Anisotropic host-inclusion systems: the role of symmetry breaking strains

Mineral host-inclusion systems can retain crucial information regarding their geologic history. For example, we can determine their formation conditions in terms of pressure (P) and temperature (T) from elastic geobarometry. In particular, it is possible to determine the strain acting on the inclusion when still entrapped in its host by measuring changes in the Raman-peak positions with respect to those of a free crystal, which are interpreted through the inclusion phonon-mode Grüneisen tensors (Grüneisen 1926).  The calculated inclusion strains can then be used in an elastic model to calculate the pressure and temperature conditions of entrapment. A simple case is when an anisotropic crystal is contained within a quasi-isotropic host, such as quartz in garnet. When this host-inclusion system is subjected to changes in P and T the host crystal will impose a uniform strain on the inclusion, which will in turn develop deviatoric stresses. 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 in a zircon host, because symmetry breaking of the inclusion occurs as P and T change. In this case, the effect of symmetry breaking on the frequencies of phonon modes is not known and may be different from the case of structural phase transitions involving soft modes.

             Therefore, we calculated the expected deformations for a quartz inclusion in a zircon host in multiple orientations and at various geologically relevant P-T conditions. We then performed ab initio Hartee-Fock/Density Functional Theory simulations on α-quartz with the selected range of strains to (i) determine the role of the symmetry breaking strains in a completely anisotropic host-inclusion system and (ii) evaluate the possible application of the phonon-mode Grüneisen tensor when the symmetry is broken. Our results show 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 Grüneisen components for trigonal alpha quartz can be used for Raman elastic geothermobarometry in anisotropic host-inclusion systems without introducing significant errors.

 Acknowledgements: This work has been partially supported by the PRIN-MUR project “THALES” Prot.2020WPMFE9_003 and the National Science Foundation under Award No. (1952698) to JPG.

References: Grüneisen, E., 1926. Zustand des festen K¨orpers. Handbuch der Physik 1, 1–52.