Hard sphere crystal growth

We have recently confirmed that hard sphere nucleation can be well described by equilibrium techniques. We now show that while nucleation can be described by quasi equilibrium techniques, the subsequent crystal growth can not. Using both computer simulations and experiments we show that when a single hard sphere nucleus grows out many twinning defects form. These twinning defects have no chance to anneal out because the crystal keeps growing. This results in a defected nucleus consisting of many differently oriented domains. We observe a large variation in the number and size of the crystalline domains. We find that this is caused by the structure of the critical nucleus: a mostly fcc nucleus results in many small domains while a more randomly stacked nucleus results in much larger domains. We subsequently calculate the structure factors of growing nuclei and analyze these in the same manner as in light scattering experiments. We find that the multi-domain structure of these nuclei causes a significant broadening of the peaks. This results in over counting the number of nuclei and an overestimation of the nucleation rate at low super-saturation. This might solve the longstanding discrepancy between nucleation rates obtained using scattering experiments and those obtained using computer simulations.