The goal of this paper is a mathematical investigation of dilatometer experiments. These are used to detect the kinetics
of solid-solid phase transitions in steel upon cooling from the high temperature phase. Usually, the data are only used for measuring
the start and end temperature of the phase transition. In the case of several coexisting product phases, expensive microscopic
investigations have to be performed to obtain the resulting fractions of the different phases. In contrast, it is shown in this paper that in the case of at most two product phases the complete phase transition kinetics including the final phase fractions are uniquely determined by the dilatometer data. Numerical results confirm the theoretical result.
We study non-isothermal nucleation and growth phase transformations, which are described by a generalized Avrami model for the phase transition coupled with an energy balance to account for recalescence
effects. The main novelty of our work is the identification of temperature dependent nucleation rates. We prove that such rates can be uniquely identified from measurements in a subdomain and apply an optimal control approach to develop a numerical strategy for its computation.