Quartz-in-garnet and Ti-in-quartz thermobarometry: Methodology and first application to a quartzofeldspathic gneiss from eastern Papua New Guinea

Mineral inclusions are ubiquitous in metamorphic rocks and elastic models for host-inclusion pairs have become frequently used tools for investigating pressure-temperature (P-T) conditions of mineral entrapment. Inclusions can retain remnant pressures (Pinc) that are relatable to their entrapment P-T conditions using an isotropic elastic model and P-T-V equations of state for host and inclusion minerals. Elastic models are used to constrain P-T curves, known as isomekes, which represent the possible inclusion entrapment conditions. However, isomekes require a temperature estimate for use as a thermobarometer. Previous studies obtained temperature estimates from thermometric methods external of the host-inclusion system. In this study, we present the first P-T estimates of quartz inclusion entrapment by integrating the quartz-in-garnet elastic model with titanium concentration measurements of inclusions and a Ti-in-quartz solubility model (QuiG-TiQ). QuiG-TiQ was used to determine entrapment P-T conditions of quartz inclusions in garnet from a quartzofeldspathic gneiss from Goodenough Island, part of the (ultra)high-pressure terrane of Papua New Guinea. Raman spectroscopic measurements of the 128, 206, and 464 cm(-1) bands of quartz were used to calculate inclusion pressures using hydrostatic pressure calibrations (Pinchyd), a volume strain calculation (Pincv.s.), and elastic tensor calculation (Pince.t.), that account for deviatoric stress. Pinchyd values calculated from the 128, 206, and 464 cm(-1) bands' hydrostatic calibrations are significantly different from one another with values of 1.8 +/- 0.1, 2.0 +/- 0.1, and 2.5 +/- 0.1 kbar, respectively. We quantified elastic anisotropy using the 128, 206 and 464 cm(-1) Raman band frequencies of quartz inclusions and stRAinMAN software (Angel, Murri, Mihailova, & Alvaro, 2019, 234:129-140). The amount of elastic anisotropy in quartz inclusions varied by similar to 230%. A subset of inclusions with nearly isotropic strains gives an average Pincv.s. and Pince.t. of 2.5 +/- 0.2 and 2.6 +/- 0.2 kbar, respectively. Depending on the sign and magnitude, inclusions with large anisotropic strains respectively overestimate or underestimate inclusion pressures and are significantly different (<3.8 kbar) from the inclusions that have nearly isotropic strains. Titanium concentrations were measured in quartz inclusions exposed at the surface of the garnet. The average Ti-in-quartz isopleth (19 +/- 1 ppm [2 sigma]) intersects the average QuiG isomeke at 10.2 +/- 0.3 kbar and 601 +/- 6 degrees C, which are interpreted as the P-T conditions of quartzofeldspathic gneiss garnet growth and entrapment of quartz inclusions. The P-T intersection point of QuiG and Ti-in-quartz univariant curves represents mechanical and chemical equilibrium during crystallization of garnet, quartz, and rutile. These three minerals are common in many bulk rock compositions that crystallize over a wide range of P-T conditions thus permitting application of QuiG-TiQ to many metamorphic rocks.