The role of symmetry-breaking strains on quartz inclusions in anisotropic hosts: Implications for Raman elastic geobarometry

Raman elastic geobarometry for mineral host-inclusion systems is used to determine the strains acting on an inclusion still entrapped in its host by measuring its Raman wavenumber shifts which are interpreted through the phonon-mode Grüneisen tensors of the inclusion phase. The calculated inclusion strains can then be used in an elastic model to calculate the pressure and temperature conditions of entrapment. This method is applied frequently to host inclusion systems where the host is almost elastically isotropic (e.g. garnet) and the inclusion is elastically anisotropic (e.g. quartz and zircon). In this case, when the entrapment occurs under hydrostatic conditions the host will impose isotropic strains on the inclusion which in turn will develop non-hydrostatic stress. In this scenario the symmetry of the inclusion mineral is preserved and the strains in the inclusion can be measured via Raman spectroscopy using the phonon-mode Grüneisen tensor approach. However, a more complex situation arises when the host-inclusion system is fully anisotropic, such as when a quartz inclusion is entrapped within a zircon host, because the symmetry of the inclusion can be broken due to the external anisotropic strain field imposed on the inclusion by the host, which in turn will modify the phonon modes. We therefore calculated the strain states of quartz inclusions entrapped in zircon hosts in multiple orientations and at various geologically relevant pressure and temperature conditions. We then performed ab initio Hartree-Fock/Density Functional Theory (HF/DFT) simulations on α-quartz in these strain states. These HF/DFT simulations show that the changes in the positions of the Raman modes produced by strains that are expected for symmetry broken quartz inclusions in zircon are generally similar to those that would be seen if the quartz inclusions remained truly trigonal in symmetry. Therefore, the use of the trigonal phonon-mode Grüneisen tensor to determine the inclusion strains does not lead to geologically significant errors in calculated quartz inclusion entrapment pressures in zircon.