Fluctuation mechanism of normal crystal growth during solidification of binary metallic melts

A recently published theory on the solidification of a one-component melt has been extended to the more complex case of binary systems. The theory is based on the model of a two-phase transitional zone existing between the crystalline phase and the melt. The concentration of solid state atoms within each mono-atomic layer of the transitional zone are assumed to fluctuate due to thermal fluctuations. A crystal growth law has been derived expressing the crystallization velocity in terms of probability functions describing these concentrations fluctuations. When certain restricting conditions concerning the atomic interaction energies within the transitional zone and the distribution of the atoms among the solid and liquid phases at supercooling are fulfilled the crystal growth law attains a simple form predicting for small supercoolings a growth rate proportional to supercooling (linear growth law), roughly proportional to physical parameter θ_AA, and with a weak dependence on another parameter Δ.