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Abstract

The reaction rate in gas-solid systems can be affected by mechanical stresses that arise as the reaction proceeds. Stresses develop due to differences between precursor and product molar volumes and thermal expansion coefficients. Experimental evidence on the interaction of reaction rate and mechanical stress for the Ti/N2 and Ti/O2 systems is provided. A detailed and consistent mathematical model is developed for the reaction taking place at the constrained precursor/product interface. An elastic formulation for the stresses is adopted, and stress generation due to mismatches in linear thermal expansion coefficients and equivalent volume (Pilling-Bedworth ratio) for the precursor and product are considered. The effect of surface energy, which becomes significant for particle sizes below 1 μm, is also included in the model. Both experimentally and theoretically, conditions exist where the mechanical stresses exceed the strength of the material, leading to mechanical breakdown of the product layer, thus causing a discontinuity in the observed reaction rate. The entire processing history, including the reaction, temperature, and pressure profiles, plays an important role in determining the overall reaction kinetics of the powder.