Phonons in Si_(24) at simultaneously elevated temperature and pressure

Abstract

Raman spectroscopy was used to measure the frequencies of phonons in Si_(24) with an open clathrate structure at temperatures from 80 to 400 K with simultaneous pressures of 0 to 8 GPa. The frequency shifts of the different phonons were substantially different under either temperature or pressure. The quasiharmonic behavior was isolated by varying pressure at low temperatures, and the anharmonic behavior was isolated by varying temperature at low pressures. Phonon modes dominated by bond bending were anomalous, showing stiffening with temperature and softening with pressure. Both the quasiharmonic behavior and the anharmonic behavior changed markedly with simultaneous changes in temperature ΔT and pressure ΔP. With ΔT = 320 K and ΔP = 8 GPa, some frequency shifts that scaled with the product ΔT ΔP were as large as the shifts from ΔT and ΔP alone. The thermodynamic entropy of this material likely has a dependence on ΔT and ΔP that cannot be obtained by adding effects from quasiharmonicity and phonon-phonon anharmonicity.

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