William J. Boettinger, Geoffrey B. McFadden, Sam R. Coriell, R F. Sekerka, James A. Warren
A model is proposed to describe the shape change (displacement field) of a binary diffusion couple when the intrinsic (lattice) diffusivities of the two substitutional atomic species differ. As for the Kirkendall effect, the displacement is due the creation and annihilation of vacancies and their corresponding lattice sites. The classical uniaxial Kirkendall shift is obtained only if the displacements are artificially constrained to be in the diffusion direction. In the more usual experimental case when the external surfaces of the diffusion couple are traction-free, a more general displacement field is obtained that accounts for the lateral shape change data of Voight and Ruth [Journal of Physics-Condensed Matter (1995) 7: 2655-2666]. In the interdiffusion zone, near the free surfaces of the diffusion couple, the sample deforms inward and outward on opposite sides of the Matano plane. The model employs an isotropic stress-free strain rate proportional to the vacancy creation/annihilation rate. For the incompressible elastic-plastic constitutive relation employed in this paper, the displacement field, unlike the stress field, is independent of the various elastic/plastic moduli. If the lateral dimension of the diffusion couple is much larger than the diffusion distance, the lateral shape exhibits limiting behavior that is the same for cylindrical and slab geometries. In this limit, the displacement differs from the uniaxial case within a diffusion distance of the external surface. If the lateral dimension of the diffusion couple is much smaller than the diffusion distance, the displacement in the diffusion direction is one-third (one-half) of the uni-axial result for the cylindrical (slab) geometries. The model permits a determination of the geometrical requirements for precise Kirkendall shift measurements for use in determining intrinsic (lattice) diffusivities.
deformation, diffusion, Kirkendall effect, theory
, McFadden, G.
, Coriell, S.
, Sekerka, R.
and Warren, J.
Lateral Deformation of Diffusion Couples, Acta Materialia
(Accessed June 6, 2023)