microstructural analysis using x-ray diffraction · microstructural analysis using x-ray...

$: Microstructural analysis using X-ray diffraction · Microstructural analysis using X-ray diffraction ... Warren-Averbach method) ... Berlin: Springer-Verlag, 2004. 34$
11

Microstructural analysis Microstructural analysis using Xusing X--ray diffractionray diffraction

M. LeoniM. LeoniUniversità di Trento – Facoltà di IngegneriaDipartimento di Ingegneria dei Materiali e Tecnologie Industrialivia Mesiano, 77 – 38050 TrentoE-mail: [email protected]

22

Microstructural Analysis using XRDMicrostructural Analysis using XRD

ØØ XX--ray diffraction & materials science/engineering?ray diffraction & materials science/engineering?a case of study: materials for gas turbinesa case of study: materials for gas turbines

ØØ XX--ray diffraction for microstructure analysis: ray diffraction for microstructure analysis: ll what can we measure/obtain?what can we measure/obtain?ll some practical applicationssome practical applications

ØØ Additional topics Additional topics ll the mathematics behindthe mathematics behind……

33

Materials in EngineeringMaterials in EngineeringA case of study: materials for jet propulsion engines

44

Materials in EngineeringMaterials in Engineering

Turbine blades and vanes in different stages

A case of study: materials for jet propulsion engines

55

Materials in EngineeringMaterials in Engineering

Blades and vanes used in different stages of gas turbines must withstand high mechanical and thermal solicitations in hostile atmosphere (corrosion/oxidation)

A case of study: materials for jet propulsion engines

66

High temperature: why?

The quest for high temperature in gas turbinesThe quest for high temperature in gas turbines

• Jumbo-jet engines: 110°C higher Tgas à 20% increase in thrust

• Industrial GTs: 55°C higher gas temp. à 8-13% more power1-4 % higher efficiency

Power and Fuel efficiency are determined by service temperature

77

Turbine blade strengthening phaseTurbine blade strengthening phaseTheThe γγ--γγ’’ microstructure of Nimicrostructure of Ni--based based SuperalloysSuperalloys

γ-γ’ Ni3Al

88

In most metals and alloys, In most metals and alloys, yield stressyield stress ((σσyy) and elastic) and elasticmodulus drastically fall with the temperaturemodulus drastically fall with the temperature

σy(T1)σy(T2)

T1 < T2

yield stress

Yield stress vs. temperatureYield stress vs. temperature

σ

ε

99

Yield stress anomaly in L1Yield stress anomaly in L122 phasesphasesSome NiSome Ni33AlAl--type phases (L1type phases (L122) exhibit a ) exhibit a Yield Stress anomaly Yield Stress anomaly : :

σσyy increases with the temperatureincreases with the temperature

σ y

T

316 - Stainless Steel

Hastalloy - X

Ni3Al

1010

OrderOrder--disorder transformationdisorder transformation

G=HG=H--TSTS

L1L122 (Pm3m)(Pm3m) fccfcc (Fm(Fm--3m)3m)

OrderedLow T

DisorderedHigh T

Al Ni (0.75) Ni - (0.25) Al

Tc

1111

TEM TEM -- SAD in SAD in γγ−−γγ’’

γγ--NiNi33AlAl(disordered)(disordered)

γγ’’--NiNi33AlAl(ordered)(ordered)

1212

γγ--NiNi33AlAl(disordered)(disordered)

γγ’’--NiNi33AlAl(ordered)(ordered)

(200)

(020) (220)

(010)

(100)

(110)

(120)(210)

superstructurereflections

TEM TEM -- SAD in SAD in γγ−−γγ’’

1313

Dislocations in NiDislocations in Ni33AlAl

APDB (APD Boundary)

Ni Al

(111)

Dislocations in Ni3Al superlattice (b=a<101>) are unstable

Partials are separated by two Complex Stacking Faults (CSF) limiting an Anti-Phase Domain (APD) region

APD

CSF CSF(111)

and dissociate in 4 Shockley partials (b=a/6<211>) in the 111 planes.

1414

APBs have a lower energy on 100 than on 111. Thermal activation allows cross slip leading to a non-gliding (sessile) configuration

(010)(111) σ y

T

316 - Stainless Steel

Hastalloy - X

Ni3Al

KearKear--WilsdorfWilsdorf locklock

Kear-Wilsdorf lock

1515

XRD Line Profile Analysis

X-ray diffraction Line Profile Analysis

XRD LPA is ideally suited to determine size/shape of crystalline domains and content of lattice defects (e.g., dislocations, faulting, APDs)

How can we study dislocations, faulting, APBand other features of the microstructure ?

1616

Directional solidification / single crystal

High temperature: why?

The quest for high temperature in gas turbinesThe quest for high temperature in gas turbines


1717

High temperature materials in GTHigh temperature materials in GT

Gas turbine achieve high temperatures by air-cooling


1818

The quest for high temperature in gas The quest for high temperature in gas turbinesturbines

TBC: Thermal Barrier Coating


1919

Thermal Barrier Coatings (Thermal Barrier Coatings (TBCsTBCs))

• TBCs on blades à 107 gals fuel savings per year (250 plane airfleet)

• In aviation engines: à 3x longer life (at 1000-3000 US$ per blade)(data from R.L. Jones, formerly at Naval Research Laboratory, USA)

Blade performance improved by means of ceramic TBCs

2020

TBC Materials: stabilised TBC Materials: stabilised zirconiazirconiaPartially Stabilised-Zirconia (PSZ)(t/t’) or Stabilised Zirconia (c)

Y2O3-ZrO2

2121

PartiallyPartially--stabilised Zirconia TBCstabilised Zirconia TBC

20 30 40 50 60 70 80 90

0

500

1000

1500

2000

2500

3000

3500

M (1

11)

M (-

111)

In

tens

ity (

coun

ts)

2θ (degrees)

27 28 29 30 31 32 33

50

100

150

M (111)M (-111)

Inte

nsity

(co

unts

)2θ (degrees)

Quantitative Phase Analysis (QPA) of Zirconia polymorphsby X-ray Diffraction (XRD) (Rietveld method)

Tetragonal 94.0 wt%Monoclinic 6.0 wt%

2222

Air Plasma Spray (APS)Air Plasma Spray (APS)Plasma Torch

1. Powder injection2. Tubolar anode3. Catode4,6. Cooling system5. Plasma gas inlet

2323

New New TBCsTBCs: APS vs. EB: APS vs. EB--PVDPVDState-of-art: APS (Plasma Spray) New: Electron Beam-PVD

textureno texture

2424

Textured Textured TBCsTBCsMicrostructure of yttria partially stabilised zirconia TBC deposited by EB-PVD: evidence of highly textured columnar grains

Thermal as well as intrinsic (growth) stresses need be considered in coating design and production process

2525

Residual stress and textureResidual stress and textureHow can we evaluate

residual stress and texture in thin films?

X-ray diffraction is ideally suited for non-destructiveevaluation of residuals stress and texture in thin films and coatings.

Structural information must be properly considered in the modelling of the elastic behaviour of textured coatings.

2626

LINE PROFILE ANALYSISLINE PROFILE ANALYSISLPA Applications typically concern the study of:

Ø crystalline domain size and shape (and distribution) Ø generalised line defects, e.g., dislocations, disclinationsØ planar faults, e.g., twin and deformation faultsØ anti-phase domain boundaries (in ordered phases)Ø residual (micro)strain (e.g. by misfitting inclusions)Ø grain surface effects (e.g. grain surface relaxation)Ø impurities (--> lattice parameter fluctuation from grain to

grain)Ø ………..

2727

Starting from the pioneering work of Scherrer (1918), LPA developed during the ’40s and ’50s (Wilson, Warren, Bertaut), with further significant contributions by Krivoglaz and Wilkensduring the ’60s. Profile fitting techniques in the ’80s/’90s had quite an impact on LPA; however, present day traditional LPA methods are still mostly based on those early studies.

Line Profile Analysis: history

• Fourier methods (e.g., Warren-Averbach method)

• Line Breadth ‘simplified’ methods (e.g., Scherrer formula, Williamson-Hall plot)

Traditional methods are usually grouped as:

2828

Line Breadth ‘simplified’ methods

2 0 3 0 4 0 5 0 6 0

2 θ (d e g re e s )

Profile information is typically extracted as FWHM or Integral Breadth (β) – ratio between peak area and maximum intensity

0.0 0.2 0.4 0.6 0.8 1.00.00

0.01

0.02

0.03

slope=2 eintercept=1/KβL

Williamson-Hall plot

β(s)

(Å-1

)

d* (Å-1)

( )* *1 2d e dK Lβ

β = + ⋅

2929

Pattern Decomposition + LPA

2 0 3 0 4 0 5 0 6 02 θ ( d e g r e e s )

2 0 3 0 4 0 5 0 6 02 θ ( d e g r e e s )

Pattern decomposition (profile fitting) is frequently used toextract peak profile parameters by fitting suitable (but arbitrary !!) analytical functions, like, e.g., Voigt, pseudo-Voigt or PVII.

position, width, shape, intensity, asymmetry,…used in LPA (e.g., by Warren-Averbach method)

3030

Most traditional methods are based on a multiple-step procedure:

3. Application of physical models to parameters extracted from theexperimental pattern.

Traditional Line Profile Analysis

20 40 60 80 100 120 1400

1000200030004000500060007000 Sol-gel cerium oxide powder, 1h @ 400°C

Inte

nsity

(co

unts

)

2θ (degrees)

2. Extraction of line profile data (FWHM, β, Fourier coefficients, …),typically by analytical profile fitting

1. Correction of line profiles for the instrumental component/backgr.

( )2cosK Lβ

λβ θ

θ=

⋅

Scherrer formula

3131

Most traditional methods are based on a multiple-step procedure:

1. Correction of line profiles for the instrumental component/backgr.

2. Extraction of line profile data (FWHM, β, Fourier coefficients, …),typically by analytical profile fitting

3. Application of physical models to parameters extracted from theexperimental pattern.

Traditional Line Profile Analysis

Microstructural Parameters

DiffractionPattern

Profile parameters:FWHM, β,

Fourier Coeff. ...Background correction

Peak separation

IP deconvolution

LPA methods:

Scherrer formula

Williamson-Hall,

Warren-Averbach, …

3232

20 40 60 80 100 120 1400


Inte

nsity

(co

unts

)

2θ (degrees)


DiffractionPattern

WPPMPhysical Model

WPPM is based on a direct modelling of the experimental pattern, based on physical models of the microstructure and lattice defects:

Whole Powder Pattern Modelling

20 40 60 80 100 120 1400


Inte

nsity

(co

unts

)

2θ (degrees)

P.Scardi & M. Leoni, Acta Cryst. A 58 (2002) 190-200

3333

ReferencesReferencesDiffraction Analysis of Materials MicrostructureE.J. Mittemeijer & P. Scardi, editors.Berlin: Springer-Verlag, 2004.

3434

WPPM APPLICATIONSWPPM APPLICATIONS

• Ball milled Fe-Mo powder• Ball milled nickel powder• Nanocrystalline cerium oxide• Cu-Be alloy wear debris• Anti-Phase Domains in Cu3Au

3535

Main sources of broadening in this case are dislocations and domain size. Corresponding fitting parameters are:

WPPM application: Ball milled Fe-Mo

• average dislocation density ρ,

In addition: peak intensities, background coefficients (Chebyshev polynomial), lattice parameter and sample displacement. Data corrected for Lorentz-Polarization effect.

• effective outer cut-off radius Re,

(1 )hkl EDGE SCREWE EC C f C f= + −

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.350.00

0.04

0.08

0.12

0.16

0.20

0.24

0.28

0.32 CEDGE CSCREW

Fe primary slip system: 110<111>Ave

rage

Con

trast

fact

or

H = (h2k2+k2l2+l2h2)/(h2+k2+l2)2

• fraction of Edge/Screw dislocations, fE . Average contrast factor from Feelastic constant, for primary slip system 110<111>:

• mean µ and variance σ of a lognormal distribution of (spherical) domains

3636


40 60 80 100 120 140

0

500

1000

1500

2000

2500

3000

3500

4000

4500

(2 2 2)(3 1 0)(2 2 0)

(2 1 1)(2 0 0)

(1 1 0)In

tens

ity (c

ount

s)

2θ (degrees)

4 0 6 0 8 0 1 0 0 1 2 0 1 4 0

1 0

1 0 0

1 0 0 0

(2 2 2 )

(3 1 0 )(2 2 0 )

(2 1 1 )(2 0 0 )

(1 1 0 ) F e -1 .5 M o s ta r t in g p o w d e r(d is k 8 0 0 M P a )

Inte

nsity

(cou

nts)


3737


40 60 80 100 120 140

0

500

1000

1500

2000

2500

3000

(2 2 2)(3 1 0)(2 2 0)

(2 1 1)(2 0 0)

(1 1 0)In

tens

ity (c

ount

s)

2θ (degrees)

4 0 6 0 8 0 1 0 0 1 2 0 1 4 0

1 0

1 0 0

1 0 0 0

(2 2 2 )

( 3 1 0 )( 2 2 0 )

( 2 1 1 )( 2 0 0 )

(1 1 0 ) F e -1 .5 M o b a ll m il le d 1 0 0 h

Inte

nsity

(cou

nts)


3838


0 20 40 60 80 100 120 140 160 1800.00

0.02

0.04

0.06

0.08100h

70h

30h

10h 0h

grai

n di

amet

er d

istri

butio

n (a

.u.)

diameter (nm)

0 20 40 60 80 1000

20

40

60

80

100

120 0h - starting powder (compacted disk)

D α t-0.36

Mea

n cr

ysta

llite

dia

met

er (

nm)

b.m. time (h)

3939


0 10 20 30 40 50 60 70 80 90 1000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

b.m. time (h)

Dis

loca

tion

dens

ity, ρ

(x1

016 m

-2)

0

4

8

12

16

20

24

28O

uter cut-off radius (nm)

4040


0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

b.m. time (h)

Reρ1/

2

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0E

dge fraction, fE

increasing dislocationcorrelation

(1 )Edge Screwhkl hkl hklE EC C f C f= + −

4141

WPPM: ApplicationsWPPM: Applications


4242

WPPM Application: Ball-Milled Nickel

40 60 80 100 120 14010

100

1000

10000

Inte

nsity

(co

unts

)

2θ (degrees)

tq h12 h48 h96

Ni patterns at increasing ball milling time

4343

40 60 80 100 120 1400

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

22000

Inte

nsity

(co

unts

)

2θ (degrees)

40 60 80 100 120 140

100

1000

10000 12h ball milling

Inte

nsity

(co

unts

)2θ (degrees)


4444

40 60 80 100 120 1400

2000

4000

6000

8000

10000

Inte

nsity

(co

unts

)

2θ (degrees)

40 60 80 100 120 140

100

1000

10000

96h ball milling

Inte

nsity

(co

unts

)2θ (degrees)


NiON

iO

4545

0 20 40 60 80 10002468

10121416182022242628

di

sloc

atio

n de

nsity

, ρo

(x10

15 m

-2)

milling time (hour)0 20 40 60 80 100

51015202530354045505560657075

Mea

n G

rain

dia

met

er (

nm)

milling time (hour)

0 20 40 60 80 1003.5225

3.5230

3.5235

3.5240

3.5245

3.5250

latti

ce p

aram

eter

, ao

(Å)

milling time (hour)0 20 40 60 80 100

0.000

0.005

0.010

0.015

0.020

0.025

0.030

β

α

faul

t pro

babi

lity

α,β

(%

)

milling time (hour)

deformation

twin


4646

5 nm96h ball milling


4747

0 20 40 60 80 1000.00

0.04

0.08

0.12

0.16

0.20

0.24

γ

(Jm

-2)

milling time (hour)

2 ln eRD

RAGb

bγ ρ =

RD Dislocations

( )2

ln12 1Disl

Gb D Db

ργ

π ν = −

GB Dislocations

( )

2 ln 216 1Disc

G Dγ

π ν

Ω=

−

Disclinations


4848

0 20 40 60 800,00

0,02

0,04

0,06

0,08

0,10

0,12 tq h6 h12 h24 h48 h96

grai

n di

amet

er d

istr

ibut

ion

D (nm)

Spherical grain size distributions


4949

100 nm

Nickel powder ball milled for 96 h

0 10 20 300.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16 TEM WPPM

frequ

ency

D (nm)


5050



5151

WPPM: Application - Nanocrystalline Ceria

CeO2 calcinated at 400°C for 1h

Grains are almost spherical and well separated

0 2 4 6 8 10 1205

10152025303540 TEM (average over

800 grains)

Freq

uenc

yGrain diameter (nm)

5252

WPPM Application: nanocrystalline oxidesWPPM Application: nanocrystalline oxidesNanocrystalline cerium oxide from sol-gel route

20 40 60 80 100 120 140

0

1000

2000

3000

4000

5000

6000

7000

Inte

nsit

y (c

ount

s)

2θ (degrees)

• P.Scardi, Z. Kristallogr 217 (2002)• M. Leoni & P.Scardi, in Diffraction Analysis of

Materials Microstructure. E.J. Mittemeijer & P. Scardi, editors. Berlin: Springer-Verlag. 2003

5 nm

5353

WPPM Application: nanocrystalline oxidesWPPM Application: nanocrystalline oxidesNanocrystalline cerium oxide from sol-gel route

20 40 60 80 100 120 140

0

1000

2000

3000

4000

5000

6000

7000

Inte

nsit

y (c

ount

s)

2θ (degrees)

• P.Scardi, Z. Kristallogr 217 (2002)• M. Leoni & P.Scardi, in Diffraction Analysis of

Materials Microstructure. E.J. Mittemeijer & P. Scardi, editors. Berlin: Springer-Verlag. 2003

0 2 4 6 8 10 120

5

10

15

20

25

30

35

40 TEM WPPM

Freq

uenc

y

Grain diameter (nm)

5454

20 40 60 80 100 120 140

0

1000

2000

3000

4000

5000

6000

7000

Inte

nsity

(co

unts

)

2θ (degrees)

1h @400°Cρ≈1.4(9)·1016 m-2

<D> =4.4(6) nm

a0=0.54153(2) nm


> standard value for‘bulk’ ceria (0.54113 nm)

5555


0 2 4 6 8 10 12 14 16 18 200.5410

0.5411

0.5412

0.5413

0.5414

0.5415

0.5416

0.5417

ICDD JCPDS PDF #34-0394 (CeO2)

a 0 (nm

)

Average grain diameter, D (nm)

Refined cell parameters increase with decreasing average grain diameter

300 400 500 6000.5411

0.5412

0.5413

0.5414

0.5415

0.5416

0.5417

a 0 (nm

)

Calcination Temperature (°C)

5656

A core-surface grain modelgrain in polycrystalline sample

Altered corona

Disclinations

grain of powder

Unaltered core

5757

Grain surface relaxation

Yacaman et al., Surf. Sci. 486 (2001) L449-L453

Gold nanorods

5858

A core-surface grain model

2 2 2

R x

adh k lxa ex

κξ−

−

∆∆ =

+ +

∆ =

Shift of atomic layers in the outer corona

a0

a0+∆a

0 1 2 3 40.0

0.2

0.4

0.6

0.8

1.0

∆a (n

m)

position along radius (nm)

5959

WPPM and grain surface relaxationSimulation for CeO2, lognormal distribution of spheres (average 3nm, lognormal

variance 0.3), surface relaxation (A=0.05nm, affected zone B=0.3 nm), dislocations (1016 m-2, Re=3nm), twins (1%) and stacking faults (2%)

40 60 80 100 120 140

1000

2000

3000

4000

5000 W PPM - no GSR W PPM - GS R

Inte

nsit

y (a

.u.)

2θ (degrees)

Main effect of GSR is peak shift (ao changes)

6060

WPPM and grain surface relaxationWPPM GSR-WPPM°

CELL PARAMETERcell parameter (nm) 0.54153(3) 0.541134

SIZE DISTRIBUTION (spherical grains)lognormal µ 1.41(2) 1.42(1)lognormal σ 0.355(7) 0.364(6)average diameter (nm) 4.37(1) 4.40(6)

DISLOCATIONSdislocation density (m-2) 1.4(10) 1016 1.08(4) 1016

edge dislocations content (%) 50 50cutoff radius Re (nm) 2(1) 3(1)A (from elastic constants) 0.1187 0.1187B (from elastic constants) 0.1618 0.1618Wilkens parameter M 0.25(1) 0.31(3)

GRAIN SURFACE RELAXATIONrelaxation factor ξ (nm) 0.008(3)decay constant κ (nm) 0.16(4)

STATISTICAL ESTIMATORSRwp 5.51 5.58Rexp 4.67 4.67GOF 1.18 1.20

fixed !

(°) Rietveld

6161

WPPM and grain surface relaxation

6262


6363


6464

WPPM - GSR - Rietveld

Structure + Microstructure refinement

20 40 60 80 100 120 140

0

1000

2000

3000

4000

5000

6000

7000

Inte

nsit

y (c

ount

s)

2θ (degrees)

0 2 4 6 8 10 120

5

10

15

20

25

30

35

40 TEM WPPM WPPM - GSR

Rietveld

Freq

uenc

y

Grain diameter (nm)

P.Scardi, Z. Kristallogr 217 (2002)

6565



6666

WPPM Application: CuWPPM Application: Cu--Be alloyBe alloyApplications: wherever good wear resistance or high mechanical properties are desired coupled with a good electrical or thermal conductivity, such as flash welding dies or parts for electrical components

Pin-on-diskwear test:

Wear debris

6767

WPPM Application: CuWPPM Application: Cu--Be alloyBe alloyFracture tends to become unlikely in small grains (below Griffith critical length) that tend to store high deformation energy. Analogous behaviour is observed in ball milled ceramics. Cu2O has a very low specific dislocation energy (≈1/3 of MgO, 1/30 of Fe3O4), so a high dislocation density is possible. Shear modulus is just G=10.3 GPa à E ∝ Gb2

20 40 60 80 100 120 1400

1000

2000

3000

4000

5000

Inte

nsity

(co

unts

)

2θ (degrees)

WPPMmodelled phases

Cu2O - Pn-3mCu - Fm-3m(CuO - Cc )

0 10 20 30 400.00

0.02

0.04

0.06

0.08

0.10

ρ = 5 x 1016 m-2

Cu2O

dia

met

er d

istri

butio

n (a

.u.)

crystallite diameter (nm)

Wear debris are made of Cu2O (with Cu metal particles).

• Cu2O is stabilised by the very small domain size (<25 nm)

Palkar et al. Phys. Rev. B53 (1996) 2167

• High angle reflections are so broad owing to the very high dislocation density (≈1016 m-2).

0 500 1000 1500-400

-350

-300

-250

-200

-150

-100

-50

0

RT

Cu

Cu2OCuO

2Cu2O + O2

--> 4CuO

4Cu + O2 --> 2Cu2

O

∆G°=RTxln[pO2]

∆G°

[kJ]

Temperature [K]

RT stablephase is

CuO100 nm

6868



6969

WPPM Application: WPPM Application: APDsAPDs in Cuin Cu33AuAuAnti Phase Domains form during the ordering process in Cu3Au. The o/d process can be thermally activated

7070

(1) (2)

(3) (4)

APB

‘Statistical’Cu(3/4) Au(1/4)Cu

Au

WPPM Application: WPPM Application: APDsAPDs in Cuin Cu33AuAu

7171

WPPM Application: WPPM Application: APDsAPDs in Cuin Cu33AuAu

20 40 60 80 100 120 140

0

200

400

600

800

1000

1200

Cu3Au (traces of Cu

2O)

γ=8% (random + (001))

FFF F

FF

F

F

Inte

nsity

(cou

nts)

2θ (degrees)

[100]

[010]

[001]

20 30 40 50 60

0

50

100

150

200

(211

)

(210

)

(110

)

(100

)

Cu 2O

FF

Inte

nsity

(cou

nts)

2θ (degrees)

7272


DiffractionPattern

WPPMPhysical Model

Main advantages of the WPPM with respect to traditional methods

WPPM : conclusions

• correct counting statistics is used;

• problem of peak overlapping is intrinsically solved: peak profiles across thewhole pattern are simultaneously refined;

• instrumental profile component can be easily included as well as appropriatebackground functions;

• different line profile models (e.g., dislocation, faulting, APBs, etc.) can betested together (parameter correlations can be evaluated);

• structural constraints can be easily implemented: the WPPM algorithm can hosta Rietveld routine (or vice-versa) for a simultaneous structure-microstructurerefinement

• multiple phase samples can be studied (considering different microstructures)including quantitative phase analysis

microstructural analysis using x-ray diffraction · microstructural analysis using x-ray...

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