Thermal convection and related instabilities in models of crystal growth from the melt on earth and in microgravity: Past history and current status

Abstract

The paper presents a comparative study of a number of theoretical/experimental/numerical results concerning the dynamics of natural (gravitational), Marangoni and related mixed convection in various geometrical models of widely-used technologies for the production of single-crystalline materials (Horizontal and vertical Bridgman growth, Czochralski method, Floating Zone Technique). Emphasis is given to fundamental knowledge provided over the years by landmark analyses as well as to very recent contributions. Such a knowledge is of paramount importance since it is validating new, more complex models, accelerating the current trend towards predictable and reproducible phenomena and finally providing an adequate scientific foundation to industrial processes which are still conducted on a largely empirical basis. A deductive approach is followed with fluid-dynamic systems of growing complexity being treated as the discussion progresses.

On experimental and numerical prediction of instabilities in Czochralski melt flow configuration

“…All three numbers strongly depend on the flow pattern. Basing on [9,10] we assume that if all three numbers agree the numerical code can be considered as validated at least at the values of DT close to critical. For further code validation, comparisons of the whole frequency spectrum can be considered.…”

“…We assume that quantitative agreement between measured and calculated critical parameters, which is yet to be obtained, ensures correct calculation of the flow and temperature fields, at least not very far from the threshold. This assumption is based on several conclusions derived from computational stability studies [9,10], where it was stated that correct computation of the instability threshold requires a sufficient accuracy for computation of both steady-state flow and the leading unstable eigenmode. On this basis all additional information can be derived from the numerical solution without carrying out new experiments.…”

On the General Properties of Steady Gravitational Thermal Flows of Liquid Metals in Variable Cross-section Containers

“…Though such production methods differ in the shape of the container used to host the liquid and/or the direction of the applied temperature gradient (Lappa, 2005), the presence of convection of gravitational (buoyancy) nature in the melt cannot be avoided. Such flows can adversely affect the perfection and purity of the ordered crystalline structures of the solidified material (bulk convection typically leads to the formation of "striations" or "segregations", at the micro or macro scale, respectively; Dupret and Van der Bogaert, 1994; Monberg, 1994).…”

The Role of Marangoni Convection in Crystal Growth

“…Figure 22.8 shows the numerical results of the changes in the pattern of twodimensional Marangoni convection in a liquid layer with low Prandtl number Pr ¼ 0.01 for increasing values of Ma, where the cold and hot sides are on the left and on the right of each layer, and additionally both upper and lower boundaries are adiabatic [33]. Figure 22.8 shows the numerical results of the changes in the pattern of twodimensional Marangoni convection in a liquid layer with low Prandtl number Pr ¼ 0.01 for increasing values of Ma, where the cold and hot sides are on the left and on the right of each layer, and additionally both upper and lower boundaries are adiabatic [33].…”