The Lattice Vibration Specific Heat of Graphite

Recent experiments have shown that the specific heat of graphite varies as T2 instead of T3 between 15°K and 80°K. In this paper such a behavior is shown to be a consequence of the elastic anisotropy of graphite, and therefore an intrinsic property, rather than a particle size effect as suggested by Gurney, or a plate-like behavior as suggested by Komatsu and Nagamiya. The Gurney treatment is shown to be in error both as to the enumeration of modes, and as to the temperature range over which the particle size effect might be of significance. The Komatsu and Nagamiya treatment is shown to be inconsistent with elasticity theory. The present treatment employs a semirigorous analysis of the normal mode problem for the transverse vibrations, approximated for long wavelengths. It is found that experimental data from 15–1000°K can be well fitted by dividing the lattice vibrations into two types: (a) modes with atom displacements normal to the layer planes with a Debye temperature of 900°K, and (b) modes with atom displacements in the planes with a Debye temperature of 2500°K.