# The Magnetic and Other Properties of the Free Electrons in Graphite

N. Ganguli, K. S. Krishnan

## Abstract

1. Graphite crystals have a large free-electron diamagnetism, which is directed almost wholly along the hexagonal axis. Over the whole range of temperature over which measurements have been made, namely, from 90 to 1270$^{\circ}$ K, this free-electron diamagnetism of graphite per carbon atom is found to be equal to the Landau diamagnetism per electron of a free-electron gas obeying Fermi-Dirac statistics and having a degeneracy temperature of 520$^{\circ}$ K. 2. From this experimental result it is concluded (a) that the number of free or mobile electrons in graphite is just one per carbon atom; (b) that the effective mass of these electrons for motion in the basal plane is just their actual mass, showing that the movements in this plane are completely free and uninfluenced by the lattice field; (c) that on the other hand their effective mass for motion along the normal to the basal plane is enormous, about 190$^{3}$ times the actual mass, which indicates that the mobile electrons belonging to any given basal layer of carbon atoms are tightly bound to the layer, though, according to (b), they can migrate quite freely over the whole of the layer; (d) that this tight binding accounts for the observed low degeneracy temperature of the electron gas in the crystal. 3. The electron gas in graphite thus conforms to a simple model which is easily amenable to theoretical treatment, and it has a low degeneracy temperature which is conveniently accessible for experimenting. It therefore forms a suitable medium for studying the properties of an electron gas. 4. The conclusions stated in 2 are in accord with the quantal views of the electronic structure of graphite, and also with its Brillouin zones. There is one zone which can just accommodate three electrons per atom, and the energy discontinuities at all of its boundary surfaces are large. There is a bigger zone which can just accommodate all the four valency electrons, but the energy discontinuities at those of its faces that are perpendicular to the basal plane are very small.