Surface energy and the size of diamond crystals

In this work we estimate the critical size for condensation of diamond crystals produced in the detonation zone of high explosives by including a surface energy term in the Gibbs free energy and assuming that the condition of thermodynamic equilibrium is satisfied so that the concentration of reaction products is determined by minimizing the free energy. The condition for equilibrium can be written as gA=gD+6γs/ρDd, where gD is the Gibbs energy per unit mass of diamond, ρD is the density of diamond, d is the diameter of the diamond crystals, γs is the surface energy, and gA is the Gibbs energy per unit mass of other forms of carbon. From calculations of binding energy for various size tetrahedral molecules reported by Badziag, et al. the surface energy for diamond can be estimated to be about 0.6 J/m2. Preliminary calculations using approximate expressions for the Gibbs energy for diamond and graphite indicate that the critical size for condensation of diamond crystals at a pressure of 300 kb and temperature of 3000 K would be about 5 Å.