Optimization of KRS-5 single crystal growth process by calculation of temperature gradient using finite element method

Objectives. Thallium halides, in particular KRS-5 (TlBr–TlI), represent one of the most promising classes of optical crystals for applications in the mid- and far-infrared ranges. Nevertheless, the high-quality standards applied to materials used for such applications present considerable challenges in the manufacture of single thallium halide crystals. In particular, when failing to adhere to exacting growth conditions, the samples exhibit polycrystalline characteristics, rendering them unsuitable for utilization. Given the high cost of experiments carried out to ascertain the optimal conditions for growth, computer modeling may present a viable alternative. When taking such an approach to satisfy the specific requirements, it becomes possible to analyze key effects as standalone entities, thus avoiding unnecessary complications resulting from the introduction of a high number of simultaneous unknown variables. Thus, the aim of the present work is to simulate the growth conditions of KRS-5 crystal to ascertain the causes of polycrystallinity in the samples and identify the optimal parameters for obtaining single crystals. Methods. In order to solve the problem, the finite element method was used. This method is employed for the calculation of temperature distribution, mechanical stresses, convective effects, the rate of spreading of the crystallization front, deformations due to thermal expansion, and other phenomena that arise during the process of crystal formation. The MATLAB package, which includes a module for solving partial differential equations, was used to simulate the crystal growth ampoule. The problem of temperature gradient was solved in axisymmetric approximation. Results. A computer simulation was employed to calculate the temperature distribution within the material during the growth process. This was used to determine the position and shape of the crystallization front. It is established that polycrystalline samples develop as a consequence of the crystallization front assuming a flat configuration. The optimum temperature in the furnace was determined. The work demonstrated the successful growth of a KRS-5 crystal under the calculated conditions. Conclusions. The calculations used to identify the underlying cause of polycrystallinity in the samples enabled a determination of the optimal parameters for single crystal growth. On the basis of the calculations, a growth experiment was conducted on the KRS-5 sample. The obtained sample met the requisite criteria for commercial utilization.