Combined thermodynamic and kinetic model for the kinetics of M/ABu reactions

We propose a model for the reaction kinetics of metal/compound systems in which growth occurs in the form of a phase MAv of fixed composition growing in between ABu and a phase of variable composition, MBw. An example of this is the Ti/SiO2 system, where Ti5Si3 grows between SiO2 and an oxide phase, TiOw. The model takes into account the slowing and eventual cessation of the reaction upon MBw reaching a limiting, equilibrium composition of MBz. We use the Gösele and Tu kinetic model but subject it to our thermodynamic constraint. The original kinetic model yields a simple parabolic relation, x2=2kt, for diffusion-controlled growth. Our model modifies this relationship, predicting a growth law of the form kt= x2/2+ax2f∑∞n=3(1/n)(x/xf)n, with x the thickness and xf the final thickness of the MAv phase. k is the reaction rate constant for diffusion-controlled growth and a∼1. xf depends on the initial metal film thickness and the stoichiometries of all phases involved in the reaction. The model provides an explanation for previous results that observed an increasing reaction rate with increasing initial metal layer thickness.