Atomic transport via point defects in crystals. II. Atomic mobilities and dielectric relaxation

Abstract

The general formulation of the kinetic theory of isothermal solid state diffusion applicable to systems showing small degrees of vacancy and interstitial disorder that was presented in a previous paper (Franklin & Lidiard, Proc. R. Soc. Lond . A 389, 405-431 (1983)) is here extended to describe atomic transport in such isothermal systems under the influence of external scalar potential fields (for example, electric, gravitational, centrifugal fields). For steady fields the results verify the correctness of the phenomenological equations suggested for solid state transport processes by the theory of non-equilibrium thermodynamics and provide expressions for the phenomenological transport coefficients L ij in terms of microscopic quantities characterizing the defect species and their movements. In particular, it is shown that the same expressions for these transport coefficients are obtained from the atomic fluxes coming from ‘drift’ under applied fields, as from diffusion arising from imposed concentration gradients. The dielectric response function for use with time-dependent fields is also obtained. It is made up of two parts; one corresponding to the d. c. conductivity, the other to a set of Debye relaxation modes. It is demonstrated that the occurrence of association and dissociation reactions among the defects influences both the relaxation times and the strengths of these modes. A brief examination of the example of solute-vacancy pairs in a f. c. c. lattice shows that these influences can be substantial and qualitatively significant.