Nucleation and growth of crystals at the intermediate stage of phase transformations in binary melts

An exact analytical solution of integro-differential equations, which describe the phase transitions in supercooled binary melts, is constructed with allowance for fluctuating rates of crystal growth. A complete solution of the corresponding Fokker–Planck and balance equations is found for arbitrary nucleation kinetics and growth rates of crystals. In limiting cases, the obtained solutions transform to earlier known solutions for a special form of diffusivity in the space of crystal sizes and purely kinetic and “diffusion-kinetic” growth rates of nuclei.