A coupled thermodynamic/kinetic model for diffusional processes in superalloys

Abstract

A coupled thermodynamic/kinetic model for diffusional processes in superalloys is described. Use is made of the generalised force-flux equations, and therefore an accurate knowledge of thermodynamical properties of the system is a prerequisite for the calculations. Calculations can be carried out in either the lattice-fixed (Kirkendall) or the mass-invariant (Matano) frame. In order to model transformations, e.g. involving the γ and γ′ phases, the concept of an interface sub-system is introduced. The numerical accuracy and stability associated with the treatment of the moving boundary is shown to be comparable to more traditional analyses which incorporate the Murray–Landis transformation. The results from the simulations are compared with experimental information, which includes (i) concentration profiles, (ii) movement of inert markers and (iii) observations of porosity formation. Particular attention is paid to the simulation of Ni–Al–Cr interdiffusion in the f.c.c. phase, for which reliable thermodynamic and kinetic information is available. Similar comparisons have been made for precipitation reactions involving the γ′ phase, although the available information is very sparse. Observations made on a number of Ni–Ni3(Al,Ti) couples can be simulated with a reasonable degree of accuracy. Particular advantages of the method are (i) the interface between phases is treated in a novel way, which avoids numerical difficulties arising from the estimation of concentration gradients at phase boundaries, (ii) it can be readily extended to multicomponent systems, and (iii) the treatment of the Kirkendall drift of vacancies. It is clear that there is a great need for experimentation aimed at deducing kinetic data, e.g. diffusional mobilities, particularly for the γ′ phase.