Stacking in sediments of colloidal hard spheres

We use computer simulations to investigate the crystallization dynamics of sedimenting hard spheres in large systems (hundreds of thousands of particles). We show that slow sedimentation results primarily in face-centered cubic (fcc) stacked crystals, instead of random hexagonal close packed or hexagonal close packed (hcp) crystals. We also find slanted stacking faults, in the fcc regions. However, we attribute the formation of fcc to the free energy difference between fcc and hcp and not to the presence of these slanted stacking faults. Although the free energy difference between hcp and fcc per particle is small (only 10(-3) times the thermal energy), it can become considerable, when multiplied by the number of particles in each domain. The ratio of fcc to hcp obtained from dynamic simulations is in excellent agreement with well-equilibrated Monte Carlo simulations, in which no slanted stacking faults were found. Our results explain a range of experiments on colloids, in which the amount of fcc increases upon lowering the sedimentation rate or decreasing the initial volume fraction.