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 are determined by transport phenomena. Although reasonable for many materials 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 facets along the melt/crystal interface is often affected both by transport phenomena and by interfacial attachment kinetics. We present a new modeling approach which accounts for interfacial kinetic effects during melt growth of large single crystals. The isotherm condition, typically employed at the melt/crystal interface, is replaced by an equation accounting for undercooling due to interface kinetics. A finite-element algorithm, designed to accommodate its numerical mesh to the appearance of facetted interfaces, is applied to this problem. Results are presented for the simulated directional growth of oxide slabs. The interplay between evolving thermal fields and anisotropic interface kinetics is investigated. In particular, the evolution of facets and the dependence of their size on growth conditions is explored. Trends reported here are in qualitative agreement with those appearing in the literature. Discrepancies between quantitative predictions of facet sizes using a theory (see Ann. Rev. Mater. Sci. 3 (1973) 397 and references within) and those calculated in this paper can, in a number of cases, be attributed to the simplifications on which this theory is based. (C) 1999 Elsevier Science B.V. All rights reserved.