Interdiffusion: Consistency of Darken's and Onsager's Methods


Article Preview

The Nernst-Planck flux formula is used in Darken's method to obtain the interdiffusion fluxes. The effective interdiffusion potentials, derived for the independent components in the system, allow obtaining the symmetrical matrix of the interdiffusion coefficients. The transport coefficients for 2, 3 and r-component system are presented. Interpretation of obtained matrixes in the light of Onsager's theory of irreversible thermodynamics is shown. Equation for the entropy production in the interdiffusion process is displayed. The presented approach allows calculation of entropy production during interdiffusion, as well as formulating Onsager's phenomenological coefficients for the interdiffusion in an explicit form, a form which is directly correlated with the mobilities of the atoms present in the system.



Edited by:

S.V. Divinski, H. Bracht and N.A. Stolwijk




J. Dąbrowa et al., "Interdiffusion: Consistency of Darken's and Onsager's Methods", Defect and Diffusion Forum, Vol. 363, pp. 29-34, 2015

Online since:

May 2015




* - Corresponding Author

[1] E. Kirkendall and A.D. Smigelskas, Trans. AIME 171 (1947), p.130.

[2] L.S. Darken, Trans. AIME 175 (1948), p.184.

[3] M. Danielewski and K. Holly, Phys. Rev. B 50 (1994), p.13336.

[4] L. Onsager, Phys. Rev. 37 (1931), p.405.

[5] L. Onsager, Phys. Rev. 38 (1931), p.2265.

[6] C. Huang, M. Olvera de la Cruz and B.W. Swift, Macromolecules 28 (1995), p.7996.

[7] R.R. Mohanty Ph.D. thesis, Indian Institute of Science, (2009).

[8] I.V. Belova, N.S. Kulkarni, Y.H. Sohn and G.E. Murch, Philos. Mag. 93 (2013), p.3515.

[9] I.V. Belova, G.E. Murch, R. Filipek and M. Danielewski, Acta Mater. 53 (2006), p.4613.

[10] C. Truesdell and B.D. Coleman, J. Chem. Phys. 33 (1960), p.28.

[11] G.J. Hooyman and S.R. de Groot, Physica 21 (1955), p.73.

[12] J.S. Kirkaldy and D.J. Young, Diffusion in the condensed state , The Institute of Metals, London, (1985).

[13] B. Wierzba, Phys. A 391 (2012), p.56.

[14] B. Wierzba and M. Danielewski, Philos. Mag. 91 (2011), p.3228.

[15] M. Danielewski, Defect Diffus. Forum, 323-325 (2012), p.43.

Fetching data from Crossref.
This may take some time to load.