Size effect on Debye temperature of metal crystals

Understanding the physical origin of materials exhibiting different properties at the mesoscale is of great significance for the design and fabrication of multifunctional quantum devices. In this work, we proposed a simple model without any adjustable parameters to describe the size (D) dependence of Debye temperature Theta D(D) of metallic nanocrystals. Theta D(D) drops with the decrease of D, which is verified by relevant experimental and simulation results. In addition, we found that the difference in the size dependence of Theta D(D) of different metal elements is determined by the ratio of the solid/liquid interface energy gamma sl and surface stress f, and the smaller the D of the nanocrystals, the greater the influence of gamma sl/f on Theta D(D)/Theta D. Theta D(D) curve declines with the decrease of size D, and the ratio of interfacial energy gamma sl to surface stress f dominates this variation tendency.