A Simple Model for Solidification of Undercooled Metallic Samples

Abstract

A simple model for reproducing temperature recalescence behaviour in spherical undercooled liquid metallic samples, undergoing crystallization transformations, is presented. The model is applied to constant heat extraction rate, uniform but time dependent temperature distribution inside the sample (even after the start of crystallization), a classical temperature dependent rate of nucleation (including contributions from different specific heats for different phases and also a catalytic factor to model the possibility of heterogeneous distributed impurities) and the solidified grain interface velocity is taken proportional to the temperature undercooling. Different assumptions are considered for the sample transformed fraction as function of the extended volume of nuclei, like the classical Kolmogoroff, Johnson–Mehl, Avrami one (corresponding to random distribution of nuclei), the Austin–Rickett one (corresponding to some kind of clusterized distribution) and also an empirical one corresponding to some ordering in the distribution of nuclei. As an example of application, a published experimental temperature curve for a zirconium sample in the electromagnetic containerless facility TEMPUS, during the 2nd International Microgravity Laboratory Mission in 1994, is modeled. Some thermo-physical parameters of interest for Zr are discussed.