General equations for multi-component diffusion in crystalline systems were derived, within the framework of Onsager’s non-equilibrium thermodynamics, with the object of providing explicit equations for diffusion-controlled phase transformations while avoiding usual simplifying assumptions such as an independence of the fluxes of various atomic species. An additional difficulty was introduced by the fact that the concentrations of vacancies which mediated the diffusion of substitutional atoms could obey different rules; depending upon whether there was a sufficient density of sources and sinks to keep the local vacancy concentration in equilibrium. Two limiting cases were treated: in one the total vacancy number was conserved (no available sources or sinks) and in another the vacancy concentration was kept in equilibrium (dense sources and sinks). The diffusive fluxes of all components and vacancies were first expressed by the Onsager relationship. The kinetic coefficients of the Onsager relationship were derived from an extremal thermodynamic principle with respect to the atomic mobilities of individual components while taking account of constraints on fluxes which resulted from the vacancy diffusion mechanism. In the case where a dense network of vacancy sources and sinks was active, the number of lattice positions was not necessarily conserved in every region of the specimen. Fick’s second law, based on a local conservation of lattice positions, was then not applicable. By using mass conservation considerations, Fick’s second law was modified so as to account for this effect. The lattice could shrink or expand either due to the generation or annihilation of vacancies or to a change in the molar volume which was connected with a change in chemical composition. Deformation of the system was expressed quantitatively by strain rates. The equations of system evolution were derived for both lattice-fixed and laboratory-fixed frames of reference.

Diffusion in Multi-Component Systems with No or Dense Sources and Sinks for Vacancies. J.Svoboda, F.D.Fischer, P.Fratzl, A.Kroupa: Acta Materialia, 2002, 50[6], 1369-81