Continuum Theory of Amorphous Carbon Nanostructures

Carbon is often considered to be silicon of the future because of the unique properties resulting from the variety of possible structural forms. A wide range of electronic properties of carbon yields many possible applications. Classical thermodynamics successfully describes bulk equilibrium of the diamond-graphite system in a wide range of temperatures and pressures. Equilibrium in the carbon system at nanoscale, however, has not been clarified despite the significance of this information for numerous existing and possible applications of carbon in nanoelectronics. In the present paper, we analyze the transition between diamond and graphite phases using the continuum Landau theory. The theory sheds light on the details of such transitions, and more importantly, predicts a new stable phase at nanoscale that can be used in carbon-based nanodevices. We find that the transition state of a system capable of undergoing a graphite/diamond phase transition gains thermodynamic stability against the bulk phases under the conditions of a limited volume if the barrier height of the transition is below the critical value. In a large-size closed system, a heterogeneous mixture of the graphite and diamond phases is the most stable state. In a small system (below the critical size), the heterogeneous mixture is not possible and the transition state becomes the globally stable state-a phase. Based on the present analysis, we hypothesize that the transition state is associated with the amorphous phase of carbon observed experimentally. The theoretical results allow us to interpret the experiments on focused ion beam scanning irradiation of single crystal CVD diamond films, which produce highly conductive regions on the diamond surface.