Abstract:
PREDICTING the shape of growing crystals is important for industrial crystallization processes. The equilibrium form of a crystal can be determined unambiguously from a consideration of the surface free energies of the various crystallographic faces {hkl}(1), but the grow th morphology is determined by kinetic factors which are harder to predict. This morphology depends on the relative growth rates R(hld)(rel) of the crystal faces. Several theories have been advanced(2,3) to relate R(hkl)(rel) to geometric or energetic characteristics of the surfaces {hkl}, but these have met with limited success in predicting the crystal morphologies observed. Here we present a theoretical approach to the problem in which R(hkl)(rel) is determined by quantities that are accessible either from kinetic models or from computer simulations of the solid-fluid interface. The important parameters controlling the growth rate are the energy required to create a step at the crystal surface and the free-energy barrier for an adsorbed solute molecule to be incorporated into the crystal. Both can be related to the mole fraction of adsorbed solute molecules in dynamic equilibrium with those in the crystal surface. When this approach is applied to the case of urea crystals grown from aqueous solution, we predict a needle-like shape which is consistent with experimental observations.