Facetting during directional growth of oxides from the melt: coupling between thermal fields, kinetics and melt/crystal interface shapes

Implicit in most large-scale numerical analyses of crystal growth from the melt is the assumption that the melt/crystal interface shape and position a re determined by transport phenomena. Although reasonable for many material s under a variety of growth conditions, this assumption is incorrect for a number of practical systems under realistic growth conditions. Specifically , the behavior of systems (e.g, certain oxides) which tend to develop facet s along the melt/crystal interface is often affected both by transport phen omena and by interfacial attachment kinetics. We present a new modeling app roach which accounts for interfacial kinetic effects during melt growth of large single crystals. The isotherm condition, typically employed at the me lt/crystal interface, is replaced by an equation accounting for undercoolin g due to interface kinetics. A finite-element algorithm, designed to accomm odate its numerical mesh to the appearance of facetted interfaces, is appli ed to this problem. Results are presented for the simulated directional gro wth of oxide slabs. The interplay between evolving thermal fields and aniso tropic interface kinetics is investigated. In particular, the evolution of facets and the dependence of their size on growth conditions is explored. T rends reported here are in qualitative agreement with those appearing in th e literature. Discrepancies between quantitative predictions of facet sizes using a theory (see Ann. Rev. Mater. Sci. 3 (1973) 397 and references with in) and those calculated in this paper can, in a number of cases, be attrib uted to the simplifications on which this theory is based. (C) 1999 Elsevie r Science B.V. All rights reserved.