected in coating SiC1 due to formation of

nanometer pores

The Weibull modulus is related to the specimen size loading method and defects

distribution [5 14] In this study the specimen size and the loading morphology could

be excluded for one kind of SiC coating so the change of the modulus is due to the

degree of the scattering of the critical flaw size under the tensile strength The

interfacial irregularities in SiC2 became narrower and deeper (about 4 microm of depth as

shown in Fig 64(c)) after thermal treatment and they are also bigger than the pores

generated within the coating So the critical flaw in SiC2 after thermal treatments is

due to the interfacial irregularities (Table 62) with less scattered size under the

loading area than as-deposited coating which increased the Weibull modulus

However the critical defects in the other coatings include pores within the coatings

(shown in Fig 64 and Table 62) For example in SiC4 the critical flaw is only from

pores within the coating after thermal treatment due to the lack of interstitial

irregularities (Fig 64(h)) This enlarged the distribution of critical flaws after thermal

treatment which leads to the decrease of the Weibull modulus in different degree The

change of the fracture strength of the full shell depends on both Weibull modulus and

local fracture strength as discussed before [5] Our result showed that the SiC coating

deposited at low temperature of 1300 ordmC produced less critical flaws and smaller

decrease of the fracture strength of the full shell (see Table 63)


169

642 Mechanism of microstructural change

Changes in SiC coatings after thermal treatment include the formation of pores the

decreased intensity of the 2θ~335 ordm peak (crystallographic errors) in XRD the arising

of Raman peaks around 1395 cm-1

and 2715 cm-1

According to previous studies [8

10 21 25 28 29] we propose that these changes after thermal treatment could be

attributed to phase transformation or the diffusion of defects such as vacancies and

interstitials

If the 2θ~335ordm peak is from amorphous α-SiC its intensity ratio to (111) diffraction

peak would increase after heat treatment Because the presence of α-SiC phase in

β-SiC could promote the transformation of β-SiC into α-SiC [29] Conversely the

intensity of 2θ~335ordm peak decreased after thermal treatment in this work as observed

in Fig 65 and no α-SiC phase segregation (Fig 66) was found by HRTEM after

thermal treatment Furthermore the transformation from disordered α-SiC into β-SiC

after thermal treatment is also excluded because high pressure and high temperature

are needed for this process to happen [29] Therefore it is concluded that the 2θ~335ordm

peak derived from stacking faults and they could be annihilated at current

environment according to previous studies [8 28 30]

Stacking faults were surrounded by defects such as dislocations vacancies and

interstitials [10 15 31] so the high density of stacking faults in this work

corresponded to the high amount of native defects The annihilation of stacking faults

after thermal treatment indicated the reduction of these defects and it could reduce

the lattice constant In this work the decrease of the lattice constant was found after

thermal treatment as indicated by the peak shift of (111) plane in XRD results (Fig

65) and the crystallisation (ordering) was also reflected from the decreased intensity

of the 2θ~335ordm peak (Fig 65) and Raman defect peak (around 882 cm-1

) (Fig 67)

Therefore the formation of pores is due to the annealing of defects through the


170

diffusion of vacancies or interstitials which are common even in high-purity CVD

SiC [32] However diffusion of native defects depended on their concentration which

was constrained by different composition of SiC (deviation from stoichiometry) [31]

For example for the C-rich cubic SiC the dominant defect is the CSi antisite (Si atom

site was occupied by C atom in tetrahedral structure) [31]

According to above analysis the formation mechanism of pores could be governed by

different kinds of defects In SiC1 coating the smallest and least content of pores

formed after thermal treatment is most likely caused by the annealing of stacking

faults surrounded by the dislocations and vacancies which is consistent with previous

study about the thermal treatment effect on stoichiometric SiC [28] In SiC coating

with excess carbon the microstructure evolution could be more complex as

demonstrated by the presence of the graphene layer (Raman peak at 2700 cm-1

)

According to previous studies [31 33] this is attributed to the existence of the CSi

antisite and vacancies which form the vacancy cluster and antisite clusters after

thermal treatment at 2000 degC

The microstructure change in SiC3 coating is different from SiC1 The diffusion

mechanism in SiC3 was supposed to be involved with the interstitials since the single

SiC crystal precipitate was found out of the coating(Fig 68) This also resulted in

higher amount of the pores in SiC3 than in SiC1 after thermal treatment It is

proposed that the different diffusion mechanism found in stoichiometric SiC1 (Si and

C vacancies) and SiC3 (tetragonal interstitials) could be due to different deposition

conditions which produced different kinds of dominant native defects The larger

pores formed in SiC3 and SiC4 could be due to larger grain size than SiC1 and SiC2

(different deposition temperature) because most of pores were near to the grain

boundaries and triple junctions (as shown in Fig 63(d) (f) and (h)) The diffusion of

native defects also affects the interfacial irregularities and the diffusion mechanism in

SiC coatings is being studied in our research group


171

65 Conclusions

The SiC coatings deposited at temperature range of 1300-1500 degC with composition

near-to the stoichiometry were thermally treated at 2000 degC in Ar atmosphere for 1

hour to study the effect of thermal treatment on microstructure and fracture strength

The following conclusions were obtained

(1) The local (intrinsic) fracture strength decreased in a varied degree after

thermal treatment and it was due to the formation of pores along the IPyCSiC

interface and in the coatings

(2) The Weibull modulus decreased once the pores have similarbigger size

asthan interfacial irregularities and distribute uniformly within coatings while

it increased with the size of pores much smaller than interfacial irregularities

after thermal treatment

(3) After thermal treatment no phase transformation was found in SiC coatings

and the crystallographic error (2θ~335 ordm) detected by XRD was demonstrated

to be stacking faults which were annihilated during this process

(4) The formation of pores after thermal treatment was attributed to the diffusion

of intrinsic defects such as vacancies interstitials and antisites Different

content and size of pores were observed in different coatings which are

presumed to have different kinds of native defects in as-deposited coatings

produced at different conditions

(5) The vacancies are supposed to be the dominant defects in stoichiometric SiC

deposited at 1280 ordmC however in other coatings the dominant defects could

be a combination of vacancies antisites and interstitials based on Raman

results before and after thermal treatment Furthermore the diffusion of native

defects also affects interfacial roughness after thermal treatment which needs

further study


172

66 References

[1] L L Snead T Nozawa Y Katoh T S Byun S Kondo D A Petti Handbook of

SiC properties for fuel performance modeling J Nucl Mater 371 (2007) 329-77

[2] C Bellan J Dhers Evaluation of Youngrsquos modulus of CVD coatings by different



microstructure and mechanical properties in SiC coatings produced by fluidised


[4] H Zhang E Loacutepez-Honorato A Javed I Shapiro P Xiao A study of the


on TRISO fuel particles J Am Ceram Soc (2011) DOI

101111j1551-2916201105044x

[5] T S Byun J D Hunn J H Miller L L Snead J W Kim Evaluation of fracture

stress for the SiC Layer of TRISO-Coated fuel particles using a modified crush

test method Int J Appl Ceram Tech 7 (2010) 327-37

[6] G H Lohnert H Nabielek W Schenk The fuel-element of the Htr-module a

prerequisite of an inherently safe reactor Nucl Eng Des 109 (1988) 257-63

[7] I J Van Rooyen J H Neethling J Mahlangu Influence of temperature on the


comparative study Proceedings of the 4th

international topical meeting on high



[8] Y Kurata K Ikawa K Iwamoto The effect of heat-treatment on density and

structure of SiC J Nucl Mater 92 (1980) 351-53

[9] D T Goodin Accident condition performance of fuels for high-temperature

gas-cooled reactors J Am Ceram Soc 65 (1982) 238-42

[10] N Shirahata K Kijima A Nakahira K Tanaka Thermal stability of stacking

faults in Beta-SiC Sci Eng Ceram Ii 2 (1999) 623-26


173

[11] J van Rooyen J H Neethling P M van Rooyen The influence of annealing


136-46

[12] E Loacutepez-Honorato K Fu P J Meadows J Tan and P Xiao Silicon carbide

coatings resistant to attack by palladium J Am Ceram Soc 93 (2010) 4135-41

[13] E Loacutepez-Honorato H Zhang D X Yang P Xiao Silver diffusion in silicon


[14] D J Green An Introduction to the Mechanical Properties of Ceramics

Cambridge University Press Cambridge 1998

[15] H Zhang E Loacutepez-Honorato A Javed X Zhao J Tan P Xiao A Study of the


Eur Ceram Soc (2012) DOI101016jjeurceramsoc201112014

[16] H Tateyama H Noma Y Adachi M Komatsu Prediction of stacking faults in

βndashSilicon carbide X-Ray and NMR studies Chem Mater 9 (1997) 766- 72

[17] K R Carduner S S Shinozaki M J Okosz C R Peters T J Whalen

Characterization of β-Silicon carbide by silicon-29 solid-state NMR transmission

electron microscopy and powder X-ray diffraction J Am Ceram Soc 73 (1990)

2281-86

[18] httptfuni-kieldematwisamatdef_enkap_6advancedt6_3_2html

[19] S M Dong G Chollon C Larbrugere M Lahaye A Guette J L Brunee M

Couzi R Naslain and D L Jiang Characterization of nearly stoichiometric SiC


[20] M Havel D BaronL Mazerolles P Colomban Phonon confinement in SiC

nanocrystals comparison of the size determination using transmission electron

microscopy and Raman spectroscopy Appl Spet 61 (2007) 855-59

[21] V V Pujar J D Cawley Effect of stacking faults on the X-Ray diffraction

profiles of 3C-SiC powder J Am Ceram Soc 78 (1995) 774-82

[22] Y L Ward R J Young R A Shatwell Effect of excitation wavelength on the


174

Raman scattering from optical phonons in silicon carbide monofilaments J Appl

Phys 102 (2007) 023512 -17

[23] X J Li J Hayashi C Z Li FT-Raman spectroscopic study of the evolution of

char structure during the prolysis of a victorian brown coal Fuel 85 (2006)

1700-07

[24] A C Ferrari J C Meyer V Scardaci C Casiraghi M Lazzeri F Mauri S

Piscanec D Jiang K S Novoselov S Roth A K Geim Raman spectrum of

graphene and graphene layers Phys Rev Lett 97 (2006) 187401-04

[25] S Nakashima H Harima Raman investigation of SiC polytypes Phys Stat Sol

A-Appl Res 162 (1997) 39-64

[26] GKBasal Effect of flaw shape on strength of seramics J Am Ceram Soc 59

(1976) 87-8



86 (2005) 071920-22

[28] K Koumoto S Takeda CH Pai High-resolution electron microscopy

observation of stacking faults in βndashSiC J Am Ceram Soc 72 (1989) 1985-87


at high pressure and high temperature J Am Ceram Soc 84 (2001) 3013-16

[30] K Koumoto S Takeda C H Pai T Sato H Yanagida High-resolution electron

microscopy observations of stacking faults in β-SiC J Am Ceram Soc 72 (1989)

1985-87



[32] E Janzen N T Son B Magnusson A Ellison Intrinsic defects in high-purity




CHAPTER 7 Microstructure amp Mechanical Properties of PyC Coatings

175

CHAPTER 7 Microstructure and Mechanical Properties of

Pyrolytic Carbon Coatings

71 Introduction

Pyrolytic carbon (PyC) coatings forming part of the TRI-Isotropic (TRISO) fuel

particle are important for the stability of this type of nuclear fuel Without appropriate

microstructure and mechanical properties of PyC coatings the stress generated inside

the particle due to internal gas pressure andor the dimensional change (anisotropic

shrinkage or creep) introduced in this layer during irradiation process could result in

the failure of the full particle [1-5] Fundamental understanding about relationship

between mechanical properties and microstructure of PyC coatings could help to

analyse the failure mechanism and model the probability of failure of TRISO fuel

particles [1 5] However their relations in PyC are complex [3 6-8] Kaae [7] found

that mechanical properties were related to the density crystal size and anisotropy but

they are not controlled by a single variable For example Youngrsquos modulus increased

with density for isotropic carbons with constant crystallite size but decreased with

increasing anisotropy for carbon with constant density and crystalline size In a

separate work [3] density had a dominant effect on the hardness and Youngrsquos

modulus in relative low density PyC coatings whereas no controlling factor was

given for high density PyC coatings

Nano-indentation is an effective way to study microstructural effects on mechanical

properties of PyC coatings because it could help with the understanding of the

deformation mechanism and measure Youngrsquos modulus and hardness spontaneously

Among studies on mechanical properties in carbon related materials under


176

depth-sensing indentation [3 9-15] few explanations about the nature of their

deformation mechanism have been discussed [9 10 13 15] First the hysteresis was

assumed to due to the slip of graphene layers in nano-meter grains and the energy

loss was attributed to the friction between graphene layers under compression stress

[9 10] Second the dislocation pileups were assumed to be responsible for energy

loss [13] but this idea failed to account for the reversible deformation [15] The most

recent theory suggested that the origin of the hysteresis was due to the formation of

(incipient) kink bands [15] This theory was found to be a universal explanation for

most laminar structured materials but the nature of initial kink band was not clear

[15]

During pressing process of TRISO fuel particles into fuel elements they experience a

final thermal treatment of 1 h above 1800 ordmC to drive off any residual impurities and

improve thermal conductivity of the fuel compact [16] The evolution of

microstructure of carbon related materials have been widely studied [17-20] Few

researches measured changes of mechanical properties after thermal treatment [19

20] but there is a lack of understanding about effect of microstructural evolution on

mechanical properties in PyC coatings Therefore in this Chapter together with the

microstructural properties the deformation mechanism under indentation influences

on mechanical properties and their change after thermal treatment in PyC coatings are

studied


Pyrolytic carbon (PyC) was coated on alumina particles (Φ 500 μm) by fluidised bed

chemical vapour deposition by Dr Eddie Loacutepez-Honorato and PyC coatings with

different density was chosen to study the mechanical properties Table 61 gives the

density and texture (orientation angle) of PyC coatings and more about deposition

mechanism could be found in Ref [21] The number of sample sequence Ci (i=1

2hellip11) starts from highest density to lowest density with density of 19 gcm3 as


177

border line to distinguish highlow density PyC which was measured by the

Archimedes method in ethanol For thermal treatment the coatings were first

grounded into fragments and then removed the alumina kernel The fragments of PyC

were then thermal treated at 1800 degC and 2000 degC for 1 hour in argon atmosphere For

further understanding of microstructural evolution during thermal treatment sample

C5 was thermal treated at 1300 1400 1500 and 1600 degC for 1 hour

Table 71 PyC coatings with different density and orientation angle

PyC

(High density)

Density

(gcm3)

Texture(Orient-

ation angle deg)

PyC

(Low density)

Density

(gcm3)

Texture(Orient-

ation angle deg)

C1 2122plusmn0059 58 C6 1855plusmn0050 63

C2 2087plusmn0183 37 C7 1738plusmn0013 73

C3 2047plusmn0030 60 C8 1635plusmn0008 71

C4 2029plusmn0015 43 C9 1603plusmn0024 71

C5 2000plusmn0061 43 C10 1414plusmn0002 85

C11 1400plusmn0024 81

Orientation angle was obtained from the full width of half maximum of azimuthal intensity scan of

SAED pattern for more information in Ref [22] Productions of PyC coatings measurement of

orientation and density measurement are contributed by Dr Eddie Loacutepez-Honorato et al

The selected area electron diffraction (SAED) patterns were obtained with the use of a

FEG-TEM (see Chapter 3) and orientation angle was measured by the azimuthal

intensity scans of SAED pattern (selected aperture diameter of 200 nm) Further

details about this measurement were shown in a previous study [22] Transmission

electron microscopy (TEM) samples were obtained by focus ion beam milling High

resolution TEM samples were prepared by dispersing the fragments on a carbon holey

film copper grid X-ray diffraction (see Chapter 3) was used to obtain domain sizes of

PyC coatings After correction of intrinsic instrumental effect the out of plane and

in-plane domain sizes (along c-axis and a-axis in graphite crystal structure) Lc and La

were qualitatively estimated from XRD data by applying the Scherrer equation to the


178

(002) and (110) reflections respectively [23] In as-deposited PyC coatings the (110)

peak was too weak to estimate accurately on the La Raman spectroscopy (633 nm

Helium ion laser source) was performed by single spot measurements (spot size was

carefully controlled to be the same for each test) of around 2 μm diameter using a times50

objective lens The laser power of less than 05 mW (10) was used with the step

size of 60 seconds and twice accumulations For each sample 5 different positions

were measured The band fitting of the first order spectra was carried out with

GRAMS32 software

To reduce the influence of surface roughness on indentation test the PyC coatings

were ground with successive finer grades of SiC paper and polished down to a 1 microm

grid diamond paste The same nano-indentation as in Chapter 3 was used The

measurements were performed at fixed loading rate of 1 mNS reaching the

maximum load of 100 mN For each coating at least 25 indentations were conducted

on the sample surface to increase the reliability of the results The Olive and Pharr

method [24] was used to analyse all the data

73 Results

731 Microstructure of PyC coatings

In order to study the influences of microstructure on mechanical properties it is

necessary to know the nature of structure which makes one sample from another eg

disorders domain size crystallinity etc and their evolution after thermal treatment

7311 Raman spectroscopy

Figure 71 is a Raman spectroscopy for an as-deposited high density PyC coating (C5

200 gcm3) which exhibits two relatively broad Raman bands at around 1335 cm

-1

and 1600 cm-1

The first band corresponds to the D band which is attributed to double

resonant Raman scattering and represents the in-plane defects [21 25 26] The

second band is an overlap of broadened G (1580 cm-1

) and D (1620 cm-1

) bands due


179

to high disordered pyrolytic carbon [27] The G band is due to the stretching modes of

pairs of sp2 atoms in graphene planes whereas D represents the similar defects

structure as the D band [18 27] It is convenient to consider 1600 cm-1

band a single

G peak for practical purposes when comparing different samples or the overall

structural evolution of a given PyC coating [27]





According to previous studies [25-32] on fitting similar Raman spectra shown in Fig

71 a simple two-symmetric-line fit (D and G bands) could not fit it well Therefore

the Raman spectra of high density PyC coatings (C1-C5 gt 19 gcm3) were

deconvoluted into above peaks at about 1220 cm-1

1335 cm-1

1500 cm-1

and 1600

cm-1

( Fig 71) The band at about 1500 cm-1

(Drsquorsquo) is attributed to interstitial defects

which could act as coupling (covalent band) between two graphene layers or adjacent

overlapped domains [25 28] The I band at around 1220 cm-1

is due to C-C on hydro

aromatic rings [28] The Raman spectra mean the high degree of in-plane andor

out-of-plane disorders in high density PyC coatings represented mainly by the full

width at half maximum (FWHM) of the D band [28] and intensity ratio (the area ratio

of the 1500 cm-1

peak to the sum of four peaks shown in Fig 71) of the Drdquo bands

[25] respectively

D

I


180

Figure 72 is the Raman spectra of high density PyC coating C5 after thermal

treatment at temperature of 1300 1400 1600 and 1800 ordmC The FWHM of the D band

decreased significantly from about 150 cm-1

(as-deposited) to about 106 cm-1

(1400

ordmC) and then to about 40 cm-1

(1800 ordmC) Similarly the intensity ratio of the Drdquo was

reduced from about 0135 (as-deposited) to about 0110 (1400 ordmC) and then to about

0078 (1800 ordmC) Another change is the split of G and D bands after thermal treatment

at 1800 ordmC (Fig 72) The above changes indicate that disorders in high density PyC

coatings are low energy structural defects ie degree of disorder is low according to a

previous study [28]


temperatures



(a) (b)


181

After thermal treatment the degree of microstructural changes of low density PyC

coatings C6-C8 (164-186 gcm3) is slightly different from even lower density

coatings C9-C11 (140-160 gcm3) so they are described separately Figure 73 shows

Raman spectra of low density PyC coatings (a) C7 and (b) C10 before and after

thermal treatment at 1800 ordmC Similar to high density PyC the as-deposited coatings

C6-C8 contains four Raman bands After thermal treatment the FWHM of the D peak

in C7 decreased from about 120 cm-1

to 57 cm-1

and the intensity ratio of interstitial

defects was also reduced (from 0116 to 0042 Fig 73(b)) In coating C10 only

slightly decrease of FWHM of the D peak (from about 83 cm-1

to 57 cm-1

) was found

after thermal treatment at 1800 ordmC (Fig 73(b)) No split of the G and D bands was

observed in low density PyC coatings

With increase in density of PyC the FWHM of the D band the concentration of the

Drdquo band and the degree of their changes after thermal treatment increase considerably

which suggest that the disorder defects in PyC are different with variation of density

and thermal treatments change the degree of the disorder

7312 Domain sizes

Table 72 summarises the out-of-plane domain size (crystallite size perpendicular to

the graphene plane Lc) and in-plane domain size (crystallite size along the graphene

plane La) measured by XRD in PyC coatings before and after thermal treatment The

Lc is in the range of 1-3 nm in all the as-deposited coatings and it is slightly bigger in

high density (about 2-3 nm) coatings than low density (about 1-2 nm) coatings After

thermal treatment at 1800 ordmC the Lc increased significantly which is about 5 times

and 2-3 times larger than in as-deposited high density and low density PyC coatings

respectively It is 2-4 times larger in high density PyC than low density PyC coatings

The La in high density (about 6 nm) is larger than low density PyC coatings (3-4 nm)

after thermal treatment at 1800 ordmC Both Lc and La remained unchanged after thermal

treatment at 2000 ordmC in all PyC coatings (This is explained in section 741) The


182

increase of domain size indicated the ordering process in PyC coatings after thermal

treatment which may involve annealing of different kinds of disorders

Table 72 Domain size of as-deposited and thermal treated PyC coatings

Sample As deposited 1800 2000

Lc (nm) La (nm) Lc (nm) La (nm) Lc (nm) La (nm)

High density (gt19 gcm3)

C1 21 -- 112 -- 116 53

C2 21 -- 132 63 154 69

C3 22 -- 98 66 111 63

C4 24 -- 95 57 118 63

C5 20 -- 120 60 152 73

Low density (lt 19 gcm3)

C6 22 -- 50 42 56 44

C7 18 -- 38 36 50 34

C8 14 -- 31 33 27 39

C9 11 -- 27 32 31 34

C10 17 -- 24 33 27 35

C11 11 -- 27 35 27 33

7313 Evolution of crystallinity

Figure 74 is the TEM images of high density PyC (C5) before and after thermal

treatment The dark field TEM show bright areas (Fig 74(a) and (b)) that represent

graphene layers with similar orientation in the selected direction of the diffraction

pattern A decrease of the orientation angle from 43 ordm to 25 ordm is found after thermal

treatment at 1800 ordmC which is obtained from the full width at half maximum of

azimuthal intensity scan of SAED pattern (insets in Fig4(a) and (b)) A bright field

TEM image of a conical microstructure after thermal treatment (Fig 74(c) dashed

rectangle in Fig 74(b)) which shows the voids at the top of conical structures The

above observations show that thermal treatment increases anisotropy and results in the

volume shrinkage and generation of voids in high density PyC coatings


183




of 200 nm



Figure 75 is the typical HRTEM away from the top of conical growth feature (eg

OA=43 ordm

OA=25 ordm

Top

Voids

100 nm

(c)

(a) (b)

5 nm

Moireacute

fringes


184

white circle in Fig 74(c)) in high density PyC coatings (C1) before and after thermal

treatment at 1800 ordmC The wrinkled short graphene fringes in as deposited high

density PyC (Fig 75(a)) were replaced by distorted planes in a larger scale with a

bigger radius of curvature (white arrow in Fig 75(b)) The common number of

parallel layers (Fig 75(a) (002) plane white parallel lines) is 2-4 in as-deposited C1

which increased to about 30 (Fig 75(b) between white parallel lines) The moireacute

fringes were observed after thermal treatment (black arrow in Fig 75(b)) which

correspond to black bars in the bright field TEM (eg dashed black rectangle in Fig

74(c)) According to the generation mechanism of moireacute fringes [33] the on-going

ordering process along the c-axis is related to the increase of number of parallel layers

and evolution (decrease) of the inter plane distance of (002) planes

Figure 76 gives the bright field TEM and HRTEM images showing the

microstructure evolution in a low density PyC coating (C7) Globular growth features

with diameters of about 400 nm were observed in as-deposited C7 as shown in Fig

76(a) and the HRTEM image shows 2-3 layers of parallel planes (Fig 76(b)) In low

density PyC coatings the graphene fringes are longer and less oriented than in high

density coatings (reflected from orientation angle shown in Table 71 and Fig 13 in

Ref [21]]) After thermal treatment the short dark bars andor dots (as indicated by

the white arrows Fig 76(c)) were observed which is due to the moireacute fringes as

shown in Fig 76(d) The number of parallel layer increased up to 8-10 (Fig 76(d))

and it reflects the slight crystallinity after thermal treatment In the other low density

PyC coatings C9-C11 the TEM images are similar with the as-deposited low density

PyC coatings (as shown in Fig 14 and Fig 13(c) in Ref [21]) Furthermore the

orientation angle is almost the same in all low density PyC before and after thermal

treatment


185




732 Mechanical properties of PyC coatings

7321 Force-displacement curve

Figure 77 gives the force-displacement curve of PyC coatings with different density

under the maximum load of 60 mN and 100 mN by nano-indentation The unloading

curve did not completely retrace the loading curve but still returned to the origin This

process is called anelastic behaviour or hysteresis behaviour and the anelastic

reversible indentation processes with an enclosed loop are found in all the PyC

coatings

(a) (b)

100 nm 5 nm

5 nm

Sphere-like

particle

Tops

Moireacute fringes Sphere-like

particle

Top (d)


186





The maximum indentation depth in low density PyC (C6-C11 lt 19 gcm3) is deeper

than in high density PyC coatings (C1-C5 gt 19 gcm3) under the same load and the

low density PyC also shows larger hysteresis loop area The ratio of the hysteresis

energy (area within the loading-unloading loop) to total loading energy (area under

loading curve) in high density PyC is lower than in low density PyC coatings For

example the ratios of sample C3 C9 and C11 are 0243 0270 and 0292 respectively

Furthermore the deformation behaviour of all PyC coatings showed the hysteresis

behaviour after thermal treatment up to 2000 ordmC The high density PyC after thermal

treatment at 1800 ordmC (red curve in Fig 77) shows anelasticity however the ratio of

its hysteresis energy (0249) is much higher than in as-deposited coating (0174)

According to previous studies [10 34] the low ratio obtained in high density PyC

coatings under pyramidal indenter corresponds to high elasticity while low density

exhibits high hysteresis (anelasticity high viscosity))

Under indentation the hardness is defined as the mean pressure the material will

support under load according to Oliver and Pharrrsquos study [24] This pressure is equal

to the load at maximum load divided by the contact area (according to eqs (7 10 11)

hc


187

in Chapter 2) However the residual depth hf is zero and no pleastic deformation is

observed after unloading The hardness obtained by Oliver and Pharr method does not

reflect the resistance of plastic deformation of material but it could represent the

degree of unelastic deformation qualitatively Therefore the mean pressure (P) value is

used which could reflect the anelastic properties of PyC coatings

7322 Youngrsquos modulus and the mean pressure

Figure 78 gives the Youngrsquos modulus (E) and the mean pressue (P) of as-deposited

PyC coatings as a function of density For low density PyC coatings (C6-C11 lt 19

gcm3) Youngrsquos modulus and the mean pressure increase almost linearly with the

density For high density PyC coatings (C1-C5 gt 19 gcm3) both Youngrsquos modulus

and the mean pressure reach plateaus which are independent of density It indicates

that mechanical properties of high PyC coatings are dominated by other factors

which are discussed in session 744



Table 73 shows the Youngrsquos modulus and the mean pressure of PyC coatings with

different density before and after thermal treatment at 1800 and 2000 ordmC After

thermal treatment at 1800 ordmC Youngrsquos modulus decreased by around 50 and the the

mean pressure is reduced by around 69 in high density PyC coatings (C1-C5 gt19

(a) (b)


188

gcm3) whereas minor change is observed when thermal treatment temperature

further increased to 2000 ordmC Previous study [20] showed similar results about

changes of mechanical properties in high density PyC after thermal treatment at

different temperature In low density PyC coatings C6-C8 (164-186 gcm3) the

mean pressure and Youngrsquos modulus decreased by about 23 and 8 after thermal

treatment at 1800 ordmC respectively which is consistent with Rooyen et alrsquos results

[19] and further decreased by 18 and 15 by increasing thermal treatment

temperature to 2000 ordmC In low density coatings C9-C11 (140-160 gcm3) little

change in mechanical properties after thermal treatment up to 2000 ordmC was found and

it is similar as the isotropic low density PyC [20] Mechanical properties and their

change after thermal treatment in PyC coatings are different with different density

Table 73 Changes of mechanical properties of PyC coatings after thermal treatment

Sample As deposited Thermal treated at 1800 Thermal treated at 2000

P (GPa) E (GPa) P (GPa) E (GPa) P (GPa) E (GPa)

High density

C1 468plusmn025 2670plusmn119 103plusmn018 1482plusmn131 090plusmn013 1337plusmn093


C3 490plusmn036 2878plusmn117 -- -- 091plusmn026 1271plusmn125



Low density







74 Discussions

The main findings of this study can be summarised as follows 1) PyC with different

density show different full width at half maximum (FWHM) of the D band and


189

concentration of the Drsquorsquo band which suggests that they have different types of disorder

TEM observation shows longer graphene fringes with lower density PyC (Fig 13 in

Ref [21]) thermal treatments decrease the degree of disorder while PyC with higher

density (gt19 gcm3) shows higher degree of decrease 3) initial increase in PyC

density until 19 gcm3 lead to proportional increase in Youngrsquos modulus (E) and the

mean pressure (P) while further increase in density has no effect on E and P 4)

hysteresis occurred after nano-indentation of PyC while the degree of hysteresis is

controlled by the PyC density and heat treatments

741 Disorders and their changes after thermal treatment

High density PyC Coatings (C1-C5 gt 19 cmg3) The dominant in-plane disorders

are domain boundaries according to a previous study [21] which generates high

FWHM of the D band due to the low energetic disorientations (eg domains andor

graphene layers) [25 28] The Drsquorsquo band (interstitial defects) is due to the amorphous

carbon structure which is composed of mainly disordered sp2 atoms and a low

amount of sp3 atoms [27 28 35] Particularly the sp3 lines are out of plane defects

which could be formed in high density PyC coatings [36] Therefore it is assumed

that the microstructure in high density PyC is composed of disoriented nano-size

graphite domains connected by amorphous carbon

After thermal treatment the reductions of the out-of-plane defects and the tilt and

twist in graphite planes are observed which could contribute to the increase of Lc

(out-of-plane domain size) as shown in HRTEM image (Fig 75) It was supposed

that the equilibrium shear stress were generated by in-plane defects and out-of-plane

defects in PyC coatings [25] once the out-of-plane defects was reduced the in-plane

stress would tend to straighten the graphite planes Furthermore the decreases of

FWHM of the D band and the orientation angle (Fig 72 and 4) show the ordering

arrangement of graphite layers is due to the healing of in-plane disorientations The

unchanged domain size Lc could be a result of a combination of increased number of


190

parallel graphene layers and decreased inter distance of (002) plane As a conclusion

the increase of domain size Lc could be due to the coalescence of domain size andor

graphene layers through reorientation and remove of interstitial defects which

usually started at temperature of about 900-1200 ordmC [17 25] No La (in-plane domain

size) value was obtained in as-deposited PyC and the overlap of the G and the Drsquo

bands indicates it is below 4 nm above which two bands split [37] After thermal

treatment at 1800 ordmC the La is about 6 nm in high density PyC coatings (Table 72

and splitting of G and Drsquo bands was shown in Fig 72) which demonstrates the

slightly increase of La It is attributed to the annihilation of low energetic in-plane

disorientations which could usually be removed at temperature above 1500 ordmC [25]

Since the high temperature above 2000 ordmC is needed to remove the rest high energetic

in-plane defects for high density PyC according to previously study [25 28] it could

explain the La remained nearly constant after thermal treatment further increased to

2000 ordmC The ordering of graphite layers is responsible for the formation of voids (Fig

74(c)) since the ordering could reduce the volume and increase the density of PyC

coatings after thermal treatment [38]

Low density PyC Coatings (C6-C11 lt 19 cmg3) The main defect is the

5-memebered rings in coatings C9-C11 by comparing the Raman spectroscopy (Fig

73(a)) with a previous study [21] In low density coatings C6-C8 (164-186 gcm3)

the degree of in-plane disorder is less than in high density coatings but higher than

coatings C9-C11 (140-160 gcm3 indicated by the FWHM of the D band) and the

out-of-plane defects are much higher than low density PyC coatings (Fig 73) After

thermal treatment the in-plane disorder is similar as in coatings C9-C11 Therefore

the dominant in-plane defects are supposed to be a combination of domain boundaries

and 5-membered rings The slightly increase of domain size Lc in low density PyC

coatings is due to the decrease of interfacial defects through reorientation of domains

However they have much lower degree of increase of Lc than high density coatings

this could be due to low anisotropy in low density PyC coatings which makes it


191

difficult to reorient domains and remove the weak defects [17 25] The domain size

La was assumed to be unchanged since ordering in-plane disorders took place at

temperature above 2400 ordmC in low density PyC due to presence of 5-member rings

[17] It is worth to notice that the graphene fringes do not represent the in-plane

domain size in low density PyC due to the curvature caused by 5-memebered rings

[21] Due to the exist of 5-membered rings in low density PyC coatings the

microstructure is lightly affected by thermal treatment

742 Hysteresis after indentation

The increase in density of PyC leads to decrease in hysteresis after indentation and

density of PyC also dominate types and degree of disorders During indentation of

PyC hysteresis is caused by the slip of graphene planes whereas the disorders such as

interstitial defects or 5-memebered rings are supposed to be responsible for the

reversible deformation The hysteresis was also observed in other carbon materials

such as single crystal graphite [15] polycrystalline graphite [15] glassy carbon [9

10] Similar explanations about the effect of slip of graphene layers on the hysteresis

behaviour under indentation were given and it suggests that the deformation

mechanism is related to a common structure in different carbon materials which are

graphene planes

The slip of graphene planes has been demonstrated available The shear modulus (micro)

of graphite is 23 GPa (between graphene layers) [39] Based on the relation of τth= micro

30 [39 40] the theoretical shear stress (τth) of graphite is estimated to be 0077 GPa

This shear stress is much lower than the yield stress under Berkovich indenter for

graphite (03-05 GPa) [15] Under indentation the slip of graphene planes consumes

energy but recovers to the original shape after unload Lower density PyC has longer

fringes than that in higher density PyC (Fig 13 Ref [21]) therefore the panes can

slip for a longer distance under shear stresses generated by nano-indentation


192

Reversible deformation is due to presence of interstitial defects or highly curved

5-memebered rings For indentation of crystallite graphite the kink band could be

generated during the initial indentation process then reviersible deformation occurs

under further indentation [15] similar as that shown in Fig 77 In our PyC coatings

disorder in the PyC plays a similar role as the kink band in the crystallite graphite

The slip direction is parallel to the graphene planes so the in-plane defects presents at

the tilt and twist of two adjacent domains could not stop and reflect the slip Only

those defects perpendicular to the slip direction can contribute to the reversible

deformation such as interstitial defects or the highly curved 5-memebered rings

(caused fibrous graphene planes as shown in Fig 13(c) Ref [21])

After heat treatment the growths of the in-plane fringes increase the degree of the

hysteresis in PyC coatings For example the straightened graphene fringes (Fig 75)

caused by reorientation and removes of interstitials facilitate the hysteresis

significantly (the ratio of hysteresis energy to total loading energy increased from

0174 to 0249 Fig 77)

743 Mechanical property of low density PyC coatings

In as deposited low density PyC (C6-C11 gt 19 gcm3) Youngrsquos modulus and the

mean pressure are dominated by the density which is consistent with previous studies

[3 7 41] because of the effect of porous structure [3 21] As discussed in session

741 the disorders in low density PyC coatings play an important part on the stability

of microstructure which could reflect changes of mechanical properties After thermal

treatment the mechanical properties remained almost unchanged in PyC coatings

C9-C11 (140-160 gcm3) and this could be explained by the insignificant change of

microstructures at the presence of 5-membered rings The slightly decrease of

mechanical properties were found in coatings C6-C8 (164-186 gcm3) which is due

to the ordering of graphene planes through reduction of interstitial defects which

could enhance hysteresis and decrease the mean pressure No voids and change of


193

orientation was observed after thermal treatment in coatings C6-C8 so Youngrsquos

modulus is slightly affected It is concluded that the mean pressure and Youngrsquos

modulus are functions of density in as-deposited low density coatings and their

evolution after thermal treatment is controlled by disorders such as interstitials andor

5-membered rings

744 Mechanical Property of high density PyC coatings

In high density PyC coatings (C1-C5 gt 19 gcm3) Youngrsquos modulus and the mean

pressure are independent of density so they are discussed regarding to variation of

texture domain size and concentration of interstitial defects (the area ratio of the 1500

cm-1

peak to the sum of four peaks shown in Fig 71) Table 74 summarises

microstructure parameters and mechanical properties of high density PyC coatings

Mechanical properties are not controlled by domain size and orientation angle which

is converse to the previous study [41] It is found that Youngrsquos modulus and the mean

pressure in high density PyC coatings decrease with the reduction of concentration of

interstitial defects (as shown in Table 74)


density PyC (C1-C5 gt 19 gcm3)

Sample Density

(gcm3)

Texture

OA (deg)

Domain

size (nm)

IinterstialAll Pressure

(GPa)

Modulus

(GPa)

C3 2047 plusmn0030 60 22 013955plusmn000374 490plusmn036 2878plusmn117





The physical meaning of the above observation can be explained by the effect of

interstitial defects on the deformation mechanism in high density PyC coatings First

the high concentration of interstitial defects could reduce the energy consumption by

the reversible slip of graphene planes (eg in Fig 77) and it corresponds to high the


194

mean pressure in high density PyC coatings Second in-plane Youngrsquos modulus is

much higher than out-of plane Youngrsquos modulus in graphite so the bonding between

graphene planes becomes important when the orientation effect could be neglected in

high density PyC (Table 74) For example in sample C4 and C5 the high Youngrsquos

modulus was obtained in C5 which have high amount of covalent band (interstitial

defects sp2 and sp3 in Fig 71) in the direction perpendicular to graphene planes The

high concentration of interstitial defects in high density PyC could also reduce the

influences of orientation angle on the high Youngrsquos modulus This could explain the

similar Youngrsquos modulus in C1 and C5 which have different orientation angles



After thermal treatment at temperature range of 1300-1800 ordmC in C5 (about 200

gcm3) the effect of concentration of interstitial defects on mechanical properties was

again demonstrated as given in Table 75 The mechanical properties decrease

gradually with the increase of thermal treatment temperature until 1600 ordmC and then a

dramatic decrease at 1800 ordmC The decrease is related to the reduction of content of

interstitial defects (Table 75) Furthermore no other relationship between mechanical

properties and microstructural features such as FWHM of the D band intensity of D

band and G band in Raman spectroscopy is found in the current work Therefore the

concentration of interstitial defects is proposed to dominant mechanical properties of

high density PyC coatings This idea about effect of interstitial defects on mechanical

properties is similar as the cross-link theory [8] which suggested that the mechanical

properties is related to the length and number of links between domains Furthermore

Temperature (ordmC) IinterstialAll Pressure (GPa) Youngrsquos modulus (GPa)

0 013456plusmn 000561 456plusmn010 2610plusmn 036

1300 011882plusmn000906 430plusmn010 2519plusmn060






195

the significant decrease of the the mean pressure and Youngrsquos modulus after 1800 ordmC

could be due to the straightening of graphene layers and formation of voids (Fig

74(c)) respectively To conclude the mechanical properties in high density PyC

coatings before and after thermal treatment from 1300 to 1800 ordmC decrease with the

reduction of concentration of interstitial defects

74 Conclusions

Disorders in PyC coatings was characterised by Raman spectroscopy A

combination of high degree of in-plane (domain boundaries) and out-of plane

defects (interstitial defects) prevail in high density PyC while the 5-membered

rings are dominant defects in low density PyC coatings

In high density PyC coatings the significant increase of domain size Lc is

attributed to the coalescence of domainsgraphene layers through reorientation and

reduction of interstitial defects During this process the graphene planes were

straightened resulting in slightly increase of La

In low density PyC coatings the microstructure remained almost unchanged after

thermal treatment due to the presence of the 5-membered rings which need high

temperature to be reduced

The hysteresis deformation behaviour was found in all PyC coatings before and

after thermal treatment under nano-indentation The nature of hysteresis is

suggested to be Slip of graphene planes consumes energy (hysteresis loop) and

disorders (interstitial defects and highly curved 5-memebered rings in high density

and low density PyC coatings respectively) are responsible for the reversible

deformation (unloading curve back to origin)

The mean pressure and Youngrsquos modulus are functions of density in low density

PyC coatings and their changes after thermal treatment are insignificant which

are due to the almost unchanged microstructure


196

In high density PyC coatings the mean pressure and Youngrsquos modulus are

independent of density orientation angle and domain size but they are related to

the concentration of interstitial defects After thermal treatment the decrease of

mechanical properties is attributed to the reduction of interstitial defects leading

to the straightening of graphene planes and formation of voids


197

75 References


techniques thin solid films 469-70 (2004) 214-20



[3] E Loacutepez-Honorato P J Meadows P Xiao G Marsh T J Abram Structure and

mechanical properties of pyrolytic carbon produced by fluidized bed chemical

vapour deposition Nucl Eng Des 238 (2008) 3121-28

[4] G K Miller D A Petti A J Varacalle J T Maki Consideration of the effects


Nucl Mater 295 (2001) 205-12

[5] A C Kada R Gnallinger M J Driscoll S Yip D G Wilson H C No et al

Modular pebble bed reactor In Modular pebble bed reactor project University

research consortium annual report 2000

[6] G Hofmann M Wiedenmeier M Freund A Beavan J Hay G M Pharr An



[7] J L Kaae Relations between the structure and the mechanical properties of


[8] F G Emmerich C A Luengo Youngrsquos modulus of heat-treated carbons A

theory for nongraphitizing carbons Carbon 31 (1993) 333-39

[9] J S Field MVSwain The indentation characterisation of mechanical properties

of various carbon materials Glassy carbon coke and pyrolytic graphite Carbon

34 (1996) 1357-66

[10] N Iwashita Elasto-plastic deformation of glass-like carbons heat-treated at


[11] M V Swain J S Field Investigation of the mechanical properties of two glassy

carbon materials using pointed indetners Philos Mag A 74 (1996) 1085-96


198

[12] N Iwashita J S Field M V Swain Indentation hysteresis of glassy carbon

materials Philos Mag A 82 (2002) 1873-81

[13] M Sakai Y Nkano S Shimizu Elastoplastic indentation on heat-treated carbons

J Am Ceram Soc 85 (2002) 1522-28

[14] A Richter R Ries R Smith MHenkel B Wolf Nanoindentation of diamond

graphite and fullerene films Diamond Relat Mater 9 (2000) 170-84

[15] MW Barsoum A Murugaiah S R Kalidindi T Zhen Y Gogotsi Kink bands





[17] F G Emmerich Evolution with heat treatment of crystallinity in carbons Carbon

33 (1995) 1709-15

[18] M A Pimenta G Dresselhaus M S Dresselhaus L G Cancado A Jorio R

Saito Studying disorder in graphite-based systems by Raman spectroscopy Phys

Chem Chem Phys 9 (2007) 1276-91

[19] I J Van Rooyen J H Neethling J Mahlangu Influence of Temperature on the

Micro-and Nanostructures of Experimental PBMR TRISO Coated Particles A

Comparative Study Proceedings of the 4th


temperature reactor technology Washington DC USA HTR 2008-58189

[20] J C Bokros R J Price Deformation and fracture of pyrolytic carbons deposited

in a fluidized bed Carbon 3 (1966) 503-19


deposition of pyrolytic carbon-I Effect of deposition conditions on microstructure

Carbon 47 (2009) 396-10

[22] P J Meadows E Loacutepez-Honorato P Xiao Fluidized bed chemical vapour


Carbon 47 (2009) 251-62


199

[23] S Bernard O Beyssac K Benzerara N Findling G Tzvetkov G E Brown Jr

XANES raman and XRD study of anthracene-based coke and saccharose-based

chars submitted to high-temperature pyrolysis Carbon 48 (2010) 2506-16



Mater Res 7 (1992) 1564-83

[25] J N Rouzaud A Oberlin C Beny-bassez Carbon films structure and

microstructure (optical and electron microscopy Raman spectroscopy) Thin solid

film 105 (1983) 75-96

[26] S Potgieter-Vermaak N Maledi N Wagner J H P Van Heerden R Van

Grieken J HPotgieter Raman spectroscopy for the analysis of coal a review J

Raman Spectrosc 42 (2011) 123-29

[27] A C Ferrari Raman spectroscopy of graphene and graphite Disorder

electron-photon coupling doping and nonadiabatic effects Solid state commun

143 (2007) 47-57

[28] J M Vallerot X Bourrat A Mouchon G Chollon Quantitative structural and

textural assessment of laminar pyrocarbons through Raman spectroscopy electron

diffraction and few other techniques Carbon 44(2006) 1833-44

[29] G A Zickler B Smarsly NGierlinger H Peterlik O Paris A reconsideration

of the relationship between the crystallite size La of carbons determined by X-ray

diffraction and Raman spectroscopy Carbon 44 (2006) 3239-46

[30] A Cuesta P Dhamelincourt J Laureyns A Martinez-Alonso JMD Tascon

Raman microprobe studies on carbon materials Carbon 32 (1994) 1523-32

[31] A Sadezky H Muckenhuber H Grothe R Nissner U Poschl Raman




200

[32] S Yamauchi Y Kurimoto Raman spectroscopic study on pyrolyzed wood and

bark of Japanese cedar temperature dependence of Raman parameters J Wood

Sci 49 (2003) 235-40

[33] D B Williams C B Carter Transmission electron microscopy A textbook for

materials science Springer New York p 392-97

[34] M Sakai R Nowak In Bannister MJ editor Austceram 92 Ceramics adding


[35] T Jawhari A Roid J Casado Raman spectroscopic characterization of some

commercially available carbon black materials Carbon 33 (1995) 1561-5

[36] G L Dong K J Huumlttinger Consideration of reaction mechanisms leading to

pyrolytic carbon of different textures Carbon 40 (2002) 2515-28

[37] A Jorio E H Martins Ferreira M V O Moutinho F Stavale C A Achete R

B Capaz Measuring disorder in graphene with the G and D bands Phys Status

Solidi B 247 (2010) 2980-82

[38] R Piat Y Lapusta T Boumlhlke M Guellali BReznik D Gerthsen TChen R

Oberacker M J Hoffmann Microstructure-induced thermal stresses in pyrolytic

carbon matrices at temperatures up to 2900 ordmC J Eur Ceram Soc 27 (2007)

4813-20

[39] J Y Huang HRTEM and EELS studies of defects structure and amorphous-like


[40] A H Cottrell Dislocations and plastic flow in crystals Clarendon Press Oxford

1972 p 162

[41] J L Kaae Microstructures of isotropic pyrolytic carbons Carbon 13 (1975)

55-62

CHAPTER 8 Conclusions and Future Works

201


This work provides both fundamental understanding and techniqual guidance on the

mechanical properties and their relationship with microstructures of SiC and PyC

coatings in TRISO fuel particles The measurement of hardness and Youngrsquos modulus

of SiC coatings could be used in the modelling work to study the peroperty of the

failure of the fuel particlues and these results have been published The measurement

of the fracture toughness of SiC in TRISO fuel particle has solved one of the

techniqual problems in field and the study contributes to the study of the fracture

behaviour of SiC coatings The fracture strength measurement has enriched the

strength data of SiC coatings before and after thermal treatment (related paper is

under revision) The characterisation of the interfacial roughness has provided a direct

method to correlate the relationship between fracture strength and interfacial

roughness The mechanical properties of PyC coatings provide foundamental

understanding about the deformation mechanism of the PyC coatings under

indentation The effect of thermal treatment on the mechanical properties has given a

preguidance about the behaviour of the PyC coatings at high temperature

81 Conclusions

(1) In SiC coatings deposited at 1300 ordmC by fluidised bed chemical vapour deposition

the Youngrsquos modulus was an exponential function of the porosity and the high

hardness was attributed to the high density of dislocations and their interactions

The initiation and propagation of micro cracks under the confined shear stress was

found to be responsible for the mechanism of plastic deformation Based on this

hardness-related plastic deformation mechanism the variation of hardness in the

three types of SiC coating was due to different grain morphologies


202

(2) The fracture beneath the Vickers indenter consists of Palmqvist cracks as

observed using SEM in above SiC coatings Based on this crack mode Vickers

indentation fracture toughness values of 351-493 MPa m12

were obtained It was

found that stress-induced micro-cracks seem to be a mechanism for the fracture

behaviour The presence of defects such as nano-pores and less constraint grain

boundaries could generate more micro cracks which dissipated energy from the

main cracks

(3) Fracture strength measured by modified crush test give less scattered values

within a given sample by distributing the load under a contact area It has been

found that Weibull modulus and fracture strength of the full shell were

significantly affected by the ratio of radius to thickness of the coating and both of

them decrease linearly with the increase of this ratio

(4) The numericalstatistical analysis was able to characterize the interfacial

roughness of different coatings and the roughness ratio representing the

irregularities was proposed to be a unique parameter for this description The

difference of the local (intrinsic) fracture strength was dominated by the

roughness ratio and it decrease linearly with the increase of the roughness ratio

The roughness ratio has the similar effect on the difference of fracture strength of

the full shell

(5) After heat treatment at 2000 degC the local fracture strength was reduced due to the

formation of pores in the coatings which could act as the enlarged critical flaw

size The Weibull modulus decreased when the pores in SiC coatings became

critical flaws while it increased once more uniformly distributed critical flaws

along the IPyCSiC interface were formed The formation of pores was mainly

related to the annihilation of stacking faults and diffusion of intrinsic defects such

as vacancies interstitials and antisites


203

(6) The hysteresis deformation mechanism was proposed to be due to the slip of

graphene planes which constraint by interstitial defects and highly curved

5-membered rings in high density and low density PyC coatings respectively

(7) The hardness and Youngrsquos modulus were related to the concentration of

interstitial defects and density in high density and low density PyC coatings

respectively Their changes in high density PyC is more significant than in low

density PyC coatings after heat treatment over 1800 ordmC due to the annihilation of

interstitial defects and reorientation of graphene layers

82 Suggestions for future work

(1) According to current study high amount of native defects were found in SiC

deposited at low temperature and it would be interesting to study their effects on

the thermal stability in a certain range of temperature such as from 1200-2000 ordmC

The study of the diffusion of native defects in SiC could also assist the study of

diffusion behaviour of fission products because these defects are more active and

they tend to reach the equilibrium during annealing process Due to different

deposition conditions the dominant species of native defects could be different in

different coatings therefore it is also important to study the deposition effect on

thermal stability of SiC coatings

(2) Itrsquos important to know how the microstructure change of SiC coatings deposited at

low temperature after irradiation because they showed robust mechanical

properties and high resistance to fission products It has been found they have high

amount of dislocations and stacking faults which accompanied by interstitials and

vacancies as reflected from the enlarged lattice constant According to this it is

supposed that after irradiation the volume change of SiC will be small because of

the pre-exist lattice defects Therefore study of the irradiation effect (at different

operational temperature) on SiC deposited at low temperature would be

promising


204

(3) Although current study has proposed to use self-affine theory to characterize the

interfacial roughness more work about their effects on fracture strength need to

be explored For example find out if the derived linear function between

roughness ratio and fracture strength in the current study could be used to explain

the differences of fracture strength in other tests To do further demonstration it is

necessary to reduce the geometrical influence and choose SiC coatings has

similar microstructure but different IPyCSiC interface These samples could be

prepared by just changing the deposition condition of IPyC while keep it same for

SiC coatings

List of Contents

2

List of Contents

List of Contents 2

Abstract 6

Declaration 7

Copyright Statement 8

Acknowledgement 9

List of Figures 10

List of Tables 17

CHAPTER 1 Introduction 19

11 TRI-Isotropic (TRISO) fuel particles 19

12 Failure mechanism 21

121 Traditional pressure vessel failure mode 21

122 Stress concentration mode 22

13 Goals of dissertation 24

14 References 26

CHAPTER 2 Literature Review 28

21 Introduction 28

22 Microstructure of silicon carbide 29

221 Atomic structure 29

222 Defects in SiC 31

2221 Stacking faults and dislocations 31

2222 Non-stoichiometric and point defects 36

23 Properties of silicon carbide 41

231 Youngrsquos modulus 41

232 Hardness 45

233 Fracture toughness 52

234 Fracture strength 55

235 Effect of thermal treatment on SiC 59

24 Microstructure and properties of pyrolytic carbon 60

241 Microstructure of pyrolytic carbon 61

242 Mechanical properties of pyrolytic carbon 65

List of Contents

3




25 Summary 70

26 References 72


Indentation 83

31 Introduction 83


33 Results 88




34 Discussion 100




35 Conclusions 105

36 References 107


41 Introduction 112






44 Conclusions 126

45 References 127


Coatings 131

51 Introduction 131


List of Contents

4

521 Materials 132






140





54 Conclusions 149

55 References 150



61 Introduction 154


63 Results 156




64 Discussion 167



65 Conclusions 171

66 References 172


Coatings 175

71 Introduction 175


73 Results 178




List of Contents

5





74 Discussions 188





74 Conclusions 195

75 References 197


81 Conclusions 201


Abstract

6

Abstract




Huixing Zhang





































Declaration

7

Declaration




Copyright Statment

8

Copyright Statement




purposes





















Acknowledgement

9

Acknowledgement









a good researcher









tensile tests






List of Figures

10

List of Figures



matrix [5]



[10]




from Ref [18]




















List of Figures

11



[48]




















loading) [89]










List of Figures

12








indenter [110]





Indentation




















List of Figures

13







projection













reference




zone









List of Figures

14




Coatings



distribution





SiC coatings










(1)









y=1351-1150x

List of Figures

15








f ) before

























List of Figures

16






temperatures






of 200 nm












List of Tables

17

List of Tables



methods






methods









conditions


Coatings




List of Tables

18









treatment


thermal treatment






density PyC




19





















service [4]


20


matrix [5]
















21


























22










PyC layer










23





increase [3]


[10]













24















issues












25












given in Chapter 8


26

14 References






329-77







174-88



141-51



199-210



Nucl Mater 295 (2001) 205-12



MIT-ANP-PR-075




27






28


21 Introduction























29





























30




from Ref [18]









31










222 Defects in SiC








ABCACBCABChellip




32









methods

[27] [28] [24] [29] [30] [31] [32]

ESF (mJ m-1

) -15 -- -28 -6 -61 -154 -323

ISF (mJ m-1

) 12 34 -34 14 138 111 -71










33















(a) (b)

(c)


34















5cm







35





stacking faults







(a)

(b)

(c) (d)


36





























37













interphase



(a)

(b) (c)

β-SiC

β-SiC

β-SiC

β-SiC

Si

Si

025 nm

025 nm

025 nm

0 312 nm

0312 nm


38












[48]









(a) (b)


39

be estimated [49]





















40









Ef (eV) 59 68 73 11 150 147 86 110


















41
















3C-SiC a 3523 1404 2329 18196 [59]

3C-SiC b 511 128 191 10026 [1]

3C-SiC c 390 142 256 -- [60]

3C-SiC a 420 126 287 19503 [61]









42
















0 44

1 11 12

2CZ

C C

(1)






spherical


43





3

[1 ( 3 )]E

B

(2)


11 122

3

C CB

(3)

1

0 1

1 0

52( 6 )

(4)

where 0 44C 1 11 12( ) 2C C and

01

0 0

3( 2 )

5 (3 4 )

B

B

(5)










44








SiC materials [1]




0 exp( )pE E CV (6)



(322 gcm3)







45


232 Hardness

















46













Single β-SiC (001) 28 -- [67]

CVD β-SiC 207-32 325-406 [466668]

FBCVD β-SiC -- 36-42 [8]


500 nm


47















grains





(a) (b)


48




















observations [62]



49






















A

PH max (7)



50







2A

S E

(8)





51

22 11 1 i

r i

vv

E E E

(9)



υi=007[65]







11 12 1 1282 4



considered


maxmaxc

Ph h

S (11)


indenter)




strength


52



























53

















1 2

3 2( )IC

E PK

H c (12)





54

























defects




55


























56


methods

Methods L


f (MPa) Ref






Crush test -- 58-75 356-427 89

Crush test 770-1324 40-73 330-647 5

Crush test 1484-1721 135-183 1045-1091 90

L














57



loading) [89]








2

1 2

1membrane

FC

t

(13)


58

2 2

1bending

FC

t

(14)


2

1 0115004022050 C (15)

)27031exp(204412 C (16)

2 2 2 1 4

0[12(1 ) ( )]r R t (17)


where max (L





mL

f

E

m

s

F

fSdAP

00

exp1exp1

(19)

where L



dAS

m

s L

f

F

f

E


1

N

iPi (20)



59




f ) is given

L

f

m

L

f

m

F

E

L

EF

ftR

r

S

S

1

2

2

0

1

)(4

(21)










size [3 5]







diffraction





60


























61








than sp2 and sp









(a) (b)

(c) (d)


62

features









layers [102]














63
















64















) D (~1330 cm-1

) Drdquo

(~1500 cm-1

) G (~1580 cm-1




65



domains [109]

















66


mechanisms


different methods


(gcm3)

Youngrsquos modulus

(GPa)

Hardness

(GPa)

Ref

3-point-bending 150-212 310-427 -- 112

137-206 165-281 -- 116


165-203 235-270 30-44 115

155-187 70-150 05-18 115

135-212 125-346 15-48 113

















67




















68













indenter [110]









69



















dislocation glide


70





















25 Summary







71



antisite clusters








particle














72

26 References



329-77















(2007) 635-38








56 (1973) 36-41


73



Nucl Mater 374 (2008) 445-52





Nucl Mater 295 (2001) 205-12



J Nucl Mater 334 (2004) 79-89








equipment 466 (2001) 406-11




18 (1963) 161-274







74







(2003) 155204-15


25 (1969) 477-88

















(2001) 2645-51




75













Forum 527-29 (2006) 1409-12















(2001) 179-88


76











(2002) 1348-35





(2003) 155208-09


Phys Rev B 63 (2001) 201201-04










Rev 173 (1968) 787-93


77



(1991) 3685-94



Am Ceram Soc 94 (2011) 3509-14








Mater Res 7(1992)1564-83



Soc 82 (1999) 2490-96


MRS Bull 23 (1995) 22-27



Materialia 59 (2008) 995 -98



47-63



Res Soc Symp P 522 (1998) 113-18


78



Rev B 71 (2005) 174113-23















(2008) 39ndash42


Am Ceram Soc 90 (2007) 673-80










79






Acta Mater 51 (2003) 3849-60







Nucl Mater 62 (1976) 123-37



J Am Ceram Soc 90 (2007) 184-91




1974



(2009) 113-23






80



443-47











136-46



55-62





Mater Res 6 (1991) 1685-94





Carbon 47 (2009) 251-62


81











Communic 143 (2007) 47-57


















82






3630-39




1981




811-21



Carbon 33 (1995) 1709-15



881-90


83



31 Introduction




















84


















C vs 1500 o

C) FBCVD SiC [5]








discussed


85















are for


and 1500 cm-1

are acoustic SiC


and 1600 cm-1














86





C 3173 + 0029


C 3135 + 0034

S3 (SiC+Si) 10 -- 1300 o

C 3188 + 0002











XP (MTS











87




(c)

(d)


88















Tecnai TM







33 Results







89














(c) (b)

(a)


90


























load


91









92



















05 μm


93












(c)


94














[27]







95










5 nm

(a) (b)

5 nm

5 nm

(c)


96















projection





2 nm

(a)

(111)

[110]

(111)

Sessile

dislocations

(b)


97





























98















99















100











34 Discussion

















101


















Ref 25)










102




0 exp( )pE E CV (1)





















103












1 2

0 Gb (2)







2(1 )

EG

(3)


was ~03times1012






104



























105


























35 Conclusions


106


















107

36 References



329-77





















Mater Res 7 (1992) 1564-83





108

Appl Phys 40 (2007) 3985-90






Res Soc Symp P 522 (1998) 113-18



Ceram Soc 94 (2011) 3509-14







063514-22



Rev B 71 (2005) 174113-23





Ceram Soc 27 (2007) 1503-11





109








012015 J Phys Conf Ser 106 (2008) 12015-124






Technol 44 (2003) 455-59



Mater 59 (2008) 995-98






044108-20


Manchester 2010



95-101


110




p206-47





J Cryst Growth 311 (2009) 4167-70












p162-91





p264





111
















2521-43




112


SiC Coatings

41 Introduction























113





data






















114














reference [25]











115










1 2 23

3 2( ) ( )IC v

a E PK

l H c

(1)









116




zone


117




























and 672 MPa m12


118
















119






3 N 6650 13125 6475 0020368 6685 18285 11600 0023088

6900 13090 6190 0019473 6995 15470 8475 0015013

6675 11895 5220 0015749 6120 16615 10495 0019880

6695 13130 6435 0020249 6555 15935 9380 0017057

6790 12610 5820 0017997 6425 18275 11850 0023783

35 N 7195 14970 7775 0022404 7235 20790 13555 0024930

6670 14080 7410 0020721 6715 18160 11445 0019412

4 N 7770 15855 8085 0020967 7390 20240 12850 0020187

χv 002008 plusmn 000273




) were taken from

Ref 9









met




120






conditions


)

S1 (SiC) 02-2 351plusmn042

S2 (SiC + C) 02-2 403plusmn043

S3 (SiC + Si) 02-2 493plusmn016








MPa m12


49 MPa m12


347 and 672 MPa m12








121


paper

















boundary










122















123





















124























(around 33 MPa m12






125


SiC (b) S3 SiC




















126




44 Conclusions















127

45 References



(2007) 329-77



Mater 58 (2010) 2843-53










Nucl Mater 62 (1976) 123-37



J Nucl Mater 45 (1972) 261-64










128

Mater 59 (2008) 39-42


















Sci Lett 6 (1987) 897-900







Am CeramSoc 72 (1989) 904-11




129


12 (2003) 155









Ceram Soc 92 (2009) 1093-97






(1992) 3299-304









Am Ceram Soc 90 (2007) 673-80




130




Acta Mater 48 (2000) 903-10







(2003) 95-101





2000










131



51 Introduction






















132

sample





















521 Materials





133








for 5 minutes



Sample Temperature

(ordmC)

MTS

(vol )


(LMin)

Radius

Thickness (~)

S1 1300 91 05vol C3H

6 600 72

S2 1300 91 01vol C3H

6 600 76

S3 1280 91 01vol C3H

6 600 83

S4 1300 91 -- 600 85

S5 1400 19 57vol Ar 778 87

S6 1500 22 82vol Ar 700 90

S7 1500 19 89vol Ar 778 101

S8 1500 22 79vol Ar 700 112

S9 1400 19 57vol Ar 777 117

S10 1300 19 57vol Ar 778 129

S11 1500 19 89vol Ar 777 151

S12 1500 22 76vol Ar 700 158

S13 1500 19 57vol Ar 778 190










134




strengthL











factor mtRr 122







10 ordm

t


135














German)













136















(L


F

fmean value)




For Size Effect

F

f MPa

S 1 15239 2235 1784 7397 185 963

S 2 15043 1999 1599 7687 183 872

S 3 14898 1540 1446 7459 187 774

S 4 16052 2042 1620 8261 178 908

S 5 17018 2573 1810 7927 178 1018

S 6 16220 1885 1648 6953 193 855

S 7 14662 1691 1974 7755 190 1019

S 8 14905 1336 1717 7102 198 868

S 9 13040 1088 1825 6495 223 820

S10 16410 1215 1472 6801 204 722

S11 16165 1006 1430 6104 219 652

S12 14677 903 1512 6616 205 737

S13 11586 489 1762 4912 300 587


137





fracture


distribution











138













of the full shell






139


shown in Fig 53


SiC coatings














140









equation [26]

12( )

L ICf

K Z

Yc (1)







141














irregularities


142




(1)

















143










2 1 2( ) ( ( ) ( )) xh x h x x h x x (2)

















144



















ξ3 ξ12 ξ6


145




S 1 02378 05903 06250 03804

S 2 04142 06950 08333 04971

S 3 06701 06673 16666 04021

S 4 06825 05244 14583 04680

S 5 05271 06308 14581 03615

S 6 08500 06343 20833 04080

S 7 04293 05162 14583 02944

S 8 07452 05107 14583 05110

S 9 05453 06099 12500 04362

S10 06953 05490 13044 05330

S11 05806 04949 10417 05574

S12 07584 06899 16666 04550

S13 05522 02971 18750 02945

















146





























147




















148

ratio



Grain size

(μm2)

04 06 06 08 20 20 20 28 20 08 20 28 25

Porosity

(Area )

0 0 0 0 05 04 12 09 03 0 08 21 20



y=1351-1150x












149


54 Conclusions


















strength




150

55 References






Am Ceram Soc 90 (2007) 184-91



350 (2006) 182-94



(1973) 36-41






J Am Ceram Soc 90 (2007) 184-91





(2006) 3043-49







151



Ceram Soc 92 (2009) 1287-95



(2010) 5578-85



Ceram Soc 92 (2009) 1287-95


Phys Rev E 51 (1995) 131-47





E 76 (2007) 036108-14






57 (2009) 2624-30





1974



152


355 (2006) 150-62



Nucl Mater 62 (1976) 123-37



(1982) 69-77



1010029780470584002 ch13 2010



Ceram Soc 88 (2005) 2645-48



86 (2005) 071920-22



Phys 42 (2009) 145303-10










153





Phys Lett 86 (2005) 071920-22


154



61 Introduction






















155


















Sample Temperature

(oC)

MTS concentration

(vol)

Added gas

concentration

Stoichiometry








1300-1500 cm-1



156


















(TecnaiTM G2

F30 U-TWIN)

63 Results



f ) in SiC






157
















158




f ) before



f ) before










159

unchanged modulus)













treatment

Sample m (from

L

f )


L

f MPa


F

f MPa


SiC1 75 61 1445 1421 774 660

SiC2 77 89 1599 1395 872 847

SiC3 65 58 1824 1333 820 548

SiC4 74 53 1717 1443 858 587







160







161




























162





coatings










163






















164


thermal treatment

















) was attributed to



165


and 1600 cm-1











cm-1


67)





166


sample


thermal treatment

Sample Porosity ()

As 2000degC

Stoichiometry

As 2000degC

Critical Defects

As 2000degC









-1)








and 789 cm-1





167


treatment







cm-1




64 Discussion



2( )

L ICf

K Z

Yc for tensile





[27] the










168









nanometer pores




















169





and 2715 cm-1




interstitials



















) (Fig 67)



170













)

















171

65 Conclusions

























further study


172

66 References











101111j1551-2916201105044x



















173



136-46















2281-86












174


Phys 102 (2007) 023512 -17



1700-07





A-Appl Res 162 (1997) 39-64


(1976) 87-8



86 (2005) 071920-22







1985-87








175



71 Introduction






















176










[15]










studied









177








PyC

(High density)

Density

(gcm3)

Texture(Orient-

ation angle deg)

PyC

(Low density)

Density

(gcm3)

Texture(Orient-

ation angle deg)

C1 2122plusmn0059 58 C6 1855plusmn0050 63

C2 2087plusmn0183 37 C7 1738plusmn0013 73

C3 2047plusmn0030 60 C8 1635plusmn0008 71

C4 2029plusmn0015 43 C9 1603plusmn0024 71

C5 2000plusmn0061 43 C10 1414plusmn0002 85

C11 1400plusmn0024 81















178








GRAMS32 software








73 Results








-1

and 1600 cm-1




) and D (1620 cm-1

) bands due


179




band a single











1335 cm-1

1500 cm-1

and 1600

cm-1









of the 1500 cm-1


[25] respectively

D

I


180





(1400







previous study [28]


temperatures



(a) (b)


181








to 57 cm-1




to 57 cm-1

) was found







7312 Domain sizes













182







C1 21 -- 112 -- 116 53

C2 21 -- 132 63 154 69

C3 22 -- 98 66 111 63

C4 24 -- 95 57 118 63

C5 20 -- 120 60 152 73


C6 22 -- 50 42 56 44

C7 18 -- 38 36 50 34

C8 14 -- 31 33 27 39

C9 11 -- 27 32 31 34

C10 17 -- 24 33 27 35

C11 11 -- 27 35 27 33













183




of 200 nm




OA=43 ordm

OA=25 ordm

Top

Voids

100 nm

(c)

(a) (b)

5 nm

Moireacute

fringes


184

























treatment


185











coatings

(a) (b)

100 nm 5 nm

5 nm

Sphere-like

particle

Tops


particle

Top (d)


186





















hc


187




















(a) (b)


188















High density






Low density







74 Discussions




189





























190






























191


















graphene planes










192















0174 to 0249 Fig 77)














193





5-membered rings





cm-1









Sample Density

(gcm3)

Texture

OA (deg)

Domain

size (nm)


(GPa)

Modulus

(GPa)











194
































195






74 Conclusions






















196







197

75 References










Nucl Mater 295 (2001) 205-12













34 (1996) 1357-66






198




J Am Ceram Soc 85 (2002) 1522-28









33 (1995) 1709-15



Chem Chem Phys 9 (2007) 1276-91










Carbon 47 (2009) 396-10



Carbon 47 (2009) 251-62


199






Mater Res 7 (1992) 1564-83



film 105 (1983) 75-96






143 (2007) 47-57













200



Sci 49 (2003) 235-40











Solidi B 247 (2010) 2980-82




4813-20




1972 p 162


55-62


201

















81 Conclusions









202








main cracks












the full shell









203



























promising


204









SiC coatings

List of Contents

3




25 Summary 70

26 References 72


Indentation 83

31 Introduction 83


33 Results 88




34 Discussion 100




35 Conclusions 105

36 References 107


41 Introduction 112






44 Conclusions 126

45 References 127


Coatings 131

51 Introduction 131


List of Contents

4

521 Materials 132






140





54 Conclusions 149

55 References 150



61 Introduction 154


63 Results 156




64 Discussion 167



65 Conclusions 171

66 References 172


Coatings 175

71 Introduction 175


73 Results 178




List of Contents

5





74 Discussions 188





74 Conclusions 195

75 References 197


81 Conclusions 201


Abstract

6

Abstract




Huixing Zhang





































Declaration

7

Declaration




Copyright Statment

8

Copyright Statement




purposes





















Acknowledgement

9

Acknowledgement









a good researcher









tensile tests






List of Figures

10

List of Figures



matrix [5]



[10]




from Ref [18]




















List of Figures

11



[48]




















loading) [89]










List of Figures

12








indenter [110]





Indentation




















List of Figures

13







projection













reference




zone









List of Figures

14




Coatings



distribution





SiC coatings










(1)









y=1351-1150x

List of Figures

15








f ) before

























List of Figures

16






temperatures






of 200 nm












List of Tables

17

List of Tables



methods






methods









conditions


Coatings




List of Tables

18









treatment


thermal treatment






density PyC




19





















service [4]


20


matrix [5]
















21


























22










PyC layer










23





increase [3]


[10]













24















issues












25












given in Chapter 8


26

14 References






329-77







174-88



141-51



199-210



Nucl Mater 295 (2001) 205-12



MIT-ANP-PR-075




27






28


21 Introduction























29





























30




from Ref [18]









31










222 Defects in SiC








ABCACBCABChellip




32









methods

[27] [28] [24] [29] [30] [31] [32]

ESF (mJ m-1

) -15 -- -28 -6 -61 -154 -323

ISF (mJ m-1

) 12 34 -34 14 138 111 -71










33















(a) (b)

(c)


34















5cm







35





stacking faults







(a)

(b)

(c) (d)


36





























37













interphase



(a)

(b) (c)

β-SiC

β-SiC

β-SiC

β-SiC

Si

Si

025 nm

025 nm

025 nm

0 312 nm

0312 nm


38












[48]









(a) (b)


39

be estimated [49]





















40









Ef (eV) 59 68 73 11 150 147 86 110


















41
















3C-SiC a 3523 1404 2329 18196 [59]

3C-SiC b 511 128 191 10026 [1]

3C-SiC c 390 142 256 -- [60]

3C-SiC a 420 126 287 19503 [61]









42
















0 44

1 11 12

2CZ

C C

(1)






spherical


43





3

[1 ( 3 )]E

B

(2)


11 122

3

C CB

(3)

1

0 1

1 0

52( 6 )

(4)

where 0 44C 1 11 12( ) 2C C and

01

0 0

3( 2 )

5 (3 4 )

B

B

(5)










44








SiC materials [1]




0 exp( )pE E CV (6)



(322 gcm3)







45


232 Hardness

















46













Single β-SiC (001) 28 -- [67]

CVD β-SiC 207-32 325-406 [466668]

FBCVD β-SiC -- 36-42 [8]


500 nm


47















grains





(a) (b)


48




















observations [62]



49






















A

PH max (7)



50







2A

S E

(8)





51

22 11 1 i

r i

vv

E E E

(9)



υi=007[65]







11 12 1 1282 4



considered


maxmaxc

Ph h

S (11)


indenter)




strength


52



























53

















1 2

3 2( )IC

E PK

H c (12)





54

























defects




55


























56


methods

Methods L


f (MPa) Ref






Crush test -- 58-75 356-427 89

Crush test 770-1324 40-73 330-647 5

Crush test 1484-1721 135-183 1045-1091 90

L














57



loading) [89]








2

1 2

1membrane

FC

t

(13)


58

2 2

1bending

FC

t

(14)


2

1 0115004022050 C (15)

)27031exp(204412 C (16)

2 2 2 1 4

0[12(1 ) ( )]r R t (17)


where max (L





mL

f

E

m

s

F

fSdAP

00

exp1exp1

(19)

where L



dAS

m

s L

f

F

f

E


1

N

iPi (20)



59




f ) is given

L

f

m

L

f

m

F

E

L

EF

ftR

r

S

S

1

2

2

0

1

)(4

(21)










size [3 5]







diffraction





60


























61








than sp2 and sp









(a) (b)

(c) (d)


62

features









layers [102]














63
















64















) D (~1330 cm-1

) Drdquo

(~1500 cm-1

) G (~1580 cm-1




65



domains [109]

















66


mechanisms


different methods


(gcm3)

Youngrsquos modulus

(GPa)

Hardness

(GPa)

Ref

3-point-bending 150-212 310-427 -- 112

137-206 165-281 -- 116


165-203 235-270 30-44 115

155-187 70-150 05-18 115

135-212 125-346 15-48 113

















67




















68













indenter [110]









69



















dislocation glide


70





















25 Summary







71



antisite clusters








particle














72

26 References



329-77















(2007) 635-38








56 (1973) 36-41


73



Nucl Mater 374 (2008) 445-52





Nucl Mater 295 (2001) 205-12



J Nucl Mater 334 (2004) 79-89








equipment 466 (2001) 406-11




18 (1963) 161-274







74







(2003) 155204-15


25 (1969) 477-88

















(2001) 2645-51




75













Forum 527-29 (2006) 1409-12















(2001) 179-88


76











(2002) 1348-35





(2003) 155208-09


Phys Rev B 63 (2001) 201201-04










Rev 173 (1968) 787-93


77



(1991) 3685-94



Am Ceram Soc 94 (2011) 3509-14








Mater Res 7(1992)1564-83



Soc 82 (1999) 2490-96


MRS Bull 23 (1995) 22-27



Materialia 59 (2008) 995 -98



47-63



Res Soc Symp P 522 (1998) 113-18


78



Rev B 71 (2005) 174113-23















(2008) 39ndash42


Am Ceram Soc 90 (2007) 673-80










79






Acta Mater 51 (2003) 3849-60







Nucl Mater 62 (1976) 123-37



J Am Ceram Soc 90 (2007) 184-91




1974



(2009) 113-23






80



443-47











136-46



55-62





Mater Res 6 (1991) 1685-94





Carbon 47 (2009) 251-62


81











Communic 143 (2007) 47-57


















82






3630-39




1981




811-21



Carbon 33 (1995) 1709-15



881-90


83



31 Introduction




















84


















C vs 1500 o

C) FBCVD SiC [5]








discussed


85















are for


and 1500 cm-1

are acoustic SiC


and 1600 cm-1














86





C 3173 + 0029


C 3135 + 0034

S3 (SiC+Si) 10 -- 1300 o

C 3188 + 0002











XP (MTS











87




(c)

(d)


88















Tecnai TM







33 Results







89














(c) (b)

(a)


90


























load


91









92



















05 μm


93












(c)


94














[27]







95










5 nm

(a) (b)

5 nm

5 nm

(c)


96















projection





2 nm

(a)

(111)

[110]

(111)

Sessile

dislocations

(b)


97





























98















99















100











34 Discussion

















101


















Ref 25)










102




0 exp( )pE E CV (1)





















103












1 2

0 Gb (2)







2(1 )

EG

(3)


was ~03times1012






104



























105


























35 Conclusions


106


















107

36 References



329-77





















Mater Res 7 (1992) 1564-83





108

Appl Phys 40 (2007) 3985-90






Res Soc Symp P 522 (1998) 113-18



Ceram Soc 94 (2011) 3509-14







063514-22



Rev B 71 (2005) 174113-23





Ceram Soc 27 (2007) 1503-11





109








012015 J Phys Conf Ser 106 (2008) 12015-124






Technol 44 (2003) 455-59



Mater 59 (2008) 995-98






044108-20


Manchester 2010



95-101


110




p206-47





J Cryst Growth 311 (2009) 4167-70












p162-91





p264





111
















2521-43




112


SiC Coatings

41 Introduction























113





data






















114














reference [25]











115










1 2 23

3 2( ) ( )IC v

a E PK

l H c

(1)









116




zone


117




























and 672 MPa m12


118
















119






3 N 6650 13125 6475 0020368 6685 18285 11600 0023088

6900 13090 6190 0019473 6995 15470 8475 0015013

6675 11895 5220 0015749 6120 16615 10495 0019880

6695 13130 6435 0020249 6555 15935 9380 0017057

6790 12610 5820 0017997 6425 18275 11850 0023783

35 N 7195 14970 7775 0022404 7235 20790 13555 0024930

6670 14080 7410 0020721 6715 18160 11445 0019412

4 N 7770 15855 8085 0020967 7390 20240 12850 0020187

χv 002008 plusmn 000273




) were taken from

Ref 9









met




120






conditions


)

S1 (SiC) 02-2 351plusmn042

S2 (SiC + C) 02-2 403plusmn043

S3 (SiC + Si) 02-2 493plusmn016








MPa m12


49 MPa m12


347 and 672 MPa m12








121


paper

















boundary










122















123





















124























(around 33 MPa m12






125


SiC (b) S3 SiC




















126




44 Conclusions















127

45 References



(2007) 329-77



Mater 58 (2010) 2843-53










Nucl Mater 62 (1976) 123-37



J Nucl Mater 45 (1972) 261-64










128

Mater 59 (2008) 39-42


















Sci Lett 6 (1987) 897-900







Am CeramSoc 72 (1989) 904-11




129


12 (2003) 155









Ceram Soc 92 (2009) 1093-97






(1992) 3299-304









Am Ceram Soc 90 (2007) 673-80




130




Acta Mater 48 (2000) 903-10







(2003) 95-101





2000










131



51 Introduction






















132

sample





















521 Materials





133








for 5 minutes



Sample Temperature

(ordmC)

MTS

(vol )


(LMin)

Radius

Thickness (~)

S1 1300 91 05vol C3H

6 600 72

S2 1300 91 01vol C3H

6 600 76

S3 1280 91 01vol C3H

6 600 83

S4 1300 91 -- 600 85

S5 1400 19 57vol Ar 778 87

S6 1500 22 82vol Ar 700 90

S7 1500 19 89vol Ar 778 101

S8 1500 22 79vol Ar 700 112

S9 1400 19 57vol Ar 777 117

S10 1300 19 57vol Ar 778 129

S11 1500 19 89vol Ar 777 151

S12 1500 22 76vol Ar 700 158

S13 1500 19 57vol Ar 778 190










134




strengthL











factor mtRr 122







10 ordm

t


135














German)













136















(L


F

fmean value)




For Size Effect

F

f MPa

S 1 15239 2235 1784 7397 185 963

S 2 15043 1999 1599 7687 183 872

S 3 14898 1540 1446 7459 187 774

S 4 16052 2042 1620 8261 178 908

S 5 17018 2573 1810 7927 178 1018

S 6 16220 1885 1648 6953 193 855

S 7 14662 1691 1974 7755 190 1019

S 8 14905 1336 1717 7102 198 868

S 9 13040 1088 1825 6495 223 820

S10 16410 1215 1472 6801 204 722

S11 16165 1006 1430 6104 219 652

S12 14677 903 1512 6616 205 737

S13 11586 489 1762 4912 300 587


137





fracture


distribution











138













of the full shell






139


shown in Fig 53


SiC coatings














140









equation [26]

12( )

L ICf

K Z

Yc (1)







141














irregularities


142




(1)

















143










2 1 2( ) ( ( ) ( )) xh x h x x h x x (2)

















144



















ξ3 ξ12 ξ6


145




S 1 02378 05903 06250 03804

S 2 04142 06950 08333 04971

S 3 06701 06673 16666 04021

S 4 06825 05244 14583 04680

S 5 05271 06308 14581 03615

S 6 08500 06343 20833 04080

S 7 04293 05162 14583 02944

S 8 07452 05107 14583 05110

S 9 05453 06099 12500 04362

S10 06953 05490 13044 05330

S11 05806 04949 10417 05574

S12 07584 06899 16666 04550

S13 05522 02971 18750 02945

















146





























147




















148

ratio



Grain size

(μm2)

04 06 06 08 20 20 20 28 20 08 20 28 25

Porosity

(Area )

0 0 0 0 05 04 12 09 03 0 08 21 20



y=1351-1150x












149


54 Conclusions


















strength




150

55 References






Am Ceram Soc 90 (2007) 184-91



350 (2006) 182-94



(1973) 36-41






J Am Ceram Soc 90 (2007) 184-91





(2006) 3043-49







151



Ceram Soc 92 (2009) 1287-95



(2010) 5578-85



Ceram Soc 92 (2009) 1287-95


Phys Rev E 51 (1995) 131-47





E 76 (2007) 036108-14






57 (2009) 2624-30





1974



152


355 (2006) 150-62



Nucl Mater 62 (1976) 123-37



(1982) 69-77



1010029780470584002 ch13 2010



Ceram Soc 88 (2005) 2645-48



86 (2005) 071920-22



Phys 42 (2009) 145303-10










153





Phys Lett 86 (2005) 071920-22


154



61 Introduction






















155


















Sample Temperature

(oC)

MTS concentration

(vol)

Added gas

concentration

Stoichiometry








1300-1500 cm-1



156


















(TecnaiTM G2

F30 U-TWIN)

63 Results



f ) in SiC






157
















158




f ) before



f ) before










159

unchanged modulus)













treatment

Sample m (from

L

f )


L

f MPa


F

f MPa


SiC1 75 61 1445 1421 774 660

SiC2 77 89 1599 1395 872 847

SiC3 65 58 1824 1333 820 548

SiC4 74 53 1717 1443 858 587







160







161




























162





coatings










163






















164


thermal treatment

















) was attributed to



165


and 1600 cm-1











cm-1


67)





166


sample


thermal treatment

Sample Porosity ()

As 2000degC

Stoichiometry

As 2000degC

Critical Defects

As 2000degC









-1)








and 789 cm-1





167


treatment







cm-1




64 Discussion



2( )

L ICf

K Z

Yc for tensile





[27] the










168









nanometer pores




















169





and 2715 cm-1




interstitials



















) (Fig 67)



170













)

















171

65 Conclusions

























further study


172

66 References











101111j1551-2916201105044x



















173



136-46















2281-86












174


Phys 102 (2007) 023512 -17



1700-07





A-Appl Res 162 (1997) 39-64


(1976) 87-8



86 (2005) 071920-22







1985-87








175



71 Introduction






















176










[15]










studied









177








PyC

(High density)

Density

(gcm3)

Texture(Orient-

ation angle deg)

PyC

(Low density)

Density

(gcm3)

Texture(Orient-

ation angle deg)

C1 2122plusmn0059 58 C6 1855plusmn0050 63

C2 2087plusmn0183 37 C7 1738plusmn0013 73

C3 2047plusmn0030 60 C8 1635plusmn0008 71

C4 2029plusmn0015 43 C9 1603plusmn0024 71

C5 2000plusmn0061 43 C10 1414plusmn0002 85

C11 1400plusmn0024 81















178








GRAMS32 software








73 Results








-1

and 1600 cm-1




) and D (1620 cm-1

) bands due


179




band a single











1335 cm-1

1500 cm-1

and 1600

cm-1









of the 1500 cm-1


[25] respectively

D

I


180





(1400







previous study [28]


temperatures



(a) (b)


181








to 57 cm-1




to 57 cm-1

) was found







7312 Domain sizes













182







C1 21 -- 112 -- 116 53

C2 21 -- 132 63 154 69

C3 22 -- 98 66 111 63

C4 24 -- 95 57 118 63

C5 20 -- 120 60 152 73


C6 22 -- 50 42 56 44

C7 18 -- 38 36 50 34

C8 14 -- 31 33 27 39

C9 11 -- 27 32 31 34

C10 17 -- 24 33 27 35

C11 11 -- 27 35 27 33













183




of 200 nm




OA=43 ordm

OA=25 ordm

Top

Voids

100 nm

(c)

(a) (b)

5 nm

Moireacute

fringes


184

























treatment


185











coatings

(a) (b)

100 nm 5 nm

5 nm

Sphere-like

particle

Tops


particle

Top (d)


186





















hc


187




















(a) (b)


188















High density






Low density







74 Discussions




189





























190






























191


















graphene planes










192















0174 to 0249 Fig 77)














193





5-membered rings





cm-1









Sample Density

(gcm3)

Texture

OA (deg)

Domain

size (nm)


(GPa)

Modulus

(GPa)











194
































195






74 Conclusions






















196







197

75 References










Nucl Mater 295 (2001) 205-12













34 (1996) 1357-66






198




J Am Ceram Soc 85 (2002) 1522-28









33 (1995) 1709-15



Chem Chem Phys 9 (2007) 1276-91










Carbon 47 (2009) 396-10



Carbon 47 (2009) 251-62


199






Mater Res 7 (1992) 1564-83



film 105 (1983) 75-96






143 (2007) 47-57













200



Sci 49 (2003) 235-40











Solidi B 247 (2010) 2980-82




4813-20




1972 p 162


55-62


201

















81 Conclusions









202








main cracks












the full shell









203



























promising


204









SiC coatings

List of Contents

4

521 Materials 132






140





54 Conclusions 149

55 References 150



61 Introduction 154


63 Results 156




64 Discussion 167



65 Conclusions 171

66 References 172


Coatings 175

71 Introduction 175


73 Results 178




List of Contents

5





74 Discussions 188





74 Conclusions 195

75 References 197


81 Conclusions 201


Abstract

6

Abstract




Huixing Zhang





































Declaration

7

Declaration




Copyright Statment

8

Copyright Statement




purposes





















Acknowledgement

9

Acknowledgement









a good researcher









tensile tests






List of Figures

10

List of Figures



matrix [5]



[10]




from Ref [18]




















List of Figures

11



[48]




















loading) [89]










List of Figures

12








indenter [110]





Indentation




















List of Figures

13







projection













reference




zone









List of Figures

14




Coatings



distribution





SiC coatings










(1)









y=1351-1150x

List of Figures

15








f ) before

























List of Figures

16






temperatures






of 200 nm












List of Tables

17

List of Tables



methods






methods









conditions


Coatings




List of Tables

18









treatment


thermal treatment






density PyC




19





















service [4]


20


matrix [5]
















21


























22










PyC layer










23





increase [3]


[10]













24















issues












25












given in Chapter 8


26

14 References






329-77







174-88



141-51



199-210



Nucl Mater 295 (2001) 205-12



MIT-ANP-PR-075




27






28


21 Introduction























29





























30




from Ref [18]









31










222 Defects in SiC








ABCACBCABChellip




32









methods

[27] [28] [24] [29] [30] [31] [32]

ESF (mJ m-1

) -15 -- -28 -6 -61 -154 -323

ISF (mJ m-1

) 12 34 -34 14 138 111 -71










33















(a) (b)

(c)


34















5cm







35





stacking faults







(a)

(b)

(c) (d)


36





























37













interphase



(a)

(b) (c)

β-SiC

β-SiC

β-SiC

β-SiC

Si

Si

025 nm

025 nm

025 nm

0 312 nm

0312 nm


38












[48]









(a) (b)


39

be estimated [49]





















40









Ef (eV) 59 68 73 11 150 147 86 110


















41
















3C-SiC a 3523 1404 2329 18196 [59]

3C-SiC b 511 128 191 10026 [1]

3C-SiC c 390 142 256 -- [60]

3C-SiC a 420 126 287 19503 [61]









42
















0 44

1 11 12

2CZ

C C

(1)






spherical


43





3

[1 ( 3 )]E

B

(2)


11 122

3

C CB

(3)

1

0 1

1 0

52( 6 )

(4)

where 0 44C 1 11 12( ) 2C C and

01

0 0

3( 2 )

5 (3 4 )

B

B

(5)










44








SiC materials [1]




0 exp( )pE E CV (6)



(322 gcm3)







45


232 Hardness

















46













Single β-SiC (001) 28 -- [67]

CVD β-SiC 207-32 325-406 [466668]

FBCVD β-SiC -- 36-42 [8]


500 nm


47















grains





(a) (b)


48




















observations [62]



49






















A

PH max (7)



50







2A

S E

(8)





51

22 11 1 i

r i

vv

E E E

(9)



υi=007[65]







11 12 1 1282 4



considered


maxmaxc

Ph h

S (11)


indenter)




strength


52



























53

















1 2

3 2( )IC

E PK

H c (12)





54

























defects




55


























56


methods

Methods L


f (MPa) Ref






Crush test -- 58-75 356-427 89

Crush test 770-1324 40-73 330-647 5

Crush test 1484-1721 135-183 1045-1091 90

L














57



loading) [89]








2

1 2

1membrane

FC

t

(13)


58

2 2

1bending

FC

t

(14)


2

1 0115004022050 C (15)

)27031exp(204412 C (16)

2 2 2 1 4

0[12(1 ) ( )]r R t (17)


where max (L





mL

f

E

m

s

F

fSdAP

00

exp1exp1

(19)

where L



dAS

m

s L

f

F

f

E


1

N

iPi (20)



59




f ) is given

L

f

m

L

f

m

F

E

L

EF

ftR

r

S

S

1

2

2

0

1

)(4

(21)










size [3 5]







diffraction





60


























61








than sp2 and sp









(a) (b)

(c) (d)


62

features









layers [102]














63
















64















) D (~1330 cm-1

) Drdquo

(~1500 cm-1

) G (~1580 cm-1




65



domains [109]

















66


mechanisms


different methods


(gcm3)

Youngrsquos modulus

(GPa)

Hardness

(GPa)

Ref

3-point-bending 150-212 310-427 -- 112

137-206 165-281 -- 116


165-203 235-270 30-44 115

155-187 70-150 05-18 115

135-212 125-346 15-48 113

















67




















68













indenter [110]









69



















dislocation glide


70





















25 Summary







71



antisite clusters








particle














72

26 References



329-77















(2007) 635-38








56 (1973) 36-41


73



Nucl Mater 374 (2008) 445-52





Nucl Mater 295 (2001) 205-12



J Nucl Mater 334 (2004) 79-89








equipment 466 (2001) 406-11




18 (1963) 161-274







74







(2003) 155204-15


25 (1969) 477-88

















(2001) 2645-51




75













Forum 527-29 (2006) 1409-12















(2001) 179-88


76











(2002) 1348-35





(2003) 155208-09


Phys Rev B 63 (2001) 201201-04










Rev 173 (1968) 787-93


77



(1991) 3685-94



Am Ceram Soc 94 (2011) 3509-14








Mater Res 7(1992)1564-83



Soc 82 (1999) 2490-96


MRS Bull 23 (1995) 22-27



Materialia 59 (2008) 995 -98



47-63



Res Soc Symp P 522 (1998) 113-18


78



Rev B 71 (2005) 174113-23















(2008) 39ndash42


Am Ceram Soc 90 (2007) 673-80










79






Acta Mater 51 (2003) 3849-60







Nucl Mater 62 (1976) 123-37



J Am Ceram Soc 90 (2007) 184-91




1974



(2009) 113-23






80



443-47











136-46



55-62





Mater Res 6 (1991) 1685-94





Carbon 47 (2009) 251-62


81











Communic 143 (2007) 47-57


















82






3630-39




1981




811-21



Carbon 33 (1995) 1709-15



881-90


83



31 Introduction




















84


















C vs 1500 o

C) FBCVD SiC [5]








discussed


85















are for


and 1500 cm-1

are acoustic SiC


and 1600 cm-1














86





C 3173 + 0029


C 3135 + 0034

S3 (SiC+Si) 10 -- 1300 o

C 3188 + 0002











XP (MTS











87




(c)

(d)


88















Tecnai TM







33 Results







89














(c) (b)

(a)


90


























load


91









92



















05 μm


93












(c)


94














[27]







95










5 nm

(a) (b)

5 nm

5 nm

(c)


96















projection





2 nm

(a)

(111)

[110]

(111)

Sessile

dislocations

(b)


97





























98















99















100











34 Discussion

















101


















Ref 25)










102




0 exp( )pE E CV (1)





















103












1 2

0 Gb (2)







2(1 )

EG

(3)


was ~03times1012






104



























105


























35 Conclusions


106


















107

36 References



329-77





















Mater Res 7 (1992) 1564-83





108

Appl Phys 40 (2007) 3985-90






Res Soc Symp P 522 (1998) 113-18



Ceram Soc 94 (2011) 3509-14







063514-22



Rev B 71 (2005) 174113-23





Ceram Soc 27 (2007) 1503-11





109








012015 J Phys Conf Ser 106 (2008) 12015-124






Technol 44 (2003) 455-59



Mater 59 (2008) 995-98






044108-20


Manchester 2010



95-101


110




p206-47





J Cryst Growth 311 (2009) 4167-70












p162-91





p264





111
















2521-43




112


SiC Coatings

41 Introduction























113





data






















114














reference [25]











115










1 2 23

3 2( ) ( )IC v

a E PK

l H c

(1)









116




zone


117




























and 672 MPa m12


118
















119






3 N 6650 13125 6475 0020368 6685 18285 11600 0023088

6900 13090 6190 0019473 6995 15470 8475 0015013

6675 11895 5220 0015749 6120 16615 10495 0019880

6695 13130 6435 0020249 6555 15935 9380 0017057

6790 12610 5820 0017997 6425 18275 11850 0023783

35 N 7195 14970 7775 0022404 7235 20790 13555 0024930

6670 14080 7410 0020721 6715 18160 11445 0019412

4 N 7770 15855 8085 0020967 7390 20240 12850 0020187

χv 002008 plusmn 000273




) were taken from

Ref 9









met




120






conditions


)

S1 (SiC) 02-2 351plusmn042

S2 (SiC + C) 02-2 403plusmn043

S3 (SiC + Si) 02-2 493plusmn016








MPa m12


49 MPa m12


347 and 672 MPa m12








121


paper

















boundary










122















123





















124























(around 33 MPa m12






125


SiC (b) S3 SiC




















126




44 Conclusions















127

45 References



(2007) 329-77



Mater 58 (2010) 2843-53










Nucl Mater 62 (1976) 123-37



J Nucl Mater 45 (1972) 261-64










128

Mater 59 (2008) 39-42


















Sci Lett 6 (1987) 897-900







Am CeramSoc 72 (1989) 904-11




129


12 (2003) 155









Ceram Soc 92 (2009) 1093-97






(1992) 3299-304









Am Ceram Soc 90 (2007) 673-80




130




Acta Mater 48 (2000) 903-10







(2003) 95-101





2000










131



51 Introduction






















132

sample





















521 Materials





133








for 5 minutes



Sample Temperature

(ordmC)

MTS

(vol )


(LMin)

Radius

Thickness (~)

S1 1300 91 05vol C3H

6 600 72

S2 1300 91 01vol C3H

6 600 76

S3 1280 91 01vol C3H

6 600 83

S4 1300 91 -- 600 85

S5 1400 19 57vol Ar 778 87

S6 1500 22 82vol Ar 700 90

S7 1500 19 89vol Ar 778 101

S8 1500 22 79vol Ar 700 112

S9 1400 19 57vol Ar 777 117

S10 1300 19 57vol Ar 778 129

S11 1500 19 89vol Ar 777 151

S12 1500 22 76vol Ar 700 158

S13 1500 19 57vol Ar 778 190










134




strengthL











factor mtRr 122







10 ordm

t


135














German)













136















(L


F

fmean value)




For Size Effect

F

f MPa

S 1 15239 2235 1784 7397 185 963

S 2 15043 1999 1599 7687 183 872

S 3 14898 1540 1446 7459 187 774

S 4 16052 2042 1620 8261 178 908

S 5 17018 2573 1810 7927 178 1018

S 6 16220 1885 1648 6953 193 855

S 7 14662 1691 1974 7755 190 1019

S 8 14905 1336 1717 7102 198 868

S 9 13040 1088 1825 6495 223 820

S10 16410 1215 1472 6801 204 722

S11 16165 1006 1430 6104 219 652

S12 14677 903 1512 6616 205 737

S13 11586 489 1762 4912 300 587


137





fracture


distribution











138













of the full shell






139


shown in Fig 53


SiC coatings














140









equation [26]

12( )

L ICf

K Z

Yc (1)







141














irregularities


142




(1)

















143










2 1 2( ) ( ( ) ( )) xh x h x x h x x (2)

















144



















ξ3 ξ12 ξ6


145




S 1 02378 05903 06250 03804

S 2 04142 06950 08333 04971

S 3 06701 06673 16666 04021

S 4 06825 05244 14583 04680

S 5 05271 06308 14581 03615

S 6 08500 06343 20833 04080

S 7 04293 05162 14583 02944

S 8 07452 05107 14583 05110

S 9 05453 06099 12500 04362

S10 06953 05490 13044 05330

S11 05806 04949 10417 05574

S12 07584 06899 16666 04550

S13 05522 02971 18750 02945

















146





























147




















148

ratio



Grain size

(μm2)

04 06 06 08 20 20 20 28 20 08 20 28 25

Porosity

(Area )

0 0 0 0 05 04 12 09 03 0 08 21 20



y=1351-1150x












149


54 Conclusions


















strength




150

55 References






Am Ceram Soc 90 (2007) 184-91



350 (2006) 182-94



(1973) 36-41






J Am Ceram Soc 90 (2007) 184-91





(2006) 3043-49







151



Ceram Soc 92 (2009) 1287-95



(2010) 5578-85



Ceram Soc 92 (2009) 1287-95


Phys Rev E 51 (1995) 131-47





E 76 (2007) 036108-14






57 (2009) 2624-30





1974



152


355 (2006) 150-62



Nucl Mater 62 (1976) 123-37



(1982) 69-77



1010029780470584002 ch13 2010



Ceram Soc 88 (2005) 2645-48



86 (2005) 071920-22



Phys 42 (2009) 145303-10










153





Phys Lett 86 (2005) 071920-22


154



61 Introduction






















155


















Sample Temperature

(oC)

MTS concentration

(vol)

Added gas

concentration

Stoichiometry








1300-1500 cm-1



156


















(TecnaiTM G2

F30 U-TWIN)

63 Results



f ) in SiC






157
















158




f ) before



f ) before










159

unchanged modulus)













treatment

Sample m (from

L

f )


L

f MPa


F

f MPa


SiC1 75 61 1445 1421 774 660

SiC2 77 89 1599 1395 872 847

SiC3 65 58 1824 1333 820 548

SiC4 74 53 1717 1443 858 587







160







161




























162





coatings










163






















164


thermal treatment

















) was attributed to



165


and 1600 cm-1











cm-1


67)





166


sample


thermal treatment

Sample Porosity ()

As 2000degC

Stoichiometry

As 2000degC

Critical Defects

As 2000degC









-1)








and 789 cm-1





167


treatment







cm-1




64 Discussion



2( )

L ICf

K Z

Yc for tensile





[27] the










168









nanometer pores




















169





and 2715 cm-1




interstitials



















) (Fig 67)



170













)

















171

65 Conclusions

























further study


172

66 References











101111j1551-2916201105044x



















173



136-46















2281-86












174


Phys 102 (2007) 023512 -17



1700-07





A-Appl Res 162 (1997) 39-64


(1976) 87-8



86 (2005) 071920-22







1985-87








175



71 Introduction






















176










[15]










studied









177








PyC

(High density)

Density

(gcm3)

Texture(Orient-

ation angle deg)

PyC

(Low density)

Density

(gcm3)

Texture(Orient-

ation angle deg)

C1 2122plusmn0059 58 C6 1855plusmn0050 63

C2 2087plusmn0183 37 C7 1738plusmn0013 73

C3 2047plusmn0030 60 C8 1635plusmn0008 71

C4 2029plusmn0015 43 C9 1603plusmn0024 71

C5 2000plusmn0061 43 C10 1414plusmn0002 85

C11 1400plusmn0024 81















178








GRAMS32 software








73 Results








-1

and 1600 cm-1




) and D (1620 cm-1

) bands due


179




band a single











1335 cm-1

1500 cm-1

and 1600

cm-1









of the 1500 cm-1


[25] respectively

D

I


180





(1400







previous study [28]


temperatures



(a) (b)


181








to 57 cm-1




to 57 cm-1

) was found







7312 Domain sizes













182







C1 21 -- 112 -- 116 53

C2 21 -- 132 63 154 69

C3 22 -- 98 66 111 63

C4 24 -- 95 57 118 63

C5 20 -- 120 60 152 73


C6 22 -- 50 42 56 44

C7 18 -- 38 36 50 34

C8 14 -- 31 33 27 39

C9 11 -- 27 32 31 34

C10 17 -- 24 33 27 35

C11 11 -- 27 35 27 33













183




of 200 nm




OA=43 ordm

OA=25 ordm

Top

Voids

100 nm

(c)

(a) (b)

5 nm

Moireacute

fringes


184

























treatment


185











coatings

(a) (b)

100 nm 5 nm

5 nm

Sphere-like

particle

Tops


particle

Top (d)


186





















hc


187




















(a) (b)


188















High density






Low density







74 Discussions




189





























190






























191


















graphene planes










192















0174 to 0249 Fig 77)














193





5-membered rings





cm-1









Sample Density

(gcm3)

Texture

OA (deg)

Domain

size (nm)


(GPa)

Modulus

(GPa)











194
































195






74 Conclusions






















196







197

75 References










Nucl Mater 295 (2001) 205-12













34 (1996) 1357-66






198




J Am Ceram Soc 85 (2002) 1522-28









33 (1995) 1709-15



Chem Chem Phys 9 (2007) 1276-91










Carbon 47 (2009) 396-10



Carbon 47 (2009) 251-62


199






Mater Res 7 (1992) 1564-83



film 105 (1983) 75-96






143 (2007) 47-57













200



Sci 49 (2003) 235-40











Solidi B 247 (2010) 2980-82




4813-20




1972 p 162


55-62


201

















81 Conclusions









202








main cracks












the full shell









203



























promising


204









SiC coatings

List of Contents

5





74 Discussions 188





74 Conclusions 195

75 References 197


81 Conclusions 201


Abstract

6

Abstract




Huixing Zhang





































Declaration

7

Declaration




Copyright Statment

8

Copyright Statement




purposes





















Acknowledgement

9

Acknowledgement









a good researcher









tensile tests






List of Figures

10

List of Figures



matrix [5]



[10]




from Ref [18]




















List of Figures

11



[48]




















loading) [89]










List of Figures

12








indenter [110]





Indentation




















List of Figures

13







projection













reference




zone









List of Figures

14




Coatings



distribution





SiC coatings










(1)









y=1351-1150x

List of Figures

15








f ) before

























List of Figures

16






temperatures






of 200 nm












List of Tables

17

List of Tables



methods






methods









conditions


Coatings




List of Tables

18









treatment


thermal treatment






density PyC




19





















service [4]


20


matrix [5]
















21


























22










PyC layer










23





increase [3]


[10]













24















issues












25












given in Chapter 8


26

14 References






329-77







174-88



141-51



199-210



Nucl Mater 295 (2001) 205-12



MIT-ANP-PR-075




27






28


21 Introduction























29





























30




from Ref [18]









31










222 Defects in SiC








ABCACBCABChellip




32









methods

[27] [28] [24] [29] [30] [31] [32]

ESF (mJ m-1

) -15 -- -28 -6 -61 -154 -323

ISF (mJ m-1

) 12 34 -34 14 138 111 -71










33















(a) (b)

(c)


34















5cm







35





stacking faults







(a)

(b)

(c) (d)


36





























37













interphase



(a)

(b) (c)

β-SiC

β-SiC

β-SiC

β-SiC

Si

Si

025 nm

025 nm

025 nm

0 312 nm

0312 nm


38












[48]









(a) (b)


39

be estimated [49]





















40









Ef (eV) 59 68 73 11 150 147 86 110


















41
















3C-SiC a 3523 1404 2329 18196 [59]

3C-SiC b 511 128 191 10026 [1]

3C-SiC c 390 142 256 -- [60]

3C-SiC a 420 126 287 19503 [61]









42
















0 44

1 11 12

2CZ

C C

(1)






spherical


43





3

[1 ( 3 )]E

B

(2)


11 122

3

C CB

(3)

1

0 1

1 0

52( 6 )

(4)

where 0 44C 1 11 12( ) 2C C and

01

0 0

3( 2 )

5 (3 4 )

B

B

(5)










44








SiC materials [1]




0 exp( )pE E CV (6)



(322 gcm3)







45


232 Hardness

















46













Single β-SiC (001) 28 -- [67]

CVD β-SiC 207-32 325-406 [466668]

FBCVD β-SiC -- 36-42 [8]


500 nm


47















grains





(a) (b)


48




















observations [62]



49






















A

PH max (7)



50







2A

S E

(8)





51

22 11 1 i

r i

vv

E E E

(9)



υi=007[65]







11 12 1 1282 4



considered


maxmaxc

Ph h

S (11)


indenter)




strength


52



























53

















1 2

3 2( )IC

E PK

H c (12)





54

























defects




55


























56


methods

Methods L


f (MPa) Ref






Crush test -- 58-75 356-427 89

Crush test 770-1324 40-73 330-647 5

Crush test 1484-1721 135-183 1045-1091 90

L














57



loading) [89]








2

1 2

1membrane

FC

t

(13)


58

2 2

1bending

FC

t

(14)


2

1 0115004022050 C (15)

)27031exp(204412 C (16)

2 2 2 1 4

0[12(1 ) ( )]r R t (17)


where max (L





mL

f

E

m

s

F

fSdAP

00

exp1exp1

(19)

where L



dAS

m

s L

f

F

f

E


1

N

iPi (20)



59




f ) is given

L

f

m

L

f

m

F

E

L

EF

ftR

r

S

S

1

2

2

0

1

)(4

(21)










size [3 5]







diffraction





60


























61








than sp2 and sp









(a) (b)

(c) (d)


62

features









layers [102]














63
















64















) D (~1330 cm-1

) Drdquo

(~1500 cm-1

) G (~1580 cm-1




65



domains [109]

















66


mechanisms


different methods


(gcm3)

Youngrsquos modulus

(GPa)

Hardness

(GPa)

Ref

3-point-bending 150-212 310-427 -- 112

137-206 165-281 -- 116


165-203 235-270 30-44 115

155-187 70-150 05-18 115

135-212 125-346 15-48 113

















67




















68













indenter [110]









69



















dislocation glide


70





















25 Summary







71



antisite clusters








particle














72

26 References



329-77















(2007) 635-38








56 (1973) 36-41


73



Nucl Mater 374 (2008) 445-52





Nucl Mater 295 (2001) 205-12



J Nucl Mater 334 (2004) 79-89








equipment 466 (2001) 406-11




18 (1963) 161-274







74







(2003) 155204-15


25 (1969) 477-88

















(2001) 2645-51




75













Forum 527-29 (2006) 1409-12















(2001) 179-88


76











(2002) 1348-35





(2003) 155208-09


Phys Rev B 63 (2001) 201201-04










Rev 173 (1968) 787-93


77



(1991) 3685-94



Am Ceram Soc 94 (2011) 3509-14








Mater Res 7(1992)1564-83



Soc 82 (1999) 2490-96


MRS Bull 23 (1995) 22-27



Materialia 59 (2008) 995 -98



47-63



Res Soc Symp P 522 (1998) 113-18


78



Rev B 71 (2005) 174113-23















(2008) 39ndash42


Am Ceram Soc 90 (2007) 673-80










79






Acta Mater 51 (2003) 3849-60







Nucl Mater 62 (1976) 123-37



J Am Ceram Soc 90 (2007) 184-91




1974



(2009) 113-23






80



443-47











136-46



55-62





Mater Res 6 (1991) 1685-94





Carbon 47 (2009) 251-62


81











Communic 143 (2007) 47-57


















82






3630-39




1981




811-21



Carbon 33 (1995) 1709-15



881-90


83



31 Introduction




















84


















C vs 1500 o

C) FBCVD SiC [5]








discussed


85















are for


and 1500 cm-1

are acoustic SiC


and 1600 cm-1














86





C 3173 + 0029


C 3135 + 0034

S3 (SiC+Si) 10 -- 1300 o

C 3188 + 0002











XP (MTS











87




(c)

(d)


88















Tecnai TM







33 Results







89














(c) (b)

(a)


90


























load


91









92



















05 μm


93












(c)


94














[27]







95










5 nm

(a) (b)

5 nm

5 nm

(c)


96















projection





2 nm

(a)

(111)

[110]

(111)

Sessile

dislocations

(b)


97





























98















99















100











34 Discussion

















101


















Ref 25)










102




0 exp( )pE E CV (1)





















103












1 2

0 Gb (2)







2(1 )

EG

(3)


was ~03times1012






104



























105


























35 Conclusions


106


















107

36 References



329-77





















Mater Res 7 (1992) 1564-83





108

Appl Phys 40 (2007) 3985-90






Res Soc Symp P 522 (1998) 113-18



Ceram Soc 94 (2011) 3509-14







063514-22



Rev B 71 (2005) 174113-23





Ceram Soc 27 (2007) 1503-11





109








012015 J Phys Conf Ser 106 (2008) 12015-124






Technol 44 (2003) 455-59



Mater 59 (2008) 995-98






044108-20


Manchester 2010



95-101


110




p206-47





J Cryst Growth 311 (2009) 4167-70












p162-91





p264





111
















2521-43




112


SiC Coatings

41 Introduction























113





data






















114














reference [25]











115










1 2 23

3 2( ) ( )IC v

a E PK

l H c

(1)









116




zone


117




























and 672 MPa m12


118
















119






3 N 6650 13125 6475 0020368 6685 18285 11600 0023088

6900 13090 6190 0019473 6995 15470 8475 0015013

6675 11895 5220 0015749 6120 16615 10495 0019880

6695 13130 6435 0020249 6555 15935 9380 0017057

6790 12610 5820 0017997 6425 18275 11850 0023783

35 N 7195 14970 7775 0022404 7235 20790 13555 0024930

6670 14080 7410 0020721 6715 18160 11445 0019412

4 N 7770 15855 8085 0020967 7390 20240 12850 0020187

χv 002008 plusmn 000273




) were taken from

Ref 9









met




120






conditions


)

S1 (SiC) 02-2 351plusmn042

S2 (SiC + C) 02-2 403plusmn043

S3 (SiC + Si) 02-2 493plusmn016








MPa m12


49 MPa m12


347 and 672 MPa m12








121


paper

















boundary










122















123





















124























(around 33 MPa m12






125


SiC (b) S3 SiC




















126




44 Conclusions















127

45 References



(2007) 329-77



Mater 58 (2010) 2843-53










Nucl Mater 62 (1976) 123-37



J Nucl Mater 45 (1972) 261-64










128

Mater 59 (2008) 39-42


















Sci Lett 6 (1987) 897-900







Am CeramSoc 72 (1989) 904-11




129


12 (2003) 155









Ceram Soc 92 (2009) 1093-97






(1992) 3299-304









Am Ceram Soc 90 (2007) 673-80




130




Acta Mater 48 (2000) 903-10







(2003) 95-101





2000










131



51 Introduction






















132

sample





















521 Materials





133








for 5 minutes



Sample Temperature

(ordmC)

MTS

(vol )


(LMin)

Radius

Thickness (~)

S1 1300 91 05vol C3H

6 600 72

S2 1300 91 01vol C3H

6 600 76

S3 1280 91 01vol C3H

6 600 83

S4 1300 91 -- 600 85

S5 1400 19 57vol Ar 778 87

S6 1500 22 82vol Ar 700 90

S7 1500 19 89vol Ar 778 101

S8 1500 22 79vol Ar 700 112

S9 1400 19 57vol Ar 777 117

S10 1300 19 57vol Ar 778 129

S11 1500 19 89vol Ar 777 151

S12 1500 22 76vol Ar 700 158

S13 1500 19 57vol Ar 778 190










134




strengthL











factor mtRr 122







10 ordm

t


135














German)













136















(L


F

fmean value)




For Size Effect

F

f MPa

S 1 15239 2235 1784 7397 185 963

S 2 15043 1999 1599 7687 183 872

S 3 14898 1540 1446 7459 187 774

S 4 16052 2042 1620 8261 178 908

S 5 17018 2573 1810 7927 178 1018

S 6 16220 1885 1648 6953 193 855

S 7 14662 1691 1974 7755 190 1019

S 8 14905 1336 1717 7102 198 868

S 9 13040 1088 1825 6495 223 820

S10 16410 1215 1472 6801 204 722

S11 16165 1006 1430 6104 219 652

S12 14677 903 1512 6616 205 737

S13 11586 489 1762 4912 300 587


137





fracture


distribution











138













of the full shell






139


shown in Fig 53


SiC coatings














140









equation [26]

12( )

L ICf

K Z

Yc (1)







141














irregularities


142




(1)

















143










2 1 2( ) ( ( ) ( )) xh x h x x h x x (2)

















144



















ξ3 ξ12 ξ6


145




S 1 02378 05903 06250 03804

S 2 04142 06950 08333 04971

S 3 06701 06673 16666 04021

S 4 06825 05244 14583 04680

S 5 05271 06308 14581 03615

S 6 08500 06343 20833 04080

S 7 04293 05162 14583 02944

S 8 07452 05107 14583 05110

S 9 05453 06099 12500 04362

S10 06953 05490 13044 05330

S11 05806 04949 10417 05574

S12 07584 06899 16666 04550

S13 05522 02971 18750 02945

















146





























147




















148

ratio



Grain size

(μm2)

04 06 06 08 20 20 20 28 20 08 20 28 25

Porosity

(Area )

0 0 0 0 05 04 12 09 03 0 08 21 20



y=1351-1150x












149


54 Conclusions


















strength




150

55 References






Am Ceram Soc 90 (2007) 184-91



350 (2006) 182-94



(1973) 36-41






J Am Ceram Soc 90 (2007) 184-91





(2006) 3043-49







151



Ceram Soc 92 (2009) 1287-95



(2010) 5578-85



Ceram Soc 92 (2009) 1287-95


Phys Rev E 51 (1995) 131-47





E 76 (2007) 036108-14






57 (2009) 2624-30





1974



152


355 (2006) 150-62



Nucl Mater 62 (1976) 123-37



(1982) 69-77



1010029780470584002 ch13 2010



Ceram Soc 88 (2005) 2645-48



86 (2005) 071920-22



Phys 42 (2009) 145303-10










153





Phys Lett 86 (2005) 071920-22


154



61 Introduction






















155


















Sample Temperature

(oC)

MTS concentration

(vol)

Added gas

concentration

Stoichiometry








1300-1500 cm-1



156


















(TecnaiTM G2

F30 U-TWIN)

63 Results



f ) in SiC






157
















158




f ) before



f ) before










159

unchanged modulus)













treatment

Sample m (from

L

f )


L

f MPa


F

f MPa


SiC1 75 61 1445 1421 774 660

SiC2 77 89 1599 1395 872 847

SiC3 65 58 1824 1333 820 548

SiC4 74 53 1717 1443 858 587







160







161




























162





coatings










163






















164


thermal treatment

















) was attributed to



165


and 1600 cm-1











cm-1


67)





166


sample


thermal treatment

Sample Porosity ()

As 2000degC

Stoichiometry

As 2000degC

Critical Defects

As 2000degC









-1)








and 789 cm-1





167


treatment







cm-1




64 Discussion



2( )

L ICf

K Z

Yc for tensile





[27] the










168









nanometer pores




















169





and 2715 cm-1




interstitials



















) (Fig 67)



170













)

















171

65 Conclusions

























further study


172

66 References











101111j1551-2916201105044x



















173



136-46















2281-86












174


Phys 102 (2007) 023512 -17



1700-07





A-Appl Res 162 (1997) 39-64


(1976) 87-8



86 (2005) 071920-22







1985-87








175



71 Introduction






















176










[15]










studied









177








PyC

(High density)

Density

(gcm3)

Texture(Orient-

ation angle deg)

PyC

(Low density)

Density

(gcm3)

Texture(Orient-

ation angle deg)

C1 2122plusmn0059 58 C6 1855plusmn0050 63

C2 2087plusmn0183 37 C7 1738plusmn0013 73

C3 2047plusmn0030 60 C8 1635plusmn0008 71

C4 2029plusmn0015 43 C9 1603plusmn0024 71

C5 2000plusmn0061 43 C10 1414plusmn0002 85

C11 1400plusmn0024 81















178








GRAMS32 software








73 Results








-1

and 1600 cm-1




) and D (1620 cm-1

) bands due


179




band a single











1335 cm-1

1500 cm-1

and 1600

cm-1









of the 1500 cm-1


[25] respectively

D

I


180





(1400







previous study [28]


temperatures



(a) (b)


181








to 57 cm-1




to 57 cm-1

) was found







7312 Domain sizes













182







C1 21 -- 112 -- 116 53

C2 21 -- 132 63 154 69

C3 22 -- 98 66 111 63

C4 24 -- 95 57 118 63

C5 20 -- 120 60 152 73


C6 22 -- 50 42 56 44

C7 18 -- 38 36 50 34

C8 14 -- 31 33 27 39

C9 11 -- 27 32 31 34

C10 17 -- 24 33 27 35

C11 11 -- 27 35 27 33













183




of 200 nm




OA=43 ordm

OA=25 ordm

Top

Voids

100 nm

(c)

(a) (b)

5 nm

Moireacute

fringes


184

























treatment


185











coatings

(a) (b)

100 nm 5 nm

5 nm

Sphere-like

particle

Tops


particle

Top (d)


186





















hc


187




















(a) (b)


188















High density






Low density







74 Discussions




189





























190






























191


















graphene planes










192















0174 to 0249 Fig 77)














193





5-membered rings





cm-1









Sample Density

(gcm3)

Texture

OA (deg)

Domain

size (nm)


(GPa)

Modulus

(GPa)











194
































195






74 Conclusions






















196







197

75 References










Nucl Mater 295 (2001) 205-12













34 (1996) 1357-66






198




J Am Ceram Soc 85 (2002) 1522-28









33 (1995) 1709-15



Chem Chem Phys 9 (2007) 1276-91










Carbon 47 (2009) 396-10



Carbon 47 (2009) 251-62


199






Mater Res 7 (1992) 1564-83



film 105 (1983) 75-96






143 (2007) 47-57













200



Sci 49 (2003) 235-40











Solidi B 247 (2010) 2980-82




4813-20




1972 p 162


55-62


201

















81 Conclusions









202








main cracks












the full shell









203



























promising


204









SiC coatings

Abstract

6

Abstract




Huixing Zhang





































Declaration

7

Declaration




Copyright Statment

8

Copyright Statement




purposes





















Acknowledgement

9

Acknowledgement









a good researcher









tensile tests






List of Figures

10

List of Figures



matrix [5]



[10]




from Ref [18]




















List of Figures

11



[48]




















loading) [89]










List of Figures

12








indenter [110]





Indentation




















List of Figures

13







projection













reference




zone









List of Figures

14




Coatings



distribution





SiC coatings










(1)









y=1351-1150x

List of Figures

15








f ) before

























List of Figures

16






temperatures






of 200 nm












List of Tables

17

List of Tables



methods






methods









conditions


Coatings




List of Tables

18









treatment


thermal treatment






density PyC




19





















service [4]


20


matrix [5]
















21


























22










PyC layer










23





increase [3]


[10]













24















issues












25












given in Chapter 8


26

14 References






329-77







174-88



141-51



199-210



Nucl Mater 295 (2001) 205-12



MIT-ANP-PR-075




27






28


21 Introduction























29





























30




from Ref [18]









31










222 Defects in SiC








ABCACBCABChellip




32









methods

[27] [28] [24] [29] [30] [31] [32]

ESF (mJ m-1

) -15 -- -28 -6 -61 -154 -323

ISF (mJ m-1

) 12 34 -34 14 138 111 -71










33















(a) (b)

(c)


34















5cm







35





stacking faults







(a)

(b)

(c) (d)


36





























37













interphase



(a)

(b) (c)

β-SiC

β-SiC

β-SiC

β-SiC

Si

Si

025 nm

025 nm

025 nm

0 312 nm

0312 nm


38












[48]









(a) (b)


39

be estimated [49]





















40









Ef (eV) 59 68 73 11 150 147 86 110


















41
















3C-SiC a 3523 1404 2329 18196 [59]

3C-SiC b 511 128 191 10026 [1]

3C-SiC c 390 142 256 -- [60]

3C-SiC a 420 126 287 19503 [61]









42
















0 44

1 11 12

2CZ

C C

(1)






spherical


43





3

[1 ( 3 )]E

B

(2)


11 122

3

C CB

(3)

1

0 1

1 0

52( 6 )

(4)

where 0 44C 1 11 12( ) 2C C and

01

0 0

3( 2 )

5 (3 4 )

B

B

(5)










44








SiC materials [1]




0 exp( )pE E CV (6)



(322 gcm3)







45


232 Hardness

















46













Single β-SiC (001) 28 -- [67]

CVD β-SiC 207-32 325-406 [466668]

FBCVD β-SiC -- 36-42 [8]


500 nm


47















grains





(a) (b)


48




















observations [62]



49






















A

PH max (7)



50







2A

S E

(8)





51

22 11 1 i

r i

vv

E E E

(9)



υi=007[65]







11 12 1 1282 4



considered


maxmaxc

Ph h

S (11)


indenter)




strength


52



























53

















1 2

3 2( )IC

E PK

H c (12)





54

























defects




55


























56


methods

Methods L


f (MPa) Ref






Crush test -- 58-75 356-427 89

Crush test 770-1324 40-73 330-647 5

Crush test 1484-1721 135-183 1045-1091 90

L














57



loading) [89]








2

1 2

1membrane

FC

t

(13)


58

2 2

1bending

FC

t

(14)


2

1 0115004022050 C (15)

)27031exp(204412 C (16)

2 2 2 1 4

0[12(1 ) ( )]r R t (17)


where max (L





mL

f

E

m

s

F

fSdAP

00

exp1exp1

(19)

where L



dAS

m

s L

f

F

f

E


1

N

iPi (20)



59




f ) is given

L

f

m

L

f

m

F

E

L

EF

ftR

r

S

S

1

2

2

0

1

)(4

(21)










size [3 5]







diffraction





60


























61








than sp2 and sp









(a) (b)

(c) (d)


62

features









layers [102]














63
















64















) D (~1330 cm-1

) Drdquo

(~1500 cm-1

) G (~1580 cm-1




65



domains [109]

















66


mechanisms


different methods


(gcm3)

Youngrsquos modulus

(GPa)

Hardness

(GPa)

Ref

3-point-bending 150-212 310-427 -- 112

137-206 165-281 -- 116


165-203 235-270 30-44 115

155-187 70-150 05-18 115

135-212 125-346 15-48 113

















67




















68













indenter [110]









69



















dislocation glide


70





















25 Summary







71



antisite clusters








particle














72

26 References



329-77















(2007) 635-38








56 (1973) 36-41


73



Nucl Mater 374 (2008) 445-52





Nucl Mater 295 (2001) 205-12



J Nucl Mater 334 (2004) 79-89








equipment 466 (2001) 406-11




18 (1963) 161-274







74







(2003) 155204-15


25 (1969) 477-88

















(2001) 2645-51




75













Forum 527-29 (2006) 1409-12















(2001) 179-88


76











(2002) 1348-35





(2003) 155208-09


Phys Rev B 63 (2001) 201201-04










Rev 173 (1968) 787-93


77



(1991) 3685-94



Am Ceram Soc 94 (2011) 3509-14








Mater Res 7(1992)1564-83



Soc 82 (1999) 2490-96


MRS Bull 23 (1995) 22-27



Materialia 59 (2008) 995 -98



47-63



Res Soc Symp P 522 (1998) 113-18


78



Rev B 71 (2005) 174113-23















(2008) 39ndash42


Am Ceram Soc 90 (2007) 673-80










79






Acta Mater 51 (2003) 3849-60







Nucl Mater 62 (1976) 123-37



J Am Ceram Soc 90 (2007) 184-91




1974



(2009) 113-23






80



443-47











136-46



55-62





Mater Res 6 (1991) 1685-94





Carbon 47 (2009) 251-62


81











Communic 143 (2007) 47-57


















82






3630-39




1981




811-21



Carbon 33 (1995) 1709-15



881-90


83



31 Introduction




















84


















C vs 1500 o

C) FBCVD SiC [5]








discussed


85















are for


and 1500 cm-1

are acoustic SiC


and 1600 cm-1














86





C 3173 + 0029


C 3135 + 0034

S3 (SiC+Si) 10 -- 1300 o

C 3188 + 0002











XP (MTS











87




(c)

(d)


88















Tecnai TM







33 Results







89














(c) (b)

(a)


90


























load


91









92



















05 μm


93












(c)


94














[27]







95










5 nm

(a) (b)

5 nm

5 nm

(c)


96















projection





2 nm

(a)

(111)

[110]

(111)

Sessile

dislocations

(b)


97





























98















99















100











34 Discussion

















101


















Ref 25)










102




0 exp( )pE E CV (1)





















103












1 2

0 Gb (2)







2(1 )

EG

(3)


was ~03times1012






104



























105


























35 Conclusions


106


















107

36 References



329-77





















Mater Res 7 (1992) 1564-83





108

Appl Phys 40 (2007) 3985-90






Res Soc Symp P 522 (1998) 113-18



Ceram Soc 94 (2011) 3509-14







063514-22



Rev B 71 (2005) 174113-23





Ceram Soc 27 (2007) 1503-11





109








012015 J Phys Conf Ser 106 (2008) 12015-124






Technol 44 (2003) 455-59



Mater 59 (2008) 995-98






044108-20


Manchester 2010



95-101


110




p206-47





J Cryst Growth 311 (2009) 4167-70












p162-91





p264





111
















2521-43




112


SiC Coatings

41 Introduction























113





data






















114














reference [25]











115










1 2 23

3 2( ) ( )IC v

a E PK

l H c

(1)









116




zone


117




























and 672 MPa m12


118
















119






3 N 6650 13125 6475 0020368 6685 18285 11600 0023088

6900 13090 6190 0019473 6995 15470 8475 0015013

6675 11895 5220 0015749 6120 16615 10495 0019880

6695 13130 6435 0020249 6555 15935 9380 0017057

6790 12610 5820 0017997 6425 18275 11850 0023783

35 N 7195 14970 7775 0022404 7235 20790 13555 0024930

6670 14080 7410 0020721 6715 18160 11445 0019412

4 N 7770 15855 8085 0020967 7390 20240 12850 0020187

χv 002008 plusmn 000273




) were taken from

Ref 9









met




120






conditions


)

S1 (SiC) 02-2 351plusmn042

S2 (SiC + C) 02-2 403plusmn043

S3 (SiC + Si) 02-2 493plusmn016








MPa m12


49 MPa m12


347 and 672 MPa m12








121


paper

















boundary










122















123





















124























(around 33 MPa m12






125


SiC (b) S3 SiC




















126




44 Conclusions















127

45 References



(2007) 329-77



Mater 58 (2010) 2843-53










Nucl Mater 62 (1976) 123-37



J Nucl Mater 45 (1972) 261-64










128

Mater 59 (2008) 39-42


















Sci Lett 6 (1987) 897-900







Am CeramSoc 72 (1989) 904-11




129


12 (2003) 155









Ceram Soc 92 (2009) 1093-97






(1992) 3299-304









Am Ceram Soc 90 (2007) 673-80




130




Acta Mater 48 (2000) 903-10







(2003) 95-101





2000










131



51 Introduction






















132

sample





















521 Materials





133








for 5 minutes



Sample Temperature

(ordmC)

MTS

(vol )


(LMin)

Radius

Thickness (~)

S1 1300 91 05vol C3H

6 600 72

S2 1300 91 01vol C3H

6 600 76

S3 1280 91 01vol C3H

6 600 83

S4 1300 91 -- 600 85

S5 1400 19 57vol Ar 778 87

S6 1500 22 82vol Ar 700 90

S7 1500 19 89vol Ar 778 101

S8 1500 22 79vol Ar 700 112

S9 1400 19 57vol Ar 777 117

S10 1300 19 57vol Ar 778 129

S11 1500 19 89vol Ar 777 151

S12 1500 22 76vol Ar 700 158

S13 1500 19 57vol Ar 778 190










134




strengthL











factor mtRr 122







10 ordm

t


135














German)













136















(L


F

fmean value)




For Size Effect

F

f MPa

S 1 15239 2235 1784 7397 185 963

S 2 15043 1999 1599 7687 183 872

S 3 14898 1540 1446 7459 187 774

S 4 16052 2042 1620 8261 178 908

S 5 17018 2573 1810 7927 178 1018

S 6 16220 1885 1648 6953 193 855

S 7 14662 1691 1974 7755 190 1019

S 8 14905 1336 1717 7102 198 868

S 9 13040 1088 1825 6495 223 820

S10 16410 1215 1472 6801 204 722

S11 16165 1006 1430 6104 219 652

S12 14677 903 1512 6616 205 737

S13 11586 489 1762 4912 300 587


137





fracture


distribution











138













of the full shell






139


shown in Fig 53


SiC coatings














140









equation [26]

12( )

L ICf

K Z

Yc (1)







141














irregularities


142




(1)

















143










2 1 2( ) ( ( ) ( )) xh x h x x h x x (2)

















144



















ξ3 ξ12 ξ6


145




S 1 02378 05903 06250 03804

S 2 04142 06950 08333 04971

S 3 06701 06673 16666 04021

S 4 06825 05244 14583 04680

S 5 05271 06308 14581 03615

S 6 08500 06343 20833 04080

S 7 04293 05162 14583 02944

S 8 07452 05107 14583 05110

S 9 05453 06099 12500 04362

S10 06953 05490 13044 05330

S11 05806 04949 10417 05574

S12 07584 06899 16666 04550

S13 05522 02971 18750 02945

















146





























147




















148

ratio



Grain size

(μm2)

04 06 06 08 20 20 20 28 20 08 20 28 25

Porosity

(Area )

0 0 0 0 05 04 12 09 03 0 08 21 20



y=1351-1150x












149


54 Conclusions


















strength




150

55 References






Am Ceram Soc 90 (2007) 184-91



350 (2006) 182-94



(1973) 36-41






J Am Ceram Soc 90 (2007) 184-91





(2006) 3043-49







151



Ceram Soc 92 (2009) 1287-95



(2010) 5578-85



Ceram Soc 92 (2009) 1287-95


Phys Rev E 51 (1995) 131-47





E 76 (2007) 036108-14






57 (2009) 2624-30





1974



152


355 (2006) 150-62



Nucl Mater 62 (1976) 123-37



(1982) 69-77



1010029780470584002 ch13 2010



Ceram Soc 88 (2005) 2645-48



86 (2005) 071920-22



Phys 42 (2009) 145303-10










153





Phys Lett 86 (2005) 071920-22


154



61 Introduction






















155


















Sample Temperature

(oC)

MTS concentration

(vol)

Added gas

concentration

Stoichiometry








1300-1500 cm-1



156


















(TecnaiTM G2

F30 U-TWIN)

63 Results



f ) in SiC






157
















158




f ) before



f ) before










159

unchanged modulus)













treatment

Sample m (from

L

f )


L

f MPa


F

f MPa


SiC1 75 61 1445 1421 774 660

SiC2 77 89 1599 1395 872 847

SiC3 65 58 1824 1333 820 548

SiC4 74 53 1717 1443 858 587







160







161




























162





coatings










163






















164


thermal treatment

















) was attributed to



165


and 1600 cm-1











cm-1


67)





166


sample


thermal treatment

Sample Porosity ()

As 2000degC

Stoichiometry

As 2000degC

Critical Defects

As 2000degC









-1)








and 789 cm-1





167


treatment







cm-1




64 Discussion



2( )

L ICf

K Z

Yc for tensile





[27] the










168









nanometer pores




















169





and 2715 cm-1




interstitials



















) (Fig 67)



170













)

















171

65 Conclusions

























further study


172

66 References











101111j1551-2916201105044x



















173



136-46















2281-86












174


Phys 102 (2007) 023512 -17



1700-07





A-Appl Res 162 (1997) 39-64


(1976) 87-8



86 (2005) 071920-22







1985-87








175



71 Introduction






















176










[15]










studied









177








PyC

(High density)

Density

(gcm3)

Texture(Orient-

ation angle deg)

PyC

(Low density)

Density

(gcm3)

Texture(Orient-

ation angle deg)

C1 2122plusmn0059 58 C6 1855plusmn0050 63

C2 2087plusmn0183 37 C7 1738plusmn0013 73

C3 2047plusmn0030 60 C8 1635plusmn0008 71

C4 2029plusmn0015 43 C9 1603plusmn0024 71

C5 2000plusmn0061 43 C10 1414plusmn0002 85

C11 1400plusmn0024 81















178








GRAMS32 software








73 Results








-1

and 1600 cm-1




) and D (1620 cm-1

) bands due


179




band a single











1335 cm-1

1500 cm-1

and 1600

cm-1









of the 1500 cm-1


[25] respectively

D

I


180





(1400







previous study [28]


temperatures



(a) (b)


181








to 57 cm-1




to 57 cm-1

) was found







7312 Domain sizes













182







C1 21 -- 112 -- 116 53

C2 21 -- 132 63 154 69

C3 22 -- 98 66 111 63

C4 24 -- 95 57 118 63

C5 20 -- 120 60 152 73


C6 22 -- 50 42 56 44

C7 18 -- 38 36 50 34

C8 14 -- 31 33 27 39

C9 11 -- 27 32 31 34

C10 17 -- 24 33 27 35

C11 11 -- 27 35 27 33













183




of 200 nm




OA=43 ordm

OA=25 ordm

Top

Voids

100 nm

(c)

(a) (b)

5 nm

Moireacute

fringes


184

























treatment


185











coatings

(a) (b)

100 nm 5 nm

5 nm

Sphere-like

particle

Tops


particle

Top (d)


186





















hc


187




















(a) (b)


188















High density






Low density







74 Discussions




189





























190






























191


















graphene planes










192















0174 to 0249 Fig 77)














193





5-membered rings





cm-1









Sample Density

(gcm3)

Texture

OA (deg)

Domain

size (nm)


(GPa)

Modulus

(GPa)











194
































195






74 Conclusions






















196







197

75 References










Nucl Mater 295 (2001) 205-12













34 (1996) 1357-66






198




J Am Ceram Soc 85 (2002) 1522-28









33 (1995) 1709-15



Chem Chem Phys 9 (2007) 1276-91










Carbon 47 (2009) 396-10



Carbon 47 (2009) 251-62


199






Mater Res 7 (1992) 1564-83



film 105 (1983) 75-96






143 (2007) 47-57













200



Sci 49 (2003) 235-40











Solidi B 247 (2010) 2980-82




4813-20




1972 p 162


55-62


201

















81 Conclusions









202








main cracks












the full shell









203



























promising


204









SiC coatings

mechanical and microstructural study of silicon …

Documents