Mathematical model of reaction between titanium pellet and nitrogen

The reaction between titanium pellet and nitrogen was investigated, under a regime in which both chemical reaction and gas pore diffusion were important, and on the basis of this study a physicochemical model was formulated to describe the reaction system. T he chemical reaction rate expressions, determined in the chemical reaction control region, were used to interpret the experimental data in the light of the model. T he expression for effective gas diffusivity D_e, which was used as a fitting parameter for calculation of the theoretical predictions, was determined to be 1·37 × 10 ^{- 5} exp(-13000/RT) m² s ^{- 1}. Deviation was found between the predictions of the model and the experimental data as the pellet thickness was increased. This is explained by the geometrical difference between the mathematical model, with flat surfaces only, and the actual pellet with both flat and circumferential surfaces. A geometrical factor g was introduced to compensate for this difference, the value of which was calculated to be 1/( 1 + 11·47L), where L is the half thickness of the sample.