A Bond-order Theory on the Phonon Scattering by Vacancies in Two-dimensional Materials

We theoretically investigate the phonon scattering by vacancies, including the impacts of missing mass and linkages ([Image: see text]) and the variation of the force constant of bonds associated with vacancies ([Image: see text]) by the bond-order-length-strength correlation mechanism. We find that in bulk crystals, the phonon scattering rate due to change of force constant [Image: see text] is about three orders of magnitude lower than that due to missing mass and linkages [Image: see text]. In contrast to the negligible [Image: see text] in bulk materials, [Image: see text] in two-dimensional materials can be 3–10 folds larger than [Image: see text]. Incorporating this phonon scattering mechanism to the Boltzmann transport equation derives that the thermal conductivity of vacancy defective graphene is severely reduced even for very low vacancy density. High-frequency phonon contribution to thermal conductivity reduces substantially. Our findings are helpful not only to understand the severe suppression of thermal conductivity by vacancies, but also to manipulate thermal conductivity in two-dimensional materials by phononic engineering.