Relationships between atomic diffusion mechanisms and ensemble transport coefficients in crystalline polymorphs

Physical Review Letters

Volumn 112, Issue 14, 2014, Pages

  Morgan, Benjamin J ^a   Madden, Paul A ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

MOLECULAR DYNAMICS; POISSON DISTRIBUTION; TEMPERATURE;

ARRHENIUS EXPRESSIONS; ATOMIC DIFFUSIONS; COMMON STRUCTURES; CRYSTALLINE POLYMORPHS; INTRINSIC DIFFUSION; MOLECULAR DYNAMICS SIMULATIONS; PHYSICAL SIGNIFICANCE; TRANSPORT COEFFICIENT;

DIFFUSION;

EID: 84898421988     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.112.145901     Document Type: Article

References (27)

1. L.V. Azároff, J. Appl Phys. 32, 1658 (1961). 0021-8979 10.1063/1.1728414
2. J. Maier, Phys. Chem. Chem. Phys. 11, 3011 (2009). PPCPFQ 1463-9076 10.1039/b902586n
3. E.M. Chan, M.A. Marcus, S. Fakra, M. ElNaggar, R.A. Mathies, and A.P. Alivisatos, J. Phys. Chem. A 111, 12210 (2007). JPCAFH 1089-5639 10.1021/jp073474u
4. R.J. Cava and E.A. Rietman, Phys. Rev. B 30, 6896 (1984). PRBMDO 0163-1829 10.1103/PhysRevB.30.6896
5. B.J. Morgan and P.A. Madden, J. Phys. Condens. Matter 24, 275303 (2012). JCOMEL 0953-8984 10.1088/0953-8984/24/27/275303
6. P.A. Madden, K.F. O'Sullivan, and G. Chiarotti, Phys. Rev. B 45, 10206 (1992). PRBMDO 0163-1829 10.1103/PhysRevB.45.10206
7. S. Hull, Rep. Prog. Phys. 67, 1233 (2004). RPPHAG 0034-4885 10.1088/0034-4885/67/7/R05 (Pubitemid 39097234)
8. C. Tubandt and E. Lorentz, Z. Phys. Chem. 87, 513 (1914). 0044-3336
9. A. Hao, C. Gao, M. Li, C. He, X. Huang, G. Zou, Y. Tian, and Y. Ma, J. Appl. Phys. 101, 053701 (2007). JAPIAU 0021-8979 10.1063/1.2709579 (Pubitemid 46442610)
10. The necessary conditions for ionic motion to be described in terms of discrete hops are discussed in C.R.A. Catlow, Solid State Ionics 8, 89 (1983). Although diffusion in (Equation presented)-AgI can also be described as hopping between tetrahedral sites, the timescales of site residence and jump processes are of the same order of magnitude and the assumption used in simple hopping models that the residence time is much greater than the jump time is not valid. SSIOD3 0167-2738 10.1016/0167-2738(83)90069-3
11. C.R.A. Catlow, Annu. Rev. Mater. Sci. 16, 517 (1986). ARMSCX 0084-6600 10.1146/annurev.ms.16.080186.002505
12. G.H. Vineyard, J. Phys. Chem. Solids 3, 121 (1957). JPCSAW 0022-3697 10.1016/0022-3697(57)90059-8
13. F.A. Haight, Handbook of the Poisson Distribution (Wiley, New York, 1967).
14. M. Parrinello, A. Rahman, and P. Vashishta, Phys. Rev. Lett. 50, 1073 (1983). PRLTAO 0031-9007 10.1103/PhysRevLett.50.1073
15. F. Zimmer, P. Ballone, J. Maier, and M. Parrinello, J. Chem. Phys. 112, 6416 (2000). JCPSA6 0021-9606 10.1063/1.481205
16. Simulation cell volumes were (Equation presented) for (Equation presented), (Equation presented) for (Equation presented), and (Equation presented) for the high-pressure (Equation presented) phase.
17. K. Compaan and Y. Haven, Trans. Faraday Soc. 52, 786 (1956); TFSOA4 0014-7672 10.1039/tf9565200786
18. K. Compaan and Y. Haven, Trans. Faraday Soc. 54, 1498 (1958). TFSOA4 0014-7672 10.1039/tf9585401498
19. The procedure for assigning ions to lattice sites by geometric construction is described in Ref. [5].
20. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ PhysRevLett.112.145901 for details.
21. The observation that nearly all diffusion events occur between neighbouring lattice sites contradicts the proposal of Lee et al. that the dominant low-temperature diffusion mechanism in B4 AgI is pure interstitial diffusion along (Equation presented)-oriented channels of face-sharing octahedra: see J.-S. Lee, S. Adams, and J. Maier, J. Phys. Chem. Solids 61, 1607 (2000). JPCSAW 0022-3697 10.1016/S0022-3697(00)00020-2
22. V. Choulakian, R.A. Lockhart, and M.A. Stephens, Can. J. Stat. 22, 125 (1994). 0319-5724 10.2307/3315828
23. J.J. Spinelli and M.A. Stephens, Can. J. Stat. 25, 257 (1997). 0319-5724 10.2307/3315735
24. The construction of chains of diffusion events is similar to the analysis of Wolf and Catlow used to identify "causal chains" of ion trajectories in (Equation presented): M.L. Wolf and C.R.A. Catlow, J. Phys. C 17, 6635 (1984). JPSOAW 0022-3719 10.1088/0022-3719/17/36/018
25. Chains of length 2 correspond to Frenkel pair formation and immediate recombination, with no contribution to either mass or charge transport, and are discounted from this analysis.
26. J.R. Patnaik and C.S. Sunandana, J. Phys. Chem. Solids 59, 1059 (1998). JPCSAW 0022-3697 10.1016/S0022-3697(97)00243-6
27. We expect nonstoichiometric systems will also exhibit non-Poisson diffusion processes, but that these make a negligible contribution towards ensemble transport except for cases of very limited nonstoichiometry.