Kinetic model for solid diffusion with a competing surface reaction

where 8, is the thickness of diffusant initially plated on the surface of the specimen, D is the diffusivity, and c(x, t) is atomic fraction of the diffusant at (x, t). This expression is appropriate if the diffusion anneal is long compared to mSo2/4Dc'„ where c, is the solubility of the diffusant. "' In some systems, this condition cannot be met. For example, in the study of the diffusion of zinc into lead, "' it was found that surface oxidation led to back-diffusion and "humped" concentration profiles, rather than Gaussian profiles, for long diffusion times. In that work, short diffusion time ;experiments were performed, leading to the wellknown erfc solution of the diffusion equation