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. (C) 2004 Elsevier B.V. All rights reserved.