Simulation of crystal growth in multicomponent metastable alloys

Abstract

A method for predicting the regularities of crystal growth from metastable melts has been developed. The process of crystal growth from a multicomponent melt is described by the methods of nonequilibrium thermodynamics, taking into account the mutual influence of thermal and diffusion processes. The application of a new variational approach to the constructed system of equations made it possible to obtain expressions of the crystal growth rate from a multicomponent melt convenient for practical calculations. The obtained technique allowed us to analyze the features of crystal growth at high rate of crystallization front, which leads to “impurity capture” effect – deviation from equilibrium conditions at the phase interface. The developed mathematical model makes it possible to calculate the growth rate of new phase particles and to estimate the effect of metastable effects on deviation of the components’ concentration at surface of the growing crystal from equilibrium values. Thus, using the obtained method, a “metastable” phase diagram of the system under study can be constructed. The developed approach is applied to the calculation of growth of α-Fe(Si) nanocrystals during annealing of amorphous alloy Fe_73,5 Cu₁ Nb₃ Si_13,5B₉. The calculation results were compared with the results of the experiment on the alloy primary crystallization. It is shown that the concentration of Fe at the surface of the growing crystal does not significantly deviate from the equilibrium values. On the other hand, silicon atoms are captured by the crystallization front, silicon concentration at the surface of the growing nanocrystal deviates significantly from equilibrium values. The calculation has shown that after the initial crystallization of the amorphous phase, occurring at a temperature of 400 – 450 °C, the deviation of silicon concentration from equilibrium value is about 2 %, while this equilibrium value is about 13.3 %.