Stochastic and deterministic models for nucleation and growth in non-isothermal and/or non-isobaric powder transformations

The calculation of fractional conversion can be very difficult in certain cases of nucleation and growth transformations (Mampel assumptions): it has only been developed for a few shapes of grains (spheres, cylinders) and only in isobaric and isothermal conditions. Here, a stochastic model which is intrinsically independent on geometry and which stands for non-isobaric and/or non-isothermal reactions is presented. The numerical evaluation of this model can be carried out in two different ways. First a slow Monte Carlo approach which is valid for all kinds of shapes and external conditions is presented, then, a faster, more classical approach is given which allows changing external conditions but only for well-known shapes.