Semiempirical Approach to the Theory of Thermal Diffusion in Crystals

The theory of thermal diffusion is developed by defining two isothermal systems: one at a temperature such that the jump frequency is equal to that in the direction along the temperature gradient in the nonisothermal system, and another at a temperature such that the jump frequency is equal to that in the direction against the gradient. The difference between these two defined temperatures, and the existing temperature gradient, are used to define a distance parameter xc. The flux equations in a temperature gradient are then developed in a formal way using xc as an expansion parameter for interstitial impurity diffusion, substitutional impurity diffusion by a vacancy mechanism for the two extreme cases of weak binding and tight binding of the vacancy-impurity complex, and for the flux of vacancies in pure metals. xc is interpreted in such a way that it defines the region in which the maximum energy is localized in the critical configuration for a jump, and is, therefore, a measure of the spatial distribution of activation energy. The analysis is applied to existing experimental data.