Classical growth of hard-sphere colloidal crystals

The classical theory of nucleation and growth of crystals is examined for concentrated suspensions of hard-sphere colloidal particles. The work of Russel is modified, extended, and evaluated, explicitly. Specifically, the Wilson-Frenkel growth law is modified to include the Gibbs-Thomson effect and is evaluated numerically. The results demonstrate that there is a critical nucleus radius below which crystal nuclei will not grow. A kinetic coefficient determines the maximum growth velocity possible. For large values of this coefficient, quenches to densities above the melting density show interface limited growth with the crystal radius increasing linearly with time. For quenches into the coexistence region the growth is diffusion limited, with the crystal radius increasing as the square root of elapsed time. Smaller values of the kinetic coefficient produce long lived transients which evidence quasi-power-law growth behavior with exponents between one half and unity. The smaller kinetic coefficients also lead to larger crystal compression. Crystal compression and nonclassical exponents have been observed in recent experiments. The theory is compared to data from small angle scattering studies of nucleation and growth in suspensions of hard colloidal spheres. The experimental nucleation rate is much larger than the theoretically predicted value as the freezing point is approached but shows better agreement near the melting point. The crystal growth with time is described reasonably well by the theory and suggests that the experiments are observing long lived transient rather than asymptotic growth behavior. (c) 1995 The American Physical Society