Abstract. Raman elastic thermobarometry has recently been applied in many
petrological studies to recover the pressure and temperature (P–T) conditions of
mineral inclusion entrapment. Existing modelling methods in petrology either
adopt an assumption of a spherical, isotropic inclusion embedded in an
isotropic, infinite host or use numerical techniques such as the finite-element
method to simulate the residual stress and strain state preserved in the
non-spherical anisotropic inclusions. Here, we use the Eshelby solution to
develop an analytical framework for calculating the residual stress and
strain state of an elastically anisotropic, ellipsoidal inclusion in an
infinite, isotropic host. The analytical solution is applicable to any class
of inclusion symmetry and an arbitrary inclusion aspect ratio. Explicit
expressions are derived for some symmetry classes, including tetragonal,
hexagonal, and trigonal. The effect of changing the aspect ratio on residual stress is investigated,
including quartz, zircon, rutile, apatite, and diamond inclusions in garnet
host. Quartz is demonstrated to be the least affected, while rutile is the
most affected. For prolate quartz inclusion (c axis longer than a axis), the
effect of varying the aspect ratio on Raman shift is demonstrated to be
insignificant. When c/a=5, only ca. 0.3 cm−1 wavenumber variation is
induced as compared to the spherical inclusion shape. For oblate quartz
inclusions, the effect is more significant, when c/a=0.5, ca. 0.8 cm−1
wavenumber variation for the 464 cm−1 band is induced compared to the
reference spherical inclusion case. We also show that it is possible to fit
an effective ellipsoid to obtain a proxy for the averaged residual
stress or strain within a faceted inclusion. The difference between the
volumetrically averaged stress of a faceted inclusion and the analytically
calculated stress from the best-fitted effective ellipsoid is calculated to
obtain the root-mean-square deviation (RMSD) for quartz, zircon, rutile,
apatite, and diamond inclusions in garnet host. Based on the results of 500 randomly generated (a wide range of aspect ratio and random
crystallographic orientation) faceted inclusions, we show that the
volumetrically averaged stress serves as an excellent stress measure and the
associated RMSD is less than 2 %, except for diamond, which has a systematically
higher RMSD (ca. 8 %). This expands the applicability of the analytical
solution for any arbitrary inclusion shape in practical Raman measurements.
Nonisothermal viscous sintering of volcanic ash
