Bulk Crystallization of Supercooled Metal Films
Authors: Chernov Andrey A. , Pil'nik Andrey A. , Islamov Damir R. 
Published: February 2020

The overwhelming majority of modern materials are knowingly produced by crystallization from melts. Leaving apart powder metallurgy and some other technologies, the mainstream is melting and homogenizing a charge followed by its transition to a solid state. In this case, technologies based on a method of ultrafast hardening from a liquid state, the key point of which is putting a substance into a deep metastable state with a further intense phase transition, are of particular importance. This allows producing amorphous, nanocrystalline, bioactive, and other promising materials widely used in modern industry and technologies, microelectronics, medicine, etc. In particular, they can be used as durable anti-corrosion coatings. Since the quality and physicochemical properties of these materials depend directly on their morphology, the skill in controlling this morphology is an effective way of producing materials with specified functional characteristics. This requires the ability to describe in detail the kinetics of phase transitions at all stages of the process.
Like any other first-order phase transitions, crystallization occurs via fluctuation-induced nucleation and growth of centers of a new phase. Hence, the overall kinetics of such a process is determined by nucleation and the growth rate of nuclei. These quantities are related to a set of various thermodynamic and kinetic parameters that are important under specific conditions and primarily to a degree of metastability of the parent phase. The main problem here is finding the time dependence of the fraction of the crystalline phase and the size distribution of the nuclei. The kinetic theory of fluctuation-induced nucleation and crystal growth is elaborated pretty well, whereas the thermophysical aspects of this problem are poorly investigated. In particular, the effect of heat release at the phase transition on the rate of the process is insufficiently studied.
Theoretical analysis of phase transition shows that for the most cases the process can be divided into two particular stages. The first one is the nucleation stage. The majority of new phase nuclei form during this particular stage. Nonlinear nature of nucleation expressed in strong dependence of nucleation rate from the degree of metastability. At the beginning of this stage the process is conditioned by the factors producing metastability, though the stage ends due to reduction in the degree of metastability. This reduction results from the transition of a portion of material from metastable phase to stable phase accompanied by release of latent heat of phase transition. Typically the portion of the new phase is relatively small at the moment of the end of nucleation stage. This is due to the fact that formation of even small portion of a new phase is enough for significant reduction in nucleation rate. The main part of initial phase transits to stable state during the subsequent growth of crystals already formed during nucleation stage. In studying the phase transition the nucleation stage attracts great interest, but it is a problem of great complexity. It involves thermodynamics of small systems, nucleation kinetics, knowing the growth mechanism in a wide range of parameters, correct accounting for effect that assembly of crystals has on metastability, etc. Combined with account for the factors producing metastability it all leads to challenging, nonlinear mathematical problem described by the system of integro-differential equations. At this time the complete solution of this problem is yet to be found.
In current work nonequilibrium theory of bulk crystallization of melts rapidly quenched to deeply supercooled state is developed. This theory correctly takes into account the heat release due to phase transition. It is achieved by using the real temperature fields formed around crystals in kinetic equations. Limits of validity of theories using heat release obtained from global heat balance are estimated. Proposed theory allows to describe accurately the kinetics of crystal nucleation and growth in metastable liquid and to determine the microstructure of solidified material. Particular attention was paid to the mechanism of crystal growth in highly nonequilibrium conditions and with account taken of the shrinkage during solidification.
The problem of solidiﬁcation of a thin layer of metal melt brought into contact with a massive cold substrate is developed. Based on the amorphization conditions formulated, the thickness of the amorphous sublayer formed near substrate is determined. The suggested model of bulk crystallization of melt makes it possible to find the morphology of the solidiﬁed layer.
The work is supported by RFBR (grant #15-08-04474).