"Bending" of steps on rapidly grown KH2PO4 crystals due to an inhomogeneous surface supersaturation field

The surfaces of large rapidly grown KH2PO4 (KDP) crystals can exhibit the f ormation of valleys in addition to the well-known growth hillocks and assoc iated intervicinal boundaries between them. Understanding the mechanism of formation of these valleys is extremely important because they are observed to be precursors to the formation of solution inclusions on the crystal su rface. Ea situ measurements using a precision coordinate measuring machine (CMM) have been made of the surface topography of rapidly grown KDP crystal s. These measurements clearly indicate that these valleys are formed by the "bending'' of macrosteps originating from a single growth hillock. Results from numerical simulations of the hydrodynamics and mass transfer for the conditions used in the rapid growth process show that the surface supersatu ration held generated on these crystals is inhomogeneous due to the spatial ly and temporally varying boundary layer thickness on the rotating crystal surface. These numerical results are used together with a simple model for the propagation of steps in an inhomogeneous surface supersaturation field to simulate the resulting crystal surface features. The qualitative agreeme nt between the surface measurements and the numerical simulations is shown to be quite good. The dependence of the valley formation on parameters such as crystal growth rate, rotation conditions, growth hillock location, and impurity level are studied. (C) 2000 Published by Elsevier Science B.V. All rights reserved.