Theory of the a-plane thermal conductivity of graphite

Because of the weak binding and the large lattice spacing in the c-direction, the phonon spectrum of graphite is approximately two-dimensional for frequencies above f c = 4 THz. Thus one can model the a-plane thermal conductivity by a two-dimensional phonon gas. At temperatures sufficiently high for classical statistics to apply, the intrinsic phonon mean free path l i, limited by cubic anharmonicities, is the same as in three dimensions, and l i ∝ T -1f -2. The spectral specific heat in 2-D is C(f) ∝ f, as against f 2 in 3-D. Thus the spectral thermal conductivity is λ i(f) ∝ C(f)l i(f) ∝ T -1f -1, and the major contribution to the intrinsic thermal conductivity λ i comes from frequencies near f c. A numerical estimate is obtained: λ i is about 19 W-cm -1-K -1 at 300 K, in agreement with measurements on pyrolitic graphite. Scattering by grain boundaries is independent of frequency, and affects mainly phonons of low frequencies. Since these frequencies make a greater contribution, the grain boundary scattering is enhanced over the 3-D case. Scattering by point defects varies as f 3 in the 2-D case, as against f 4 in 3-D. Estimates are given for the decrease in conductivity due to grain boundaries, point defects such as vacancies, and their combined effect. © 2001 Technomic Publishing Co., Inc.