Limits of applicability of the “diffusion-controlled product growth” kinetic approach to modeling SHS

In modeling SHS in condensed systems, it is typically considered that a solid and a liquid reactant (a molten metal) are separated by a solid product interlayer, and diffusion in this layer is the rate-controlling stage (a “solid-solid-liquid mechanism”). However, in most cases modeling is performed not with real diffusion data (activation energy E and preexponent D0) for the product phase but with fitting parameters which are chosen to match the calculated and measured thermal characteristics of the SHS wave. In this work, a system of kinetic, thermodynamic and structural estimates is developed for evaluating the validity of this approach for particular SHS systems/conditions using available experimental data on both diffusion in the product phase and characteristics of the SHS wave. A classical Ti-C system is chosen as an example. Change in geometry of a unit reaction cell due to melting and spreading of the metallic reactant is taken into account, and different situations arising within this concept are analyzed. It is demonstrated that the “diffusion-controlled growth” kinetics is not applicable to SHS of interstitial compounds in the wave propagation regime because it cannot provide sufficient heat release for sustaining SHS and the final product structure will disagree with experimental data known in literature. As an alternative, a “solid-liquid mechanism” of phase formation during SHS is grounded, which implies a direct contact of a metallic melt with a solid reactant. A micromechanistic criterion for a changeover of these interaction routes is obtained, which is important for SHS in the thermal explosion mode.