Derivation of expressions for interdiffusion and intrinsic diffusion flux in presence of chemical potential gradient in a multicomponent system with composition dependent molar volume

Abstract

Abstract It has been generally accepted and often mentioned in the text books that gradient in chemical potential of a species is the fundamental driving force for its diffusion. However, a general derivation of the interrelation between the diffusion flux of a component and chemical potential gradients in a non-ideal solution is lacking. Although there have been various studies in the literature reporting such interrelations for a binary system, they all assume constant molar volume. In a non-ideal system though molar volume changes with composition. Hence, in the present work, kinetic theory is used to derive a relation between diffusion flux and the chemical potential gradients for a multicomponent system with composition dependent molar volume. It is shown that the velocity of the marker as measured in a diffusion couple experiment should consist of the drift velocity (UN) due to change in molar volume accompanied by diffusion as well as the Kirkendall velocity caused by vacancy equilibration process. For the assumption of volume change occurring only in the direction of diffusion, the Kirkendall velocity is same as the marker velocity measured in a diffusion couple. However, if the lattice is allowed to relax in all directions, the contribution of UN to the marker velocity can be significant. This is shown to be as high as 20% for Cu in a Cu-Ni diffusion couple.