Calculation of Phenomenological Coefficients by Monte Carlo Computer Simulation Methods

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In this paper we first review the principal indirect and direct Monte Carlo methods for calculating the Onsager phenomenological transport coefficients in solid state diffusion. We propose a new Monte Carlo method that makes use of a steady state calculation of a flux of atoms that is driven by a difference in chemical potential of the atoms between a source and a sink plane. The method is demonstrated for the simple cubic one component lattice gas with nearest neighbour interactions. The new method gives results in good agreement with a Monte Carlo method based on Einsteinian expressions for the phenomenological coefficients.

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27-34

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January 2006

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© 2006 Trans Tech Publications Ltd. All Rights Reserved

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[1] J. Philibert: Atom Movements: Diffusion and Mass Transport in Solids, (Editions de Physique, Les Ulis 1991).

Google Scholar

[2] A.R. Allnatt and A.B. Lidiard: Atomic Transport in Solids, (Cambridge University Press, Cambridge 1993).

Google Scholar

[3] J.R. Manning: Diffusion Kinetics for Atoms in Crystals. (Van Nostrand, Princeton, NJ 1968).

Google Scholar

[4] G.E. Murch and J.C. Dyre: CRC Crit. Rev. Sol. St. Mat. Sci. Vol. 15 (1989), p.345.

Google Scholar

[5] A.R. Allnatt: J. Phys. C: Solid State Phys. Vol. 14 (1981), p.5453 and p.5467.

Google Scholar

[6] C.C. Wang and S.A. Akbar: Acta Metall et Mater. Vol. 41 (1993), p.2807.

Google Scholar

[7] M. Nastar, V. Yu. Dobretsov and G. Martin: Phil. Mag. A Vol. 80 (2000), p.155.

Google Scholar

[8] J.R. Manning: Phys. Rev. B Vol. 4 (1971), p.1111.

Google Scholar

[9] L.K. Moleko, A.R. Allnatt and E.L. Allnatt: Phil. Mag. A Vol. 59 (1989), p.141.

Google Scholar

[10] T. Wichmann, K.G. Wang and K.W. Kehr: J. Phys. A: Math. Gen. Vol. 27 (1994), p. L263.

Google Scholar

[11] B. Widom: J. Chem. Phys. Vol. 39 (1963), p.2808.

Google Scholar

[12] G.E. Murch and R.J. Thorn: J. Comput. Phys. Vol. 29 (1978), p.237.

Google Scholar

[13] M. Bowker and D.A. King: Surf. Sci. Vol. 72 (1978), p.208.

Google Scholar

[14] G.E. Murch and R.J. Thorn: Phil. Mag. Vol. 36 (1977), p.529.

Google Scholar

[15] G.E. Murch: Phil. Mag. A Vol. 46 (1982), p.151.

Google Scholar

[16] K.W. Kehr, K. Binder and S.M. Reulein: Phys. Rev. B Vol. 39 (1989), p.4891.

Google Scholar

[17] G.E. Murch and R.J. Thorn: Phil. Mag. A Vol. 39 (1979), p.259.

Google Scholar

[18] A.R. Allnatt: J. Phys. C Vol. 15 (1982), p.5605.

Google Scholar

[19] Z. Qin and G.E. Murch: Phil. Mag. A Vol. 70 (1994), 481.

Google Scholar

[20] H. Sato and R. Kikuchi: J. Chem. Phys. Vol. 55 (1971), p.677.

Google Scholar

[21] P. Argyrakis and A.A. Chumak: Phys. Rev. B Vol. 66 (2002), p.54303.

Google Scholar

[22] G.E. Murch: Phil. Mag. A Vol. 41 (1980), p.157.

Google Scholar

[23] R. Kutner: Phys. Lett. A, Vol. 81 (1981), p.239.

Google Scholar

[24] G.E. Murch: Diffusion in Crystalline Solids, ed: by G.E. Murch and A.S. Nowick (Orlando, Fl. Academic Press 1984) p.379.

Google Scholar

[25] R.A. McKee: Phys. Rev. B Vol. 23 (1981), p.1609.

Google Scholar