Size-induced acoustic hardening and optic softening of Ramn phonons

TL;DR

This paper explains the size-induced acoustic hardening and optical softening in nanostructures using the bond order-length-strength correlation, clarifying the mechanisms behind these phenomena across various materials.

Contribution

It introduces a unified theoretical explanation for size-dependent phonon shifts in nanostructures based on the BOLS correlation, resolving previous controversies.

Findings

Optical softening results from surface atomic cohesive energy weakening.

Acoustic hardening is mainly due to intergrain interactions.

Predictions agree with experimental data for multiple nanomaterials.

Abstract

It has been puzzling that the Raman optical modes shift to lower frequency (or termed as optical mode softening) associated with creation of Raman acoustic modes that shift to higher energy (or called as acoustic hardening) upon nanosolid formation and size reduction. Understandings of the mechanism behind the size-induced acoustic hardening and optic softening have been quite controversial. On the basis of the recent bond order-length-strength (BOLS) correlation [Phys. Rev. B 69 045105 (2004)], we show that the optical softening arises from atomic cohesive energy weakening of surface atoms and the acoustic mode hardening is predominated by intergrain interaction. Agreement between predictions and observations has been reached for Si, CdS, InP, TiO2, CeO2, and SnO2 nanostructures with elucidation of vibration frequency of the corresponding isolated dimers. Findings further evidence the impact of bond order loss to low-dimensional systems and the essentiality of the BOLS correlation in describing the behavior of nanostructures.