  Diamonds melt at temperatures above 4000 K. There are no measurements of the
steady-state rate of the reverse process: diamond nucleation from the melt,
because experiments are difficult at these extreme temperatures and pressures.
Using numerical simulations, we estimate the diamond nucleation rate and find
that it increases by many orders of magnitude when the pressure is increased at
constant supersaturation. The reason is that an increase in pressure changes
the local coordination of carbon atoms from three-fold to four-fold. It turns
out to be much easier to nucleate diamond in a four-fold coordinated liquid
than in a liquid with three-fold coordination, because in the latter case the
free-energy cost to create a diamond-liquid interface is higher. We speculate
that this mechanism for nucleation control is relevant for crystallization in
many network-forming liquids. On the basis of our calculations, we conclude
that homogeneous diamond nucleation is likely in carbon-rich stars and unlikely
in gaseous planets.
