Variable Intrinsic Diffusivities in Ternary and Higher Alloys

Abstract

Two different attempts to describe the interdiffusion process in a multi-component system showing concentration dependent intrinsic diffusivities are compared. In the first case the type of a function which can be used to approximate the intrinsic diffusivity is postulated. An alternative way using thermodynamic data to calculate the intrinsic diffusivities is also demonstrated. Using both these approaches and the Generalised Darken’s Method (GDM) the interdiffusion processes in the Ni-Pd and Ni-Fe-Cr systems are analysed. A comparison of the theoretically calculated drift velocity with the experimental markers’ velocity obtained from a ‘multi-foil’ diffusion experiment in Pd-Ni diffusion couple is presented. Introduction In many real systems the intrinsic diffusivities of the components may very with the composition This concentration dependence of diffusion coefficient becomes particularly important when the concentration difference across a diffusion couple is large. Determination of variable (concentration dependent) intrinsic diffusivities even for a simplest multi-component system, i.e., for a binary system is still a subject of many theoretical and experimental studies [1,2]. An important step forward in the determination of the intrinsic diffusivities was achieved by the introducing the ‘multi-foil’ diffusion experimental technique by Heumann and Walther [3]. From one diffusion annealing experiment giving the markers’ shift in a wide concentrations’ range and using the Darken’s [4] and BoltzmanMatano [5,6] or Sour and Freise [7] analysis the intrinsic diffusivities as a function of concentration can be calculated. Unfortunately, this methodology can be used only for the binary systems. Therefore, working out a method which will enable to calculate the intrinsic diffusivities in ternary and higher systems are very desirable. In this paper the GDM is used to describe the diffusion processes in multicomponent systems and when the intrinsic diffusivities are functions of the elements’ concentrations. The approximated solution of the GDM using Faedo-Galerkin’s method has been obtained [8] and the appropriate computer program has been written [9]. Two methods have been used to calculate the concentration dependent intrinsic diffusivities. In the first method a certain type of function has been used to approximate the intrinsic diffusivities of Ni and Pd in Ni-Pd system. These functions and the GDM were subsequently used to calculate the concentration profiles of the components and the drift (marker) velocity in the interdiffusion zone and were compared with the experimental results. The alternative method using the thermodynamic data and the ‘diffusion path’ calculated on the basis of the GDM has been used for modelling the interdiffusion process in the Ni-Fe-Cr diffusion couples. It has been shown that in both of these cases the problem of determining the variable intrinsic diffusivities can be resolved using the Inverse Method [10,11].