We have carried out ab initio hybrid Hartree-Fock/Density Functional Theory simulations to determine the structure and vibrational modes of zircon, ZrSiO4, as a function of different applied strains. The changes in phonon-mode wavenumbers are approximately linear in the unit-cell strains, and have been fitted to determine the components of the phonon-mode Grüneisen tensors of zircon which reproduce the change in measured Raman shifts with pressure. They can therefore be used to convert Raman shifts measured from zircon inclusions in metamorphic rocks into strains that in turn can be used to determine the metamorphic conditions at the time that the inclusion was trapped. Due to the strong anisotropy in the thermal pressure of zircon, the phonon-mode Grüneisen tensor is not able to reproduce the temperature-induced changes in Raman shifts. Because zircon inclusions are normally measured at room conditions this does not prevent the calculation of their entrapment conditions.

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