Energy Bands in Graphite

Abstract

THE graphite crystal is known to consist of parallel planes of carbon atoms. The planes are about 3.35 A. apart, indicating¹ that the binding between them is of long-range, or Van der Waals, type. In each plane the atoms form a regular hexagonal pattern of side 1.42 A. The closeness of this value to that for aromatic systems such as benzene (1.39 A.) or coronene² (1.41 A.) makes it clear that in any one plane the binding consists of : (i) basic o-type bonds resembling ordinary chemical single bonds, symmetrical around each C-C direction, and effectively localized in this region ; and (ii) mobile (or conduction, or ¶-) electrons, which are not localized, and the symmetry of which relative to the basal plane is the same as that of a separate 2p_z-atomic orbital, the z direction lying perpendicular to the plane. The existence of these second electrons gives the metallic character to graphite, and their behaviour may be studied by methods essentially similar to those used^2,3,4 for condensed hydrocarbons. These methods correspond, in usual metal theory, to the 'tight-binding approximation'.