Debye Temperature and Specific Heat

6d oc t)1 jd [28]. For nanostructures, the 0d drops with size because of depression. 

Generally, the specific heat is regarded as a macroscopic quantity integrated over all bonds of the specimen and is the amount of energy required to raise the temperature of the substance by 1 K. However, in dealing with the representative bond of the entire specimen, one has to consider the specific heat per bond that is obtained by dividing the bulk-specific heat by the total number of bonds involved. Depending critically on the 0d and the T, the specific heat varies with both object size and the temperature of measurement. The effect of body size on the specific 

The rise of the absorption and the loss of thermal waves with specific wave vectors explain the decrease of specific heat in the small volumes. Lu et al. [31] calculated the size effects on the specific heat of Al thin films by employing the Prasher s approach [34] and derived that the reduction of phonon states was not the main reason causing the size effect on specific heat but a thin layer of Al oxide was responsible for it. 

The heat capacity per unit volume is defined as the ratio of an infinitely small amount of heat 8E added to the body to the corresponding small increase in its temperature 6T when the volume remains unchanged. The specific heat approximates the extended Debye model  

respectively. Therefore, the heat capacity in the low-temperature limit becomes  

---