Theoretical estimation of surface Debye temperature of nano structured material

The estimation of Debye temperature (TD) exploiting phonon is very important. In this work an attempt has been made to estimate TD for solids in a simple phenomenological approach. The ultimate goal is to estimate TD for nano structured material. The objective of this present work is to extend Debye model for nano-structured material and hence to extract the contribution to surface specific heat and surface Debye temperature. An empirical relation between TD and surface Debye temperature (TDS) is proposed. Lindemann melting criterion is also extended towards nano structure. The overall results obtained are compared and found to be in good agreement.