We constructed a continuum theory of carbon phases based on the Landau theory of phase transitions. Our theory ties up many seemingly unrelated data on the carbon system. Transformations between graphite, diamond, and liquid-carbon are described by the Landau– Gibbs free-energy which depends on two order parameters: crystallization and structural. The barrier-height and gradient-energy coefficients were calculated from the nucleation data obtained in the studies of diamond/graphite and diamond/liquid-carbon systems. The boundary of the absolute stability of the graphitic phase was interpreted as the spinodal point of the free-energy, which allowed us to calculate the pressure dependence of the barrier-height coefficient. The continuum model yielded a value of 1.66 J/m2 for the graphite/liquid-carbon interface energy, which continues the trend of the elements of Group IV. We also analyzed stability of nanostructured amorphous carbon and interpreted it as the transition state of the free-energy function. This conjecture helped us to explain results of the experiments on the focused ion-beam irradiation of CVD-diamond nanofilms. The present theory may be used for the large-scale modeling of graphite and diamond crystallization; it can also be extended to include other structural modifications of carbon or an entirely different element such as silicon.
Umantsev, Alexander and Akkerman, Zinoviy, "Continuum Theory of Carbon Phases" (2009). Faculty Working Papers. 13.