Semiconductivity and Diamagnetism of Polycrystalline Graphite and Condensed Ring Systems

Abstract

The analysis of results obtained from studies of electric resistivity as a function of temperature, and sample preparation, and of other available evidence, leads to a clarification of the electronic processes in the class of substances extending from condensed ring molecular solids to polycrystalline graphite. In all these solids, the electric current flows preferentially along the benzene-ring planes. Scattering of electrons is due to thermal lattice vibrations and to the boundaries of molecular planes, where electrons pass through potential barriers into the neighboring crystallites. These barriers are quite transparent in polycrystalline graphite and baked carbons, since the flow occurs along the carbon-carbon bonds, but are quite opaque in molecular solids where the barriers are due to the presence of foreign atoms attached at the periphery of the molecules.In contrast with the infinite graphite crystal, systems of benzene-rings of finite dimensions possess a finite energy gap between the filled and the conduction bands, the energy gap steadily decreasing with increase of molecular size---from about 1 ev for molecules several benzene rings wide, to 0.2-0.3 ev for systems 30-40A in diameter and to 0.05 ev for graphite crystallites with diameters of the order of 1000A. When in the process of carbonization, foreign atoms are removed from peripheries, the carbon atoms left with free, unattached valencies play a role of donors, that is, become a source of conduction (excess) electrons. The concentration of such excess electrons increases as long as gases are driven out from the carbons, but starts decreasing as a result of growth of crystallite size for samples treated to higher temperatures. The complete interpretation of the dependence of resistivity on temperature is based on a combination of these three factors: scattering, concentration of the excess electrons, and concentration of holes and electrons activated from the lower band (over the energy gap).The anisotropic component of the diamagnetism of condensed ring systems has a twofold origin: (1) diamagnetism of the filled band (closed shell) of resonance ($\ensuremath{\pi}$) electrons, which is proportional to the number of benzene rings in a molecule; and (2) the Landau diamagnetism of the free electrons and holes. The contribution of the Landau diamagnetism is by far the larger of the two for graphite, but decreases fast with the crystallite size and becomes negligible for molecules with diameters of 30A or below, due to an increase in the effective mass of carriers.