Amplitude and Frequency of Skin Atom Vibration

At a given temperature, the vibrational amplitude and frequency of a given atom follow Einstein s relation, ii ccoxf /2z = k T, which yields the magnitude of vibration x oc The frequency and magnitude of vibration for an surface 

The vibrational amplitude of an atom at the surface is indeed greater [54, 55] than that of a bulk atom while the frequency is lower. The magnitude and frequency are sensitive to the m value and vary insignificantly with the curvature of a spherical dot when K 3. 

The BOLS correlation and the scaling relation correlate the size-created and stiffened LFR phonons to the intergrain interaction. The size-softened optical phonons result from interaction between the undercoordinated neighboring atoms in the skin. The coordination reduction enhancement of the phonon frequencies of the Eg mode of Ti02 and the G mode of GNR is dictated by the interaction between undercoordinated dimers. The size-induced phonon relaxation follows a K fashion. Decoding the size dependency of the Raman optical redshift leads to vibrational information of Si, InP, CdS, CdSe, TiOz, CeOa, and Sn02 dimers and their bulk shifts. 

Takagahara, Electron-phonon interactions and excitonic dephasing in semiconductor nanocrystals. Phys. Rev. Lett. 71(21), 3577-3580 (1993) 

Kanzawa, S. Hayashi, K. Yamamoto, Raman scattering from acoustic phonons confined in Si nanocrystals. Phys. Rev. B 54(12), R8373-R8376 (1996) 

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