Phonon mode Griineisen parameters

The pressure-dependence of ZnO phonon-mode frequencies measured by Raman scattering was reported in [37, 130]. From that the Griineisen parameters 7j... 

Table 3.6. Griineisen parameters of the zone-center phonon modes of ZnO [37] ...

Elastic constants depend on pressure and temperature because of the anharmonicity of the interatomic potentials. From the dependence of bulk and shear moduli on hydrostatic and uniaxial pressure, third order elastic constants and Griineisen parameters may be determined. Griineisen parameter shows the effect of changing volume, V, on the phonon mode frequencies, co. 

Thermal Expansion and Griineisen Parameter. Specific-heat calculations usually neglect interactions of phonon states or different vibrational modes (harmonic approximation). However, thermal expansion arises from such interactions. The coefficient of thermal expansion a is calculated fiom oscillatory equations by assuming asymmetric binding potentials. At decreasing temperature, vibrations become more harmonic, and t 0 for T -> 0. Above T = 0, not only phonon states of the same mode interact, but also those of different modes. 

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