radiation damage accumulation and associated mechanical hardening in thin films and bulk ...

303 Pages·2016·22.74 MB·English

RADIATION DAMAGE ACCUMULATION AND ASSOCIATED
MECHANICAL HARDENING IN THIN FILMS AND BULK
MATERIALS
A Thesis
Presented to
The Academic Faculty
by
Aaron Yehudah Dunn
In Partial Fulfillment
of the Requirements for the Degree
Doctor of Philosophy in the
Woodruff School of Mechanical Engineering
Georgia Institute of Technology
May 2016
Copyright (cid:13)c 2016 by Aaron Yehudah Dunn
RADIATION DAMAGE ACCUMULATION AND ASSOCIATED
MECHANICAL HARDENING IN THIN FILMS AND BULK
MATERIALS
Approved by:
Professor Laurent Capolungo, Advisor Professor Chaitanya Deo
Woodruff School of Mechanical Nuclear and Radiological Engineering,
Engineering Woodruff School of Mechanical
Georgia Institute of Technology Engineering
Georgia Institute of Technology
Professor David McDowell R´emi Dingreville, Ph.D.
Woodruff School of Mechanical Structural and Thermal Analysis
Engineering, School of Materials Science Sandia National Laboratories
and Engineering
Georgia Institute of Technology
Professor Naresh Thadhani Enrique Mart´ınez-Saez, Ph.D.
School of Material Science and Material Science and Technology Division
Engineering Los Alamos National Laboratory
Georgia Institute of Technology
Date Approved: February 25, 2016
To my grandfather, Yehudah Ashkenazi, whose scientific curiosity was unparalleled.
To my parents, Revill and Sara, for their ever-constant support of my scientific endeavors.
To Ed Davis and Don Haynes, two of the greatest teachers around, who have influenced
myself and countless others to fearlessly pursue our passions.
ACKNOWLEDGEMENTS
I would like to thank my advisor Laurent Capolungo for his excellent and thorough support
of my work; R´emi Dingreville and Enrique Mart´ınez-Saez for their support during my time
spent at Sandia National Laboratories and Los Alamos National Laboratories as well as
their scientific contributions and advice throughout this process; all of the people that
have collaborated with me over the course of my studies including Mathieu McPhie, Laura
Agudo-Merida, Ignacio Martin-Bragado, Brittany Muntifering, Khalid Hattar, and Blas
Uberuaga; my outstanding labmates at Georgia Tech: Manas Upahyay, Pierre-Alexandre
Juan, Nicolas Bertin, Cameron Sobie, and Laura Leclercq; and my friends, fellow students,
and bandmates Chris Bishop, Peter McKeon, and Matthew Jordan.
iv
TABLE OF CONTENTS
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
LIST OF ABBREVIATIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix
SUMMARY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx
I INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Perspective: current and future nuclear industry . . . . . . . . . . . 1
1.1.2 Extreme environments for nuclear materials: radiation and temper-
ature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.3 Materialsinuse andunder developmentfornuclearapplicationsand
their microstructural changes under irradiation . . . . . . . . . . . 5
1.1.4 Multi-scale modeling: link between atomic-level material behavior
and macroscopic mechanical properties . . . . . . . . . . . . . . . . 6
1.2 Scientific questions and innovation. . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Scope of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
II RADIATIONDAMAGE,RADIATIONEFFECTS,ANDASSOCIATED
MODELING TOOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1 Radiation damage and radiation effects in metals . . . . . . . . . . . . . . 11
2.1.1 Primary radiation damage . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.2 Defect types and behaviors . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.3 Influence of irradiation conditions on damage accumulation . . . . 18
2.1.4 Influence of pre-irradiated microstructure on damage accumulation 19
2.1.5 Radiation effects: hardening, swelling, and embrittlement. . . . . . 22
2.2 Models of radiation defects and damage accumulation . . . . . . . . . . . . 25
2.2.1 Ab-initio and atomistic models . . . . . . . . . . . . . . . . . . . . 25
2.2.2 Rate theory and cluster dynamics models . . . . . . . . . . . . . . 28
2.2.3 Kinetic Monte Carlo models . . . . . . . . . . . . . . . . . . . . . . 33
2.2.4 Comparison of defect evolution in CD and OKMC models . . . . . 36
2.3 Stochastic cluster dynamics as a method for addressing the limitations of
CD and OKMC models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
v
III SPATIALLY RESOLVED STOCHASTIC CLUSTER DYNAMICS . . 40
3.1 Motivation: computational efficiency with complex models . . . . . . . . . 40
3.2 Derivation of the method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.1 Rate theory background . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.2 Sink strengths in cluster dynamics . . . . . . . . . . . . . . . . . . 45
3.2.3 Reaction rates in units of s−1 inside discrete volume elements . . . 57
3.2.4 Spatially resolved rate equations . . . . . . . . . . . . . . . . . . . . 58
3.2.5 Application of the kinetic Monte Carlo algorithm . . . . . . . . . . 61
3.3 Simulating radiation damage in the form of displacement cascades . . . . . 63
3.3.1 Method 1: Single volume element implantation . . . . . . . . . . . 64
3.3.2 Method 2: Distributed cascade implantation . . . . . . . . . . . . . 65
3.3.3 Method 3: Adaptive meshing . . . . . . . . . . . . . . . . . . . . . 68
3.4 Synchronous parallel SRSCD . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.4.1 Scaling of synchronous parallel SRSCD . . . . . . . . . . . . . . . . 84
3.4.2 Limiting cases of kinetic Monte Carlo domains . . . . . . . . . . . . 94
3.5 Validation of SRSCD by comparison to other simulation techniques . . . . 98
3.5.1 Comparison with rate theory: Frenkel pair implantation . . . . . . 98
3.5.2 Comparison with OKMC: cascade damage in Cu . . . . . . . . . . 101
3.5.3 Comparison with OKMC: Frenkel pairs and helium in α-Fe . . . . 108
3.5.4 Resistivity recovery in electron-irradiated iron: comparison with
OKMC, MFRT, and experiment . . . . . . . . . . . . . . . . . . . . 109
3.6 Summary of Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
IV THE INFLUENCE OF IRRADIATION CONDITIONS AND MATE-
RIAL MICROSTRUCTURE ON DEFECT ACCUMULATION . . . . 117
4.1 Irradiation and microstructural regimes of interest . . . . . . . . . . . . . . 117
4.2 Allowed defects and migration/binding energies in α-Fe . . . . . . . . . . . 119
4.3 Helium and displacement damage under ion irradiation conditions: appli-
cation to thin films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.3.1 Helium desorption from low-temperature implanted and annealed
iron thin films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.3.2 Mechanisms of helium desorption through He V cluster migration 128
m n
vi
4.3.3 Effective helium diffusivity in irradiated α-Fe thin films . . . . . . . 131
4.3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
4.4 Neutron damage accumulation over long timescales: application to bulk
materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
4.4.1 Description of simulation and methodology . . . . . . . . . . . . . . 147
4.4.2 Investigationofinteractionsbetweendisplacementcascadesanddefects149
4.4.3 The impact of PKA energy on damage accumulation . . . . . . . . 152
4.4.4 The effect of traps for SIA loops on microstructure . . . . . . . . . 152
4.4.5 Damage accumulation in neutron-irradiated α-Fe: comparison to
experimental results. . . . . . . . . . . . . . . . . . . . . . . . . . . 157
4.4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
4.5 The impact of grain boundaries on defect accumulation: application to
nanocrystalline metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
4.5.1 The effect of grain size on damage content in nanocrystalline α-Fe . 161
4.5.2 Investigating defect behaviors inside grain boundaries: methodology 164
4.5.3 Impact of grain boundary defect energetics on damage accumulation 170
4.5.4 Analysis of correlations between grain boundary defect behaviors
and damage accumulation . . . . . . . . . . . . . . . . . . . . . . . 186
4.5.5 Discussion: void denuded zones in irradiated metals . . . . . . . . . 198
4.5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
4.6 Summary of Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
V USING SRSCD IN THE CONTEXT OF MULTISCALE MODELING
AND EXPERIMENTAL DESIGN . . . . . . . . . . . . . . . . . . . . . . . 203
5.1 Multiscale modeling of irradiation hardening in metals . . . . . . . . . . . 203
5.2 Damage-induced hardening in neutron-irradiated bulk iron . . . . . . . . . 206
5.2.1 Mesoscale irradiation hardening model . . . . . . . . . . . . . . . . 207
5.2.2 Application: Irradiation hardening of Fe . . . . . . . . . . . . . . . 213
5.2.3 Choice of hardening model . . . . . . . . . . . . . . . . . . . . . . . 222
5.2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
5.3 Using ions to reproduce neutron damage: investigating the equivalence be-
tween dose rate and temperature . . . . . . . . . . . . . . . . . . . . . . . 225
5.3.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
5.3.2 Results: Temperature Shift ∆T . . . . . . . . . . . . . . . . . . . 228
P
vii
5.3.3 Using vacancy concentration as a metric for equivalent damage . . 233
5.3.4 Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . . 234
5.4 Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
VI CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
APPENDIX A — DERIVATION OF KINETIC MONTE CARLO AL-
GORITHM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
APPENDIXB —DEMONSTRATIONOFEQUIVALENCEOFSTOCHAS-
TICANDDETERMINISTICAPPROACHESTORATETHEORYPROB-
LEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
APPENDIX C — DEMONSTRATION OF EQUIVALENCE OF SERIAL
AND PARALLEL KINETIC MONTE CARLO ALGORITHMS . . . 253
APPENDIX D — APPLICATION OF SERIAL AND PARALLEL KMC
ALGORITHMS TO GENERAL COUPLED INITIAL-VALUE PROB-
LEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
APPENDIX E — PRINCIPAL COMPONENTS OF THE CORRELA-
TION MATRIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
viii
LIST OF TABLES
1 Reaction rates for vacancy and interstitial reactions in a finite volume ele-
ment, size V. N indicates the absolute number of species i present in the
i
volume. All rates are in units of s−1. 3D SIA indicates that the SIA cluster
is approximated as a sphere that migrates in three dimensions, 1D SIA indi-
cates that the SIA cluster is approximated as a circular dislocation loop that
migrates in one dimension. In the migration reaction, species X migrates
from volume element i to j, with boundary surface area A and separation
ij
L .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
ij
2 Constants used in Table 1 for calculating reaction rates in SRSCD. Material
constants for α-Fe are given. . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3 MaximumnumberofreactionsinSRSCDinsideasinglevolumeelementwith
n mobile defect types and m stationary defect types. . . . . . . . . . . . . . 69
4 Comparison of simulation box sizes, computation times, and number of steps
of SRSCD simulations using the adaptive meshing algorithm. Results of
these simulations are presented in the following sections. . . . . . . . . . . . 80
5 Material and experimental parameters used in the simulation of Stoller et al.
[207]. Interstitials were assumed perfectly bound to interstitial clusters and
could not dissociate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
6 Material and experimental constants used in the simulation of Caturla et al.
[39] for Cu. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
7 MigrationandbindingparametersusedinSRSCDsimulations. Thediffusion
of HeV and HeV clusters are taken from the values found for Nb, which is
3
assumed to be similar to the behavior of Fe. He V clusters with m/n ≤ 0.5
m n
areassumedtoactasvacancyclustersonly, anddonotallowHedissociation.
VacancyandheliumbindingenergiesinHe V form/n > 0.5aretakenfrom
m n
[216]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
8 Material parameters used in experiment [231] and rate theory [162] studies
of helium desorption from Fe foils . . . . . . . . . . . . . . . . . . . . . . . . 122
9 Migration and binding parameters used in spatially resolved stochastic rate
theory simulation of Helium desorption from Fe foil. The diffusion of HeV
and HeV clusters are taken from the values found for Nb, which is assumed
3
to be similar to the behavior of Fe. For the binding energy of vacancies
to large He V clusters, the He was not taken into account. A functional
m n
form for this binding energy exists [216] but does not apply to clusters where
m << n. Most large HeV clusters in this simulation are of this type. . . . . 124
10 Table of implantation conditions used in simulations. The effect of changing
each parameter on effective diffusivity of helium was studied. . . . . . . . . 134
ix
11 Simulation parameters for neutron irradiation of coarse-grained iron. Pa-
rameters are chosen to match the experiment of Eldrup et al. [67]. Cascade
energy and SIA loop trap density are treated as parameters and their effect
on defect microstructure is discussed in the next section. . . . . . . . . . . . 148
12 Cascade energies (in keV) and volumes (in nm3) used in this simulation.
Cascade volumes were used to determine the probability of ballistic mixing
of defects in the cascade with defects already present in the material. . . . . 151
13 Average binding energies for single vacancies and single interstitials on a
variety of grain boundary types in α-Fe (from Tschopp et al. [225]). All
binding energies are given in eV. . . . . . . . . . . . . . . . . . . . . . . . . 168
14 Grain boundary properties varied in sensitivity analyses carried out in this
section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
15 Correlations between defect binding and migration energies in grain bound-
ariesandmetricsfordamageaccumulationinsimulationsofFrenkelpairirra-
diation of nanocrystalline α-Fe, using simulation parameters given in Section
4.5.2.2. All correlation results are reported in the range [−1,1] . . . . . . . 192
16 (16a) The four eigenvectors of the correlation matrix R most responsible
for the variance in the output variables, referred to a principal components.
Varianceinv d , fori ∈ [1,3000], isgivenbyλ . (16b)Communalityvalues
kj ij k
between output variables and principal components. Communality indicates
the percentage of variation in each output variable that is explained by a
given principal component. . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
17 Iron properties (values taken from Koester et al. [113]) . . . . . . . . . . . . 208
18 Defect concentration parameters (see equation (108)) . . . . . . . . . . . . . 212
19 Rate-dependent parameters (see equation (108)) . . . . . . . . . . . . . . . 219
20 Allowed reactions in problem 5.9 . . . . . . . . . . . . . . . . . . . . . . . . 256
21 Reactions and rates in the converted chaotic system . . . . . . . . . . . . . 259
22 Principal components v and variances λ of the correlation matrix R (top),
k k
and communality of the output variables for each principal component. . . 262
x