Murnaghan Equation Research Articles

Pargasite at high pressure and temperature

The P–T phase stability field, the thermoelastic behavior and the P-induced deformation mechanisms at the atomic scale of pargasite crystals, from the “phlogopite peridotite unit” of the Finero mafic–ultramafic complex (Ivrea-Verbano Formation, Italy), have been investigated by a series of in situ experiments: (a) at high pressure (up to 20.1 GPa), by single-crystal synchrotron X-ray diffraction with a diamond anvil cell, (b) at high temperature (up to 823 K), by powder synchrotron X-ray diffraction using a hot air blower device, and (c) at simultaneous HP–HT conditions, by single-crystal synchrotron X-ray diffraction with a resistive-heated diamond anvil cell (P max = 16.5 GPa, T max = 1200 K). No phase transition has been observed within the P–T range investigated. At ambient T, the refined compressional parameters, calculated by fitting a second-order Birch–Murnaghan Equation of State (BM-EoS), are: V 0 = 915.2(8) A3 and K P0,T0 = 95(2) GPa (β P0,T0 = 0.0121(2) GPa−1) for the unit-cell volume; a 0 = 9.909(4) A and K(a) P0,T0 = 76(2) GPa for the a-axis; b 0 = 18.066(7) A and K(b) P0,T0 = 111(2) GPa for the b-axis; c 0 = 5.299(5) A and K(c) P0,T0 = 122(12) GPa for the c-axis [K(c) P0,T0 ~ K(b) P0,T0 > K(a) P0,T0]. The high-pressure structure refinements (at ambient T) show a moderate contraction of the TO4 double chain and a decrease of its bending in response to the hydrostatic compression, along with a pronounced compressibility of the A- and M(4)-polyhedra [K P0, T0(A) = 38(2) GPa, K P0, T0(M4) = 79(5) GPa] if compared to the M(1)-, M(2)-, M(3)-octahedra [K P0, T0(M1,2,3) ≤ 120 GPa] and to the rigid tetrahedra [K P0, T0(T1,T2) ~ 300 GPa]. The thermal behavior, at ambient pressure up to 823 K, was modelled with Berman’s formalism, which gives: V 0 = 909.1(2) A3, α0 = 2.7(2)·10−5 K−1 and α1 = 1.4(6)·10−9 K−2 [with α0(a) = 0.47(6)·10−5 K−1, α0(b) = 1.07(4)·10−5 K−1, and α0(c) = 0.97(7)·10−5 K−1]. The petrological implications for the experimental findings of this study are discussed.

Pressure-induced phase transformation of CsPbI3 by X-ray diffraction and Raman spectroscopy

ABSTRACTThe structural transformation of cesium lead iodine (CsPbI3) has been investigated in diamond anvil cells up to ∼15 GPa at room temperature by employing synchrotron radiation X-ray diffraction and Raman spectroscopy. One reversible transformation from orthorhombic (Pnma) to monoclinic (P21/m) phase has been observed at 3.9 GPa. Isothermal pressure–volume relationship of orthorhombic CsPbI3 is well fitted by the third-order Birch–Murnaghan equation of state with K0 = 14(3) GPa, K′0 = 6(2) and V0 = 891(7) Å3. The ultralow value of bulk modulus K0 demonstrates the high compressible nature of CsPbI3, similar to those of organic–inorganic metal halide perovskites. The present results provide essential information on the intrinsic properties and stability of CsPbI3, which may be applied in photovoltaic devices.

Single-crystal equations of state of magnesiowüstite at high pressures

Solid solutions of (Mg,Fe)O with high iron enrichment may be an important component of ultralow-velocity zones at Earth’s core-mantle boundary. However, to date there have been few high-precision studies on the elastic properties of these materials. In this study we present results on the compression of (Mg_(0.22)Fe_(0.78))O magnesiowustite in both neon and helium pressure media using single-crystal diffraction to ~55 GPa. In addition, our sample was characterized by time-domain synchrotron Mossbauer spectroscopy at ambient pressure using an extended time range that resulted in vastly improved energy resolution. The combination of these high-resolution techniques tightly constrains the presence of a defect-structure component at room pressure due to 4.7 mol% tetrahedrally coordinated ferric iron, resulting in a renormalized composition of (Mg_(0.215)Fe_(0.762)□_(0.023))O. Both high-pressure diffraction data sets are well described by a third-order Birch-Murnaghan equation of state. The best fit-parameters for a crystal with cubic structure in helium are K_(0T) = 148(3) GPa, K′_(0T) = 4.09(12), and V0 = 78.87(6) A^3. Increasing differential stress in the neon-containing sample chamber was correlated with increasing apparent distortion of the initially cubic unit cell, requiring a lower-symmetry hexagonal cell to fit the data above ~20 GPa. For fit equations of state, we determine the pressure-dependent correlation ellipses for the equation of state parameters and compare with previously published single-crystal diffraction data from (Mg,Fe)O crystals in a helium medium. We make two main observations from the data sets using a helium pressure medium: K_(0T) decreases as a function of increasing iron content from periclase to wustite and K′_(0T) is consistent with an approximately constant value of 4.0 that is independent of iron content, at least up to the iron concentration measured here. In combination with previously reported thermal parameters, we compute the density of magnesiowustite with this composition at core-mantle boundary conditions and discuss the implications.

Elastic constants of boron hydrogen chains in monoclinic crystal

Full-potential linearized augmented plane waves (FPLAPW), density functional theory within the generalized gradient and local density approximations methods are used to determine the ground state structure and to calculate the elastic constants of two phases of boron hydrogen chains in monoclinic crystalline form. The ground state structures are subjected to different strains to find the thirteen elastic constants of both phases by fitting the total energies E (V0,ε) with Birch—Murnaghan equation of state. Young's modulus shows that the anti-phase structure is stiffer than the in-phase one. The calculated ductility index using Pugh's (B/G) ratio found to be less than 0.5 for both phases indicating that they are brittle material.

High pressure structural phase transitions in Ho: Eu2O3

Structural stability and phase transitions in mixed rare earth sesquioxides (Eu1−xHox)2O3 crystallizing in the cubic bixbyite structure were investigated under high pressure using angle dispersive X-ray diffraction technique. Studies on various compositions of the mixed oxide show that when the average cationic radius, RRE (where, RRE = xRHo+(1−x)REu) is equivalent to or below 0.9164 Å, the system undergoes a cubic to monoclinic transition as a function of pressure, whereas, when RRE equivalent to or above 0.9220 Å it is observed to prefer a transition from cubic to hexagonal structure. Based on our detailed investigations, a pressure-concentration (P−x) phase diagram for (Eu1−xHox)2O3 up to a pressure of 15 GPa is constructed. The bulk moduli for the parent and high pressure phases are calculated from the Birch-Murnaghan equation of state fit to the experimental pressure volume data and are reported. Structural analysis based on refinement has revealed that, an increasing structural rigidity of the cubic phase with decreasing RRE leads to an increase in the transition pressure and bulk moduli except for 0.4 ≤ x ≤ 0.6. The observed significant reduction in bulk moduli and transition pressure for 0.4 ≤ x ≤ 0.6 is due to the increased micro strain/internal pressure developed upon doping.

Experimental evidence for the survival of augite to transition zone depths, and implications for subduction zone dynamics

(Ca,Mg)-rich clinopyroxenes are abundant in Earth’s upper mantle and subduction zones. Experimental studies on the thermoelastic properties of these minerals at simultaneous high pressure and high temperature are important for constraining of the composition and structure of the Earth. Here, we present a synchrotron-based single-crystal X-ray diffraction study of natural diopside-dominated augite [(Ca 0.89 Na 0.05 Mg 0.06 )(Mg 0.74 Fe 0.11 Al 0.14 Ti 0.01 )(Si 1.88 Al 0.12 )O 6.00 ] at P and T to ~27 GPa and 700 K. The experiment simulates conditions in cold subducting slabs, and results indicate that augite is stable over this pressure and temperature range. A third-order high-temperature Birch-Murnaghan equation was fit with the pressure-volume-temperature data, yielding the following thermoelastic parameters: K T0 = 111(1) GPa, K ′ T0 = 4.1(1), (∂ K 0 /∂ T ) P = −0.008(5) GPa/K and α T = 4(1)×10 −5 K −1 +2(3)×10 −8 K −2 T. A strain analysis shows that the compression along the three principal stress directions is highly anisotropic with ɛ1:ɛ2:ɛ3 = 1.98:2.43:1.00. Additionally, high-pressure structural refinements of room-temperature polyhedral geometry, bond lengths and O3-O3-O3 angle were investigated to ~27 GPa at ambient temperature. Pressure dependences of polyhedral volumes and distortion indicate that the substitution of Al 3+ for Si 4+ significantly changes the compressional behavior of the T O 4 -tetrahedron in augite. Density calculations of this augite along a subducting slab geotherm suggest that augite as well as other common clinopyroxenes would promote slab stagnations at transition zone depths if they are metastably preserved in significant quantities.

Investigation of structural and multiferroic properties of three phases of BiFeO3 using modified Becke Johnson potential technique

Electronic band structure, ferroelectric and ferromagnetic properties of Cubic, Tetragonal and Rhombohedral (hexagonal axis) phases of multiferroic BiFeO3 compound has been investigated using first-principles calculations under the generalized gradient (GGA) and TB-mBJ semi local (Tran-Blaha modified Becke-Johnson) potential approximations using WIEN2k code. For this purpose, the total energies were calculated as a function of reduced volumes and the data were fitted to Brich Murnaghan equation. The estimated ground state parameters are found to be comparable with those of experimental ones. The semiconducting behavior of the material was obtained using TB-mBJ method in the spin polarized mode. Analysis of the density of states indicates that the valence band consists of Fe-d and O-p states, while the conduction band is composed of Fe-d and Bi-p states. The analysis of electron localization function shows that stereochemically active lone-pair electrons are present at Bi sites of Rhombohedral and Tetragonal phases and are responsible for the displacements of Bi atoms from the centro-symmetric to the non-centrosymmetric structure leading to the exhibition of ferroelectricity. Further, it has been concluded that the “lone pair” may have been formed due to the hybridization of 6s and 6p atomic orbitals with 6s2 electrons filling one of the resulting orbitals in Bi. The Polarization and the magnetic properties including susceptibility were obtained. The calculated magnetic moments at the iron sites are not integer values, since Fe electrons have a hybridization interaction with the neighboring O ions.

Elastic properties of CaCO3 high pressure phases from first principles**Project supported by the National Natural Science Foundation of China (Grant Nos. 41174071, 41373060, 41374096, and 41403099) and the Seismic Fund of Institute of Earthquake Science, China Earthquake Administration (CEA) (Grant Nos. 2012IES0408, 2014IES0407, and 2016IES0101).

Elastic properties of three high pressure polymorphs of CaCO3 are investigated based on first principles calculations. The calculations are conducted at 0 GPa–40 GPa for aragonite, 40 GPa–65 GPa for post-aragonite, and 65 GPa–150 GPa for the -h-CaCO structure, respectively. By fitting the third-order Birch–Murnaghan equation of state (EOS), the values of bulk modulus and pressure derivative are 66.09 GPa and 4.64 for aragonite, 81.93 GPa and 4.49 for post-aragonite, and 56.55 GPa and 5.40 for -h-CaCO, respectively, which are in good agreement with previous experimental and theoretical data. Elastic constants, wave velocities, and wave velocity anisotropies of the three high-pressure CaCO phases are obtained. Post-aragonite exhibits 25.90%–32.10% anisotropy and 74.34%–104.30% splitting anisotropy, and -h-CaCO shows 22.30%–25.40% anisotropy and 42.81%–48.00% splitting anisotropy in the calculated pressure range. Compared with major minerals of the lower mantle, CaCO high pressure polymorphs have low isotropic wave velocity and high wave velocity anisotropies. These results are important for understanding the deep carbon cycle and seismic wave velocity structure in the lower mantle.

Structural stability of high entropy alloys under pressure and temperature

The stability of high-entropy alloys (HEAs) is a key issue before their selection for industrial applications. In this study, in-situ high-pressure and high-temperature synchrotron radiation X-ray diffraction experiments have been performed on three typical HEAs Ni20Co20Fe20Mn20Cr20, Hf25Nb25Zr25Ti25, and Re25Ru25Co25Fe25 (at. %), having face-centered cubic (fcc), body-centered cubic (bcc), and hexagonal close-packed (hcp) crystal structures, respectively, up to the pressure of ∼80 GPa and temperature of ∼1262 K. Under the extreme conditions of the pressure and temperature, all three studied HEAs remain stable up to the maximum pressure and temperatures achieved. For these three types of studied HEAs, the pressure-dependence of the volume can be well described with the third order Birch-Murnaghan equation of state. The bulk modulus and its pressure derivative are found to be 88.3 GPa and 4 for bcc-Hf25Nb25Zr25Ti25, 193.9 GPa and 5.9 for fcc-Ni20Co20Fe20Mn20Cr20, and 304.6 GPa and 3.8 for hcp-Re25Ru25Co25Fe25 HEAs, respectively. The thermal expansion coefficient for the three studied HEAs is found to be in the order as follows: fcc-Ni20Co20Fe20Mn20Cr20 > bcc-Hf25Nb25Zr25Ti25 ≈ hcp-Re25Ru25Co25Fe25.

40 years of mineral elasticity: a critical review and a new parameterisation of equations of state for mantle olivines and diamond inclusions

Elasticity is a key property of materials, not only for predicting volumes and densities of minerals at the pressures and temperatures in the interior of the Earth, but also because it is a major factor in the energetics of structural phase transitions, surface energies, and defects within minerals. Over the 40 years of publication of Physics and Chemistry of Minerals, great progress has been made in the accuracy and precision of the measurements of both volumes and elastic tensors of minerals and in the pressures and temperatures at which the measurements are made. As an illustration of the state of the art, all available single-crystal data that constrain the elastic properties and pressure–volume–temperature equation of state (EoS) of mantle-composition olivine are reviewed. Single-crystal elasticity measurements clearly distinguish the Reuss and Voigt bulk moduli of olivine at all conditions. The consistency of volume and bulk modulus data is tested by fitting them simultaneously. Data collected at ambient pressure and data collected at ambient temperature up to 15 GPa are consistent with a Mie–Grunesien–Debye thermal-pressure EoS in combination with a third-order Birch–Murnaghan (BM) compressional EoS, the parameter V 0 = 43.89 cm3 mol−1, isothermal Reuss bulk modulus $$K_{\text{TR,0}} = 126.3(2){\text{ GPa}}$$ , $$K^{\prime}_{\text{TR,0}} = 4.54(6)$$ , a Debye temperature $$\theta_{\text{D}} = 644(9)\;{\text{K}}$$ , and a Gruneisen parameter γ 0 = 1.044(4), whose volume dependence is described by q = 1.9(2). High-pressure softening of the bulk modulus at room temperature, relative to this EoS, can be fit with a fourth-order BM EoS. However, recent high-P, T Brillouin measurements are incompatible with these EoS and the intrinsic physics implied by it, especially that $$\left( {\frac{{\partial K^{\prime}_{\text{TR}} }}{\partial T}} \right)_{P} > 0$$ . We introduce a new parameterisation for isothermal-type EoS that scales both the Reuss isothermal bulk modulus and its pressure derivative at temperature by the volume, $$K_{\text{TR}} (T,P = 0) = K_{\text{TR,0}} \left[ {\frac{{V_{0} }}{V(T)}} \right]^{{\delta_{\text{T}} }}$$ and $$K^{\prime}_{\text{TR}} (T,P = 0) = K^{\prime}_{\text{TR,0}} \left[ {\frac{V(T)}{{V_{0} }}} \right]^{{\delta^{\prime}}}$$ , to ensure thermodynamic correctness at low temperatures. This allows the elastic softening implied by the high-P, T Brillouin data for mantle olivine to be fit simultaneously and consistently with the same bulk moduli and pressure derivatives (at room temperature) as the MGD EoS, and with the additional parameters of α V0 = 2.666(9) × 10−5 K−1, $$\theta_{\text{E}} = 484(6)$$ , $$\delta_{\text{T}}$$ = 5.77(8), and $$\delta^{\prime}$$ = −3.5(1.1). The effects of the differences between the two EoS on the calculated density, volume, and elastic properties of olivine at mantle conditions and on the calculation of entrapment conditions of olivine inclusions in diamonds are discussed, and approaches to resolve the current uncertainties are proposed.

Structural stability and phase transition of Bi2Te3 under high pressure and low temperature

Structural stability and phase transition of topological insulator Bi2Te3 were studied via angle-dispersive synchrotron radiation X-ray diffraction under high pressure and low temperature condition. The results manifest that the R-3m phase (phase I) is stable at 8K over the pressure range up to 10GPa and phase transition occurs between 8K and 45K at 8GPa. According to the Birch-Murnaghan equation of state, the bulk modulus at ambient pressure B0 was estimated to be 45 ± 3GPa with the assumption of B0′ = 4. The structural robustness of phase I at 8K suggests that the superconductivity below 10GPa is related to phase I. Topological properties of superconducting Bi2Te3 phase under pressure were discussed.

Li0.5Ni0.5Mn2O4 spinel: Its synthesis, structure and high pressure properties

A new Li-Ni-Mn spinel of the composition Li0.5Ni0.5Mn2O4 was successfully prepared by thermal decomposition of citrate complexes followed by quenching from 1048 K. The distribution of cations in this oxide was deduced from X-ray powder diffraction and XPS measurements. High pressure powder X-ray diffraction measurements were performed up to pressures of approximately 6 GPa. The cubic spinel phase remained stable within the pressure range of this study. The bulk modulus calculated from the second order Birch–Murnaghan equation of state with the data following from our study was B0 = 136 (3) GPa, while the initial volume was V0 = 578.4 (3) Å3. The obtained bulk modulus fits into the general trend of compressibility increasing with growing lithium content at tetrahedral sites. The result of the experiment reported here has provided the first proof of the earlier postulated tendency.

Synchrotron X-Ray Diffraction Studies on the New Generation Ferromagnetic Semiconductor Li(Zn,Mn)As under High Pressure**Supported by the National Natural Science Foundation and the Ministry of Science and Technology of China, the National Natural Science Foundation of China under Grant No U1530402, the U.S. Department of Energy of Office of Science under Grant No DE-AC02-06CH11357, the DOE-NNSA under Grant No DE-NA0001974, the

The pressure effect on the crystalline structure of the I–II–V semiconductor Li(Zn,Mn)As ferromagnet is studied using in situ high-pressure x-ray diffraction and diamond anvil cell techniques. A phase transition starting at ∼11.6 GPa is found. The space group of the high-pressure new phase is proposed as Pmca. Fitting with the Birch–Murnaghan equation of state, the bulk modulus and its pressure derivative of the ambient pressure structure with space group of are GPa and , respectively.

Pressure-induced structural modifications of rare-earth hafnate pyrochlore

Complex oxides with the pyrochlore (A2B2O7) and defect-fluorite ((A,B)4O7) structure-types undergo structural transformations under high-pressure. Rare-earth hafnates (A2Hf2O7) form the pyrochlore structure for A = La–Tb and the defect-fluorite structure for A = Dy–Lu. High-pressure transformations in A2Hf2O7 pyrochlore (A = Sm, Eu, Gd) and defect-fluorite (A = Dy, Y, Yb) were investigated up to ~50 GPa and characterized by in situ Raman spectroscopy and synchrotron x-ray diffraction (XRD). Raman spectra at ambient pressure revealed that all compositions, including the defect-fluorites, have some pyrochlore-type short-range order. In situ high-pressure synchrotron XRD showed that all of the rare earth hafnates investigated undergo a pressure-induced phase transition to a cotunnite-like (orthorhombic) structure that begins between 18 and 25 GPa. The phase transition to the cotunnite-like structure is not complete at 50 GPa, and upon release of pressure, the hafnates transform to defect-fluorite with an amorphous component. For all compositions, in situ Raman spectroscopy showed that disordering occurs gradually with increasing pressure. Pyrochlore-structured hafnates retain their short-range order to a higher pressure (30 GPa vs. <10 GPa) than defect-fluorite-structured hafnates. Rare earth hafnates quenched from 50 GPa show Raman spectra consistent with weberite-type structures, as also reported for irradiated rare-earth stannates. The second-order Birch–Murnaghan equation of state fit gives a bulk modulus of ~250 GPa for hafnates with the pyrochlore structure, and ~400 GPa for hafnates with the defect-fluorite structure. Dy2Hf2O7 is intermediate in its response, with some pyrochlore-type ordering, based on Raman spectroscopy and the equation of state, with a bulk modulus of ~300 GPa. As predicted based on the similar ionic radius of Zr4+ and Hf4+, rare-earth hafnates show similar behavior to that reported for rare earth zirconates at high pressure.

Pressure-Driven Isostructural Phase Transition in InNbO4: In Situ Experimental and Theoretical Investigations.

The high-pressure behavior of technologically important visible-light photocatalytic semiconductor InNbO4, adopting a monoclinic wolframite-type structure at ambient conditions, was investigated using synchrotron-based X-ray diffraction, Raman spectroscopic measurements, and first-principles calculations. The experimental results indicate the occurrence of a pressure-induced isostructural phase transition in the studied compound beyond 10.8 GPa. The large volume collapse associated with the phase transition and the coexistence of two phases observed over a wide range of pressure shows the nature of transition to be first-order. There is an increase in the oxygen anion coordination number around In and Nb cations from six to eight at the phase transition. The ambient-pressure phase has been recovered on pressure release. The experimental pressure-volume data when fitted to a Birch-Murnaghan equation of states yields the value of ambient pressure bulk modulus as 179(2) and 231(4) GPa for the low- and high-pressure phases, respectively. The pressure dependence of the Raman mode frequencies and Grüneisen parameters was determined for both phases by experimental and theoretical methods. The same information is obtained for the infrared modes from first-principles calculations. Results from theoretical calculations corroborate the experimental findings. They also provide information on the compressibility of interatomic bonds, which is correlated with the macroscopic properties of InNbO4.

Anomalous lattice compressibility of hexagonal Eu2O3

Monoclinic Eu2O3 was investigated in a Mao-Bell type diamond anvil cell using angle dispersive x-ray diffraction up to a pressure of 26 GPa. Pressure induced structural phase transition from monoclinic to hexagonal phase was observed at 4.3 GPa with 2% volume collapse. Birch –Murnaghan equation of state fit to the pressure volume data yielded a bulk modulus of 159(9) GPa and 165(6) GPa for the monoclinic and hexagonal phases respectively. Equation of state fitting to the structural parameters yielded an axial compressibility of βa > βc > βb for the parent monoclinic phase, showing the least compressibility along b axis. Contrary to the available reports, an anomalous lattice compressibility behavior is observed for the high pressure hexagonal phase, characterized by pronounced hardening of a axis above 15 GPa. The observed incompressible nature of the hexagonal a axis in the pressure range 15–25 GPa is found to be compensated by doubling the compressibility along the c axis.

Structural stability of ultra-high temperature refractory material MoSi2 and Mo5Si3 under high pressure**Project supported by the Joint Fund of the National Natural Science Foundation of China and the Chinese Academy of Sciences (Grant No. U1332104).

In-situ angle dispersive x-ray diffraction (ADXRD) with synchrotron radiation source is performed on an ultra-high temperature refractory of MoSi2 and Mo5Si3 by using a diamond anvil cell (DAC) at room temperature. While the pressure-induced volume reduction is almost constant, the value of the bulk modulus increases with the decrease of molybdenum content in the system. According to the Brich–Murnaghan equation, the bulk modulus 222.1 (2.1) GPa with its pressure derivative 4 of MoSi2, and the bulk modulus 308.4 (7.6) GPa with its pressure derivative 0.7 (0.1) of Mo5Si3 are obtained. The experimental data show that MoSi2 has distinct anisotropic behavior, Mo5Si3 is less anisotropic than MoSi2. The result shows that MoSi2 and Mo5Si3 have the structural stabilities under high pressure. When the pressure reaches up to 41.1 GPa, they can still maintain their body-cantered tetragonal structures.

P-V-T behavior of FeO(OH) and MnO(OH)

The P-V-T behavior of FeO(OH) and MnO(OH) has been determined under high pressure and high temperature up to 7.5 GPa and 500 °C using a MAX 80 cubic anvil high-pressure apparatus. The samples, synthetic goethite, α-FeO(OH), respectively, a natural groutite/manganite, α-MnO(OH)/γ-MnO(OH), specimen were mixed with Vaseline to ensure hydrostatic pressure-transmitting conditions, and NaCl served as an internal standard for pressure calibration. Energy-dispersive diffraction patterns were collected at a fixed 2θ angle (θ ≈ 4.52°). At pressures >7.1 GPa and temperatures >310 °C, respectively, P > 6.3 GPa and T > 350 °C, the transformation goethite ↔ e-FeO(OH) was observed. Between 400 and 450 °C, the sample dehydrated to magnetite due to the reducing conditions caused by the graphite-tube furnace. By fitting a Birch–Murnaghan equation of state to the data, the bulk modulus of goethite was determined as (112.26 ± 2.26) GPa, (K′ = 4), VT,0 = (138.79 ± 0.10) A3·exp [∫(0.497 ± 0.103) × 10−4 dT], (∂KT/∂T)P = (–0.033 ± 0.020) GPa K−1. For e-FeO(OH), the values K = (142.8 ± 15.1) GPa, V0 = (66.18 ± 0.16) A3, (K′ = 4), were obtained. Groutite and manganite are more compressible than their Fe analogues. K(groutite) = (84.0 ± 2.9) GPa, V0 = (139.92 ± 0.13) A3, (K′ = 4). K(manganite) = (82.2 ± 3.0) GPa, V0 = (135.37 ± 0.15) A3, (K′ = 4). Groutite disappeared at P ≈ 5.5 GPa and T = 300 °C, only manganite remained. At T > 400 °C, the sample dehydrated first to Mn3O4 [II] and then to manganosite (MnO) again pointing to reducing conditions.

Compressibility and high-pressure structural behavior of Mg2Fe2O5

The compressibility and structural behavior of the novel Mg 2 Fe 2 O 5 oxide has been investigated by in situ single-crystal X-ray diffraction in a diamond-anvil cell up to a pressure of 17 GPa. The bulk compressibility of Mg 2 Fe 2 O 5 can be described using a second-order Birch-Murnaghan equation of state (BM2 EoS) with V 0 = 352.4(2) A 3 and K 0 = 171(4) GPa. Three linear BM2 EoS were used to describe the axial compressibility of Mg 2 Fe 2 O 5 , which was found to be highly anisotropic. The a and b lattice parameters have very similar compressibilies, with a 0 = 2.8917(11) A and linear modulus M a = 572(16) GPa and b 0 = 9.736(3) A and linear modulus M b = 583(15) GPa, respectively. The c -axis is the most compressible direction as indicated by the smaller linear modulus [ c 0 = 12.520(15) A and M c = 404(28) GPa]. The Mg 2 Fe 2 O 5 structure consists of edge-sharing octahedra alternating with layers of trigonal prisms. The compression behavior of the M-O bonds of the M1 and M2 octahedra and of the M3 prisms depend on their location in either an edge-sharing environment, which makes them stiffer, or a corner-sharing environment where they have more freedom to distort and compress. The main compression mechanism consists of a polyhedral tilting around the M2-O1-M2 angle, which decreases with increasing pressure. Mg 2 Fe 2 O 5 has recently been added to the list of stable end-members of phases with M 4 O 5 stoichiometry, making it a potentially relevant phase in the Earth’s upper mantle and transition zone. To develop thermodynamic activity-composition models for high-pressure phases, it is crucial to know the accurate elastic parameters of each individual end-member. Currently these have only been measured for Mg 2 Fe 2 O 5 (this study) and Fe 4 O 5 .

Effects of water on P-V-T equation of state of pyrope

High-pressure single-crystal/powder synchrotron X-ray diffraction was carried out on a hydrous pure magnesium pyrope (Mg3Al2Si3O12) containing 900ppmw H2O, synthesized at 4.0GPa and 1300K. The pressure-volume (P-V) single-crystal data from room pressure to 9.81GPa at ambient temperature were fitted by a third-order Birch-Murnaghan equation of state (BM-EoS) yielding a unit-cell volume of V0=1505.14±0.38Å3, an isothermal bulk modulus of K0=160±3GPa and its pressure derivative K′0=5.2±0.4. When fixing K'0=4.0, the data yielded V0=1504.58±0.32Å3 and K0=166±2GPa. The pressure-volume-temperature (P-V-T) EoS of the synthetic hydrous pyrope was also measured at temperatures up to 900K and pressures up to 16.75GPa, using a diamond anvil cell in conjunction with in situ synchrotron angle-dispersive powder X-ray diffraction. The P-V data at room temperature and in a pressure range of 0.0001–14.81GPa were then analyzed by a third-order BM-EoS and yielded V0=1505.35±0.25Å3, K0=161±2GPa, K′0=5.0±0.3. With K'0 fixed to 4.0, we also obtained V0=1505.04±0.29Å3 and K0=167±1GPa. Consequently, we fitted the P-V-T data with the high-temperature third-order BM-EoS approach and obtained the thermoelastic parameters of V0=1505.4±0.3Å3, K0=162±1GPa, K′0=4.9±0.2, the temperature derivative of the bulk modulus (∂K0/∂T)P=−0.018±0.004GPaK−1, and the thermal expansion coefficient at ambient conditions α0=(3.2±0.1)×10−5K−1. These properties were consistent with the thermal pressure EoS analysis. These new results on hydrous pyrope were also compared with previous studies of anhydrous pyrope. The main effect of hydration on pyrope is to decrease K0 and increase K'0 by increasing the vacancies or unoccupied volume in the structure. The entire dataset enabled us to examine the thermoelastic properties of important mantle garnets and this data has further applications for modeling the P-T conditions in the upper mantle of the Earth’s interior using deep mineral assemblages.