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Using diamond anvil cells with temperature control, we measured Raman spectra on materials at elevated temperatures and pressures. The shifts of individual Raman peaks, Δω, were fit to functions of the form
Δω = A P + B T + C P² + D PT
where P and T are pressure and temperature. The first two terms, proportional to P and T, are the well-known quasiharmonic and anharmonic phonon shifts. Our interest is in the cross-term proportional to the product PT. These cross-terms show how pure anharmonicity depends on pressure, and how simultaneous P and T may be important to the free energy.

For Si₂₄ with the clathrate structure, the largest Δω for a bending mode of B_3g symmetry was actually from the cross term in PT, even though the temperature range was only 320 K and the pressure range was 8 GPa. Monoclinic ZrO₂, over a pressure range of 3 GPa and a temperature range of 320K, showed several modes with a large PT cross term. DFT calculations revealed that these modes were oxygen-dominated, with bending-type displacement patterns and negative Grueneisen parameters. The entropy of Si₂₄ and ZrO₂ may have a dependence on the product of P and T [PRB 95, 094306 (2017)].