Dynamics of the Graphite Lattice

The distribution of frequencies of normal vibrations in the graphite lattice has been obtained in closed form for low temperatures in the two-dimensional approximation for the values (α, β, 0) and (α, β, α/2) of the force constants (α, β, γ) for nearest, second-nearest, and third-nearest neighbors. The frequencies run from 0 to a finite value ωmax, with two logarithmic peaks in their density. The specific heat has been calculated for two special sets of force constant ratios. Deviations from T2 dependence set in at temperatures much lower than predicted by Debye theory. Comparison with experiment leads to a numerical value for θ=ℏωmax/k, from which ωmax, and therefore also α and one of the macroscopic elastic constants, c44, may be calculated. θ and ωmax appear very sensitive to the assumed force constant ratios, c44 less so.