Theoretical analysis of cross-plane lattice thermal conduction in graphite*

A theoretical analysis of the cross-plane lattice thermal conduction in graphite is performed by using first-principles calculations and in the single-mode relaxation time approximation. The out-of-plane phonon acoustic mode ZA and optical mode ZO ′ have almost 80% and 20% of contributions to cross-plane heat transfer, respectively. However, these two branches have a small part of total specific heat above 300 K. Phonons in the central 16% of Brillouin zone contribute 80% of cross-plane transport. If the group velocity angle with respect to the graphite layer normal is less than 30°, then the contribution is 50% at 300 K. The ZA phonons with long cross-plane mean free path are focused in the cross-plane direction, and the largest mean free path is on the order of several micrometers at room temperature. The average value of cross-plane mean free path at 300 K is 112 nm for ZA phonons with group velocity angle with respect to the layer normal being less than 15°. The average value is dropped to 15 nm when phonons of all branches in the whole Brillouin zone are taken into account, which happens because most phonons have small or even no contributions.