Size-induced acoustic hardening and optic softening of phonons in InP,CeO2,SnO2, CdS, Ag, and Si nanostructures

Abstract

It has long been a puzzle that the Raman optical modes shift to lower frequency (or termed optical mode softening or redshift) associated with the creation of Raman acoustic modes that shift to higher energy (or called acoustic hardening or blueshift) upon a nanosolid being formed and its size being reduced. Understandings of the mechanism behind the size-induced Raman shifts have been quite controversial. On the basis of the bond-order--length--strength (BOLS) correlation mechanism [Phys. Rev. B 69, 045105 (2004)], we show that the optical softening arises from atomic cohesive energy weakening of atoms in the surface skins, whereas the acoustic mode hardening is predominated by intergrain interactions. Agreement between predictions and observations has been realized for Ag, Si, CdS, InP, ${\mathrm{TiO}}_{2}$, ${\mathrm{CeO}}_{2}$, and ${\mathrm{SnO}}_{2}$ nanostructures with elucidation of vibration frequencies of the corresponding isolated dimers from fitting the optical softening.