Statistical theories of atomic transport in crystalline solids

Abstract

This review is concerned with the fundamentals of the theory of the transport of atoms through crystalline solids, such as may result from the existence of gradients of chemical and isotopic composition, electrical potential, stress, temperature, etc. The main emphasis is on the statistical description of these processes via the theory of mobile lattice imperfections-vacancies and interstitial atoms. Only processes taking place in the bulk of the solid are considered, i.e. enhanced diffusion and migration in the vicinity of dislocations, grain boundaries and other interfaces are not discussed. The various statistical theories available at the present time are reviewed against the phenomenological framework provided by nonequilibrium thermodynamics. One object of this work is to demonstrate the interrelations among the different theories and to disclose where they are equivalent. Another is to show that the means are now available to calculate all the phenomenological transport coefficients which arise in the nonequilibrium thermodynamics of these processes in terms of the assumed properties of the defects, their interactions with solute atoms, etc. Although this review is thus primarily concerned with the theory of atomic transport at an abstract level, the physical aspects of the subject are referred to throughout. Explicit solutions of the transport equations, however, are not considered.