Modeling the mass transfer processes in the growth of KDP crystals from solution

Finding the conditions of high-speed single crystal growth with an appropriate quality is a priority for the industrial production of crystalline materials. Crystals of potassium dihydrogen phosphate (KDP) are important optical materials, they are grown from an aqueous solution and an increase in the rate of growth and quality of a single crystal is of great practical importance. In this paper, mathematical simulation of hydrodynamic and mass transfer processes in growing KDP crystals is performed. The flow and mass transfer are modeled within the framework of continuous medium, which is considered as an aqueous 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 non-flowing and flowing crystallizers. The mathematical model is considered in a conjugate formulation with allowance for mass transfer in the «solution—crystal» system. Local features of hydrodynamics and mass transfer in a solution near the surface of a growing crystal are determined, which can affect on the local (for a particular place and direction) crystal growth rate and the formation of defects. The requirements to the crystallizers that provide the «necessary» hydrodynamics in the solution are discussed. Its validation is shown for the flow around a long horizontal plate simulating the growing facet of the crystal. The rate of precipitation of salt was evaluated by the proposed mathematical model, which matches the calculation of solution flow according to the Navier-Stokes equations for an incompressible fluid with a thermodynamic condition for the normal growth of a face under conditions of two-dimensional nucleation. The action of the flowing crystallizers was analyzed for various solution inflows (axial and ring) and its outflow through the axial bottom hole.