Transport phenomena in crystal growth from solution

Abstract This is a review of the role of transport phenomena in crystal growth from solution. Transport phenomena are normally taken to include fluid motion (convection), heat transfer and mass transfer. These prosesses strongly influence growth rate, crystal morphology, and defect formation. Mass transfer arises primarily from concentration gradients, but can also be caused by a temperature gradient (Soret effect), an electric field, acceleration of gravity, etc. In solutions, mass transfer is strongly enhanced by convection; the motion of the solution carries material with it. Similarly, convection can be caused by a variety of driving forces; a pressure gradient, mechanical forces, buoyancy, electric fields, and even the growth of the crystal itself. Except in liquid metals, heat transfer in liquids is also strongly enhanced by convection. It is important to realize that the simple form of Fick's first law is often not valid in crystal growth from solutions, i.e. the mass transfer flux is not necessarily equal to the product of a concentration gradient and a diffusion coefficient. In multicomponent systems the flux of a component depends on the concentration gradients of all the other constituents. It is possible for a component to move from a region where its concentration is low to a region where its concentration is high. If the component is charged, its movement is also strongly influenced by an electric field, which may be generated by the diffusion process itself. The flux of a solute into the surface of the crystal equals the growth rate, and includes a contribution caused by the movement of the solution toward the crystal surface. This convective contribution has the effect of increasing the growth rate beyond that predicted by Fick's first law, especially when the solubility is large. It is also important to note that the stagnant film model for heat and mass transfer in the presence of convection is a fiction and can lead to erroneous predictions. There is no unstirred layer near the surface of the crystal. With convection, the mass transport rate is not proportional to the diffusion coefficient and the heat transfer rate is not proportional to the thermal conductivity. The operational challenge in crystal growth from solutions is to maximize the growth rate without trapping the solution as inclusions in the crystal. Constitutional supercooling is always present in solution growth, but does not prevent growth without interface breakdown. High quality crystals can be grown from solutions because step propagation is faster than step generation, as manifested by the presence of facets. Faceted growth can become unstable when step trains decelerate, which occurs when steps begin in regions of high supersaturation and move to regions of low supersaturation. In order to avoid this condition, either crystals must be grown very slowly or well-controlled vigorous convection must be used. However if one desires to avoid inclusion formation in the transition from dissolution to growth, it is advantageous to grow in the absence of convection so that the transition from dissolution to growth may be made gradual.