Simulation of Crystal Growth in Multicomponent Metastable Alloys

Abstract

A technique is developed for predicting the patterns of crystal growth from metastable melts. Using nonequilibrium thermodynamics methods, a crystal growth process from a multicomponent melt is described, which considers the interaction between thermal and diffusion processes. The application of a new variation approach to the constructed equation system has made it possible to obtain expressions for the crystal growth rate from a multicomponent melt, which is convenient for practical calculations. The developed technique has made it possible to analyze the crystal growth features at a high motion speed of the crystallization front, which leads to an “impurity capture” effect, i.e., the deviation from the equilibrium conditions at the interface. The developed mathematical model makes it possible to: calculate the growth rate of new phase particles, as well as evaluate the influence of metastable effects upon the deviation of component concentrations near the growing crystal’s surface from equilibrium values. Thus, with the use of the developed method, a “metastable” phase diagram of the system under study can be constructed. The approach under development has been applied to the calculation of the α-Fe(Si) nanocrystal growth in the course of the annealing of amorphous Fe_73.5Cu₁Nb₃Si_13.5B₉ alloy. The calculation results are compared with the experiment results on the alloy’s primary crystallization. It has been shown that the iron concentration at the growing crystal’s surface insignificantly deviates from the equilibrium values. On the other hand, silicon atoms are captured by the crystallization front; the silicon concentration at the growing nanocrystal’s surface significantly deviates from the equilibrium values. After the primary crystallization of the amorphous phase occurring in the temperature range from 400 to 450°C, calculations show that the silicon concentration’s deviation from the equilibrium value should be about 2%, whereas the equilibrium concentration value amounts to about 13.3%.