Modeling of nano-modified binary alloy crystallization processes

A mathematical model of nonequilibrium crystallization of a binary aluminum alloy (Al-Si) with modifying refractory nanosized particles, which are the centers of nucleation of the crystalline phase, is proposed. The model describes thermodynamic processes, as well as heterogeneous nucleation and crystallization of $\alpha$-component and $\beta$-component of the melt. The nucleation of the crystalline phase occurs on the surface of the nanoparticles during the supercooling of the melt. The liquidus temperature in the melt depends on the concentration of the dissolved alloying component, which is determined from the non-equilibrium lever equation. When the metal is cooled down to eutectic temperature, the crystallization of the alloy $\alpha$-component takes place, followed by crystallization of the $\beta$-component if the cooling continues. The growth rate of the crystal phase is proportional to the supercooling. The volume of the solid phase formed around the nucleus determines the size of the grain structure in the solidified alloy. Numerical simulation of melt solidification in cylindrical mold is carried out. The parameters of heat exchange of the melt-mold system with the environment are determined in experiments. The features of the heterogeneous nucleation and crystallization kinetics during the melt cooling are considered. It is determined that the conditions of nucleation, crystallization rate, supercooling and solidification time differ significantly within the cast. According to the results obtained, it is found out that as the melt cools, there is a volume-sequential crystallization of the metal. The area with the finest structure of the solidified metal is located near the wall of the mold. The estimation of the grain structure size in the cast is consistent with the experimental results. The reliability of the proposed model is confirmed by comparing the results of numerical calculation with the data of a physical experiment on measuring the temperature during solidification of the melt and studying the properties of the cast.