The Effect of a Substitutional Solute Element on the Diffusivity of an Interstitial Solute Element in a Dilute Ternary Alloy

Abstract

A model is developed to explain the dependence of the diffusion coefficient of an interstitial solute upon the concentration of substitutional solute. In the model, substitutional solute atoms act as traps for diffusing interstitial atoms and thus decrease the number of atomic jumps through the lattice of the solvent, but diffusion can also take place by jumps out of traps and within overlapping traps. Two parameters are used to develop the theory: the size of the trap around a substitutional atom, and the interstitial-substitutional solute binding energy. Three terms are shown to contribute to the magnitude of the interstitial diffusivity. The first term is for atomic jumps in the host lattice and from lattice into traps. The second is for jumps from traps to host lattice. The third is for jumps which occur entirely within traps. The theory predicts a marked initial decrease of the interstitial diffusion coefficient as a function of the substitutional concentration. After this initial decrease, the diffusivity goes through a minimum, and the position of this minimum depends upon the trap radius.