We present an assessment of the thermo-elastic behaviour of rutile based on X-ray diffraction data and direct elastic measurements available in the literature. The data confirms that the quasi-harmonic approximation is not valid for rutile because rutile exhibits substantial anisotropic thermal pressure, meaning that the unit-cell parameters change significantly along isochors. Simultaneous fitting of both the diffraction and elasticity data yields parameters of KTR0= 205.14(15) GPa, KSR0= 207.30(14) GPa, $K_{TR0}^{\prime} $= 6.9(4) in a 3rd-order Birch-Murnaghan Equation of State for compression, αV0= 2.526(16) × 10–5 K–1, Einstein temperature θE = 328(12) K, Anderson-Grüneisen parameter δT = 7.6(6), with a fixed thermal Grüneisen parameter γ = 1.4 to describe the thermal expansion and variation of bulk modulus with temperature at room pressure. This Equation of State fits all of the available data up to 7.3 GPa at room temperature, and up to 1100 K at room pressure within its uncertainties. We also present a series of formulations and a simple protocol to obtain thermodynamically consistent Equations of State for the volume and the unit-cell parameters for stiff materials, such as rutile. In combination with published data for garnets, the Equation of State for rutile indicates that rutile inclusions trapped inside garnets in metamorphic rocks should exhibit negative residual pressures when measured at room conditions.

Here we report the first results from elastic geobarometry applied to a kyanite inclusion entrapped within an eclogitic diamond (from Voorspoed mine, South Africa) using micro‐Raman and Fourier transform infrared spectroscopy, electron microprobe analysis, ab initio calculations, and finite element modeling. Application of elastic geobarometry to very elastically anisotropic kyanite inclusions is challenging, as current models do not allow for elastic anisotropy. In order to minimize the effects of anisotropy, we have explored the effects of deviatoric stress on Raman modes via ab initio density functional theory. The results allowed us to select the Raman mode (at ca. 638 cm−1) that is the least sensitive to deviatoric stress. The shift of this band in the inclusion while still trapped within the diamond relative to the inclusion in air (once liberated) was used under hydrostatic approximation to determine a residual pressure on the inclusion of 0.184 ± 0.045 GPa and an entrapment pressure of 5.2 ± 0.3 GPa (~160 km depth) for an FTIR N‐aggregation residence temperature of 1119 ± 50 °C. This is the first geothermobarometric determination for a diamond from the Voorspoed kimberlite. It overlaps with P–T estimates obtained by traditional chemical geobarometry for diamonds from other kimberlites from the Kaapvaal craton, suggesting that the hydrostatic approximation does not introduce significant errors in the geobarometric evaluation. Our protocol of Raman peak selection can be used for geobarometry of further kyanite‐bearing diamonds and may provide a guide for more robust geobarometry of other types of mineral inclusions in diamonds, both eclogitic and peridotitic.

A thermal-pressure equation of state has been determined for zircon (ZrSiO4) that characterizes its thermoelastic behavior at metamorphic conditions. New pressure-volume (P-V) data from a "Mud-Tank" zircon have been collected from 1 bar to 8.47(1) GPa using X-ray diffraction, and elastic moduli were measured from room temperature up to 1172 K by resonance ultrasound spectroscopy. These data were fitted simultaneously with temperature-volume (T-V) data from the literature in EosFit7c using a new scaling technique. The parameters of a third order Birch-Murnaghan EoS with a Mie-Grüneisen-Debye model for thermal pressure has compressional EoS parameters K0T = 224.5(1.2) GPa, K0T¢ = 4.90(31) with a fixed initial unit-cell volume V0 = 39.26 cm 3 /mol and thermal parameters g0 = 0.868(15), q = 2.37(80), and QD = 848(38) K. EoS parameters that describe the variation of unit-cell parameters with pressure and temperature were determined using an isothermal-type EoS. This new EoS confirms that zircons are stiffer than garnets and exhibit a much lower thermal expansion. This results in steep isomekes between This is the peer-reviewed, final accepted version for American Mineralogist, published by the Mineralogical Society of America.The published version is subject to change. Cite as Authors (Year) Title. American Mineralogist, in press.

Diamonds and their inclusions are unique fragments of deep Earth, which provide rare samples from inaccessible portions of our planet. Inclusion-free diamonds cannot provide information on depth of formation, which could be crucial to understand how the carbon cycle operated in the past. Inclusions in diamonds, which remain uncorrupted over geological times, may instead provide direct records of deep Earth’s evolution. Here, we applied elastic geothermobarometry to a diamond-magnesiochromite (mchr) host-inclusion pair from the Udachnaya kimberlite (Siberia, Russia), one of the most important sources of natural diamonds. By combining X-ray diffraction and Fourier-transform infrared spectroscopy data with a new elastic model, we obtained entrapment conditions, P trap = 6.5(2) GPa and T trap = 1125(32)–1140(33) °C, for the mchr inclusion. These conditions fall on a ca. 35 mW/m 2 geotherm and are colder than the great majority of mantle xenoliths from similar depth in the same kimberlite. Our results indicate that cold cratonic conditions persisted for billions of years to at least 200 km in the local lithosphere. The composition of the mchr also indicates that at this depth the lithosphere was, at least locally, ultra-depleted at the time of diamond formation, as opposed to the melt-metasomatized, enriched composition of most xenoliths.

A new micro‐furnace equipped with an H‐shaped resistance heater has been developed to conduct in situ single‐crystal X‐ray diffraction experiments at high temperature. The compact design of the furnace does not restrict access to reciprocal space out to 2θ = 60°. Therefore, unit‐cell parameters and intensity data can be determined to a resolution of 0.71 Å with Mo radiation. The combined use of mineral phases with well characterized lattice expansion (e.g. pure Si and SiO2 quartz) and a small‐diameter (0.025 mm) K‐type thermocouple allowed accurate temperature calibration from room temperature to about 1273 K and consequent evaluation of thermal gradients and stability. The new furnace design allows temperatures up to about 1273 K to be reached with a thermal stability better than ±5 K even at the highest temperatures. Measurements of the lattice thermal expansion of pure silicon (Si), pure synthetic grossular garnet (Ca3Al2Si3O12) and quartz (SiO2) are presented to demonstrate the performance of the device. Its main advantages and limitations and important considerations for using it to perform high‐temperature diffraction measurements are discussed.