Debye temperature and stiffness of carbon and boron nitride polymorphs from first principles calculations

Abstract

A theoretical investigation has been made on the phonon spectrum and heat capacity of polymorphs of carbon and boron nitride with special interests on the variation of Debye temperature and stiffness with temperature. A part of optical phonon branches of graphite exhibits higher frequencies than those of diamond. As a consequence, graphite shows smaller heat capacity and higher Debye temperature than diamond above a crossover temperature of $1000\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. This supports experimental reports of heat capacity although available experimental data are widely scattered. The higher Debye stiffness of graphite at above $1000\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ is not contradictory to the fact that conventional stiffness of diamond is much larger than that of graphite, since the Debye stiffness is determined by both acoustic and optical phonons, whereas only acoustic phonons contribute to the conventional stiffness. The same trend was found between hexagonal and cubic boron nitrides with a crossover temperature of $600\phantom{\rule{0.3em}{0ex}}\mathrm{K}$.