Kinetic Monte Carlo Simulations for Solid State Ionics: Case Studies with the MOCASSIN Program

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Kinetic Monte Carlo simulations are a useful tool to predict and analyze the ionic conductivity in crystalline materials. We present here the basic functionalities and capabilities of our recently published Monte Carlo software for solid state ionics called MOCASSIN, exemplified by simulations of several model systems and real materials. We address the simulation of tracer correlation factors for various structures, the correlation in systems with complex migration mechanisms like interstitialcy or vehicle transport, and the impact of defect interactions on ionic conductivity. Simulations of real materials include a review of oxygen vacancy migration in doped ceria, oxygen interstitial migration in La-rich melilites, and proton conduction in acceptor doped fully hydrated barium zirconate. The results reveal the impact of defect interactions on the ionic conductivity and the importance of the defect distribution. Combinations of these effects can lead to unexpected transport behavior in solid state ionic materials, especially for multiple mobile species. Kinetic Monte Carlo simulations are therefore useful to interpret experimental data which shows unexpected behavior regarding the dependence on temperature and composition.

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Diffusion Foundations (Volume 29)

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117-142

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April 2021

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© 2021 Trans Tech Publications Ltd. All Rights Reserved

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[1] G.W. King, Monte-Carlo method for solving diffusion problems, Ind. Eng. Chem. 43(11) (1951) 2475-2478.

DOI: 10.1021/ie50503a021

Google Scholar

[2] P. Flinn, G. McManus, Monte Carlo calculation of the order-disorder transformation in the body-centered cubic lattice, Phys. Rev. 124(1) (1961) 54.

DOI: 10.1103/physrev.124.54

Google Scholar

[3] J.R. Beeler, Displacement Spikes in Cubic Metals. I. a-Iron, Copper, and Tungsten, Phys. Rev. 150(2) (1966) 470-487.

DOI: 10.1103/physrev.150.470

Google Scholar

[4] J.R. Beeler, Radiation effects, computer experiments, North-Holland Pub. Co. ; Elsevier Science Pub. Co. distributor, Amsterdam ; New York, (1983).

Google Scholar

[5] C. Bennett, B. Alder, Persistence of vacancy motion in hard sphere crystals, J. Phys. Chem. Solids 32(9) (1971) 2111-2122.

DOI: 10.1016/s0022-3697(71)80388-8

Google Scholar

[6] H.J. De Bruin, G.E. Murch, Diffusion correlation effects in non-stoichiometric solids, Philos. Mag. A 27(6) (1973) 1475-1488.

DOI: 10.1080/14786437308226902

Google Scholar

[7] G.E. Murch, 7 - Simulation of Diffusion Kinetics with the Monte Carlo Method, in: G.E. Murch, A.S. Nowick (Eds.), Diffusion in Crystalline Solids, Academic Press1984, pp.379-427.

DOI: 10.1016/b978-0-12-522662-2.50012-1

Google Scholar

[8] A.F. Voter, Introduction to the kinetic monte carlo method, in: K.E. Sickafus, E.A. Kotomin, B.P. Uberuaga (Eds.), Radiation Effects in Solids, Springer Netherlands, Dordrecht, 2007, p.1–23.

Google Scholar

[9] D.J. Fisher, Monte Carlo diffusion studies, Trans Tech Publications, Pfaffikon, Switzerland, (2015).

Google Scholar

[10] G.E. Murch, I. Belova, Monte Carlo Methods in Solid State Diffusion, Handbook of Solid State Diffusion, Volume 1 (2017).

DOI: 10.1016/b978-0-12-804287-8.00009-9

Google Scholar

[11] N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller, Equation of State Calculations by Fast Computing Machines, J. Chem. Phys. 21(6) (1953) 1087–1092.

DOI: 10.2172/4390578

Google Scholar

[12] G.E. Murch, Monte Carlo calculation as an aid in teaching solid-state diffusion, Am. J. Phys. 47(1) (1979) 78.

DOI: 10.1119/1.11678

Google Scholar

[13] D.T. Gillespie, A general method for numerically simulating the stochastic time evolution of coupled chemical reactions, J. Comp. Phys. 22(4) (1976) 403-434.

DOI: 10.1016/0021-9991(76)90041-3

Google Scholar

[14] S.A. Serebrinsky, Physical time scale in kinetic Monte Carlo simulations of continuous-time Markov chains, Phys. Rev. E 83(3) (2011).

DOI: 10.1103/physreve.83.037701

Google Scholar

[15] S. Plimpton, A. Thompson, A. Slepoy, SPPARKS kinetic Monte Carlo simulator, (2012).

Google Scholar

[16] J. Purton, J.C. Crabtree, S. Parker, DL_MONTE: a general purpose program for parallel Monte Carlo simulation, Mol. Sim. 39(14-15) (2013) 1240-1252.

DOI: 10.1080/08927022.2013.839871

Google Scholar

[17] M.J. Hoffmann, S. Matera, K. Reuter, kmos: A lattice kinetic Monte Carlo framework, Comp. Phys. Comm. 185(7) (2014) 2138-2150.

DOI: 10.1016/j.cpc.2014.04.003

Google Scholar

[18] M. Leetmaa, N.V. Skorodumova, KMCLib: A general framework for lattice kinetic Monte Carlo (KMC) simulations, Comput. Phys. Commun. 185(9) (2014) 2340-2349.

DOI: 10.1016/j.cpc.2014.04.017

Google Scholar

[19] B. Morgan, A Python Lattice-Gas Monte Carlo Module, J. Open Source Soft. 2(13) (2017) 247.

DOI: 10.21105/joss.00247

Google Scholar

[20] S. Eisele, S. Grieshammer, MOCASSIN: Metropolis and kinetic Monte Carlo for solid electrolytes, J. Comp. Chem. 41(31) (2020) 2663-2677.

DOI: 10.1002/jcc.26418

Google Scholar

[21] A. Van der Ven, G. Ceder, M. Asta, P.D. Tepesch, First-principles theory of ionic diffusion with nondilute carriers, Phys. Rev. B 64(18) (2001).

DOI: 10.1103/physrevb.64.184307

Google Scholar

[22] I.V. Belova, G.E. Murch, Tracer correlation factors in the random alloy, Philosophical Magazine A 80(7) (2000) 1469-1479.

DOI: 10.1080/01418610008212131

Google Scholar

[23] G.E. Murch, The Haven Ratio in Fast Ionic Conductors, Solid State Ionics 7(3) (1982) 177-198.

DOI: 10.1016/0167-2738(82)90050-9

Google Scholar

[24] H. Sato, R. Kikuchi, Cation Diffusion and Conductivity in Solid Electrolytes. I, J. Chem. Phys. 55(2) (1971) 677-702.

Google Scholar

[25] A.R. Allnatt, E.L. Allnatt, Computer simulation of phenomenological coefficients for atom transport in a random alloy, Philos. Mag. A 49(5) (1984) 625-635.

DOI: 10.1080/01418618408233291

Google Scholar

[26] G.E. Murch, Z. Qin, Tracer and collective correlation factors in solid state diffusion, Defect and Diffusion Forum 109 (1994) 1-18.

DOI: 10.4028/www.scientific.net/ddf.109-110.1

Google Scholar

[27] A.D. Murray, G.E. Murch, C.R.A. Catlow, A new hybrid scheme of computer simulation based on Hades and Monte Carlo: Application to ionic conductivity in Y3+ doped CeO2, Solid State Ionics 18-19 (1986) 196-202.

DOI: 10.1016/0167-2738(86)90111-6

Google Scholar

[28] A. Oaks, D. Yun, B. Ye, W.-Y. Chen, J.F. Stubbins, Kinetic Monte Carlo model of defect transport and irradiation effects in La-doped CeO2, J. Nucl. Mater. 414(2) (2011) 145-149.

DOI: 10.1016/j.jnucmat.2011.02.030

Google Scholar

[29] P.P. Dholabhai, S. Anwar, J.B. Adams, P. Crozier, R. Sharma, Kinetic lattice Monte Carlo model for oxygen vacancy diffusion in praseodymium doped ceria: Applications to materials design, J. Solid. State. Chem. 184(4) (2011) 811–817.

DOI: 10.1016/j.jssc.2011.02.004

Google Scholar

[30] P.P. Dholabhai, S. Anwar, J.B. Adams, P.A. Crozier, R. Sharma, Predicting the optimal dopant concentration in gadolinium doped ceria: a kinetic lattice Monte Carlo approach, Model. Simul. Mater. Sci. Eng. 20(1) (2011) 015004.

DOI: 10.1088/0965-0393/20/1/015004

Google Scholar

[31] P.P. Dholabhai, J.B. Adams, A blend of first-principles and kinetic lattice Monte Carlo computation to optimize samarium-doped ceria, J. Mater. Sci. 47(21) (2012) 7530-7541.

DOI: 10.1007/s10853-012-6398-y

Google Scholar

[32] S. Grieshammer, B.O.H. Grope, J. Koettgen, M. Martin, A combined DFT + U and Monte Carlo study on rare earth doped ceria, Phys. Chem. Chem. Phys. 16(21) (2014) 9974.

DOI: 10.1039/c3cp54811b

Google Scholar

[33] J. Koettgen, S. Grieshammer, P. Hein, B.O.H. Grope, M. Nakayama, M. Martin, Understanding the ionic conductivity maximum in doped ceria: trapping and blocking, Phys. Chem. Chem. Phys. 20 (2018) 14291-14321.

DOI: 10.1039/c7cp08535d

Google Scholar

[34] S. Grieshammer, S. Eisele, J. Koettgen, Modeling Oxygen Ion Migration in the CeO2-ZrO2-Y2O3 Solid Solution, J. Phys. Chem. C 122(33) (2018) 18809-18817.

DOI: 10.1021/acs.jpcc.8b04361

Google Scholar

[35] J.O. Nilsson, M. Leetmaa, O.Y. Vekilova, S.I. Simak, N.V. Skorodumova, Oxygen diffusion in ceria doped with rare-earth elements, Phys. Chem. Chem. Phys. 19(21) (2017) 13723-13730.

DOI: 10.1039/c6cp06460d

Google Scholar

[36] R. Krishnamurthy, Y.G. Yoon, D. Srolovitz, R. Car, Oxygen diffusion in yttria‐stabilized zirconia: a new simulation model, J. Am. Ceram. Soc. 87(10) (2004) 1821-1830.

DOI: 10.1111/j.1151-2916.2004.tb06325.x

Google Scholar

[37] R. Pornprasertsuk, P. Ramanarayanan, C.B. Musgrave, F.B. Prinz, Predicting ionic conductivity of solid oxide fuel cell electrolyte from first principles, J. Appl. Phys. 98(10) (2005) 103513.

DOI: 10.1063/1.2135889

Google Scholar

[38] E. Lee, F. Prinz, W. Cai, Enhancing ionic conductivity of bulk single-crystal yttria-stabilized zirconia by tailoring dopant distribution, Physical Review B 83(5) (2011).

DOI: 10.1103/physrevb.83.052301

Google Scholar

[39] J.-P. Eufinger, M. Daniels, K. Schmale, S. Berendts, G. Ulbrich, M. Lerch, H.-D. Wiemhöfer, J. Janek, The model case of an oxygen storage catalyst - non-stoichiometry, point defects and electrical conductivity of single crystalline CeO2-ZrO2-Y2O3 solid solutions, Phys. Chem. Chem. Phys. 16(46) (2014) 25583–25600.

DOI: 10.1039/c4cp03704a

Google Scholar

[40] K. Momma, F. Izumi, VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data, J. Appl. Crystallogr. 44(6) (2011) 1272-1276.

DOI: 10.1107/s0021889811038970

Google Scholar

[41] J. Schuett, T.K. Schultze, S. Grieshammer, Oxygen Ion Migration and Conductivity in LaSrGa3O7 Melilites from First Principles, Chem. Mater. 32(11) (2020) 4442-4450.

DOI: 10.1021/acs.chemmater.9b04599

Google Scholar

[42] M. Rozumek, P. Majewski, H. Schluckwerder, F. Aldinger, K. Künstler, G. Tomandl, Electrical Conduction Behavior of La1+xSr1−xGa3O7-δ Melilite-Type Ceramics, J . Am. Ceram. Soc. 87(9) (2004) 1795–1798.

DOI: 10.1111/j.1551-2916.2004.01795.x

Google Scholar

[43] M. Rozumek, P. Majewski, L. Sauter, F. Aldinger, La1+xSr1-xGa3O7-δ Melilite-Type Ceramics - Preparation, Composition, and Structure, J. Am. Ceram. Soc. 87(4) (2004) 662–669.

DOI: 10.1111/j.1551-2916.2004.00662.x

Google Scholar

[44] F. Wei, H. Gasparyan, P.J. Keenan, M. Gutmann, Y. Fang, T. Baikie, J.B. Claridge, P.R. Slater, C.L. Kloc, T.J. White, Anisotropic oxide ion conduction in melilite intermediate temperature electrolytes, J. Mater. Chem. A 3(6) (2015) 3091–3096.

DOI: 10.1039/c4ta05132g

Google Scholar

[45] F.M. Draber, C. Ader, J.P. Arnold, S. Eisele, S. Grieshammer, S. Yamaguchi, M. Martin, Nanoscale percolation in doped BaZrO3 for high proton mobility, Nat. Mater. (2019).

DOI: 10.1038/s41563-019-0561-7

Google Scholar