Kinetics of bulk crystallization in a supercooled metallic melt: Nucleation stage

This paper presents a model of the overall crystallization of a supercooled melt that correctly takes into account the change in the degree of metastability of the parent phase during nucleation and the growth of centers of a new phase. The paper examines single-component melts of pure metals that are instantaneously supercooled. We demonstrate that the growth rate of non-interacting spherical particles is a composite function of time mediated by the melt temperature at the interface boundary. It is shown that at the nucleation stage, fundamentally different scenarios for phase transitions are possible. This is determined by the relationship between the duration of this stage and the characteristic time required to reach the heat-transfer-limited stage of crystal growth. The difference between these scenarios is that, in the first scenario, the temperature field in the melt during nucleation is practically uniform, whereas in the second scenario it is significantly nonuniform. We derived a nonlinear equation for melt supercooling, at which nucleation begins, depending on the cooling rate for a given nucleation probability. In addition, an integral equation for an excluded volume is obtained, where new crystallization centers cannot nucleate. Simple analytical dependencies for the duration of nucleation and the number of crystallization centers, as functions of melt supercooling, were derived for a wide range of Stefan numbers.