Abstract
A new, relatively simple and highly efficient modification of the directional melt crystallization method in the form of a multi-cassette process has been considered. This study is based on Russian Patents and technological studies conducted at National Research and Technological University MISiS. As a result, mathematical models of a multi-cassette method have been developed for 3D radiation and conduction analysis of thermal processes in the entire volume of the heating unit and 2D analysis of convection and conduction heat exchange in a separate cassette. Parameters have been calculated on the basis of these mathematical models for clarifying the effect of heating unit component arrangement and dimensions on the formation of thermal fields in cassette units, the effect of vertical homogeneity of heat supply to the cassette unit and heating power reduction rate during crystallization on the shape of the crystallization front, as well as the effect of small asymmetry in cassette design and violation of cassette bottom cooling homogeneity on convection and asymmetrical heat transfer. Application of the conductive and radiative heat exchange model to the entire heating unit has allowed us to calculate process parameters on the basis of which we have analyzed the effect of heating unit components, their arrangement and temperature on the heat exchange conditions at the cassette unit boundaries. Application of the convective and conductive model to one growth cassette has shown that asymmetrical design and boundary thermal conditions as well as unstable vertical temperature gradient lead to the formation of convection vortices and substantial crystallization front deviation from planar shape. Calculations on the basis of the convective mass exchange model have shown that an increase in the crystallization rate by one order of magnitude greatly increases the tellurium flow into the crystal thus substantially altering the melt composition in the vicinity of the crystallization front and hence serving as a potential origin of dendrite growth. The authenticity of the calculation results has been verified in a number of tests aimed at analyzing the effect of heat and mass transport on crystallization front shape for cassette cooling rates that are typical of polycrystalline bismuth telluride growth processes.
Highlights
Study of the plastic formation in the production of thermoelectric material based on bismuth telluride // Russ
The parametric calculations carried out on their basis were aimed to the identifying an influence of locations and sizes of the hot zone components to a thermal field in the cassette unit; the establishing an influence of vertical heat supply equability to the cassette unit and an influence of heating power decrease during the plate crystallization, as well as to the determining an influence of small cassette design distortions and violation of cooling uniformity in its bottom part on the occurrence of convection and asymmetrical thermal field
By means of the conductive−radiative heat transfer model for the entire hot zone there were carried out parametric calculations and it was analyzed an influence of hot zone components on the heat exchange conditions at the cassette unit boundaries
Summary
Математическое моделирование тепловых процессов при кассетной кристаллизации халькогенидов. В результате были разработаны математические модели многокассетного метода, позволяющие как трехмерный радиационно−кондуктивный анализ тепловых процессов во всем объеме теплового узла, так и двумерный анализ конвективно−кондуктивного теплообмена в отдельной кассете. Этот метод получил развитие в работе [9], в которой предложен способ выращивания методом направленной кристаллизации кристаллической пластины с более совершенной кристаллической структурой, имеющей меньшие углы разориентации плоскостей спайности за счет более эффективного управления ориентацией плоскостей спайности как на стадии зарождения кристаллов, так и в процессе роста. В работе [11] на основе математического моделирования выполнен сравнительный анализ двух основных технологических подходов для получения ТЭ материалов на основе теллурида висмута: равноканального углового прессования [12] и кассетной кристаллизации методом Бриджмена.
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