|M.Sc Student||Meir Arye (Leib)|
|Subject||Internal Radiation Heat Transfer During the Growth of|
Sapphire Crystal Domes
|Department||Department of Chemical Engineering||Supervisor||Professor Simon Brandon|
At Rotem Industries a production line for growth of sapphire domes has been operating during the last two decades.
Large high quality single crystals are grown by the gradient solidification method (GSM); the growth is carried out in double-wall molybdenum crucibles and perfect crystals, free of grain boundaries and scattering centers are produced.
Unfortunately, the high temperatures associated with sapphire growth (melting point ~20400C) and the sensitivity of the process to the working parameters, limit the understanding and possible improvement of this process. In this case experimental analysis is very difficult and it is necessary to augment this approach with numerical analysis techniques.
The main goal for this work is the production and application of a finite-element-based tool for the numerical analysis of thermal fields in the crucibles during the growth. It is intended for this tool to be coupled to another global heat transport algorithm, developed (elsewhere) for the analysis of heat transport within the furnace in which the growth crucibles are placed.
The finite element model consists of four domains: a transparent inner domain in which heat flows solely by radiation between surfaces, two opaque crucibles in which heat transport is dominated by conduction, the transparent crystal in which heat flows by combined conduction and non participating radiation, and the optically thick melt in which heat flows via conduction and participating radiation mechanisms; both the P1 and the Rosseland methods were selected for the calculation of participating radiation in the melt.
The following techniques are used in the final model: Radiation heat transfer between surfaces is calculated by means of direct element-by-element integration; this new technique shows very good results in the current work. The P1 approximation is used to model the radiation in the melt. The Marshak boundary condition is applied for the opaque molybdenum surfaces. In this work we suggest an improvement for these boundary conditions, which can be applied to handle radiation through the melt/crystal interface. The Rosseland approach is also used to describe inner radiation phenomena in the melt. For this purpose a general form for the slip boundary condition is derived
Results show significant dependence of the thermal field on the absorbtivity of the melt, the boundary conditions and the physical parameters (medium conductivity, boundary emissivity etc).
The algorithm developed here, which employs realistic inner and outer boundary conditions, is able to predict temperature fields and melt/crystal interface shapes existing during crystal growth. In order to further improve the realistic nature of the results, future work will include coupling the boundary conditions to an existing global analysis algorithm.