NONEQUILIBRIUM VACANCY ENTRAPMENT BY RAPID SOLIDIFICATION

A complete, self-consistent theory is presented of vacancy entrapment at a rapidly advancing solidification front. This consists of heat conduction equations for the solid and liquid regions, a vacancy diffusion equation for the solid region, and boundary conditions at the liquid/solid interface expressed in the form of heat and vacancy fluxes. These dynamic fluxes, which connect the two phases and provide explicit coupling between enthalpy and vacancy concentration, describe the generation of the latent heat of fusion and the creation and annihilation of vacancies at the interface. This system of equations is specialized to the case of spherical, rapidly solidifying metal droplets, and solved by two methods. Firstly, solutions are given in the form of a set of integral equations that incorporate the boundary conditions as integral kernels. Temperature and vacancy concentration profiles calculated numerically show the existence of distinct, undercooling- and heat extraction-dominated solidification regimes, with large vacancy supersaturations achieved in the former case. Secondly, the system of equations is transformed into a set of algebraic and first-order ordinary differential equations by use of polynomial expressions for the profiles, and is solved to give the time evolution of the temperature and vacancy concentration at the moving interface.