Growth kinetics and melt convection

A phase-field model have been developed, which fits into the framework of the lattice Boltzmann model. Calculations for the growth of monocomponent dendrites and comparison with analytic results have proven its applicability. The phase-field model has been extented to describe the melt/solid system of binary alloys. This model has been applied to perform first calculations of the microstructure evolving during the Czochralski growth of GeSi single crystals.

[1]  W. Miller,et al.  CRYSTAL GROWTH KINETICS AND FLUID FLOW , 2003 .

[2]  Gustav Amberg,et al.  Phase-field simulation of dendritic growth in a shear flow , 1998 .

[3]  Sauro Succi,et al.  Towards a Renormalized Lattice Boltzmann Equation for Fluid Turbulence , 2002 .

[4]  M. Ode,et al.  Phase–field model for solidification of Fe–C alloys , 2000 .

[5]  Toshio Suzuki,et al.  Phase-field model for binary alloys. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  S Succi,et al.  Lattice Boltzmann model for anisotropic liquid-solid phase transition. , 2001, Physical review letters.

[7]  A. Karma,et al.  Quantitative phase-field modeling of dendritic growth in two and three dimensions , 1996 .

[8]  A. Karma,et al.  Phase-field simulations of dendritic crystal growth in a forced flow. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  D. Wolf-Gladrow.  Lattice-Gas Cellular Automata and Lattice Boltzmann Models: An Introduction , 2000 .

[10]  C. Hsu,et al.  Efficient adaptive phase field simulation of dendritic growth in a forced flow at low supercooling , 2002 .

[11]  William N. Gill,et al.  Selection of a length scale in unconstrained dendritic growth with convection in the melt , 1993 .

[12]  Wheeler,et al.  Phase-field model for isothermal phase transitions in binary alloys. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[13]  Pierre Lallemand,et al.  Lattice Gas Hydrodynamics in Two and Three Dimensions , 1987, Complex Syst..