ABSTRACT
We have studied the evolution of cellular structures in Ge 1-x Si x single-crystal growth as a function of process parameters. Because these structures are much larger than those occurring during the solidification of metals, we developed a modified phase-field method, which is able to handle these structure within reasonable computer times using the real material parameters. The model has been tested for computing equilibrium shapes of crystals, dendritic growth, and cellular growth of Ni x Cu 1-x. We also performed classical molecular dynamics calculations in order to compute the diffusion coefficients of Si and Ge in melts of various compositions.
Subject(s)
Biophysics/methods , Crystallization , Germanium/chemistry , Silicon/chemistry , Anisotropy , Copper/chemistry , Materials Testing , Models, Biological , Nickel/chemistry , Polymers/chemistry , ThermodynamicsABSTRACT
A phase-field lattice kinetic model is presented for the numerical simulation of the dendritic growth of a pure crystal in the presence of thermal transport. A finite-difference scheme for the phase field is combined with an explicit lattice kinetic scheme for the temperature field. The resulting scheme is advanced in time with an adaptive time-marching procedure which permits us to achieve long simulation times with larger time steps than explicit finite-difference and previous kinetic methods. The method is demonstrated for the case of dendritic growth of a single crystal over a wide range of Stefan and capillarity numbers.
