An nth-order Gaussian energy distribution model for sintering

Although it is well known that the rate of sintering is governed by deceleratory kinetics, it is often difficult to fit power-law and nth-order reaction models over broad time-temperature ranges. This work shows that a phenomenological model combining a reaction order with an activation energy distribution can correlate surface area as a function of sintering time and temperature over a greater range of those variables. Qualitatively, the activation energy distribution accounts for the dependence of free energy on particle size and material defects, while the reaction order accounts for geometric factors such as a distribution of diffusion lengths. The model is demonstrated for sintering of hydroxyapatite using data of Bailliez and Nzihou [S. Bailliez, A. Nzihou, Chem. Eng. J. 98 (2004) 141-152].