Optical and Acoustic Grüneisen Parameter of Nano-sized Particles

Abstract

Theoretical size dependence optical and acoustic Grüneisen parameter γop(r ) and γac(r) at room temperature (300 K) are calculated for Si nanoparticles using modified Debye-Einstein approximation model. The obtained results are used for studying the total Grüneisen parameter γ(θD(r),θE(r)). All parameters forming the model including Debye’s θD (r,T) and Einstein’s θE (r,T) temperatures and lattice volume are calculated according to their nanoscale size dependence. These values θE (r,T) and θD (r,T) for Silicon decrease with decreasing nanoparticle size, except for lattice volume and Grüneisen parameter which increases to about 2.9 times of its bulk lattice volume and total Grüneisen parameter to about 2.45 compared with bulk value when the particle diameter reaches lower than 5 nm.

Keywords

• Grüneisen Parameter
• Debye’s Temperature
• Einstein’s Temperature
• Acoustic and Optical Branch
• Nanoparticle