Solute transfer in zone refining

Solute Transfer in Zone Refining of Eutectic-Forming Mixtures... 

This study has been conducted with the objectives 1) to analyze and determine the effect of the free convective mixing in the melted zone upon the over-all solute transfer process in zone refining under various conditions and 2) to take into account the solute transfer both in the melted zone and in the adjacent P.S.Z. (mushy region) in predicting the rate of over-all solute transfer. The temperature distribution, composition, zone travel speed, zone dimension and other important parameters are considered in this study. 

The porous medium, namely the P.S.Z., possesses a certain filtration capacity to filter out the solute. This corresponds to the rate of forward mass transfer across the P.S.Z. in zone refining. 

The thickness of a partially solidified zone (mushy region) in zone refining under most experimental conditions has been determined. The transfer of solute within this zone is, no doubt, most important in determining the overall solute transfer. All the zone refining theories have failed to take this most important factor into account. 

The "Filtration Model" as proposed in this study represents the overall rate of the solute transfer (macro-segregation) in zone refining very well for a wide range of experimental conditions. 

Several elementary aspects of mass diffusion, heat transfer and fluid flow are considered in the context of the separation and control of mixtures of liquid metals and semiconductors by crystallization and float-zone refining. First, the effect of convection on mass transfer in several configurations is considered from the viewpoint of film theory. Then a nonlinear, simplified, model of a low Prandtl number floating zone in microgravity is discussed. It is shown that the nonlinear inertia terms of the momentum equations play an important role in determining surface deflection in thermocapillary flow, and that the deflection is small in the case considered, but it is intimately related to the pressure distribution which may exist in the zone. However, thermocapillary flows may be vigorous and can affect temperature and solute distributions profoundly in zone refining, and thus they affect the quality of the crystals produced. 

The preceding discussion assumes that no convection exists in the melt, and this is rarely, if ever, the case. Next we shall consider two approaches which account for convection in the melt, a transport mechanism which is especially important in mass transfer because Dl is small and even weak convection markedly alters solute concentration profiles and may cause macrosegregation. First we shall discuss film theory which is a very simple approach that gives qualitative information and often provides considerable physical insight into the mechanisms involved. Second, we shall discuss a simplified model of zone refining. 

In the application of the Dlrlchlet type boundary conditions at the overlapping boundary lines between the Inner zone, crown zone and shoulder zones, the temperature In the neighboring region at the previous time step was used as the known temperature at first and this was repeated a few times to refine the values of temperature. The heat transfer coefficients needed In the application of Neumann type boundary conditions were determined by trial and error by repeating the solutions several times. 

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