Theory of the Lattice Vibration of Graphite

Abstract

A theory of the lattice vibration and specific heat of graphite, which has a typical lamellar structure, is worked out using the Born-von Karman method. Four types of restoring forces are assumed; the first and second ones are associated with changes in the bond lengths and bond angles of the honey-comb net planes, respectively, the third with change in distance between neighoring atoms on adjacent net planes, and the fourth with the bending of the net planes. We have obtained modes whose polarizations are parallel and perpendicular to the planes. The former are essentially two-dimensional, but the latter are of more complex characters and play a particular role in the temperature range 45° to 100°K. As our main interest is in this and higher temperature ranges, we neglect the shearing forces between neighboring net planes which are effective at much lower temperatures. For small wave numbers, our theory naturally reduces to the semi-continuum theory developed by Komatsu and Nagamiya (1951) and Komatsu (1...