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A computer rimulauoo is conducted to smdy single-crystal growth by the travelingsolvent method (TSM) using a pseudo-steady-state model. The model. which ts govemed by momentum, heat, and mass balances in the system. is solved by a Bnite-volume/Newton method.Flow patterns, temperature and solute distributions, and unknown melWsolid interfaces are calculated simultaneously. The model is mainly developed for binary compounds for which the solubility of solvent in solid materials is negtigible. In such a system an integrability condition, which results from an overall solvent balance, is required to ensure the unique solution of solute fields in the computation. Sample calculations are reponed for CdTe. a 11-VI-compound semicandudor. grown from Te solvent. Due to strong couplmg of solute and tempemme fields and Rurd Row, as well as phase equilibrium, the effect of convection on the interface morphology and zone positron IS significant in such a system. Through computer simulation, the effects of some process parmeters, including the growth speed. heater temperature, and initial solvent volume, on interface shapes, convective mass uansfer, and constitutional supercooling at different degrees of convection xe also demonstrated. C JV Lan and D T Yang hlodel descriptionThe steady-state TSM growth of a binary-compound crystal is simulated using a pseudosteady-state model (PSSM). The PSSM mainly neglects the evolution of the system caused by the displacement of the ampoule in the furnace. This approximation is usually valid for the TSM system, because of the sufficiently small growth rates used. So, when a steady State is reached the growth rate is equal to the ampoule pulling speed. If heating is axisymmetic, the physical domain for the feed, the solution zone, the crystal, and the ampoule can be taken as shown in figure 1. The RHS of figure 1 shows an effective ambient-temperature distribution for computation. As it is, it can be treated as a two-dimensional model. The flow, temperature, and solute fields, as well as the shapes of the feed front (the feedsolution interface, hf(r)) and the growth front (solutiodcrystal interface, hC(r)), are represented in the cylindrical coordinate system ( r , z).The solubility of the solvent in the feed and the crystal is neglected, while the feed and growth fronts are assumed to be in equilibrium. Since the density difference between

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Computer simulation is conducted to study vertical zone-melting crystal growth. The model, which is gouemed by momentum and heat transfer in the system, is solved by a finite volume/Newton method with an implementation of the pseudo-arclength continuation. Single crystal growth of NaNDJ in a computer-controlledtransparent multizone furnace is simulated as examples. The calculated results show that natural convection induced by the buoyancy force affects melt-solid interfaces significantly, which is consistent with the obseruation during crystal growth experiments. Along the solution bmncb, mulliple steady states are observed, and they are accompanied by the inversion of the upper me/l-feed interface.

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