Melt boundaries

Accumulation rate of x in the slag = removal rate through melt boundary layer ... 

Here, we have assumed that resistance is in the melt boundary layer. However, resistance in the slag boundary layer can also be taken into account. Then kt is replaced by a total mass transfer coefficient that is obtained by summing the two resistances. 

Miki et al. [12] gave a relationship between the yield of Si and the attained phosphorus concentration during vacuum treatment at 1823K, see Fig. 1.10. This result is based on the assumptions that (1) there is no resistance in the melt boundary layer, (2) a perfect vacuum is maintained. 

According to equation (3.6.59) the obtained data should be represented by a straight line in the —log sMe0 —f(S) coordinates. Such a dependence for the case of PbO is presented in Fig. 3.6.8. From equation (3.6.59) it follows that the surface energy at a solid oxide-ionic melt boundary can be calculated from the slope of the —log sMe0 — /(.S ) dependence according to the equation... 

Laser Beam Machining, Fig.1 Overview of laser machining processes and their typical laser-matter interaction times and power densities. The red line marks the 1 kJ/cm energy density level, where most processes are distributed. The dotted line indicates the melt boundary of metals (Reprinted from Meijer et al. (2002), with permission from Elsevier)... 

Computations based on the extended 3D model of the hot zone have shown, in particular, that the distribution of the temperature and of the heat at the melt/cmcible and the crystal/melt boundaries are essentially nonstationary and greatly deviate from the axisymmetric ones [37, 38]. Note that strong spatial and temporal nonuniformity of the heat flux at the crystal/melt interface (and, hence, of the growth rate) is probably a cause of striations in the resistivity and the oxygen level in the grown crystals. 

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