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Mathematical Simulation of Crystal Growing in Water-Salt Solutions

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Abstract

A detection of the conditions of high-rate single crystal growth with an appropriate quality is a priority for an industrial production of crystalline materials. The crystals of potassium dihydrogen phosphate (KDP) are the important optical materials. They are growing from water-salt solutions. The flow and mass transfer are modeled within the framework of continuous medium, which is considered as a water solution of a special salt-potassium dihydrogen phosphate. This salt dissolves in water to a saturation level at a high temperature. Then, such supersaturated solution is used to grow crystals at lower temperatures in static crystallizers (without inflow and outflow) and in continuous-flow crystallizers. The mathematical model is considered in a conjugate formulation with taking into an account of mass transfer in “solution–crystal” system. The local features of hydrodynamics and mass transfer in a solution near a surface of growing crystal are established, which may affect to a local (for a particular place and direction) crystal growth rates and a defect formation. The requirements to the crystallizers for providing a “necessary” solution hydrodynamics are discussed. The validation of this model is shown for the task of flow around a long horizontal plate, which simulating the growing crystal facet. The rate of salt precipitation is estimated by means of proposed mathematical model, in which a solution flow and salt concentration are calculated by solving Navier-Stokes and mass transfer equations for an incompressible fluid. Then the calculated salt flux on crystal surface is applied in a thermodynamic relationship for a normal growth of facets under conditions of two-dimensional nucleation. The action of continuous-flow crystallizers was analyzed for various solution inflows (axial and ring) and its outflow through the bottom hole.

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Funding

The present work was supported by the Ministry of Science and Higher Education within the framework of the Russian State Assignment under contract No. AAAA-A20-120011690136-2.

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Authors and Affiliations

  1. Ishlinsky Institute for Problems in Mechanics of Russian Academy of Sciences, 119526, Moscow, Russia

    A. I. Prostomolotov & N. A. Verezub

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  1. A. I. Prostomolotov
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  2. N. A. Verezub
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Correspondence to A. I. Prostomolotov or N. A. Verezub.

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Prostomolotov, A., Verezub, N.A. Mathematical Simulation of Crystal Growing in Water-Salt Solutions. Mech. Solids 57, 883–892 (2022). https://doi.org/10.3103/S002565442204015X

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