Mass Transfer Problems in Ionic Crystals with Charge Neutrality

Abstract

Both diffusional creep and sintering involve mass transport of the stoichiometric group of atoms AαBβ. The driving force in each case is external to the lattice, being applied mechanical stress in the case of diffusional creep and surface tension in the case of sintering. It is assumed that point defect mechanisms are involved in the diffusion process. Herring has considered the case of diffusional creep by lattice diffusion where charge effects are absent. The analogous case of creep by grain-boundary diffusion, which becomes the important process at small grain size, has also been treated. [A. L. Ruoff, Materials Science Center Rept. No. 298, Cornell University, Ithaca, New York; and R. L. Coble, J. Appl. Phys. 34, 1679 (1963)]. The diffusional creep of a polycrystalline specimen is here formulated exactly and terms which must be dropped to obtain Herring's expression (for either metallic or ionic crystals) are directly specified. It is then shown that Herring's equations apply to a pure ionic crystal when the conduction is purely ionic and space-charge effects can be ignored if the tracer diffusion coefficient D in Herring's equations is replaced by DM, and the atomic volume Ω in his equations is replaced by the molecular volume VM of the diffusing ``molecule'' of AαBβ. If A atoms have the smallest tracer diffusion coefficient DTa0, then DM=DTa0/faα, where fa is the correlation factor.