Diamonds melt at temperatures above 4000 K. There are no measurements of the steady-state rate of the\ud reverse process, i.e., diamond nucleation from the melt, because experiments are difficult at these extreme\ud temperatures and pressures. Using numerical simulations, we estimate the diamond nucleation rate and\ud find that it increases by many orders of magnitude when the pressure is increased at constant supersaturation.\ud The reason is that by increasing the pressure the local coordination of the liquid changes from\ud threefold to fourfold, and we show that the free-energy cost to create a diamond-liquid interface is lower in\ud the fourfold than in the threefold liquid. We speculate that this mechanism for nucleation control is\ud relevant for crystallization in many network-forming liquids. We conclude that homogeneous diamond\ud nucleation is likely in carbon-rich stars and unlikely in gaseous planets
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