Abstract
Materials for nuclear applications are subjected to extremely stringent conditions. The incoming energetic particles create different types of defects in the material that modify the system microstructure. These defects diffuse and interact with each other and pre-existing features in the material, leading to alterations of the material properties, and even to failure. To deploy reliable materials for such extreme applications, a deep understanding of the microstructural changes and their relation to material properties is critically required. Synergistic experimental and theoretical studies are paramount to gain such crucial knowledge. In this work we review one theoretical venue developed over the years to first understand and then predict the material response upon irradiation: an object kinetic Monte Carlo (OKMC) approach parameterized to first-principles data. We review the theory behind the kinetic Monte Carlo (KMC) algorithm and the specifics of the OKMC as a mesoscale methodology. We describe density functional theory (DFT) as an ab initio approach that can accurately calculate parameters required by the OKMC as input data to be able to analyze the microstructure evolution of the system. Finally, we show two applications lengthily studied in the literature: the microstructural evolution of both ferritic steels and tungsten under diverse irradiation conditions.
This is a preview of subscription content, log in via an institution.
References
Abe H, Kuramoto E (1999) Interaction of solutes with irradiation-induced defects of electron-irradiated dilute iron alloys. J Nucl Mater 271–272:209–213
Arsenlis A, Cai W, Tang M, Rhee M, Oppelstrup T, Hommes G, Pierce TG, Bulatov VV (2007) Enabling strain hardening simulations with dislocation dynamics. Model Simul Mater Sci Eng 15:553–595
Athènes M, Bulatov VV (2014) Path factorization approach to stochastic simulations. Phys Rev Lett 113(23):230601
Baldwin M, Doerner R (2008) Helium induced nanoscopic morphology on tungsten under fusion relevant plasma conditions. Nucl Fusion 48(3):035001, 00193
Becke AD (1988) Density-functional exchange-energy approximation with correct asymptotic-behavior. Phys Rev A 38(6):3098–3100
Becquart C, Domain C (2007) Ab initio calculations about intrinsic point defects and He in W. Nucl Instrum Methods Phys Res Sect B Beam Interact Mater Atoms 255(1):23–26
Becquart C, Domain C (2009) A density functional theory assessment of the clustering behaviour of He and H in tungsten. J Nucl Mater 386–388:109–111
Becquart CS, Domain C (2010) Modeling microstructure and irradiation effects. Metall Mater Trans A 42A:852
Becquart C, Domain C, Sarkar U, DeBacker A, Hou M (2010) Microstructural evolution of irradiated tungsten: ab initio parameterisation of an OKMC model. J Nucl Mater 403(1–3): 75–88
Becquart CS, Barthe MF, De Backer A (2011) Modelling radiation damage and He production in tungsten. Phys Scripta T145:014048
Bertin N, Upadhyay MV, Pradalier C, Capolungo L (2015) A FFT-based formulation for efficient mechanical fields computation in isotropic and anisotropic periodic discrete dislocation dynamics. Model Simul Mater Sci Eng 23(6):065009
Bortz AB, Kalos MH, Lebowitz JL (1975) A new algorithm for Monte Carlo simulation of Ising spin systems. J Comput Phys 17:10–18
Castin N, Bakaev A, Bonny G, Sand A, Malerba L, Terentyev D (2017) On the onset of void swelling in pure tungsten under neutron irradiation: an object kinetic Monte Carlo approach. J Nucl Mater 493:280–293
Castin N, Bonny G, Bakaev A, Ortiz C, Sand A, Terentyev D (2018) Object kinetic Monte Carlo model for neutron and ion irradiation in tungsten: impact of transmutation and carbon impurities. J Nucl Mater 500:15–25
Caturla MJ, Soneda N, Alonso E, Wirth BD, de la Rubia TD, Perlado JM (2000) Comparative study of radiation damage accumulation in Cu and Fe. J Nucl Mater 276:13
Ceperley DM, Alder BJ (1980) Ground state of the electron gas by a stochastic method. Phys Rev Lett 45(7):4
Chatterjee A, Vlachos DG (2007) An overview of spatial microscopic and accelerated kinetic Monte Carlo methods. J Comput-Aided Mater Des 14(2):253–308
Correa AA, Kohanoff J, Artacho E, Sánchez-Portal D, Caro A (2012) Nonadiabatic forces in ion-solid interactions: the initial stages of radiation damage. Phys Rev Lett 108(21):213201
Dai Y, Victoria M (1997) Defect cluster structure and tensile properties of copper single crystals irradiated with 600 MeV protons. MRS Proc 439:319–324
De Backer A, Sand A, Ortiz CJ, Domain C, Olsson P, Berthod E, Becquart CS (2016) Primary damage in tungsten using the binary collision approximation, molecular dynamic simulations and the density functional theory. Phys Scripta T167:014018
Domain C, Becquart CS, Malerba L (2004) Simulation of radiation damage in Fe alloys: an object kinetic Monte Carlo approach. J Nucl Mater 335:121
Draeger EW, Andrade X, Gunnels JA, Bhatele A, Schleife A, Correa AA (2017) Massively parallel first-principles simulation of electron dynamics in materials. J Parallel Distrib Comput 106: 205–214
Elcock EW (1959) Vacancy diffusion in ordered alloys. Proc Phys Soc 73:250
Elcock EW, McCombie CW (1957) Vacancy diffusion in binary ordered alloys. Phys Rev Lett Editor 109:605
El-Mellouhi F, Mousseau N, Lewis LJ (2008) Kinetic activation-relaxation technique: an off-lattice self-learning kinetic Monte Carlo algorithm. Phys Rev B 78:153202
Eyring H, Walter J, Kimball GE (1944) Quantum chemistry, 1st edn. Wiley, New York
Feibelman PJ (1990) Diffusion path for an Al adatom on Al(001). Phys Rev Lett 65(6):729–732
Fernandez N, Ferro Y, Kato D (2015) Hydrogen diffusion and vacancies formation in tungsten: density functional theory calculations and statistical models. Acta Mater 94:307–318
Fichthorn KA, Lin Y (2013) A local superbasin kinetic Monte Carlo method. J Chem Phys 138(16):164104
Fu CC, Dalla Torre J, Willaime F, Bocquet J-L, Barbu A (2005) Multiscale modelling of defect kinetics in irradiated iron. Nature Mater 4:68
Gámez L, Gámez B, Caturla MJ, Terentyev D, Perlado JM (2011) Object Kinetic Monte Carlo calculations of irradiated Fe-Cr dilute alloys: the effect of the interaction radius between substitutional Cr and self-interstitial Fe. Nucl Instrum Methods Phys Res Sect B Beam Interact Mater Atoms 269(14):1684–1688
Gharaee L, Marian J, Erhart P (2016) The role of interstitial binding in radiation induced segregation in W-Re alloys. J Appl Phys 120(2):025901
Gibson MA, Bruck J (2000) Efficient exact stochastic simulation of chemical systems with many species and many channels. J Phys Chem A 104(9):1876–1889
Gillespie D (1976) A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J Comput Phys 22:403–434
Gillespie D (1977) Exact stochastic simulation of coupled chemical reactions. J Phys Chem 81:2340–2361
Gilmer GH, Bennema P (1972) Simulation of crystal growth with surface diffusion. J Appl Phys 43(4):1347–1360
Glensk A, Grabowski B, Hickel T, Neugebauer J (2015) Understanding anharmonicity in FCC materials: from its origin to ab initio strategies beyond the quasiharmonic approximation. Phys Rev Lett 114(19):195901
Grabowski B, Hickel T, Neugebauer J (2007) Ab initio study of the thermodynamic properties of nonmagnetic elementary FCC metals: exchange-correlation-related error bars and chemical trends. Phys Rev B 76(2)
Grabowski B, Hickel T, Neugebauer J (2011) Formation energies of point defects at finite temperatures. Phys Status Solidi B 248(6):1295–1308, 00049. https://doi.org/10.1002/pssb.201046302
Hanusse P, Blanche A (1981) A Monte Carlo method for large reaction diffusion systems. J Chem Phys 74:6148
Heinisch HL (1990) Computer simulation of high energy displacement cascades. Radiat Eff Defects Solids 113:53
Henkelman G, Jonsson H (1999) A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives. J Chem Phys 111(15):7010–7022, 01295
Henkelman G, Jonsson H (2000) Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. J Chem Phys 113(22) 9978–9985
Henkelman G, Jonsson H (2001) Long time scale kinetic Monte Carlo simulations without lattice approximation and predefined event table. J Chem Phys 115(21):9657
Henkelman G, Uberuaga BP, Jonsson H (2000) A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J Chem Phys 113(22):9901–9904
Henriksson KOE, Nordlund K, Krasheninnikov A, Keinonen J (2005) Difference in formation of hydrogen and helium clusters in tungsten. Appl Phys Lett 87(16):163113
Hohenberg P, Kohn W (1964) Inhomogenous electron gas. Phys Rev B 136:864–B871
Huang G-Y, Juslin N, Wirth BD (2016) First-principles study of vacancy, interstitial, noble gas atom interstitial and vacancy clusters in BCC-W. Comput Mater Sci 123:121–130
Huang CH, Gharaee L, Zhao Y, Erhart P, Marian J (2017) Mechanism of nucleation and incipient growth of Re clusters in irradiated W-Re alloys from kinetic Monte Carlo simulations. Phys Rev B 96:094108
Huang CH, Gilbert MR, Marian J (2018) Simulating irradiation hardening in tungsten under fast neutron irradiation including Re production by transmutation. J Nucl Mat 499:204–215
Hudson TS, Dudarev SL, Caturla MJ, Sutton AP (2005) Effects of elastic interactions on post-cascade radiation damage evolution in kinetic monte carlo simulations. Philos Mag 85:661–675
Hunter A, Saied F, Le C, Koslowski M (2011) Large-scale 3D phase field dislocation dynamics simulations on high-performance architectures. Int J High Perform Comput Appl 25(2): 223–235, 00026
Jiménez F, Ortiz C (2016) A GPU-based parallel object kinetic monte carlo algorithm for the evolution of defects in irradiated materials. Comput Mater Sci 113:178–186
Kampen NGV (1992) Stochastic processes in physics and chemistry, 2nd edn. Elsevier, Amsterdam
Kohn W, Sham LJ (1965) Self-consistent equations including exchange and correlation effects. Phys Rev 140(4A):1133
Körmann F, Dick A, Grabowski B, Hallstedt B, Hickel T, Neugebauer J (2008) Free energy of bcc iron: integrated ab initio derivation of vibrational, electronic, and magnetic contributions. Phys Rev B 78(3):033102
Langreth DC, Mehl MJ (1983) Beyond the local-density approximation in calculations of ground-state electronic properties. Phys Rev B 28(4):1809–1834
Lasa A, Tahtinen SK, Nordlund K (2014) Loop punching and bubble rupture causing surface roughening A model for W fuzz growth. EPL (Europhys Lett) 105(2):25002, 00010
Lu G-H, Zhou H-B, Becquart CS (2014) A review of modelling and simulation of hydrogen behaviour in tungsten at different scales. Nucl Fusion 54(8):086001
Malerba L, Caro A, Wallenius J (2008) Multiscale modelling of radiation damage and phase transformations: The challenge of FeCr alloys. J Nucl Mater 382:112–125
Martin-Bragado I, Tian S, Johnson M, Castrillo P, Pinacho R, Rubio J, Jaraiz M (2006) Modeling charged defects, dopant diffusion and activation mechanisms for TCAD simulations using kinetic Monte Carlo. Nucl Instrum Methods Phys Res Sect B Beam Interact Mater Atoms 253(1–2):63–67
Martin-Bragado I, Rivera A, Valles G, Gomez-Selles JL, Caturla MJ (2013) MMonCa: an object kinetic Monte Carlo simulator for damage irradiation evolution and defect diffusion. Comput Phys Commun 184(12):2703–2710, 00037
Martinez E, Uberuaga BP (2015) Mobility and coalescence of stacking fault tetrahedra in cu. Sci Rep 5:9084
Martínez E, Marian J, Kalos M, Perlado J (2008) Synchronous parallel kinetic Monte Carlo for continuum diffusion-reaction systems. J Comput Phys 227(8):3804–3823, 00032
Martínez E, Monasterio PR, Marian J (2011) Billion-atom synchronous parallel kinetic monte carlo simulations of critical 3D Ising systems. J Comp Phys 230:1359–1369
Mason DR, Yi X, Kirk MA, Dudarev SL (2014) Elastic trapping of dislocation loops in cascades in ion-irradiated tungsten foils. J Phys Condens Matter 26(37):375701
Maury F, Lucasson P, Lucasson A, Faudot F, Bigot J (1987) A study of irradiated FeCr alloys: deviations from Matthiessen’s rule and interstitial migration. J Phys F Metal Phys 17(5): 1143–1165
Nguyen-Manh D, Dudarev S (2006) Multi-scale modelling of defect behavior in BCC transition metals and iron alloys for future fusion power plants. Mater Sci Eng A 423(1–2):74–78
Niklasson A, Tymczak C, Challacombe M (2006) Time-reversible born-oppenheimer molecular dynamics. Phys Rev Lett 97(12):123001
Novotny MA (1995) Monte Carlo algorithms with absorbing Markov chains: fast local algorithms for slow dynamics. Phys Rev Lett 74(1):1
Oda T, Zhu D, Watanabe Y (2015) Kinetic Monte Carlo simulation on influence of vacancy on hydrogen diffusivity in tungsten. J Nucl Mater 467:439–447
Ohsawa K, Goto J, Yamakami M, Yamaguchi M, Yagi M (2010) Trapping of multiple hydrogen atoms in a tungsten monovacancy from first principles. Phys Rev B 82(18):184117
Olsson P (2009) Ab initio study of interstitial migration in Fe-Cr alloys. J Nucl Mater 386–388: 86–89
Olsson P, Domain C, Wallenius J (2007) Ab initio study of Cr interactions with point defects in bcc Fe. Phys Rev B 75:014110
Olsson P, Becquart CS, Domain C (2016) Ab initio threshold displacement energies in iron. Mater Res Lett 4(4):219–225
Opplestrup T, Bulatov V, Gilmer G, Kalos M, Sadigh B (2006) First-passage Monte Carlo algorithm: diffusion without all the Hops. Phys Rev Lett 97(23):230602
Perdew JP, Chevary JA, Vosko SH, Jackson KA, Pederson MR, Singh DJ, Fiolhais C (1992) Atoms, molecules, solids, and surfaces: applications of the generalized gradient approximation for exchange and correlation. Phys Rev B 46(11):6671–6687
Perini A, Jacucci G, Martin G (1984) Cluster free energy in the simple-cubic Ising model. Phys Rev B 29(5):2689–2697
Schulze TP (2002) Kinetic Monte Carlo simulations with minimal searching. Phys Rev E 65(3):036704
Shim Y, Amar J (2005a) Rigorous synchronous relaxation algorithm for parallel kinetic Monte Carlo simulations of thin film growth. Phys Rev B 71(11):115436
Shim Y, Amar JG (2005b) Semirigorous synchronous sublattice algorithm for parallel kinetic monte carlo simulations of thin film growth. Phys Rev B 71:125432
Sholl DS, Steckel JA (2009) Density functional theory a practical introduction. Wiley, Hoboken
Slepoy A, Thompson AP, Plimpton SJ (2008) A constant-time kinetic Monte Carlo algorithm for simulation of large biochemical reaction networks. J Chem Phys 128(20):205101
Söderlind P, Yang LH, Moriarty JA, Wills JM (2000) First-principles formation energies of monovacancies in BCC transition metals. Phys Rev B 61(4):2579–2586
Sørensen MR, Voter AF (2000) Temperature-accelerated dynamics for simulation of infrequent events. J Chem Phys 112(21):9599–9606
Subramanian G, Perez D, Uberuaga BP, Tomé CN, Voter AF (2013) Method to account for arbitrary strains in kinetic Monte Carlo simulations. Phys Rev B 87(14):144107
Suzudo T, Yamaguchi M, Hasegawa A (2014) Stability and mobility of rhenium and osmium in tungsten: first principles study. Model Simul Mater Sci Eng 22(7):075006
Takaki S, Fuss J (1983) Dedek HKU, Schultz H. The resistivity recovery of high purity and carbon doped iron following low electron irradiation. Rad Eff 79:87–122
Trushin O, Karim A, Kara A, Rahman TS (2005) Self-learning kinetic Monte Carlo method: application to Cu(111). Phys Rev B 72:115401
Uberuaga BP, Hoagland RG, Voter AF, Valone SM (2007) Direct Transformation of Vacancy Voids to Stacking Fault Tetrahedra. Phys Rev Lett 99:135501
Uberuaga BP, Martínez E, Perez D, Voter AF (2018) Discovering mechanisms relevant for radiation damage evolution. Comput Mater Sci 147:282–292
Valles G, González C, Martin-Bragado I, Iglesias R, Perlado J, Rivera A (2015a) The influence of high grain boundary density on helium retention in tungsten. J Nucl Mater 457:80–87
Valles G, Cazalilla AL, Gonzalez C, Martin-Bragado I, Prada A, Iglesias R, Perlado J, Rivera A (2015b) A multiscale approach to defect evolution in tungsten under helium irradiation. Nucl Instrum Methods Phys Res Sect B Beam Interact Mater Atoms 352:100–103
Valles G, Panizo-Laiz M, González C, Martin-Bragado I, González-Arrabal R, Gordillo N, Iglesias R, Guerrero C, Perlado J, Rivera A (2017a) Influence of grain boundaries on the radiation-induced defects and hydrogen in nanostructured and coarse-grained tungsten. Acta Mater 122:277–286
Valles G, Martin-Bragado I, Nordlund K, Lasa A, Björkas C, Safi E, Perlado J, Rivera A (2017b) Temperature dependence of underdense nanostructure formation in tungsten under helium irradiation. J Nucl Mater 490:108–114
Vattré A, Jourdan T, Ding H, Marinica M-C, Demkowicz MJ (2016) Non-random walk diffusion enhances the sink strength of semicoherent interfaces. Nat Commun 7:10424
Vineyard GH (1957) Frequency factors and isotope effects in solid state rate processes. J Phys Chem Solids 3(1–2):121–127
Voter AF (1997) Hyperdynamics: accelerated molecular dynamics of infrequent events. Phys Rev Lett 78(20):3908
Voter AF (1998) Parallel replica method for dynamics of infrequent events. Phys Rev B 57(22):R13985
Voter AF (2007) Introduction to the kinetic Monte Carlo method, Ch. 1. Springer, Dordrecht
Voter AF, Doll JD (1984) Transition state theory description of surface self-diffusion: comparison with classical trajectory results. J Chem Phys 80:5832
Voter AF, Doll JD (1985) Dynamical corrections to transition state theory for multistate systems: surface self-diffusion in the rare-event regime. J Chem Phys 82:80–92
Was GS (2007) Fundamentals of radiation materials science. Springer, Berlin/Heidelberg/New York
Wen M, Takahashi A, Ghoniem NM (2009) Kinetics of self-interstitial cluster aggregation near dislocations and their influence on hardening. J Nucl Mater 392:386–395
Witt WC, del Rio BG, Dieterich JM, Carter EA (2018) Orbital-free density functional theory for materials research. J Mater Res 33:1–19
Xu L, Henkelman G (2008) Adaptive kinetic monte carlo for first-principles accelerated dynamics. J Chem Phys 129:114104
Xu D, Wirth BD, Li M, Kirk MA (2012) Defect microstructural evolution in ion irradiated metallic nanofoils: kinetic Monte Carlo simulation versus cluster dynamics modeling and in situ transmission electron microscopy experiments. Appl Phys Lett 101(10):101905, 00009
Young WM, Elcock EW (1966) Monte carlo studies of vacancy migration in binary ordered alloys: I. Proc Phys Soc 89:735
Zhang J, Zhang H, Ye H, Zheng Y (2016) Free-end adaptive nudged elastic band method for locating transition states in minimum energy path calculation. J Chem Phys 145(9):094104
Zhu T, Li J, Samanta A, Kim HG, Suresh S (2007) Interfacial plasticity governs strain rate sensitivity and ductility in nanostructured metals. Proc Natl Acad Sci 104(9):3031–3036
Zinkle SJ, Farrell K (1989) Void swelling and defect cluster formation in reactor-irradiated copper. J Nucl Mater 168:262–267
Acknowledgements
The authors thank Malvin H. Kalos, Alfredo Caro, Frédéric Soisson, Vasily Bulatov, Blas Uberuaga, Arthur F. Voter, and Danny Perez for many useful discussions. E.M. wants to thank Gustavo Esteban for useful comments on the manuscript. E.M. acknowledges the support of the U.S. DOE, Office of Science, Advanced Scientific Computing Research and Fusion Energy Sciences through the Scientific Discovery through Advanced Computing (SciDAC) project on Plasma-Surface Interactions for this work. This research used resources provided by the LANL Institutional Computing Program. LANL, an affirmative action/equal opportunity employer, is operated by Los Alamos National Security, LLC, for the National Nuclear Security Administration of the US DOE under contract DE-AC52-06NA25396.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this entry
Cite this entry
Martínez, E., Caturla, M.J., Marian, J. (2018). DFT-Parameterized Object Kinetic Monte Carlo Simulations of Radiation Damage. In: Andreoni, W., Yip, S. (eds) Handbook of Materials Modeling. Springer, Cham. https://doi.org/10.1007/978-3-319-50257-1_137-1
Download citation
DOI: https://doi.org/10.1007/978-3-319-50257-1_137-1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-50257-1
Online ISBN: 978-3-319-50257-1
eBook Packages: Springer Reference Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics