Features of the Use of Equilibrium State Diagrams for Description of Crystal Growth from Metastable Melts

Abstract

The crystallization of metastable metal alloys is characterized by a high rate of the crystallization front, which leads to the effect of "impurity capture" and deviation from the local equilibrium near the surface of the growing crystal. To calculate the growth rate of the crystalline nuclei, a method was developed for prediction of deviation of the components’ concentration near the crystal surface from the equilibrium values. A crystal nucleus was considered to be growing from the initial multicomponent phase, due to interphase transition of the components through its surface. It became possible to distinguish the equilibrium and non-equilibrium effect of the nucleus growth rate by decomposing the molar rate of the product formation near equilibrium, as a function of the molar concentration of the components in the Taylor series and limiting with the linear members. The practical calculations were carried out for the crystallization of the amorphous alloy Fe73,5Cu1Nb3Si13,5B9 of the FINEMET type. The local deviations were investigated for the silicon concentration from the equilibrium values at the surface of the growing crystal.

Variational theory of crystal growth and its application for analysis of forming processes for metastable phases in overcooled metallic melts with eutectic composition

“…Then the layer of atoms B, limiting diffusion of the component A to the nucleus surface, would be created near this surface. As a result, such nucleus could not grow [4], what occurs at usual cooling conditions of eutectic melts.…”

“…Thereby the equilibrium lines can be approximated in the low temperatures area. The examples of building of such lines were considered in several researches, e. g. [4,16]. In our case, the lines E S OZ and OA S continue the lines Z L O и A L O and correspond to the values of components concentrations which are established near nuclei surface for local equilibrium.…”

“…impurity trapping, and the melt composition near its surface corresponds to concentration of impurity B in the point c 1 [4]. Thereby, simultaneous growth of "equilibrium" nuclei of A and Z E phases as well as metastable nuclei of Z phase, occur during cooling of the melt with eutectic composition, i. e. phase transformation takes plaсe: Initial melt → A +Z +Z E It is important to note that in the case of nuclei Z forming the local equilibrium condition is not executed, thereby use of the equations ( 1) and Onsager principle is not correct.…”

“…Conventional theoretical models uses assumption about local equilibrium near the growing crystal surface in description of crystallization processes in such systems [4]. However, this assumption is valid only in the case when crystal growth is limited by diffusion transfer of the components from initial melt.…”

“…In particular, deviation from the local equilibrium conditions on the boundary "melt -crystal" is observed [2,[4][5][6][7]. At the same time, these deviations have non-linear feature, and the methods of linear non-equilibrium thermodynamics become not valid for description of this system.…”