Numerical simulations of flow and mass transfer during potassium dihydrogen phosphate single crystal growth via the three-dimensional motion growth method

A novel solution-based crystal growth method, namely, the three-dimensional motion growth method (3D MGM) is proposed to effectively utilize convection for simultaneous enhancement of morphological stability and mass transfer. To evaluate this new growth method, numerical simulations of flow and mass transfer are carried out on growth of potassium dihydrogen phosphate (KDP) crystals subjected to 3D MGM. The supersaturation field of the crystal surface is presented as functions of translational velocity and distance since it is critically involved in the processes of morphological instability and inclusion formation; the dependences of surface supersaturation on the solution flow surrounding the crystal surface are analyzed in detail. The correlations between thickness of the solute boundary layer and translational velocity and distance are described. The roles of natural and forced convection in mass transfer under different conditions are discussed, with results showing that the effects of natural convection are significant only at low translational velocities. The Damkohler number is introduced to measure the significance of mass transport limitations in the solution system of 3D MGM crystal growth, where it implies that with the increase of translational velocity, the limitations in mass transport decrease. Comparisons with the traditional rotating-crystal method indicate that 3D MGM has advantages in terms of the distribution homogeneity of surface supersaturation. The model of steps moving on the prismatic face demonstrates that the step-train propagates more stably on the crystal surface when the 3D MGM is applied.