Lateral deformation of diffusion couples

A model is used to describe the shape change of a binary diffusion couple when the diffusivities of the two species differ. The classical uniaxial Kirkendall shift is obtained only if the displacement is constrained to be in the diffusion direction. For traction-free conditions at the external surfaces of a diffusion couple, a more general displacement field is obtained that accounts for the lateral shape change data of Voigt and Ruth [Journal of Physics-Condensed Matter 7 (1995) 2655-2666]. The model employs an isotropic stress-free strain rate and equal and constant partial molar volumes. In this case the displacement field is shown to be independent of the various elastic/plastic moduli. Depending on the lateral dimension of the diffusion couple, the displacement in the diffusion direction can be reduced by up to a factor of three compared to the case of a pure uniaxial displacement.