A high P-T single-crystal X-ray diffraction study of thermoelasticity of MgSiO3 orthoenstatite

P-V-T data of MgSiO₃ orthoenstatite have been measured by single-crystal X-ray diffraction at simultaneous high pressures (in excess of 4.5 GPa) and temperatures (up to 1000 K). The new P-V-T data of the orthoenstatite, together with previous compression data and thermal expansion data, are described by a modified Birch-Murnaghan equation of state for diverse temperatures. The fitted thermoelastic parameters for MgSiO₃ orthoenstatite are: thermal expansion ?α/?P with values of a=2.86(29)×10^-5 K^-1 and b=0.72(16)×10^-8 K^-2; isothermal bulk modulus K _{T o} =102.8(2) GPa; pressure derivative of bulk modulus K′=?K/?P=10.2(1.2); and temperature derivative of bulk modulus K=?K/?T=-0.037(5) GPa/K. The derived thermal Grüneisen parameter is γ _th=1.05 for ambient conditions; Anderson-Grüneisen parameter is δ _{T o} =11.6, and the pressure derivative of thermal expansion is ?α/?P=-3.5×10^-6K^-1 GPa^-1. From the P-V-T data and the thermoelastic equation of state, thermal expansions at two constant pressures of 1.5 GPa and 4.0 GPa are calculated. The resulting pressure dependence of thermal expansion is Δα/ΔP=-3.2(1)× 10^-6 K^-1 GPa^-1. The significantly large values of K′, K, δ _T and ?α/?P indicate that compression/expansion of MgSiO₃ orthoenstatite is very sensitive to changes of pressure and temperature.     

P-V-T equation of state of magnesiowüstite (Mg0.6Fe0.4)O

The lattice parameter of magnesiowüstite (Mg_0.6Fe_0.4)O has been measured up to a pressure of 30 GPa and a temperature of 800 K, using an external heated diamond anvil cell and diffraction using X-rays from a synchrotron source. The experiments were conducted under quasi-hydrostatic condition, using neon as a pressure transmitting medium. The experimental P-V-T data were fitted to a thermal-pressure model with the isothermal bulk modulus at room temperature K _T0 = 157 GPa, (?K _TO /?P) _T =4, (?K _T /?T) _P =-2.7(3) × 10^-2 GPa/K, (?K _T /?T) _v =-0.2(2) × 10^-2 GPa/K and the Anderson-Grüneisen parameter δ _T =4.3(5) above the Debye temperature. The data were also fitted to the Mie-Grüneisen thermal equation of state. The least-squares fit yields the Debye temperature θ _DO = 500(20) K, the Grüneisen parameter γ ₀=1.50(5), and the volume dependence q=1.1(5). Both thermal-pressure models give consistent P-V-T relations for magnesiowüstite to 140 GPa and 4000 K. The P-V-T relations for magnesiowüstite were also calculate by using a modified high-temperature Birch-Murnaghan equation of state with a δ _t of 4.3. The results are consistent with those calculated by using the thermal-pressure model and the Mie-Grüneisen relation to 140 GPa and 3000 K.     

Hydrostatic compression of γ-Mg2SiO4 to mantle pressures and 700 K: Thermal equation of state and related thermoelastic properties

P-V-T equations of state for the γ phase of Mg₂SiO₄ have been fitted to unit cell volumes measured under simultaneous high pressure (up 30 GPa) and high temperature (up to 700 K) conditions. The measurements were conducted in an externally heated diamond anvil cell using synchrotron x-ray diffraction. Neon was used as a pressure medium to provide a more hydrostatic pressure environment. The P-V-T data include 300 K-isothermal compression to 30 GPa, 700 K-compression to 25 GPa and some additional data in P-T space in the region 15 to 30 GPa and 300 to 700 K. The isothermal bulk modulus and its pressure derivative, determined from the isothermal compression data, are 182(3) GPa and 4.2(0.3) at T=300 K, and 171(4) GPa and 4.4(0.5) at T=700 K. Fitting all the P-V-T data to a high-temperature Murnaghan equation of state yields: K _TO=182(3.0) GPa, K _TO=4.0(0.3), ?K _T /?T)₀=?2.7(0.5)×10^?2 GPa/K and (?² K _T /?P?T)₀=5.5(5.2)×10^?4/K at the ambient condition.     

Compressibility of calcium ferrite-type MgAl2O4

 In situ X-ray diffraction experiments of calcium ferrite-type MgAl₂O₄ have been carried out using a diamond anvil cell combined with synchrotron radiation and an imaging plate X-ray detector under hydrostatic pressures up to 9 GPa. The observed unit-cell volumes at various pressures were fitted to the Birch-Murnaghan equation of state, yielding a bulk modulus of K _{T 0}= 241(3) GPa when K′ _{T 0}=4 is assumed. This relatively large bulk modulus of calcium ferrite-type MgAl₂O₄ is consistent with that expected from the systematic relation between bulk modulus and molar volume for the most compounds possessing fcc oxygen packing. Received March 5, 1996/Revised, accepted October 15, 1996     

Refractive index and compressibility of Di64An36 glass over a pressure range of 0–5.0 GPa

Data on the refractive index, density, and bulk modulus variations of Di₆₄An₃₆ glass, which is used as a model basalt melt, were obtained with a polarization interference microscope and a high-pressure diamond anvil cell at ambient temperature and pressure up to 5.0 GPa. An anomalous decrease in the bulk modulus, K _t , was observed in the pressure range 0?C1.0 GPa. The values of the zero-pressure isothermal bulk modulus, K _t,0 = 22.2, and variation of the bulk modulus with pressure, ??K _t /??P = 11.35, were derived using a linear equation relating K _t and P over the pressure range with the normal behavior of the compressibility. A comparison of our results with previous data on other glasses and melts showed that the bulk moduli of silicate glasses are similar to those of corresponding melts. The values of the pressure coefficient of the bulk moduli, ??K _t /??P, for glasses derived from linear equations are 2.5 times higher than the pressure derivative of the bulk modulus, K?? _T , derived using the Birch-Murnaghan equation for corresponding melts. The difference in ??K _t /??P and K?? _T has an effect on the compressibility of glasses and melts. The compressibility of glasses up to 5.0 GPa calculated as (d ? d ₀)/d is almost two times lower than that of corresponding melts.     

Single-crystal hydrostatic compression of synthetic pyrope, almandine, spessartine, grossular and andradite garnets at high pressures

The compression of synthetic pyrope Mg₃Al₂ (SiO₄)₃, almandine Fe₃Al₂(SiO₄)₃, spessartine Mn₃Al₂ (SiO₄)₃ grossular Ca₃Al₂(SiO₄)₃ and andradite Ca₃Fe₂ (SiO₄)₃ was studied by loading the crystals together in a diamond anvil cell. The unit-cell parameters were determined as a function of pressure by X-ray diffraction up to 15 GPa using neon as a pressure transmitting medium. The unit-cell parameters of pyrope and almandine were measured up to 33 and 21 GPa, respectively, using helium as a pressure medium. The bulk moduli, K _{T 0}, and their first pressure derivatives, K _{T 0} ^′, were simultaneously determined for all five garnets by fitting the volume data to a third order Birch-Murnaghan equation of state. Both parameters can be further constrained through a comparison of volume compressions between pairs of garnets, giving for K _{T 0} and K _{T 0} ^′ 171(2) GPa and 4.4(2) for pyrope, 185(3) GPa and 4.2(3) for almandine, 189(1) GPa and 4.2 for spessartine, 175(1) GPa and 4.4 for grossular and 157(1) GPa and 5.1 for andradite, where the K _{T 0} ^′ are fixed in the case of spessartine, grossular and andradite. Direct comparisons of the unit-cell volumes determined at high pressures between pairs of garnets reveal anomalous compression behavior for Mg²⁺ in the 8-fold coordinated triangular dodecahedron in pyrope. This agrees with previous studies concerning the compression behaviors of Mg²⁺ in 6-fold coordinated polyhedra at high pressures. The results show that simple bulk modulus–volume systematics are not obeyed by garnets. Received: 29 July 1998 / Revised, accepted: 7 April 1999     

Equation of state of hexagonal aluminous phase in basaltic composition to 63 GPa at 300 K

A laser-heated diamond-anvil cell that is capable of operating up to a pressure of 63 GPa, with X-ray diffraction facilities using a synchrotron radiation source at the SPring-8, has been developed to observe the compressibility of a hexagonal aluminous phase, [K_0.15Na_1.66Ca_0.11Mg_1.29Fe²⁺ _0.86Al_3.13Ti_0.09Si_1.98] _Σ9.27O₁₂. The hexagonal aluminous phase is a potassium host mineral from the subducted oceanic crust in the Earth's lower mantle. A sample was heated using a YAG laser at each pressure increment to relax the deviatoric stress in the sample. X-ray diffraction measurements were carried out at 300 K using an angle-dispersive technique. Pressure was measured using an internal platinum pressure calibrant. The observed unit-cell volumes were used to obtain a third-order Birch–Murnaghan equation of state: unit-cell volume V _o=185.94(±16) ų, density ρ _o=4.145 g/cm³, and bulk modulus K _o=198(±3) GPa when the first pressure is derivative of the bulk modulus K ^′ _o is fixed to 4. The density of hexagonal aluminous phase is lower than that of coexisting Mg-perovskite in the subducted oceanic crust.     

The compressibility of a natural apatite

In-situ synchrotron X-ray diffraction (XRD) experiments of a natural apatite with the formula of Ca₅(PO₄)₃F_0.94Cl_0.06 were carried out using a diamond anvil cell and angle-dispersive technique at Photon Factory (PF), Japan. Pressure–volume data were collected up to 7.12 GPa at 300 K. The pressures were determined from the ruby fluorescence spectra shift. The unit-cell parameters and volume decreased systematically with increasing pressure, and a reliable isothermal bulk modulus and its pressure derivative were obtained in this study. The third-order Birch–Murnaghan equation of state yielded the isothermal bulk modulus of K_T=91.5(38) GPa, its pressure derivative K_T= 4.0(11), and the zero-pressure volume V₀=524.2(3) ų.     

High-temperature and high-pressure equation of state for the hexagonal phase in the system NaAlSiO4 – MgAl2O4

Thermal equation of state of an Al-rich phase with Na_1.13Mg_1.51Al_4.47Si_1.62O₁₂ composition has been derived from in situ X-ray diffraction experiments using synchrotron radiation and a multianvil apparatus at pressures up to 24 GPa and temperatures up to 1,900 K. The Al-rich phase exhibited a hexagonal symmetry throughout the present pressure–temperature conditions and the refined unit-cell parameters at ambient condition were: a=8.729(1) Å, c=2.7695(5) Å, V ₀=182.77(6) Å³ (Z=1; formula weight=420.78 g/mol), yielding the zero-pressure density ρ₀=3.823(1) g/cm³ . A least-square fitting of the pressure-volume-temperature data based on Anderson’s pressure scale of gold (Anderson et al. in J Appl Phys 65:1534–543, 1989) to high-temperature Birch-Murnaghan equation of state yielded the isothermal bulk modulus K ₀=176(2) GPa, its pressure derivative K ₀ ^′ =4.9(3), temperature derivative (?K _T /?T) _P =?0.030(3) GPa K^?1 and thermal expansivity α(T)=3.36(6)×10^?5+7.2(1.9)×10^?9 T, while those values of K ₀=181.7(4) GPa, (?K _T /?T) _P =?0.020(2) GPa K^?1 and α(T)=3.28(7)×10^?5+3.0(9)×10^?9 T were obtained when K ₀ ^′ was assumed to be 4.0. The estimated bulk density of subducting MORB becomes denser with increasing depth as compared with earlier estimates (Ono et al. in Phys Chem Miner 29:527–531 2002; Vanpeteghem et al. in Phys Earth Planet Inter 138:223–230 2003; Guignot and Andrault in Phys Earth Planet Inter 143–44:107–128 2004), although the difference is insignificant (<0.6%) when the proportions of the hexagonal phase in the MORB compositions (～20%) are taken into account.     

The nonlinear anomalous lattice elasticity associated with the high-pressure phase transition in spodumene: a high-precision static compression study

The high-pressure behavior of the lattice elasticity of spodumene, LiAlSi₂O₆, was studied by static compression in a diamond-anvil cell up to 9.3 GPa. Investigations by means of single-crystal XRD and Raman spectroscopy within the hydrostatic limits of the pressure medium focus on the pressure ranges around ~3.2 and ~7.7 GPa, which have been reported previously to comprise two independent structural phase transitions. While our measurements confirm the well-established first-order C2/c–P2₁/c transformation at 3.19 GPa (with 1.2% volume discontinuity and a hysteresis between 0.02 and 0.06 GPa), both unit-cell dimensions and the spectral changes observed in high-pressure Raman spectra give no evidence for structural changes related to a second phase transition. Monoclinic lattice parameters and unit-cell volumes at in total 59 different pressure points have been used to re-calculate the lattice-related properties of spontaneous strain, volume strain, and the bulk moduli as a function of pressure across the transition. A modified Landau free energy expansion in terms of a one component order parameter has been developed and tested against these experimentally determined data. The Landau solution provides a much better reproduction of the observed anomalies than any equation-of-state fit to data sets truncated below and above P _tr, thus giving Landau parameters of K ₀ = 138.3(2) GPa, K′ = 7.46(5), λ _V  = 33.6(2) GPa, a = 0.486(3), b = −29.4(6) GPa and c = 551(11) GPa.     

Equation of state and pressure-induced structural changes in mirabilite (Na2SO4·10H2O) determined from ab initio density functional theory calculations

We have carried out ab initio calculations using density functional theory to determine the bulk elastic properties of mirabilite, Na₂SO₄·10H₂O, and to obtain information on structural trends caused by the application of high pressure up to ~60 GPa. We have found that there are substantial isosymmetric discontinuous structural re-organisations at ~7.7 and ~20 GPa caused by changes in the manner in which the sodium cations are coordinated by water molecules. The low-pressure and intermediate-pressure phases both have sodium in sixfold coordination but in the high-pressure phase the coordination changes from sixfold to sevenfold. These coordination changes force a re-arrangement of the hydrogen-bond network in the crystal. The trend is towards a reduction in the number of hydrogen bonds donated to the sulphate group (from twelve down to six over the range 0–60 GPa) and an increase in hydrogen bonding amongst the Na-coordinated water molecules and the two interstitial water molecules. Ultimately, we observe proton transfers from the interstitial waters (forming OH^? ions) to two of the Na-coordinated waters (forming a pair of H₃O⁺ ions). The equation of state in the athermal limit of the low-pressure phase of mirabilite, parameterised by fitting an integrated form of the third-order Birch-Murnaghan expression to the calculated energy as a function of unit-cell volume, yields the zero-pressure unit-cell volume, V ₀ = 1468.6(9) ų, the incompressibility, K ₀ = 22.21(9) GPa, and the first pressure derivative K ₀′ = (?K/?P)₀ = 5.6(1).     

Compressibility of Ca3Al2Si3O12 perovskite up to 55 GPa

Compressibility of perovskite-structured Ca₃Al₂Si₃O₁₂ grossular (GrPv) was investigated at high pressure and high temperature by means of angle-dispersive powder X-ray diffraction using a laser-heated diamond anvil cell. We observed the Pbnm orthorhombic distortion for the pure phase above 50 GPa, whereas below this pressure, Al-bearing CaSiO₃ perovskite coexists with an excess of corundum. GrPv has a bulk modulus (K ₀ = 229 ± 5 GPa; \(K_{0}^{{\prime }}\) fixed to 4) almost similar to that reported for pure CaSiO₃ perovskite. Its unit-cell volume extrapolated to ambient conditions (V ₀ = 187.1 ± 0.4 Å³) is found to be ~2.5 % larger than for the Al-free phase. We observe an increasing unit-cell anisotropy with increasing pressure, which could have implications for the shear properties of Ca-bearing perovskite in cold slabs subducted into the Earth’s mantle.     

Compressibility of strontium orthophosphate Sr<Subscript>3</Subscript>(PO<Subscript>4</Subscript>)<Subscript>2</Subscript> at high pressure

High pressure in situ synchrotron X-ray diffraction experiment of strontium orthophosphate Sr₃(PO₄)₂ has been carried out to 20.0 GPa at room temperature using multianvil apparatus. Fitting a third-order Birch–Murnaghan equation of state to the P–V data yields a volume of V ₀ = 498.0 ± 0.1 Å³, an isothermal bulk modulus of K _T  = 89.5 ± 1.7 GPa, and first pressure derivative of K _T ′ = 6.57 ± 0.34. If K _T ′ is fixed at 4, K _T is obtained as 104.4 ± 1.2 GPa. Analysis of axial compressible modulus shows that the a-axis (K _a  = 79.6 ± 3.2 GPa) is more compressible than the c-axis (K _c  = 116.4 ± 4.3 GPa). Based on the high pressure Raman spectroscopic results, the mode Grüneisen parameters are determined and the average mode Grüneisen parameter of PO₄ vibrations of Sr₃(PO₄)₂ is calculated to be 0.30(2).     

A high-pressure neutron diffraction study of the ferroelastic phase transition in RbCaF3

The fluoroperovskite phase RbCaF₃ has been investigated using high-pressure neutron powder diffraction in the pressure range ~0–7.9 GPa at room temperature. It has been found to undergo a first-order high-pressure structural phase transition at ~2.8 GPa from the cubic aristotype phase to a hettotype phase in the tetragonal space group I4/mcm. This transition, which also occurs at ~200 K at ambient pressure, is characterised by a linear phase boundary and a Clapeyron slope of 2.96 × 10^?5 GPa K^?1, which is in excellent agreement with earlier, low-pressure EPR investigations. The bulk modulus of the high-pressure phase (49.1 GPa) is very close to that determined for the low-pressure phase (50.0 GPa), and both are comparable with those determined for the aristotype phases of CsCdF₃, TlCdF₃, RbCdF₃, and KCaF₃. The evolution of the order parameter with pressure is consistent with recent modifications to Landau theory and, in conjunction with polynomial approximations to the pressure dependence of the lattice parameters, permits the pressure variation of the bond lengths and angles to be predicted. On entering the high-pressure phase, the Rb–F bond lengths decrease from their extrapolated values based on a third-order Birch–Murnaghan fit to the aristotype equation of state. By contrast, the Ca–F bond lengths behave atypically by exhibiting an increase from their extrapolated magnitudes, resulting in the volume and the effective bulk modulus of the CaF₆ octahedron being larger than the cubic phase. The bulk moduli for the two component polyhedra in the tetragonal phase are comparable with those determined for the constituent binary fluorides, RbF and CaF₂.     

Compressional behavior of omphacite to 47 GPa

Omphacite is an important mineral component of eclogite. Single-crystal synchrotron X-ray diffraction data on natural (Ca, Na) (Mg, Fe, Al)Si₂O₆ omphacite have been collected at the Advanced Photon Source beamlines 13-BM-C and 13-ID-D up to 47 GPa at ambient temperature. Unit cell parameter and crystal structure refinements were carried out to constrain the isothermal equation of state and compression mechanism. The third-order Birch–Murnaghan equation of state (BM3) fit of all data gives V ₀ = 423.9(3) Å³, K _T0 = 116(2) GPa and K _T0′ = 4.3(2). These elastic parameters are consistent with the general trend of the diopside–jadeite join. The eight-coordinated polyhedra (M2 and M21) are the most compressible and contribute to majority of the unit cell compression, while the SiO₄ tetrahedra (Si1 and Si2) behave as rigid structural units and are the most incompressible. Axial compressibilities are determined by fitting linearized BM3 equation of state to pressure dependences of unit cell parameters. Throughout the investigated pressure range, the b-axis is more compressible than the c-axis. The axial compressibility of the a-axis is the largest among the three axes at 0 GPa, yet it quickly drops to the smallest at pressures above 5 GPa, which is explained by the rotation of the stiffest major compression axis toward the a-axis with the increase in pressure.     

Structural change of GeO2 under pressure

Pressure-induced amorphization of α-quartz type GeO₂ was studied with a newly developed X-ray diffraction system which consists of a 4-circle goniometer and a curved position sensitive detector. Single-crystal diffraction was measured under pressurs up to 7.3 GPa at room temperature in order to investigate pretransitional phenomena. Diffraction intensity and line width of the diffraction profiles showed no remarkable change up to 5.9 GPa. However, no sharp diffraction line was observed at pressures over 6.5 GPa. The bulk modulus at 0.1 MPa and its pressure derivative of α-quartz type GeO₂ were determined to be K _T =32.8(3.3) GPa and K′ _T =6.0(2.0), respectively. In situ microscopic observations of the amorphization transformation was also performed. The large volume change due to amorphization was observed and estimated to be about 10%.     

Single-crystal x-ray diffraction of brucite to 14 GPa

Single-crystal brucite, Mg(OH)₂, was studied to 14 GPa in a quasi-hydrostatic pressure medium using a diamond anvil cell and energy-dispersive synchrotron x-ray diffraction. The parameters of a third-order Birch-Murnaghan equation of state fit to the data are: K _OT=42(2) GPa, and (?K _OT/?P)_T= 5.7(5). The bulk modulus is significantly lower than that obtained in recent shock compression and powder x-ray diffraction experiments under non-hydrostatic conditions. No evidence was found for a transition involving the Mg -O sub-structure over the pressure range of these experiments. This implies that the structural change previously identified at high pressure by Raman spectroscopy probably involves rearrangement of hydrogen atoms, leaving the Mg — O substructure largely unaffected.     

Compression of Fe3C to 30 GPa at room temperature

Polycrystalline Fe₃C (cementite) was compressed in a neon pressure medium to 30.5 GPa at 300 K using diamond-anvil cell techniques. Angular dispersive X-ray diffraction of Fe₃C was measured using monochromatic synchrotron radiation and imaging plates. No phase transition was observed up to the highest pressure studied. The pressure–volume data were fitted to a third-order Birch–Murnaghan equation of state. With V ₀ constrained to a measured value of 155.28 ų, the best fit yielded a 300-K isothermal bulk modulus K ₀ = 174 ± 6 GPa, and its pressure derivative at constant temperature K ₀ ^′ =(K ₀ /P) _T = 4.8±0.8.     

Thermal equation of state of synthetic orthoferrosilite at lunar pressures and temperatures

Iron-rich orthopyroxene plays an important role in models of the thermal and magmatic evolution of the Moon, but its density at high pressure and high temperature is not well-constrained. We present in situ measurements of the unit-cell volume of a synthetic polycrystalline end-member orthoferrosilite (FeSiO₃, fs) at simultaneous high pressures (3.4–4.8 GPa) and high temperatures (1,148–1,448 K), to improve constraints on the density of orthopyroxene in the lunar interior. Unit-cell volumes were determined through in situ energy-dispersive synchrotron X-ray diffraction in a multi-anvil press, using MgO as a pressure marker. Our volume data were fitted to a high-temperature Birch–Murnaghan equation of state (EoS). Experimental data are reproduced accurately, with a  $\varDelta P$ Δ P  standard deviation of 0.20 GPa. The resulting thermoelastic parameters of fs are: V ₀ = 875.8 ± 1.4 Å³, K ₀ = 74.4 ± 5.3 GPa, and $\frac{{\text d}K}{{\text d}T} = -0.032 \pm 0.005\,\hbox{GPa K}^{-1}$ d K d T = - 0.032 ± 0.005 GPa K - 1 , assuming ${K}^{\prime}_{0} = 10 $ K 0 ′ = 10 . We also determined the thermal equation of state of a natural Fe-rich orthopyroxene from Hidra (Norway) to assess the effect of magnesium on the EoS of iron-rich orthopyroxene. Comparison between our two data sets and literature studies shows good agreement for room-temperature, room-pressure unit-cell volumes. Preliminary thermodynamic analyses of orthoferrosilite, FeSiO₃, and orthopyroxene solid solutions, (Mg_1?x Fe _x ) SiO₃, using vibrational models show that our volume measurements in pressure–temperature space are consistent with previous heat capacity and one-bar volume–temperature measurements. The isothermal bulk modulus at ambient conditions derived from our measurements is smaller than values presented in the literature. This new simultaneous high-pressure, high-temperature data are specifically useful for calculations of the orthopyroxene density in the Moon.     

Structure and nuclear density distribution in the cheralite—CaTh(PO4)2: studies of its behaviour under high pressure (36?GPa)

The crystal structure of the cheralite—CaTh(PO₄)₂—has been revisited by neutron diffraction and its behaviour under high pressure investigated by X-ray diffraction up to 36?GPa. The neutron diffraction data at ambient pressure gave a more accurate determination of the Ca/Th cation position than previous XRD data, taking advantage that the neutron scattering lengths of calcium and thorium are of same order of magnitude. The nuclear density distribution was also determined using the maximum entropy method (MEM) confirming that the two cations are not located at the same position in the unit cell but are slightly displaced from one another along a specific direction in order to minimize the electrostatic repulsion with the surrounding phosphorus atoms. At high pressure, the compound did not show any phase transition or amorphization. From the evolution of the unit-cell volume as a function of the pressure, the zero-pressure bulk modulus B₀ and its pressure derivative B₀ ^′ have been determined by fitting the experimental compressibility curve to the Birch–Murnaghan equation of state. The results are B₀?=?140(2) GPa and B ₀ ^′ ?=?4.4(4) GPa.