Modeling to determine the size and dimension effects on Debye temperature in metallic crystals

In the present work, a thermodynamic top-down qualitative approach is formulated to study the effect of size reduction and shape on Debye temperature of metallic nanocrystals. The model formulation consider the impact of size, shape, dimension, solid-liquid interfacial energy γSL and surface stress 𝑓 on the thermodynamic property. It is noted that ratio of solid-liquid interfacial energy γSL and surface stress 𝑓 is directly proportional to the Debye temperature of nanostructures. Debye temperature of metallic nanocrystals show progressive reduction with decrease in size of the crystal and drop in Debye temperature is drastic below the size range of 10 nm. The model results are observed in good consistency with the compared simulated and experimental data. The shape and dimensionality of the nanostructure results in change in the surface area to volume ratio in nanostructures and thus has a wide impact on the thermodynamic property.