▎ 摘　　要

The phonon density of states of graphene based materials have been studied using density functional theory. Substitution of the carbon atoms with carbon isotopes may result in the appearance of gaps in the phonon density of states. Wider gaps are introduced when selected carbon atoms are replaced with germanium atoms. The effect of the percentage of germanium atoms substituting carbon atoms in graphene has also been studied. The results presented here may find application in the design of efficient thermoelectric materials. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4717746]