[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