Energetical preference of diamond nanoparticles.

Abstract

The energetical advantage of diamond in comparison with graphite caused by small particle sizes is established by modeling and computation of free energy. The results, obtained for low external pressure, P\ensuremath{\simeq}0, and for temperatures up to 1100 \ifmmode^\circ\else\textdegree\fi{}C, indicate that diamond is the stable modification of carbon, and graphite is the metastable one at small particle sizes which are less than the boundary of stability regions of these phases. The models of crystal charge lattices have been determined to compute lattice energies by summation of pair interaction potentials acting between elements (ions, electrons) of the charge lattices. The diamond charge lattice is presented by an ion-electron lattice of negative bond charges and positive ions. The graphite charge lattice consists of hexagonal ion-electron nets and collectivized conduction electrons located between the nets. The consideration of conduction electrons in the graphite model provides the stable graphite structure because the attraction between the conduction electrons and hexagonal nets compensates for the repulsive forces acting between the nets. Mechanisms of the nucleation of diamond and graphite have been considered to determine the structure of clusters forming these phases. The considered mechanism of nucleation of diamond clusters consists in the forming of octagonal carbon clusters with the following transformation of the octagonal clusters to the ten-atomic-diamond clusters. The octagonal clusters consist of the same fragments of carbon atoms as the fragments forming the graphite nets. But the difference is that diamond crystals are generated from an octagon of atoms and the graphite clusters are formed from hexagons. The intersection of size dependences of free energies of diamond and graphite indicates the size-related stabilization of diamond nanoparticles. The established boundaries of the stability regions of diamond and graphite are 10.2 nm at room temperature, 6.1 nm at 525 \ifmmode^\circ\else\textdegree\fi{}C, 4.8 nm at 800 \ifmmode^\circ\else\textdegree\fi{}C, and 4.3 nm at 1100 \ifmmode^\circ\else\textdegree\fi{}C. \textcopyright{} 1996 The American Physical Society.