Crystal nucleation and liquid-liquid transition in deeply supercooled silicon

The possibility of a liquid-liquid phase transition in several network-forming liquids such as water, silica and silicon has been intensely investigated over several years. In the majority of cases these putative transitions occur at conditions far below the melting temperature. Under such conditions, the kinetics of crystallisation in principle poses a challenge towards observing such a transition. In fact, it has been argued, on the basis of reversible free energy calculations, that the evidence points instead towards slow, but spontaneous, crystallisation. Robust evidence of well-defined metastable liquid states and a liquid-liquid transition has been found for a number of models of water. These studies also show a clear free energy barrier to crystallisation under the relevant conditions. We study crystal nucleation in liquid silicon through computer simulations of a classical model, with the aim of answering the specific question of whether a well-defined metastable liquid exists under the relevant conditions. We find, that indeed a barrier to crystallisation exists, and that the choice of order parameter is crucial. We also discuss the effect of changes in the microscopic structure of the liquid on the free energy barriers to crystallisation.