Vacancy and self-interstitial atomic diffusion coefficients in concentrated solid solution alloys can have a non-monotonic concentration dependence. Here, the kinetics of monovacancies and ⟨100⟩ dumbbell interstitials in Ni–Fe alloys are assessed using lattice kinetic Monte Carlo (kMC). The non-monotonicity is associated with superbasins, which impels using accelerated kMC methods. Detailed implementation prescriptions for first passage time analysis kMC (FPTA-kMC), mean rate method kMC (MRM-kMC), and accelerated superbasin kMC (AS-kMC) are given. The accelerated methods are benchmarked in the context of diffusion coefficient calculations. The benchmarks indicate that MRM-kMC underestimates diffusion coefficients, while AS-kMC overestimates them. In this application, MRM-kMC and AS-kMC are computationally more efficient than the more accurate FPTA-kMC. Our calculations indicate that composition dependence of migration energies is at the origin of the vacancy’s non-monotonic behavior. In contrast, the difference between formation energies of Ni–Ni, Ni–Fe, and Fe–Fe dumbbell interstitials is at the origin of their non-monotonic diffusion behavior. Additionally, the migration barrier crossover composition—based on the situation where Ni or Fe atom jumps have lower energy barrier than the other one—is introduced. KMC simulations indicate that the interplay between composition dependent crossover of migration energy and geometrical site percolation explains the non-monotonic concentration-dependence of atomic diffusion coefficients.
REFERENCES
1.
Y.
Zhang
, T. T.
Zuo
, Z.
Tang
, M. C.
Gao
, K. A.
Dahmen
, P. K.
Liaw
, and Z. P.
Lu
, “Microstructures and properties of high-entropy alloys
,” Prog. Mater. Sci.
61
, 1
–93
(2014
).2.
J.-W.
Yeh
, “Alloy design strategies and future trends in high-entropy alloys
,” Jom
65
, 1759
–1771
(2013
).3.
E. J.
Pickering
and N. G.
Jones
, “High-entropy alloys: A critical assessment of their founding principles and future prospects
,” Int. Mater. Rev.
61
, 183
–202
(2016
).4.
B.
Gludovatz
, A.
Hohenwarter
, D.
Catoor
, E. H.
Chang
, E. P.
George
, and R. O.
Ritchie
, “A fracture-resistant high-entropy alloy for cryogenic applications
,” Science
345
, 1153
–1158
(2014
).5.
D. B.
Miracle
and O. N.
Senkov
, “A critical review of high entropy alloys and related concepts
,” Acta Mater.
122
, 448
–511
(2017
).6.
C.-Y.
Cheng
, Y.-C.
Yang
, Y.-Z.
Zhong
, Y.-Y.
Chen
, T.
Hsu
, and J.-W.
Yeh
, “Physical metallurgy of concentrated solid solutions from low-entropy to high-entropy alloys
,” Curr. Opin. Solid State Mater. Sci.
21
, 299
–311
(2017
).7.
C.
Lu
, T.
Yang
, K.
Jin
, N.
Gao
, P.
Xiu
, Y.
Zhang
, F.
Gao
, H.
Bei
, W. J.
Weber
, K.
Sun
et al., “Radiation-induced segregation on defect clusters in single-phase concentrated solid-solution alloys
,” Acta Mater.
127
, 98
–107
(2017
).8.
K.
Jin
, C.
Lu
, L. M.
Wang
, J.
Qu
, W. J.
Weber
, Y.
Zhang
, and H.
Bei
, “Effects of compositional complexity on the ion-irradiation induced swelling and hardening in Ni-containing equiatomic alloys
,” Scr. Mater.
119
, 65
–70
(2016
).9.
Y.
Shi
, B.
Yang
, and P. K.
Liaw
, “Corrosion-resistant high-entropy alloys: A review
,” Metals
7
, 43
(2017
).10.
Y.
Zhang
, S.
Zhao
, W. J.
Weber
, K.
Nordlund
, F.
Granberg
, and F.
Djurabekova
, “Atomic-level heterogeneity and defect dynamics in concentrated solid-solution alloys
,” Curr. Opin. Solid State Mater. Sci.
21
, 221
–237
(2017
).11.
T.
Abram
and S.
Ion
, “Generation-IV nuclear power: A review of the state of the science
,” Energy Policy
36
, 4323
–4330
(2008
).12.
J.-W.
Yeh
and S.-J.
Lin
, “Breakthrough applications of high-entropy materials
,” J. Mater. Res.
33
, 3129
–3137
(2018
).13.
K. L.
Murty
and I.
Charit
, “Structural materials for Gen-IV nuclear reactors: Challenges and opportunities
,” J. Nucl. Mater.
383
, 189
–195
(2008
).14.
Y.
Zhang
, T.
Egami
, and W. J.
Weber
, “Dissipation of radiation energy in concentrated solid-solution alloys: Unique defect properties and microstructural evolution
,” MRS Bull.
44
, 798
–811
(2019
).15.
G.
Velişa
, M. W.
Ullah
, H.
Xue
, K.
Jin
, M. L.
Crespillo
, H.
Bei
, W. J.
Weber
, and Y.
Zhang
, “Irradiation-induced damage evolution in concentrated Ni-based alloys
,” Acta Mater.
135
, 54
–60
(2017
).16.
F.
Granberg
, K.
Nordlund
, M. W.
Ullah
, K.
Jin
, C.
Lu
, H.
Bei
, L.
Wang
, F.
Djurabekova
, W.
Weber
, and Y.
Zhang
, “Mechanism of radiation damage reduction in equiatomic multicomponent single phase alloys
,” Phys. Rev. Lett.
116
, 135504
(2016
).17.
R. K.
Adair
, “Neutron cross sections of the elements
,” Rev. Mod. Phys.
22
, 249
(1950
).18.
L. R.
Greenwood
, “A new calculation of thermal neutron damage and helium production in nickel
,” J. Nucl. Mater.
115
, 137
–142
(1983
).19.
L. S.
Darken
, “Diffusion, mobility and their interrelation through free energy in binary metallic systems
,” Trans. AIME
175
, 184
–201
(1948
).20.
J. R.
Manning
, “Cross terms in the thermodynamic diffusion equations for multicomponent alloys
,” Metall. Mater. Trans. B
1
, 499
–505
(1970
).21.
A. D.
Le Claire
, “Solute diffusion in dilute alloys
,” J. Nucl. Mater.
69-70
, 70
–96
(1978
).22.
T.
Helander
and J.
Ågren
, “A phenomenological treatment of diffusion in Al–Fe and Al–Ni alloys having B2-bcc ordered structure
,” Acta Mater.
47
, 1141
–1152
(1999
).23.
K.-Y.
Tsai
, M.-H.
Tsai
, and J.-W.
Yeh
, “Sluggish diffusion in Co–Cr–Fe–Mn–Ni high-entropy alloys
,” Acta Mater.
61
, 4887
–4897
(2013
).24.
D.
Rohrberg
, K.-H.
Spitzer
, L.
Dörrer
, A. J.
Kulińska
, G.
Borchardt
, A.
Fraczkiewicz
, T.
Markus
, M. H. G.
Jacobs
, and R.
Schmid-Fetzer
, “Host atom diffusion in ternary Fe-Cr-Al alloys
,” Metall. Mater. Trans. A
45
, 269
–279
(2014
).25.
J.
Dąbrowa
, W.
Kucza
, G.
Cieślak
, T.
Kulik
, M.
Danielewski
, and J.-W.
Yeh
, “Interdiffusion in the fcc-structured Al-Co-Cr-Fe-Ni high entropy alloys: Experimental studies and numerical simulations
,” J. Alloys Compd.
674
, 455
–462
(2016
).26.
C. G.
Schön
, M. A.
Tunes
, R.
Arróyave
, and J.
Ågren
, “On the complexity of solid-state diffusion in highly concentrated alloys and the sluggish diffusion core-effect
,” Calphad
68
, 101713
(2020
).27.
A.
Paul
, “Comments on “sluggish diffusion in Co–Cr–Fe–Mn–Ni high-entropy alloys” by K.Y. Tsai, M.H. Tsai and J.W. Yeh, Acta Materialia 61 (2013) 4887–4897
,” Scr. Mater.
135
, 153
–157
(2017
).28.
W.
Kucza
, J.
Dąbrowa
, G.
Cieślak
, K.
Berent
, T.
Kulik
, and M.
Danielewski
, “Studies of “sluggish diffusion” effect in Co-Cr-Fe-Mn-Ni, Co-Cr-Fe-Ni and Co-Fe-Mn-Ni high entropy alloys; determination of tracer diffusivities by combinatorial approach
,” J. Alloys Compd.
731
, 920
–928
(2018
).29.
Y. N.
Osetsky
, A. V.
Barashev
, and Y.
Zhang
, “On the mobility of defect clusters and their effect on microstructure evolution in fcc Ni under irradiation
,” Materialia
4
, 139
–146
(2018
).30.
L. K.
Béland
, P.
Brommer
, F.
El-Mellouhi
, J.-F.
Joly
, and N.
Mousseau
, “Kinetic activation-relaxation technique
,” Phys. Rev. E
84
, 046704
(2011
).31.
M.
Trochet
, N.
Mousseau
, L. K.
Béland
, and G.
Henkelman
, “Off-lattice kinetic Monte Carlo methods
,” in Handbook of Materials Modeling: Methods: Theory and Modeling
(Springer, Cham
, 2019
), pp. 1
–29
.32.
L. K.
Béland
, G. D.
Samolyuk
, and R. E.
Stoller
, “Differences in the accumulation of ion-beam damage in Ni and NiFe explained by atomistic simulations
,” J. Alloys Compd.
662
, 415
–420
(2016
).33.
Y. N.
Osetsky
, L. K.
Béland
, and R. E.
Stoller
, “Specific features of defect and mass transport in concentrated fcc alloys
,” Acta Mater.
115
, 364
–371
(2016
).34.
S.
Mahmoud
and N.
Mousseau
, “Long-time point defect diffusion in ordered nickel-based binary alloys: How small kinetic differences can lead to completely long-time structural evolution
,” Materialia
4
, 575
–584
(2018
).35.
Y. N.
Osetsky
, L. K.
Béland
, A. V.
Barashev
, and Y.
Zhang
, “On the existence and origin of sluggish diffusion in chemically disordered concentrated alloys
,” Curr. Opin. Solid State Mater. Sci.
22
, 65
–74
(2018
).36.
Y.
Osetsky
, A. V.
Barashev
, L. K.
Béland
, Z.
Yao
, K.
Ferasat
, and Y.
Zhang
, “Tunable chemical complexity to control atomic diffusion in alloys
,” npj Comput. Mater.
6
, 1
–8
(2020
).37.
Y.
Shim
and J. G.
Amar
, “Semirigorous synchronous sublattice algorithm for parallel kinetic Monte Carlo simulations of thin film growth
,” Phys. Rev. B
71
, 125432
(2005
).38.
M.
Merrick
and K. A.
Fichthorn
, “Synchronous relaxation algorithm for parallel kinetic Monte Carlo simulations of thin film growth
,” Phys. Rev. E
75
, 011606
(2007
).39.
T.
Tian
and K.
Burrage
, “Binomial leap methods for simulating stochastic chemical kinetics
,” J. Chem. Phys.
121
, 10356
–10364
(2004
).40.
A.
Chatterjee
, D. G.
Vlachos
, and M. A.
Katsoulakis
, “Binomial distribution based τ-leap accelerated stochastic simulation
,” J. Chem. Phys.
122
, 024112
(2005
).41.
A.
Chatterjee
and D. G.
Vlachos
, “Multiscale spatial Monte Carlo simulations: Multigriding, computational singular perturbation, and hierarchical stochastic closures
,” J. Chem. Phys.
124
, 064110
(2006
).42.
J.
Goutsias
, “Quasiequilibrium approximation of fast reaction kinetics in stochastic biochemical systems
,” J. Chem. Phys.
122
, 184102
(2005
).43.
A.
Samant
and D. G.
Vlachos
, “Overcoming stiffness in stochastic simulation stemming from partial equilibrium: A multiscale Monte Carlo algorithm
,” J. Chem. Phys.
123
, 144114
(2005
).44.
Y.
Cao
, D. T.
Gillespie
, and L. R.
Petzold
, “The slow-scale stochastic simulation algorithm
,” J. Chem. Phys.
122
, 014116
(2005
).45.
M. A.
Novotny
, “Monte Carlo algorithms with absorbing Markov chains: Fast local algorithms for slow dynamics
,” Phys. Rev. Lett.
74
, 1
–5
(1995
).46.
J.
Munoz
, M.
Novotny
, and S.
Mitchell
, “Rejection-free Monte Carlo algorithms for models with continuous degrees of freedom
,” Phys. Rev. E
67
, 026101
(2003
).47.
B.
Puchala
, M. L.
Falk
, and K.
Garikipati
, “An energy basin finding algorithm for kinetic Monte Carlo acceleration
,” J. Chem. Phys.
132
, 134104
(2010
).48.
A.
Chatterjee
and A. F.
Voter
, “Accurate acceleration of kinetic Monte Carlo simulations through the modification of rate constants
,” J. Chem. Phys.
132
, 194101
(2010
).49.
S. T.
Chill
, M.
Welborn
, R.
Terrell
, L.
Zhang
, J.-C.
Berthet
, A.
Pedersen
, H.
Jónsson
, and G.
Henkelman
, “Eon: Software for long time simulations of atomic scale systems
,” Modell. Simul. Mater. Sci. Eng.
22
, 055002
(2014
).50.
G.
Henkelman
, B. P.
Uberuaga
, and H.
Jónsson
, “A climbing image nudged elastic band method for finding saddle points and minimum energy paths
,” J. Chem. Phys.
113
, 9901
–9904
(2000
).51.
G.
Henkelman
and H.
Jónsson
, “Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points
,” J. Chem. Phys.
113
, 9978
–9985
(2000
).52.
Y. N.
Osetsky
, A. V.
Barashev
, L. K.
Béland
, K.
Ferasat
, Z.
Yao
, and Y.
Zhang
, “Sluggish and chemically biased diffusion by interstitial atoms in Ni-Fe random alloys
” (unpublished).53.
G.
Bonny
, D.
Terentyev
, R. C.
Pasianot
, S.
Poncé
, and A.
Bakaev
, “Interatomic potential to study plasticity in stainless steels: The FeNiCr model alloy
,” Modell. Simul. Mater. Sci. Eng.
19
, 085008
(2011
).54.
S.
Zhao
, G. M.
Stocks
, and Y.
Zhang
, “Defect energetics of concentrated solid-solution alloys from ab initio calculations: Ni 0.5 Co 0.5, Ni 0.5 Fe 0.5, Ni 0.8 Fe 0.2 and Ni 0.8 Cr 0.2
,” Phys. Chem. Chem. Phys.
18
, 24043
–24056
(2016
).55.
M. G.
Evans
and M.
Polanyi
, “Further considerations on the thermodynamics of chemical equilibria and reaction rates
,” Trans. Faraday Soc.
32
, 1333
–1360
(1936
).56.
N.
Mousseau
, L. K.
Béland
, P.
Brommer
, J.-F.
Joly
, F.
El-Mellouhi
, E.
Machado-Charry
, M.-C.
Marinica
, and P.
Pochet
, “The activation-relaxation technique: Art nouveau and kinetic art
,” J. At., Mol., Opt. Phys.
2012
, 14
.57.
M.
Trochet
, L. K.
Béland
, J.-F.
Joly
, P.
Brommer
, and N.
Mousseau
, “Diffusion of point defects in crystalline silicon using the kinetic activation-relaxation technique method
,” Phys. Rev. B
91
, 224106
(2015
).58.
J.
Piochaud
, T.
Klaver
, G.
Adjanor
, P.
Olsson
, C.
Domain
, and C.
Becquart
, “First-principles study of point defects in an fcc Fe-10Ni-20Cr model alloy
,” Phys. Rev. B
89
, 024101
(2014
).59.
K. A.
Fichthorn
and Y.
Lin
, “A local superbasin kinetic Monte Carlo method
,” J. Chem. Phys.
138
, 164104
(2013
).60.
Y.
Lin
and K. A.
Fichthorn
, “The diffusion of a Ga atom on GaAs (001) β 2 (2 × 4): Local superbasin kinetic Monte Carlo
,” J. Chem. Phys.
147
, 152711
(2017
).61.
L. K.
Béland
and N.
Mousseau
, “Long-time relaxation of ion-bombarded silicon studied with the kinetic activation-relaxation technique: Microscopic description of slow aging in a disordered system
,” Phys. Rev. B
88
, 214201
(2013
).62.
L. K.
Béland
, Y. N.
Osetsky
, R. E.
Stoller
, and H.
Xu
, “Slow relaxation of cascade-induced defects in Fe
,” Phys. Rev. B
91
, 054108
(2015
).63.
X.
Xu
, J.
Wang
, J.-P.
Lv
, and Y.
Deng
, “Simultaneous analysis of three-dimensional percolation models
,” Front. Phys.
9
, 113
–119
(2014
).64.
S. J.
Rothman
, L. J.
Nowicki
, and G. E.
Murch
, “Self-diffusion in austenitic Fe-Cr-Ni alloys
,” J. Phys. F: Met. Phys.
10
, 383
–398
(1980
).65.
L.
Barnard
and D.
Morgan
, “Ab initio molecular dynamics simulation of interstitial diffusion in Ni–Cr alloys and implications for radiation induced segregation
,” J. Nucl. Mater.
449
, 225
–233
(2014
).66.
S.
Zhao
, Y.
Osetsky
, and Y.
Zhang
, “Preferential diffusion in concentrated solid solution alloys: NiFe, NiCo and NiCoCr
,” Acta Mater.
128
, 391
–399
(2017
).67.
C.
Lu
, T.
Yang
, L.
Niu
, Q.
Peng
, K.
Jin
, M. L.
Crespillo
, G.
Velisa
, H.
Xue
, F.
Zhang
, P.
Xiu
et al., “Interstitial migration behavior and defect evolution in ion irradiated pure nickel and Ni-xFe binary alloys
,” J. Nucl. Mater.
509
, 237
–244
(2018
).68.
X.
Wang
, K.
Jin
, D.
Chen
, H.
Bei
, Y.
Wang
, W. J.
Weber
, Y.
Zhang
, and K. L.
More
, “Effects of Fe concentration on helium bubble formation in NiFex single-phase concentrated solid solution alloys
,” Materialia
5
, 100183
(2019
).69.
Y.
Zhang
, G. M.
Stocks
, K.
Jin
, C.
Lu
, H.
Bei
, B. C.
Sales
, L.
Wang
, L. K.
Béland
, R. E.
Stoller
, G. D.
Samolyuk
et al., “Influence of chemical disorder on energy dissipation and defect evolution in concentrated solid solution alloys
,” Nat. Commun.
6
, 8736
(2015
).70.
71.
G.
Henkelman
and H.
Jónsson
, “Long time scale kinetic Monte Carlo simulations without lattice approximation and predefined event table
,” J. Chem. Phys.
115
, 9657
–9666
(2001
).72.
L.
Xu
and G.
Henkelman
, “Adaptive kinetic Monte Carlo for first-principles accelerated dynamics
,” J. Chem. Phys.
129
, 114104
(2008
).73.
L.
Xu
, D.
Mei
, and G.
Henkelman
, “Adaptive kinetic Monte Carlo simulation of methanol decomposition on Cu (100)
,” J. Chem. Phys.
131
, 244520
(2009
).74.
J.-F.
Joly
, L. K.
Béland
, P.
Brommer
, F.
El-Mellouhi
, and N.
Mousseau
, “Optimization of the kinetic activation-relaxation technique, an off-lattice and self-learning kinetic Monte-Carlo method
,” J. Phys.: Conf. Ser.
341
, 012007
(2012
).75.
L. K.
Béland
, Y. N.
Osetsky
, R. E.
Stoller
, and H.
Xu
, “Kinetic activation–relaxation technique and self-evolving atomistic kinetic Monte Carlo: Comparison of on-the-fly kinetic Monte Carlo algorithms
,” Comput. Mater. Sci.
100
, 124
–134
(2015
).© 2020 Author(s).
2020
Author(s)
You do not currently have access to this content.
