Raman spectroscopy determination of the Debye temperature and atomic cohesive energy of CdS, CdSe, Bi2Se3, and Sb2Te3 nanostructures

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We have formulated the size and temperature dependence of the phonon relaxation dynamics for CdS, CdSe, Bi2Se3, and Sb2Te3 nanostructures based on the framework of bond order–length–strength correlation, core-shell configuration, and local bond averaging approach. The Raman shifts are correlated directly to the identities (nature, order, length, and energy) of the representative bond of the specimen without needing involvement of the Grüneisen mode parameters or considering the processes of phonon decay or multi-phonon resonant scattering. Quantitative information of the Debye temperature, the atomic cohesive energy, the reference frequencies from which the Raman shifts proceed, and the effective coordination numbers of the randomly sized particles, as well as the length and energy of the representative bond, has been obtained. It is clarified that the size-induced phonon softening arises intrinsically from the cohesive weakening of the undercoordinated atoms in the skin up to three atomic layers and the thermally derived phonon softening results from the thermally lengthening and weakening of bonds. Developed approach empowers the Raman technique in deriving quantitative and direct information regarding bond stiffness relaxation with applied stimuli such as coordination, mechanical, thermal, and chemical environment, which are crucial to practical applications.