Size dependent Debye temperature and mean square displacements of nanocrystalline Au, Ag and Al

In the present work the size dependent Debye Temperature (θD) and Mean Square Displacements (MSDs) of nanocrystalline Au, Ag and Al are determined. Size dependent melting temperature (Tm) of these nanoparticles is determined by the expression derived by Nanda et al. following liquid drop model. The size dependent lattice contraction is properly accounted following Qi and Wang. The Debye temperatures are determined from the values of melting temperatures by Lindemann theory of melting. The calculated values of relative Debye temperature change for nanophase Au are agreeing well with the experiments. The procedure is extended to determine the MSDs of Au, Ag and Al for sizes ranging from 2 nm to 50 nm at 300 K. The results show that the size effect on θD and MSDs are predominant in the sizes ranging from 2 nm to 10 nm.