SHOCK SYNTHESIS OF SILICIDES .2. THERMODYNAMICS AND KINETICS

A thermodynamic and kinetic analysis of shock-induced reactions in the (Nb or Mo)-Si systems provides a framework for the extraordinarily high reaction rates and a quantitative interpretation of the experimental results obtained in Part I. The thermodynamic analysis is conducted by adding the heat of reaction to the shock energy; increases in shock pressure, temperature, and velocity are predicted. At the particle level, melting at the silicon-metal interface is found to be a necessary condition for the initiation of reaction; heat conduction calculations enable the prediction of a critical molten (Si) region size for which the heat generated through the reaction exceeds the heat lost to the unreacted regions. The calculation of melt fraction (of Si) as a function of shock energy coupled with critical melt pool sizes enables the determination of a minimum shock energy for the initiation of shock-induced reaction. At the local level, the reaction kinetics can be rationalized through the production of a liquid-phase reaction product (NbSi2), the formation of spherical nodules (approximately 2 mum diameter) of this product through interfacial tension and their subsequent solidification (in times of 1-5 ns). The heat generated by the reaction is sufficient to melt niobium along the interface which facilitates both the expulsion of the NbSi2 nodules into the liquid Si, and the generation of fresh Nb interface for further reaction. In addition, the dissolved Nb enriches the surrounding Si liquid, promoting more NbSi2 reaction and formation.