A simple yet general model of binary diffusion coefficients emerged from a comprehensive assessment of 18 binary systems

Abstract

This study is the most comprehensive test to date aiming at defining the optimal number of fitting parameters for a reliable mathematical description of the diffusion behavior of a binary solid solution. Our systematic test of 18 diverse binary systems has yielded a surprisingly simple model with only one fitting parameter/constant which can be evaluated from experimental diffusion data. The rest of the quantities in the model are the self-diffusion and impurity (dilute) diffusion coefficients of the pure elements and the thermodynamic factor which can be computed from a CALPHAD thermodynamic assessment of the pertinent binary system. The 1-parameter Z-Z-Z model has been demonstrated to be very reliable and robust since the 18 binary systems tested in this study include very asymmetrical systems such as Co-Pd and Fe-Pd as well as Nb-Ti whose experimental diffusion coefficient data cover ~9 orders of magnitude and over a temperature range spanning ~1200°C (from ~800°C to ~2000°C). The Z-Z-Z model allows both tracer and intrinsic diffusion coefficients to be reliably computed for any composition at any temperature after the sole constant is evaluated from the interdiffusion or all experimental diffusion data. Extension of such a simple and robust model from binary to ternary and higher order systems will lead to a substantial reduction of fitting parameters and an enhancement of the reliability of future multicomponent diffusion (atomic mobility) databases for simulation of kinetic processes in materials.