Understanding solid phase interactions: the use of tracer isotopes

Abstract

The problem being considered is that of phase formation in systems where a solid layer grows on a substrate from the chemical interaction of that substrate with another material. Starting from the classical diffusion equations an attempt is made to understand what contributions can be made from the use of isotope tracers. Except in two quite rare cases: that of interstitial diffusion without exchange with the lattice (as in the oxidation of silicon), and that of diffusion by a nearly pure grain boundary process the information to be gathered is extremely limited. The formulation of the problem leads to somewhat complicated derivations. It is shown, however, that the solutions arrived at express correctly the physical competition between two simultaneous phenomena: the growth of the layer and the mixing of the isotopes. This competition is expressed not in kinetic terms, which are the same for both processes, but in thermodynamic terms which relate to the different driving forces. In cases where the isotope does not belong to the most mobile species it acts as a fine inert marker. The model, with minor modifications, is shown to apply as well to such special cases as the formation of SiO 2.