Theory of the Specific Heat of Graphite

The graphite crystal is considered as a system of thin elastic plates spaced at a constant distance. An elastic force is assumed to act between each neighboring plates in such a way that a local change of the spacing between them produces at that point a tension or a pressure normal to the plates whose magnitude is proportional to that change. The vibrations of this system are assumed to be separable into independent parts: the bending vibrations in which the displacements occur normal to the planes of the plates, and the extensional and shearing vibrations in which the displacements occur parallel to them. The frequency distributions of their normal modes are studied. The values of the elastic constants of the plates that determine the latter vibrations are derived from the force constants of benzene molecule, while the value of the bending modulus of the plate is determined by fitting the calculated specific heat curve with the observed one. The constants of the elastic force acting between neighboring plates are derived from the measured elastic constants of graphite (mainly the compressibility). Small contributions of the electronic specific heat and the C p – C v correction are added to obtain the total specific heat. The result is in good agreement with experiment.