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 w ork of Russel is modified, extended, and evaluated, explicitly. Specif ically, 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 wil l not grow. A kinetic coefficient determines the maximum growth veloci ty possible. For large values of this coefficient, quenches to densiti es above the melting density show interface Limited growth with the cr ystal radius increasing linearly with time. For quenches into the coex istence region the growth is diffusion limited, with the crystal radiu s increasing as the square root of elapsed time. Smaller values of the kinetic coefficient produce long lived transients which evidence quas i-power-law growth behavior with exponents between one half and unity. The smaller kinetic coefficients also lead to larger crystal compress ion. Crystal compression and nonclassical exponents have been observed in recent experiments. The theory is compared to data from small angl e scattering studies of nucleation and growth in suspensions of hard c olloidal 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 tha t the experiments are observing long lived transient rather than asymp totic growth behavior.