Impact of variation in size, shape and dimension of nanomaterial on Debye temperature and Raman frequency

A simple unified thermodynamic approach is developed to determine the effect of size on Raman frequency of nanomaterials. The model approach is based on the Bond energy model developed to determine cohesive energy of nanomaterials with respect to bulk material. The model formulation includes the size, dimension and shape of nanomaterial. The model approach is obtained extending the relation used to determine the effect of size and shape on Debye temperature of nanomaterials. Raman Frequency variation with size is studied for Si, CdSe, InP, CeO2, SnO2, ZnO nanocrystals. It is noted from the model calculations that Raman frequency of nanocrystals drop with decrease in the size at nano level resulting in Raman red shift. The experimental data of previous workers is found in good agreement with model results. The approach is further used to determine the Raman frequency variation with size and shape in nanoparticles and nanowires of varied shapes and nanofilms. Depending on the surface atoms to volume ratio in nanomaterials of varied shapes, variation in Raman frequency is studied and good consistency with the available data confirms the validity of the formulation.