Model for sintering polydispersed glass particles

We propose a model to describe the sintering kinetics of polydispersed glass particles, having no adjustable parameter. The model is based on three sintering stages: a pure `Frenkelʹ (F) first step, a mixed `Frenkel/Mackenzie–Shuttleworthʹ stage, and a third, pure `Mackenzie–Shuttleworthʹ (MS) step. The model considers sample shrinkage as the sum of the partial shrinkage of several clusters, each consisting of equally sized particles and each showing independent F or MS behavior. The overall set of clusters mimics the specimenʹs real particle size distribution. We then introduce the concept of neck forming ability – ξr, which allows the formation of necks among particles of different sizes, relaxing the clustering condition. Using experimental physical parameters: particle size distribution, viscosity, surface energy, and the theoretical ξr, the model describes well the sintering kinetics of an alumino-borosilicate glass powder having polydispersed, irregular shaped particles in a variety of temperatures. The sintering kinetics of the real powder is slower, but not far from the calculated kinetics of a monodispersed distribution containing only particles of average size. Thus the model provides a tool for estimating the sintering kinetics of real glass powders, for any size distribution and temperature, thus minimizing the number of laboratory experiments.