Diffusion and creep in multi-component alloys with non-ideal sources and sinks for vacancies

Diffusion in single-phase multi-component crystalline systems can be characterized by three attributes: (i) the vacancy mechanism of diffusion for 'slowly' diffusing substitutional components (ii) the existence of non-ideal sources and sinks for vacancies and (iii) the 'quick' diffusion of atoms of interstitial components. The first attribute leads to a constraint amongst fluxes of vacancies and substitutional components. The second attribute causes the non-uniform generation/annihilation of vacancies in the system being accompanied by dissipation and contributing to local swelling or shrinkage. The third attribute concerns the change of lattice constants due to the change of the concentration of interstitials and, therefore, also contributes to local swelling and shrinkage. The evolution equations for these systems have been derived from the conservation laws and the thermodynamic extremal principle. The equations represent an extension of evolution equations for multi-component systems with ideal or no sources and sinks for vacancies derived in a previous paper [Svoboda J, Fischer FD, Fratzl P, Kroupa A. Acta Mater 50 (2002) 1369]. Both diffusion and vacancy generation/annihilation are supposed to be proportional to driving forces of a chemical and mechanical nature. The appropriate evolution equations are derived, and it is shown that diffusion and vacancy generation or annihilation in isotropic materials depend on two different sets of driving forces and, thus, they can be considered as independent processes. Two relevant kinetic coefficients can be introduced for an isotropic body: the bulk and shear viscosities. However, the deformation state caused by the generation/annihilation of vacancies at grain boundaries is highly anisotropic