Chemical potential of carbon in the low pressure synthesis of diamond

The low pressure synthesis of diamond is analyzed with the activity and the chemical potential of carbon, which are the criteria for the transfer of carbon from one phase to another. The atomic hydrogen hypothesis for preferential etching of graphite over diamond is equivalent to the assumption that the chemical potential of carbon in the gas phase is larger than that in diamond and smaller than that in graphite, which is contradictory to the well-established stability of graphite with respect to diamond. The chemical potential of carbon between diamond and graphite is shown to be reversed when the size of the carbon cluster is sufficiently small. The number of atoms in the carbon clusters that make diamond more stable than graphite is estimated to be similar to 104 at 1200 K and 2700 Pa from the reported values of the surface energy data. This number is much smaller than those for the other systems where the formation of metastable phases is the rule rather than an exception. The role of gas activation is probably to decrease the surface energy ratio of graphite to diamond and thus to increase this number, thus inducing the dominant formation of diamond.