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 ((Formula presented.)) 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 ((Formula presented.)), a volume strain calculation ((Formula presented.)), and elastic tensor calculation ((Formula presented.)), that account for deviatoric stress. (Formula presented.) 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 ~230%. A subset of inclusions with nearly isotropic strains gives an average (Formula presented.) and (Formula presented.) 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 [2σ]) intersects the average QuiG isomeke at 10.2 ± 0.3 kbar and 601 ± 6°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.
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