nuclear fuels and materials - 151-2017-00l · nuclear fuels and materials - 151-2017-00l ⌸lecture...

WIR SCHAFFEN WISSEN – HEUTE FÜR MORGEN

Nuclear Fuels and Materials - 151-2017-00L

Manuel A. Pouchon :: Head of LNM :: Paul Scherrer Institut

Master of Nuclear Engineering ‐ Spring Semester 2016

Lecture 5: Adv. Systems, New Damage Mech. (Creep, ..) New Materials

Nuclear Fuels and Materials - 151-2017-00L ⌸ Lecture 5 - Page 2/83

o Components, Materials, Requirements: • LWRs• Advanced systems• new damage mechanism

o Creep / Stress rupture• Basics / Stages• Diffusion creep / Dislocation creep / Grain Boundary Sliding• Rupture• Norton‘s Creep Law / Monkman-Grant plot• Increase creep properties

o New Materials• Ferritic-Martensitic / Intermetallics / ODS / Ceramics• Example “Irradiation Creep”

o Additions / Repetition• Water chemistry / Galvanic Corrosion• Strengthening of metallic materials• Plastic Deformation• Stress Behavior• Dislocations / Burgers Vector

TOC


• Temperature 320 (400)• Thermal neutrons• Loads (static, dynamic)• Water as coolant

Materials related boundary conditions for LWRs


http://dx.doi.org/10.1016/j.actamat.2012.11.004

Materials in PWR


prio 1 prio 2

• Google the materials of the different components

•Which kind of steels where?

•Why?

•Make a list

Homework


Component Material Mass (MT)

Materials Issues

Fuel • UO2

• (U,Pu)O2

100 Fission gas release; fission product swelling; thermal conductivity decrease with burnup

Cladding,spacer grids

• Zircaloy:1.5 Sn; 0.5 (Fe, Ni, Cr); 0.1 O; bal Zr

25 Waterside corrosion and hydriding; embrittlement, growth; pellet-claddinginteraction; creep; fretting

Neutron absorbers • Ag-Cd-In (PWR), • B4C (BWR); • Gd2O3 (both)

~1 Embrittlement, thermal-mechanical fatigue

Reactor Pressure Vessel • Low-alloy steel:2 Cr ; 1 Mo; bal Fe

400 - 500 Radiation embrittlement

Steam Generator(PWR only)

• Low-alloy steel • Inconel: 60 Ni; 25 Cr; 15 Fe

Tube plugging, cracking, denting; leakage fromthe primary coolant to the secondary loop water

Reactor Internals • Stainless Steel:18 Cr; 8 Ni; bal Fe;

• Inconel

Swelling/creep, Stress-Corrosion Cracking, Fatigue

Ex-core components, primary piping

• Stainless steel - Stress-corrosion cracking (esp. BWR)

Valves, pumps • Stainless steel;• stellite: high Co conc.

- Cobalt dissolution => activation in core=> deposition in primary circuit

Components, Materials, Mass, Materials Issues


• Proliferation• Sustainability• Closure of fuel cycle• Safety

Demands for advanced reactors


(10-12y) R&D (~1B€) before 1st prototype of techno demo (source CEA, F. Carré)

Gen IV systems

Sodium Fast Reactor

Molten Salt Reactor

Gas Fast Reactor

Supercritical Water-cooled ReactorVery High Temperature Reactor

Lead FastReactor


SFR GFR LFR VHTR SCWR MSR Fusion

CoolantT(oC)

Liquid Na,few bars

He, 70 bars, 480-850

Lead alloys, 550-800

He, 70 bars, 600-1000

Water, 24 MPa, 280-550

Molten salt,500-720

He, 80 bar,300-480 / Pb-17, 480-700

Core Structures

Wrapper F/M steelsCladdingAFMA F/M ODS

Fuel & core structuresSiCf/SiC composite

Target, Wondow, CladdingF/M steels ODS

Core GraphiteControl rodsC/C SiC/SiC

Cladding & core structuresNi based Alloys & F/M steels

Core structureGraphite Hastelloy

First wall BlanketF/M steels ODS SiCf/SiC

Temp. (oC) 390 – 700 600 – 1200 350 – 480 600 – 1600 350 – 620 700 – 800 500 - 625

DoseCladding200 dpa

60/90 dpaCladding~100 dpa

7/25 dpa

~100 dpa+ 10 ppm He & 45 ppm H per dpa

Other components

IHX or turbineNi alloys

IHX or turbineNi alloys

Source CEA

Structural Materials in Advanced Systems


• Combined cycle plants (electricity and heat)• VHTR gas cooled, thermal neutrons, up to 1000 C gas temperature,

direct/indirect cycle)• Closing the fuel cycle • Fast spectrum (SFR, GFR)• Other projects: LMR, ADS, Traveling Wave, MSR, SCWR• Small medium Sized Reactors (SMR)

Advanced nuclear plants –current priorities

Nuclear Fuels and Materials - 151-2017-00L ⌸ Lecture 5 - Page 11/83March 2011

Delivering Nuclear Solutions for America’s Energy Challenges

Industrial Application

District Heating

Seawater Desalination

Petroleum Refining

Oil Shale and Oil Sand

Processing

Cogeneration of Electricity and Steam

Steam Reforming of Natural Gas

Hydrogen Production

800-

1000

°C

100

300

200

1000

400

600

500

700

900

800

LWRs

80-2

00°C

250-

550°

C

300-

600°

C

500-

900°

C

350-

800°

C

VHTR

NGNP

Potential Contribution of Fission Reactors to Process Heat Industries


March 2011Delivering Nuclear Solutions for America’s Energy Challenges

Existing Plants – Assuming 25% penetration of process heat & power market - - - 2.7 quads*

Coal‐to‐Liquids (24 – 100,000 bpd new plants )

Petrochemical

(170 plants in U.S.)

Fertilizers/Ammonia

(23 plants in U.S.–NH3 production)

Petroleum Refining

(137 plants in U.S.)

Oil Sands/Shale

* Quad = 1x1015 Btu (293 x 106 MWth) annual energy consumptionHydrogen Production

Growing and New Markets – Potential for 9.3 quads of HTGR Process Heat & Power

Oil Sands/Shale

Potential U.S. Market for HTGRs


VHTR – Potential applications

Oil companies • Refinery• De-supfurization of heavy oils• Production of gas• Coal gasification • Extraction from oil shales and tar-

sands

Metallurgy• Steel making

Chemical industry• Hydrogen production• Ethylen production• Styren production• …

Others• Sea water desalination• District heating

Other industries• Production of other metals

(aluminum, …)• Glass making

Electricity• Electricity production

Cement industries• Production of cements• Production of lime

Paper mill• Production of paste• Drying

Process heat for industry


March 2011 Delivering Nuclear Solutions for America’s Energy Challenges

Nuclear IslandPresent or future generationProcess heat and/or electricity

Nuclear IslandPresent or future generationProcess heat and/or electricity

Renewable‐Electric IntegrationElectrolysis or co‐electrolysis driverAdditional electricity to grid

Renewable‐Electric IntegrationElectrolysis or co‐electrolysis driverAdditional electricity to grid

Hydrogen Generation PlantUpgrade of fossil and bio feedstocksCatalytic feedstock for coal to liquids

Hydrogen Generation PlantUpgrade of fossil and bio feedstocksCatalytic feedstock for coal to liquids

Liquid Fuels & Chemicals PlantCoal and biomass to liquidsProcess chemicals

Liquid Fuels & Chemicals PlantCoal and biomass to liquidsProcess chemicals

Carbon FeedstockCoalBiomass

Carbon FeedstockCoalBiomass

Re-thinking Energy — Hybrid Energy Systems


• Dow needs high temperatures in its unit operations. As high as 1000 oC to crack ethane to ethylene

Requires > 3,700 MW & > 22 Million Lbs/h (9979 t/h) of steam to operate

• ~40% of Dow’s energy use is for conversion of petrochemical feedstocks (natural gas components ethane/butane and liquids such as naphtha) to ethylene

At $8/MMBTU natural gas equivalent fuel cost, DOW steam and power bill alone is ~$5 Billion per year

This alone equates to 14 MM tons per year of CO2 alone

• It is not just about EnergyPetrochemical Industry’s raw materials are energy, natural gas liquids, naphtha Dow’s world-wide feedstock & energy demand is almost ~1 MM BBL/day,

estimated cost of ~$32 billion in 2008 (~ 45% total annual operating costs and expenses)

Production shifting overseas.

• Energy Plan America: http://energy.doe.com/perspectives/plan.htm

1 btu = 1055 joulesMM = million metricbbl = barrel

DOW Chemical – Real Example


Delivering Nuclear Solutions for America’s Energy Challenges

U.S. Europe Africa Asia

Past • Peach Bottom (P)• St. Vrain (P)

• AVR (.de, PB)• THTR‐300 (.de, PB)

Cancelled • PBMR (.za, PB)

Operating • HTTR (.jp, P)

• HTR‐10 (.cn, PB)

UnderConstruction

• HTR‐PM (.cn, PB)

Planned NGNP • Allegro (GFR, fast)

(V)HTR current situation


Influence of advanced fuel cycle on life‐time and radio‐toxicity of high level waste (ALI : annual limit on intake)

Concepts for advanced fuel recycling. Option 1 consists of two aqueous separation steps where U, Pu, and Np are extracted in one stage and the minor actinides are extracted in another stage. The GANEX process releases U, Pu, and the minor actinides in one process step. For both options, only the fission products (FP) have to be disposed

Advanced Fuel Cycles


U.S. Europe Russia Asia

Past • Clementine (mercury)

• EBR I/II• SEFOR• FFTF

• Dounreay (DFR, PFR)• Rhapsodie• Superphénix1250 MWe (‐1997)

• Phénix (‐2009)

• BN‐350

Cancelled • Clinch River• IFR

• SNR‐300 (De)

Operating • BN‐600 • Joyo (Jp)• FBTR (In)• Monju (Jp)• CEFR (Cn)

UnderConstruction

• BN‐800 (testing) • PBFR (In)

Planned • ASTRID• ALFRED (lead)

• Allegro (helium)

• BN‐1200 (constr. 2016)

• BN‐1800 (constr. 2020)

• Toshiba S4 (Jp)• JSFR (Jp)• Kalimer (Kr)

SFR-projects


Temperature/Dose exposures


Requirements for materials in future nuclear systems

Technical challenges& Leading physical phenomena

60-year lifetime Fast neutron damage (fuel and core materials)

• Effect of irradiation on microstructure, phase instability, precipitation• Swelling growth, hardening, embrittlement• Effect on tensile properties (yield strength, UTS, elongation…)• Irradiation creep and creep rupture properties• Hydrogen and helium embrittlement

High temperature resistance (SFR > 550°C, V/HTR > 850-950°C)• Effect on tensile properties (yield strength, UTS, elongation…)• High temperature embrittlement• Effect on creep rupture properties• Creep fatigue interaction• Fracture toughness

Corrosion resistance (primary coolant, power conversion, H2 production)• Corrosion and stress-corrosion cracking

(IGSCC, IASCC, hydrogen cracking & chemical compatibility…) F. Carré, CEAF. Carré, CEA


• Thermal creep• Swelling• Irradiation creep • HT-Helium embrittlement• Low Cycle Fatigue• HT corrosion• Crack Growth• Interactions

Most important new damage mechanisms






TOC


• What is creep and stress rupture• Creep laws: Norton law, Monkman Grant rule• Creep of metals and alloys: ferritic, martensitic, austenitic,

nickel-base (solid solution, nickelbase (gamma prime), ODS, intermetallics, refractory alloys

• Creep damage• Extrapolation of creep data• Creep crack growth

Creep and stress rupture


1. Collapse at the ideal strength -(flow when the ideal shear strength is exceeded).

2. Low-temperature plasticity by dislocation glide -(a) limited by a lattice resistance (or Peierls' stress); (b) limited by discrete obstacles; (c) limited by phonon or other drags; and (d) influenced by adiabatic heating.

3. Low-temperature plasticity by twinning.4. Power-law creep by dislocation glide, or glide-plus-climb -

(a) limited by glide processes; (b) limited by lattice-diffusion controlled climb (“high-temperature creep”); (c) limited by core diffusion controlled climb (“low-temperature creep”); (d) power-law breakdown, (the transition from climb-plus-glide to glide alone); (e) Harper-Dorn creep; (f) creep accompanied by dynamic recrystallization.

5. Diffusional Flow -(a) limited by lattice diffusion (“Nabarro-Herring creep”); (b) limited by grain boundary diffusion (“Coble creep”); and (c) interface-reaction controlled diffusional flow.

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The mechanisms may superimpose in complicated ways.

5 types of deformation mechanisms


Thermal creep testing


• Creep occurs under load at high temperature.• Boilers, gas turbine engines, and ovens are some of the systems

that have components that experience creep.• An understanding of high temperature materials behavior is

beneficial in evaluating failures in these types of systems. • Failures involving creep are usually easy to identify due to the

deformation that occurs.• Failures may appear ductile or brittle. Cracking may be either transgranular or intergranular.

• While creep testing is done at constant temperature and constant load actual components may experience damage at various temperatures and loading conditions.

http://www.materialsengineer.com/CA-Creep-Stress-Rupture.htm

Creep and Stress-rupture (1)


• High temperature progressive deformation of a material at constant stress is called creep.

• High temperature is a relative term that is dependent on the materials being evaluated.

• A typical creep curve is shown below: In a creep test a constant load is applied to a tensile specimen maintained at a constant temperature. Strain is then measured over a period of time. The slope of the curve, identified in the figure, is the strain rate of the test during stage II or the creep rate of the material.

• Primary creep, Stage I, is a period of decreasing creep rate. Primary creep is a period of primarily transient creep. During this period deformation takes place and the resistance to creep increases until stage II.

• Secondary creep, Stage II, is a periodof roughly constant creep rate.Stage II is referred to as steady state creep.

• Tertiary creep, Stage III, occurs when there is a reduction in cross sectionalarea due to necking or effective reduction in area due to internal void formation.

http://www.materialsengineer.com/CA-Creep-Stress-Rupture.htm

Creep and Stress-rupture (2)


Temperaturen Dependance

Dynamic recrystallization replaces deformed by undeformed material, permitting a new wave of primary creep, thus accelerating the creep rate.


Stress Dependence

Power-law creep involving cell-formation by climb. Power-law creep limited by glide processes alone is also possible.

Power-law breakdown: glide contributes increasingly to the overall strain-rate.

Diffusional flow by diffusional transport through and round the grains. The strain-rate may be limited by the rate of diffusion or by that of an interface reaction.


Creep mechanisms (schematically)


Different creep regimes


Deformation mechanisms involved in creep include:

• viscous creep: for amorphous solids

• vacancies or atoms : diffusion

• dislocations : slip

• grain boundaries : grain rotation, grain boundary sliding

Basics


Viscous creep for amorphous solids such as many types of plastics is a diffusion dependent processthat is enhanced by increasing the temperature, i.e., thermally activated process, and follows the Arrhenius equation.

Q/RT.

Ae

Where Q is the activation energy for creep in cal/mol, R is the gas constant, and T is the absolute temperature in K.

As seen before, during creep A depends on the applied stress.

Viscous Creep


for amorphous solids

Viscous Creep Illustration

https://upload.wikimedia.org/wikipedia/commons/thumb/9/93/Laminar_shear.svg/800px-Laminar_shear.svg.pnghttps://upload.wikimedia.org/wikipedia/commons/thumb/9/93/Laminar_shear.svg/800px-Laminar_shear.svg.png


In crystalline materials, creep occurs either by• diffusional-

or • dislocation-

creep

Diffusional creep involves the motion of vacancies and this may occur primarily through the grains or along the grain boundaries.

Vacancy motion through the grains is called the Nabarro-Herring mechanism.

Vacancy motion along the grain boundaries is called the Coble mechanism.

Diffusional Creep


Note that the vacancies and atoms move in opposite directions.

Diffusional Creep: Illustration


These strain rates are given by

Nabarro-Herring/RT)(Q

22

.

eTd

Av

Coble/RT)(Q

32

.

eTd

Ab

Where • d is the diameter of the grain,• Qv is the activation energy of self or volume diffusion, and• Qb is the activation energy for grain boundary diffusion, which is usually

half that of self or volume diffusion.• A2 is a material constant.

Diffusional Creep: Equations


In crystalline materials, dislocation creep involves the motion of dislocations where dislocation climb is an important factor.

Dislocation climb means that the edge of the extra plane of atoms move to another plane parallel to the previous plane that it was before.

This dislocation motion also involves the diffusion of vacancies and thus the strain rate is thermally activated having the form,

Dislocation creep

Where m varies from one material to another and is typically on the order of 5.

Thus creep can become quite complex.

More sophisticated methods are often applied to creep by using the Sherby-Dorn parameter and Larson-Miller parameter.

(Q/RT).

eT

A m

Dislocation Creep


Dislocation Creep: Illustration


http://www.tf.uni‐kiel.de/matwis/amat/def_en/http://www.tf.uni‐kiel.de/matwis/amat/def_en/kap_5/backbone/r5_3_3.html

Dislocation Climb


Only • solid solution hardening and • precipitation hardening

remain effective at elevated temperatures to help prevent creep.

Grain boundary sliding during creep causes

a) the creation of voids at an inclusion trapped at the grain boundary and

b) the creation of a void at a triple point where 3 grains are in contact.

Creep


c

time

tertiary

creep

Creep damage starts

Tertiary Creep


• Stress rupture testing is similar to creep testing except that thestresses used are higher than in a creep test.

• Stress rupture testing is always done until failure of the material.• In creep testing the main goal is to determine the minimum creep rate in stage II.

Once a designer knows the materials will creep and has accounted for this deformation a primary goal is to avoid failure of the component.

• Stress rupture tests are used to determine the time to cause failure. Data is plotted log-log as in the charts below. A straight line is usually obtained at each temperature. This information can then be used to extrapolate time to failure for longer times.

• Changes in slope of the stress rupture line are due to structural changes in the material. It is significant to be aware of these changes in material behavior, because they could result in large errors when extrapolating the data.

Creep and Stress-rupture


Modified 9Cr-1Mo ferritic-martensitic steel

Creep rupture Data: Example T91 VHTR RPV steel


Norton‘s Creep Lawσ = A. ε̇n . exp (U/kT)

Monkman Grant Rulet F . ε̇ = Const

ε̇…. secondary creep ratet F … time to fracture

Important creep laws


Norton’s Law for TiAl as an example


Monkman-Grant plot


Temperature limits of RPV materials


Effect Consequence in material Kind of degradation in component

Displacement damageFormation of point defect clusters and dislocation loops

Hardening, embrittlement

Irradiation-induced segregationDiffusion of detrimental elements to grain boundaries

Embrittlement, grain boundary cracking

Irradiation-induced phase transitions

Formation of phases not expected according to phase diagram, phase dissolution

Embrittlement, softening

SwellingVolume increase due to defect clusters and voids

Local deformation, eventually residual stresses

Irradiation creep Irreversible deformationDeformation, reduction of creep life

Helium formation and diffusionVoid formation (inter- and intra-crystalline)

Embrittlement, loss of stress rupture life and creep ductility

Radiation Damage


USC: ultra supercritical coal

Boiler Materials for USC plants


Change matrix tohigher creep resistance (austenitic / fcc)

Change matrix tohigher creep resistance (austenitic / fcc)

Change other austenitic system e.g. Ni‐base (solid solution, precipitation hardening)

Change other austenitic system e.g. Ni‐base (solid solution, precipitation hardening)

Change to higher melting points and deformation mechanisms (refractory alloys, intermetallics )

Change to higher melting points and deformation mechanisms (refractory alloys, intermetallics )

Change to ceramicsChange to ceramics

Introduce stable obstacles to dislocation movement (oxide dispersoids, nano‐clusters)

Introduce stable obstacles to dislocation movement (oxide dispersoids, nano‐clusters)

Possibilities to increase creep properties

Possibilities to increase creep properties

Increase Creep Properties






TOC


• Graphite (as moderator and core material)• Ferritic-martensitic 9 -12%Cr steels• Austenitic superalloys• Oxide dispersion strengthened steels• Intermetallics• Refractory alloys• Ceramics (bulk, reinforced)

Materials for advanced fission and fusion plants


http://www.threeplanes.net/tmartensite.html

Tempered Matensite


Development of ferritic-martensitic steels


Advanced Metallic Materials (ODS)


Intermetallics (Titanium-aluminide)


Graphite SiC/SiC

Ceramic materials


Irradiation Creep Experiment


kT

QneB

Thermal and irradiation creep


kT

QneB

Irradiation creep

Biased flow of point defects (interstitials and vacancies) to sinks

Thermal Creep

Dislocation slip and climb

Diffusion flow

Grain boundary sliding

strongly temperature‐dependence

power law stress‐dependence

n=1 or 2 ?

m 1 or 1/2 ?

Principle of Creep

mnKB

SDBB 0

K: dpa / rate

Thermal Creep – Irradiation Creep


Comparison of irradiation creep compliance B0 as a function of irradiation temperature T. • The large black and grey‐filled symbols indicate light‐ion irradiations before and after damage efficiency correction, respectively:

• He‐implanted ODS PM2000 (•, •) and 19Cr‐ODS (▲,▲)• p‐irradiated ODS Ni‐20Cr‐1ThO2 (■,■), p‐irradiated martensitic DIN1.4914 (◆,◆).

• The small symbols indicate neutron irradiations to doses below 25 dpa (filled symbols) and above 25 dpa (empty symbols):

• ODS MA957 (▼, ▼ ), HT9 ( ■ , ■), HT9 (•), F82H ( ▲), Fe‐16Cr (◆).

neutrons

ions

Irradiaton Creep Compliance (update)


Graphite

HTR‐10 core


Single grain:

without creep

with creepJ.F.B. Payne, NNL

Graphite: anisotropy


CTE: Coefficient of Thermal Expansion

Graphite Irradiation behavior


Graphite Irradiation behavior


Pyrolytic carbon (PyC)






TOC


Addition: Corrosion Groups


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Addition: Water Chemistry


At anodic sites:

Zn Zn2+ + 2e

Al Al3+ + 3e ;

Fe Fe 2+ + 2e

At the Cathodic sites:

2H+ + 2e H2

O2+ 4H+ + 4e 2H2O

O2 + 2H2O + 4e 4OH-

Addition: Water Chemistry


Cathodic Protections

• By controlling the electrode potential so that the metal becomes immune orpassive (cathodic or anodic protection)

• By reducing the rate of corrosion with the aid of corrosion inhibitors added to theenvironment

• By applying an organic or inorganic protective coating• By proper materials selection, designing components

Anodic ProtectionKeeping material in anodic/passive range

Corrosion Protection Methods


Mechanism At Room Temperature At high Temperature

Grain hardening Fully operative Diffusion processes and grain boundary sliding become important, large grains show better properties

Dislocation hardening operative Annealing of dislocationSolid solution strengthening

operative operative

Particle strengthening Orowan bowing or cutting Mainly climbingOrder effects Moderate influence Dislocation movement

through ordered lattice difficult due to diffusion effects

Strengthening of metallic materials


Low temperature

lattice resistance

discrete obstacles resistance

High temperaturePower-law creep involving cell-formation by climb

Power-law breakdown: glide contributes increasingly

Dynamic recrystallization replaces deformed by undeformed material

Diffusional flow by diffusional transport through and round the grains

Overview: Plastic Deformation


Typical for many

Metals and alloysCarbon steels (RT)

Bulk ceramics

Fiber reinforced

ceramics

Single Crystal

Stress-strain behaviour


(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.

The stress-strain curve for an aluminum alloy


http://dolbow.cee.duke.edu/TENSILE/tutorial/node4.html

Stress-strain behaviour


http://dolbow.cee.duke.edu/TENSILE/tutorial/node3.html

Stress Strain: Engineering – Real


In many materials, the yield stress is not very well defined and for this reason a standard has been developed to determine its value.

The standard procedure is to project a line parallel to the initial elastic region starting at 0.002 strain. The 0.002 strain point is often referred to as the 0.2% offset strain point.

0.2% offset strain point


Is a vector, that represents the magnitude and direction of the lattice distortion of dislocation in a crystal lattice

Burgers Vector


The perfect crystal in a) is cut and sheared one atom spacing in b) and c). The line along which the shearing occurs is a screw dislocation. A Burgers vector b is required to close a loop of equal atom spacings around the screw dislocation.

Dislocation: Screw


The perfect crystal in a) is cut and an extra plane of atoms is inserted in b). The bottom edge of the extra plane is an edge dislocation in c). A Burgers vector b is required to close a loop of equal atom spacings around the edge dislocation.

a) b) c)

Dislocation: Edge


A mixed dislocation showing a screw dislocation at the front of the crystal gradually changing to an edge dislocation at the side of the crystal. Note that the line direction of the dislocation is parallel to the Burgers vector of the screw dislocation and perpendicular to the edge dislocation.

Dislocation: Mixed

nuclear fuels and materials - 151-2017-00l · nuclear fuels and materials - 151-2017-00l ⌸lecture...

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