Size effects on Debye temperature, Einstein temperature, and volume thermal expansion coefficient of nanocrystals

Based on a size-dependent root of mean square amplitude (rms) model, the size-dependent Debye temperatures of nanocrystals are modeled without any adjustable parameter by considering both Lindemann’s criterion and Mott’s equation. In terms of this model, the Debye temperatures depend on both size and interface conditions, which lead to related applications on size effects of the Einstein temperature and the volume thermal expansion coefficient. It is found that the model’s predictions are in good agreement with available experimental and computer simulation results.