Criteria for the existence of local equilibria in supercooled melts

The paper is intended for researchers studying of supercooled metallic melts. It addresses an important theoretical problem: the possibility of establishing local thermodynamic equilibrium at the phase boundary during crystallization from a supercooled melt. Such processes play a crucial role in determining the microstructure of materials during solidification, particularly under rapid cooling conditions characteristic of modern metallurgical and powder technologies. During supercooling, nuclei of a new, solid phase begin to form in the melt. To mathematically describe the growth of such nuclei, it is necessary to specify boundary conditions that define the composition of the adjacent liquid phase. Traditional models assume that local equilibrium can be established near the nucleus and that its parameters can be derived from the equilibrium phase diagram. However, as demonstrated by our study of binary systems, local equilibrium may, in some cases, be fundamentally unattainable. This article presents a theoretical analysis of the conditions under which equilibrium may or may not be established. The analysis considers chemical potentials of the components in both the solid nucleus and the liquid melt. Based on the equilibrium phase diagram of the corresponding macrosystem, one can infer the relative chemical potentials of the components in each phase. It is shown that when the nucleus consists of a single component, local equilibrium is always possible in principle. However, when the nucleus is a solution, equilibrium may only be realized under specific thermodynamic conditions. In such cases, the application of first-kind boundary conditions becomes invalid, and it is necessary to take into account the rates of chemical reactions involved in the interphase transfer of each component.