Engineering Physics Annotation << Back Calculation and Experimental Study of the State of the Thermal System in the Process of Synthesis of Fluoride Single Crystals in a Carbon-Graphite Thermal Unit Using the HDS Method Yusim V.A., Sarkisov A.E., Meksheneva Zh.V., Trubin A.E., Chanturia G.T., Bulanova T.A., Bulanov V.A. The paper presents a non-stationary three-dimensional full-size mathematical model of SrF2 single crystal synthesis by the HDS method in a carbon-graphite thermal unit using various graphite crucibles. The model describes the transient behavior of the crystal-melt, melt-gas and crystal-gas boundaries. The temperature distribution in growth crucibles of various shapes and sizes with the synthesized material at their various displacements relative to the initial state was also described. To calculate signifi cant changes in the shape of the crystallization front at the crystal-melt boundary and changes in the state of the system during the growth of a single crystal, block-structured grids were used. Each gird block is consisted of separate blocks. Each separate block is ordered three-dimensional array of conventionally cubic cells. The fi nite-difference schemes of the 1st and 2nd order were used, embedded in the used fl ow simulation package in the SolidWorks program. Additionally, a number of applied experiments were conducted to determine the state of thermal processes in the UTU under study and various crucibles during single crystal synthesis. The obtained data were compared with the data of mathematical modeling. Keywords: 3D model, SrF2 , single crystal synthesis, growth unit. DOI: 10.25791/infizik.3.2025.1463 Pp. 03-16.