High-pressure neutron diffraction study on H–D isotope effects in brucite

A neutron powder diffraction study of hydrogenated and deuterated brucite was conducted at ambient temperature and at pressures up to 9 GPa, using a Paris–Edinburgh high-pressure cell at the WAND instrument of the ORNL High Flux Isotope Reactor. The two materials were synthesized by the same method and companion measurements of neutron diffraction were conducted under the same conditions. Our refinement results show that the lattice-parameters of the a axis, parallel to the sheets of Mg–O octahedra, decrease only slightly with pressure with no effect of H–D substitution. However, the c axis of Mg(OD)₂ is shorter and may exhibit greater compressibility with pressure than that of Mg(OH)₂. Consequently, the unit-cell volume of deuterated brucite is slightly, but systematically smaller than that of hydrogenated brucite. When fitted to a third-order Birch–Murnaghan equation in terms of the normalized unit-cell volume, values of the bulk modulus for hydrogenated and deuterated brucite (K ₀ = 39.0 ± 2.8 and 40.4 ± 1.3 GPa, respectively) are, however, indistinguishable from each other within the experimental errors. The measured effect of H–D substitution on the unit-cell volume also demonstrates that brucite (and other hydrous minerals) preferentially incorporate deuterium over hydrogen under pressure, suggesting that the distribution of hydrogen isotopes in deep-earth conditions may differ significantly from that in near-surface environments.     

Structure and compressibility of synthetic ZnAl2O4 (gahnite) under high-pressure conditions, from synchrotron X-ray powder diffraction

 The structural behavior of synthetic gahnite (ZnAl₂O₄) has been investigated by X-ray powder diffraction at high pressure (0–43 GPa) and room temperature, on the ID9 beamline at ESRF. The equation of state of gahnite has been derived using the models of Birch–Murnaghan, Vinet and Poirier–Tarantola, and the results have been mutually compared (the elastic bulk modulus and its derivatives versus P determined by the third-order Birch–Murnaghan equation of state are K ₀=201.7(±0.9) GPa, K ^′ ₀=7.62(±0.09) and K ^″ ₀=−0.1022 GPa⁻¹ (implied value). The compressibilities of the tetrahedral and octahedral bond lengths [0.00188(8) and 0.00142(5) GPa⁻¹ at P=0, respectively], and the␣polyhedral volume compressibilities of the four-␣and␣sixfold coordination sites [0.0057(2) and 0.0041(2) GPa⁻¹ at P=0, respectively] are discussed. Received: 15 January 2001 / Accepted: 23 April 2001     

Equations of state of CaSiO3 Perovskite: a molecular dynamics study

The molar volumes and bulk moduli of CaSiO₃ perovskite are calculated in the temperature range from 300 to 2,800 K and the pressure range from 0 to 143 GPa using molecular dynamics simulations that employ the breathing shell model for oxygen and the quantum correction in addition to the conventional pairwise interatomic potential models. The performance of five equations of state, i.e., the Keane, the generalized-Rydberg, the Holzapfel, the Stacey–Rydberg, and the third-order Birch–Murnaghan equations of state are examined using these data. The third-order Birch–Murnaghan equation of state is found to have a clear tendency to overestimate the bulk modulus at very high pressures. The Stacey–Rydberg equation of state degrades slightly at very high pressures along the low-temperature isotherms. In comparison, the Keane and the Holzapfel equations of state remain accurate in the whole temperature and pressure range considered in the present study. K ₀′ derived from the Holzapfel equation of state also agrees best with that calculated independently from molecular dynamics simulations. The adiabatic bulk moduli of CaSiO₃ perovskite along lower mantle geotherms are further calculated using the Keane and the Mie-Grüneisen–Debye equations of state. They are found to be constantly higher than those of the PREM by ~5%, and also very similar to those of the MgSiO₃ perovskite. Our results support the view that CaSiO₃ perovskite remains invisible in the Earth’s lower mantle.     

Compressibility of synthetic glaucophane

The compressibilities of two synthetic glaucophane samples were measured over the range of 0–10 GPa at ambient temperature in a diamond-anvil cell at the Cornell High-Energy Synchrotron Source (CHESS). The pressure–volume data were fitted to the Birch–Murnaghan equation of state taking care to include only data with a minimum of deviatoric stress. When using a second-order truncation, both samples yielded essentially identical values of the bulk modulus K ₀, which had an average value of 91.8 ± 1.3 GPa. Maximum compression was observed approximately along the a* axis as shown by the strain ellipsoid and supported by the a axis showing the highest compressibility. These results agree closely with the earlier study of a natural glaucophane single-crystal by Comodi et al. (Eur J Mineral 3:485–499, 1991), suggesting that the substitution of about 20–30 mol.% of Fe for Mg and Al in the structure may not significantly change its compressibility.     

In situ neutron diffraction study of deuterated portlandite Ca(OD)2 at high pressure and temperature

The structure of deuterated portlandite, Ca(OD)₂, has been investigated using time-of-flight neutron diffraction at pressures up to ∼4.5 GPa and temperatures up to ∼823 K. Rietveld analysis of the data reveals that with increasing pressure, unit-cell parameter c decreases at a rate about 4.5 times larger than that for a, which is largely due to rapid contraction of the interlayer spacing in this pressure range. Fitting of the determined cell volumes to the third-order Birch–Murnaghan equation of state yields a bulk modulus (K ₀) of 32.2 ± 1.0 GPa and its first derivative (K ₀′) of 4.4 ± 0.6. Moreover, on compression, hydrogen-mediated interatomic interactions within the interlayer become strengthened, as reflected by decreases in interlayer D···O and D···D distances with increasing pressure. Correspondingly, D–D, the distance between the three equivalent sites over which D is disordered, increases, suggesting a pressure-induced hydrogen disorder. This behavior is similar to that reported in brucite at elevated pressure. On heating at ∼2.1 GPa, cell parameter c increases more rapidly than a, as expected. However, because of the pressure effect, the thermal expansion coefficients, particularly along c, are much smaller than those at ambient pressure. With increasing temperature, the three partially occupied D sites become further apart, and the D-mediated interactions, mainly the interlayer D···D repulsion, become weakened.     

Pressure-induced structural transition in Ln2Zr2O7 (Ln = Ce, Nd, Gd) pyrochlores

The structural behavior under pressure of three lanthanide pyrochlore zirconates Ln₂Zr₂O₇ (Ln³⁺ = Ce, Nd and Gd) has been investigated by X-ray diffraction up to 50 GPa. For all three compounds, a symmetry reduction from cubic to monoclinic is observed under increasing pressure dependant on a pressure value that increases with the ionic radius of the lanthanide ions, r _Ln. The cubic and monoclinic phases coexist over a wide pressure range which increases with r _Ln. The zero-pressure bulk modulus of the cubic phase, B ₀, and its pressure derivative, B ₀′, have been determined by fitting the experimental compressibility curves to the Birch–Murnaghan equation of state.     

The compressibility and high pressure structure of diopside from first principles simulation

The structure of diopside (CaMgSi₂O₆) has been calculated at pressures between 0 and 25 GPa using the planewaves and pseudopotentials approach to density functional theory. After applying a pressure correction of 4.66 GPa to allow for the under-binding usually associated with the generalized gradient approximation, cell parameters are in good agreement with experiment. Fitting to the third-order Birch–Murnaghan equation of state yields values of 122 GPa and 4.7 for the bulk modulus and its pressure derivative. In addition to cell parameters, our calculations provide all atomic positional parameters to pressures considerably beyond those currently available from experiment. We have analyzed these data in terms of polyhedral rigidity and regularity and find that the most compressible Ca polyhedron becomes markedly less anisotropic above 10 GPa. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Equation of state, elasticity, and shear strength of pyrite under high pressure

 Physical properties including the equation of state, elasticity, and shear strength of pyrite have been measured by a series of X-ray diffraction in diamond-anvil cells at pressures up to 50 GPa. A Birch–Murnaghan equation of state fit to the quasihydrostatic pressure–volume data obtained from laboratory X-ray source/film techniques yields a quasihydrostatic bulk modulus K _0T =133.5 (±5.2) GPa and bulk modulus first pressure derivative K ^′ _0T =5.73 (±0.58). The apparent equation of state is found to be strongly dependent on the stress conditions in the sample. The stress dependency of the high-pressure properties is examined with anisotropic elasticity theory from subsequent measurements of energy-dispersive radial diffraction experiments in the diamond-anvil cell. The calculated values of K _0T depend largely upon the angle ψ between the diffracting plane normal and the maximum stress axis. The uniaxial stress component in the sample, t=σ₃−σ₁, varies with pressure as t=−3.11+0.43P between 10 and 30 GPa. The pressure derivatives of the elastic moduli dC ₁₁/dP=5.76 (±0.15), dC ₁₂/dP=1.41 (±0.11) and dC ₄₄/dP=1.92 (±0.06) are obtained from the diffraction data assuming previously reported zero-pressure ultrasonic data (C ₁₁=382 GPa, C ₁₂=31 GPa, and C ₄₄=109 GPa). Received: 21 December 2000 / Accepted: 11 July 2001     

The effect of composition and cation ordering on the compressibility of columbites up to 7 GPa

The unit-cell parameters of two columbite samples along the (Fe,Mn)Nb₂O₆ solid solution were measured by means of high-pressure single-crystal X-ray diffraction up to pressures of 7 GPa. The compressional behaviour of these minerals was studied as a function of composition and degree of order. The P–V data of all the samples were fitted with a third-order Birch–Murnaghan equation of state. For the two samples with different compositions but identical degree of order the substitution of Mn for Fe causes a decrease of the bulk modulus K _T0, from 153(1) to 146(1) GPa, without any effect on the pressure first derivative K′. For the two samples with the same composition, cation ordering causes an increase of the bulk modulus from 149(1) to 153(1) GPa and of the pressure first derivative from 4.1(2) to 4.8(3). The compressional behaviour is anisotropic with a linear axial compressibility scheme β _b > β _c ≥ β _a for all samples, regardless of composition and degree of order. Such anisotropy increases sligthly with increasing Mn content.     

Elasticity and equation of state of Li<Subscript>2</Subscript>B<Subscript>4</Subscript>O<Subscript>7</Subscript>

A single crystal X-ray diffraction study on lithium tetraborate Li₂B₄O₇ (diomignite, space group I4₁ cd) has been performed under pressure up to 8.3 GPa. No phase transitions were found in the pressure range investigated, and hence the pressure evolution of the unit-cell volume of the I4₁ cd structure has been described using a third-order Birch–Murnaghan equation of state (BM-EoS) with the following parameters: V ₀  = 923.21(6) ų, K ₀  = 45.6(6) GPa, and K′ = 7.3(3). A linearized BM-EoS was fitted to the axial compressibilities resulting in the following parameters a ₀  = 9.4747(3) Å, K _0a  = 73.3(9) GPa, K′ _a  = 5.1(3) and c ₀  = 10.2838(4) Å, K _0c  = 24.6(3) GPa, K′ _c  = 7.5(2) for the a and c axes, respectively. The elastic anisotropy of Li₂B₄O₇ is very large with the zero-pressure compressibility ratio β _0c /β _0a  = 3.0(1). The large elastic anisotropy is consistent with the crystal structure: A three-dimensional arrangement of relatively rigid tetraborate groups [B₄O₇]²⁻ forms channels occupied by lithium along the polar c–axis, and hence compression along the c axis requires the shrinkage of the lithium channels, whereas compression in the a direction depends mainly on the contraction of the most rigid [B₄O₇]²⁻ units. Finally, the isothermal bulk modulus obtained in this work is in general agreement with that derived from ultrasonic (Adachi et al. in Proceedings-IEEE Ultrasonic Symposium, 228–232, 1985; Shorrocks et al. in Proceedings-IEEE Ultrasonic Symposium, 337–340, 1981) and Brillouin scattering measurements (Takagi et al. in Ferroelectrics, 137:337–342, 1992).     

An X-ray diffraction study of shock-wave-densified SiO<Subscript>2</Subscript> glasses

 The densification and structural changes in SiO₂ glass compressed up to 43.4 GPa by shock experiments are investigated quantitatively by the X-ray diffraction technique. Direct structural data (average Si–O and Si–Si distances and Si–O–Si angles, coordination number of the Si atom) of these shock-densified SiO₂ glasses have been obtained by analyzing the radial distribution function curves, RDF(r), calculated with X-ray diffraction data. The coordination number of all densified glasses is about 4 and shows almost no pressure variation. The SiO₂ glass has shown density increase of 11% at a shock compression of 26.3 GPa. This density evolution could not be explained by the coordination change. The reduction of the average Si–O–Si angle (144° at 0 GPa to 136° at 26.3 GPa) obtained from RDF(r) data may account for this density increase. This Si–O–Si angle change may be caused by shrinkage of the network structure and the increase of small rings of SiO₄ tetrahedra. For higher shock pressure, a decrease in the Si–O–Si angle to 140° was observed. This is consistent with the decrease in density at 32.0 and 43.2 GPa. This decrease in the Si–O–Si angle and density could be attributed to an annealing effect due to high after-shock residual temperature. This pressure dependence of average Si–O–Si angles in shock-densified SiO₂ glass agrees with the results of our previous Raman spectroscopic study. On the other hand, the pressure variation for the first sharp diffraction peak (FSDP) was analyzed to estimate the evolution of intermediate range structures. It is suggested that the mean d value (d _m ) obtained from the position of FSDP strongly depends on the shock and residual temperature, as well as shock pressure. Received: 29 June 2001 / Accepted: 14 November 2001     

The influence of pressure on the structure and dynamics of hydrogen bonds in zoisite and clinozoisite

Density functional theory calculations have been used to study the pressure-induced changes of the hydrogen bond of Fe-free orthozoisite and clinozoisite and the concomitant shifts of the OH-stretching frequencies. Two independent parameter-free lattice dynamical calculations have been employed. One was based on a plane-wave basis set in conjunction with norm-conserving pseudopotentials and a density functional perturbation theory approach, while the other used a localised basis set and a finite displacement algorithm for the lattice dynamical calculations. Both models confirm the unusually large pressure-induced red-shift found experimentally (−33.89 cm⁻¹/GPa) in orthozoisite, while the pressure-induced shifts in clinozoisite are much smaller (−5 to −9 cm⁻¹/GPa). The atomistic model calculations show that in orthozoisite the nearly linear O–H⋯O arrangement is compressed by about 8% on a pressure increase to 10 GPa, while concomitantly the O–H distance is significantly elongated (by 2.5% at 10 GPa). In clinozoisite, the O–H⋯O arrangement is kinked at ambient conditions and remains kinked at high pressures, while the O-H distance is elongated by only 0.5% at 10 GPa. The current calculations confirm that correlations between the distances and dynamics of hydrogen bonds, which have been established at ambient conditions, cannot be used to infer hydrogen positions at high pressures.     

Visualization-based analysis of structural and dynamical properties of simulated hydrous silicate melt

We have explored first-principles molecular dynamics simulation data for hydrous MgSiO₃ liquid (with 10 wt% water) to gain insight into its structural and dynamical behavior as a function of pressure (0–150 GPa) and temperature (2,000–6,000 K). By visualizing/analyzing a number of parameters associated with short- and mid-range orders, we have shown that the melt structure changes substantially on compression. The speciation of the water component at low pressures is dominated by the isolated structures (with over 90% hydrogen participated) consisting of hydroxyls, water molecules, O–H–O bridging and four-atom (O–H–O–H and H–O–H–O) groups, where every oxygen atom may be a part of polyhedron or free (i.e., bound to only magnesium atom). Hydroxyls favor polyhedral sites over magnesium sites whereas molecular water is almost entirely bound to magnesium sites, and also interpolyhedral bridging (Si–O–H–O–Si) dominates other types of bridging. Water content is shown to enhance and suppress, respectively, the proportions of hydroxyls and molecular water. As compression increases, these isolated structures increasingly combine with each other to form extended structures involving a total of five or more O and H atoms and also containing threefold coordination species, which together consume over 80% hydrogen at the highest compression studied. Our results show that water lowers the mean coordination numbers of different types including all cation–anion environments. The hydrous melt tends to be more tetrahedrally coordinated but with the Si–Si network being more disrupted compared to the anhydrous melt. Protons increase the content of non-bridging oxygen and decrease the contents of bridging oxygen as well as oxygen triclusters (present at pressures above 10 GPa). The calculated self-diffusion coefficients of all atomic species are enhanced in the presence of water compared to those of the anhydrous melt. This is consistent with the prediction that water depolymerizes the melt structure at all pressures. Our analysis also suggests that proton diffusion involves two processes—the transfer of H atoms (requiring the rupture and formation of O–H bonds) and the motion of hydroxyls as hydrogen carriers (requiring the rupture and formation of Si–O and/or Mg–O bonds). Both the processes are operative at low compression whereas only the first process is operative at high compression.     

Compression behaviors of distorted rutile-type hydrous phases, MOOH (M?=?Ga, In, Cr) and CrOOD

X-ray diffraction measurements of distorted rutile-type oxyhydroxides β-GaOOH, InOOH, β-CrOOH, and β-CrOOD were taken at a maximum pressure of up to 35 GPa under quasi-hydrostatic conditions, at ambient temperature. Anomalies in the evolution of the relative lattice constants and the axial ratios of β-GaOOH, InOOH, and β-CrOOD suggest anisotropic stiffening along the a- and/or b-axes where the hydrogen bond is formed. The changes were observed at 15 GPa in β-GaOOH and InOOH and at 4 GPa in β-CrOOD. The pressures were higher in oxyhydroxides that have longer O…O distances of the hydrogen bond at ambient pressure. In contrast, such stiffening behavior was not observed in CrOOH, which has a significant short O…O distance and strong hydrogen bond. The stiffening behaviors observed in the present study can be attributed to the symmetrization of the hydrogen bonds in oxyhydroxides, as was previously found in δ-AlOOH(D).     

Do carbonate liquids become denser than silicate liquids at pressure? Constraints from the fusion curve of K<Subscript>2</Subscript>CO<Subscript>3</Subscript> to 3.2 GPa

Brackets on the melting temperature of K₂CO₃ were experimentally determined at 1.86 ± 0.02 GPa (1,163–1,167°C), 2.79 ± 0.03 GPa (1,187–1,195°C), and 3.16 ± 0.04 GPa (1,183–1,189°C) in a piston-cylinder apparatus. These new data, in combination with published experiments at low pressure (<0.5 GPa), establish the K₂CO₃ fusion curve to 3.2 GPa. On the basis of these experiments and published thermodynamic data for crystalline and liquid K₂CO₃, the high-pressure density and compressibility of K₂CO₃ liquid were derived from the fusion curve. The pressure dependence of the liquid compressibility (K′₀ = dK ₀/dP, where K ₀ = 1/β₀) is between 16.2 and 11.6, with a best estimate of 13.7, in a third-order Birch–Murnaghan equation of state (EOS). This liquid K′₀ leads to a density of 2,175 ± 36 kg/m³ at 4 GPa and 1,500°C, which is ∼30% lower than that reported in the literature on the basis of the falling-sphere method at the same conditions. The uncertainty in the liquid K′₀ leads to an error in melt density of ± 2% at 4 GPa; the error decreases with decreasing pressure. With a K′₀ of 13.7, the compressibility of K₂CO₃ at 1,500°C and 1 bar (K ₀ = 3.8 GPa) drops rapidly with increasing pressure ( ), which prevents a density crossover with silicate melts, such as CaAlSi₂O₈ and CaMgSi₂O₆, at upper mantle depths.     

The influence of the Jahn–Teller effect at Fe<Superscript>2+</Superscript> on the structure of chromite at high pressure

The crystal structure of chromite FeCr₂O₄ was investigated to 13.7 GPa and ambient temperature with single-crystal X-ray diffraction techniques. The unit-cell parameter decreases continuously from 8.3832 (5) to 8.2398 (11) Å up to 11.8 GPa. A fit to the Birch–Murnaghan equation of state (EoS) based on the P–V data gives: K ₀ = 209 (13) GPa, K′ = 4.0 (fixed), and V ₀ = 588 (1) ų. The FeO₄ tetrahedra and CrO₆ octahedra are compressed isotropically with pressure with their Fe–O and Cr–O bond distances decreasing from 1.996 (6) to 1.949 (7) Å and from 1.997 (3) to 1.969 (7) Å, respectively. The tetrahedral site occupied by the Fe²⁺ cation is more compressible than the octahedral site occupied by the Cr³⁺ cation. The resulting EoS parameters for the tetrahedral and the octahedral sites are K ₀ = 147 (9) GPa, K′ = 4.0 (fixed), V ₀ = 4.07 (1) ų and K ₀ = 275 (24) GPa, K′ = 4.0 (fixed), V ₀ = 10.42 (2) ų, respectively. A discontinuous volume change is observed between 11.8 and 12.6 GPa. This change indicates a phase transition from a cubic (space group Fd-[`3]{\overline{3}} m) to a tetragonal structure (space group I4₁ /amd). At the phase transition boundary, the two Cr–O bonds parallel to the c-axis shorten from 1.969 (7) to 1.922 (17) Å and the other four Cr–O bonds parallel to the ab plane elongate from 1.969 (7) to 1.987 (9) Å. This anisotropic deformation of the octahedra leads to tetragonal compression of the unit cell along the c-axis. The angular distortion in the octahedron decreases continuously up to 13.7 GPa, whereas the distortion in the tetrahedron rises dramatically after the phase transition. At the pressure of the phase transition, the tetrahedral bond angles along the c-axis direction of the unit cell begin decreasing from 109.5° to 106.6 (7)°, which generates a “stretched” tetrahedral geometry. It is proposed that the Jahn–Teller effect at the tetrahedrally coordinated Fe²⁺ cation becomes active with compression and gives rise to the tetrahedral angular distortion, which in turn induces the cubic-to-tetragonal transition. A qualitative molecular orbital model is proposed to explain the origin and nature of the Jahn–Teller effect observed in this structure and its role in the pressure-induced phase transition.     

Synchrotron X-ray analysis of norbergite, Mg2.98Fe0.01Ti0.02Si0.99O4(OH0.31F1.69) structure at high pressure up to 8.2?GPa

The natural norbergite, Mg_2.98Fe_0.01Ti_0.02Si_0.99O₄(OH_0.31F_1.69) is examined by synchrotron X-ray diffraction analysis at pressures up to 8.2 GPa. The measured linear compressibilities of the crystallographic axes are β _a  = 2.18(4) × 10⁻³, β _b  = 2.93(7) × 10⁻³, and β _c  = 2.77(7) × 10⁻³ (GPa⁻¹), respectively and the calculated isothermal bulk modulus of the norbergite is K _T = 113(2) GPa based on the Birch–Murnaghan equation of state assuming a pressure derivative of K′ = 4. The crystal structures of norbergite are refined at room temperature and pressures of 4.7, 6.3, and 8.2 GPa, yielding R values for the structure refinements of 4.6, 5.3, and 5.3%, respectively. The bulk moduli of the polyhedral sites are 293(15) GPa for the tetrahedron, 106(5) GPa for the M2 octahedron, 113(2) GPa for the M3 octahedron, and 113(3) GPa for the total void space. The bulk modulus exhibits a good linear correlation with the filling factor for polyhedral sites in structures of the humite minerals and forsterite, reflecting the Si⁴⁺ + 4O²⁻ ⇔ □ + 4(OH, F)⁻ substitution in the humite minerals. Moreover, two simply linear trends were observed in the relationship between bulk modulus and packing index for natural minerals and dense hydrous magnesium silicate minerals. This relationship would reflect that the differences in compression mechanism were involved with hydrogen bonding in these minerals. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Effect of incorporation of iron and aluminum on the thermoelastic properties of magnesium silicate perovskite

In situ X-ray diffraction measurements of Fe- and Al-bearing MgSiO₃-rich perovskite (FeAl-Pv), which was synthesized from a natural orthopyroxene, were performed at pressures of 19–32 GPa and temperatures of 300–1,500 K using a combination of a Kawai-type apparatus with eight sintered-diamond anvils and synchrotron radiation. Two runs were performed using a high-pressure cell with two sample chambers, and both MgSiO₃ perovskite (Mg-Pv) and FeAl-Pv were synthesized simultaneously in the same cell. Thus we were able to measure specific volumes (V/V ₀) of Mg-Pv and FeAl-Pv at the same P−T conditions. At all the measurement conditions, values of the specific volume of FeAl-Pv are consistent with those of Mg-Pv within 2 Standard Deviation, strongly suggesting that effect of incorporation of iron and aluminum on the thermoelastic properties of magnesium silicate perovskite is undetectable in this composition, pressure, and temperature range. Two additional runs were performed using a high-pressure cell that has one sample chamber and unit-cell volumes of FeAl-Pv were measured at pressures and temperatures up to 32 GPa and 1,500 K, respectively. All the unit-cell volume data of FeAl-Pv perovskite were fitted to the high temperature Birch–Murnaghan equation of state and a complete set of thermoelastic parameters of this perovskite was determined with an assumption of K′ _300,0 = 4. The determined parameters are K _300,0 = 243(3) GPa, (∂K _T,0/∂T) _P = −0.030(8) GPa/K, a ₀ = 2.78(18) × 10⁻⁵ K⁻¹, and b ₀ = 0.88(28) × 10⁻⁸ K⁻², where a ₀ and b ₀ are the coefficients of the following expression describing the zero-pressure thermal expansion: α _T,0 = a ₀ + b ₀ T. The equation-of-state parameters of FeAl-Pv are in good agreement with those of MgSiO₃ perovskite at the conditions corresponding to the uppermost part of the lower mantle.     

Eutectic temperatures and melting relations in the Fe–O–S system at high pressures and temperatures

We have investigated melting relations in the Fe–O–S ternary system in the pressure range of 15–27 GPa and 1873 K. Subsolidus phase relations are Fe, Fe₃S₂, and FeO up to 17 GPa and Fe, Fe₃S, and FeO above this pressure. The eutectic temperature slightly decreases from ambient pressure to 17 GPa, whereas increases above this pressure. The eutectic temperature in this study is 100 K lower than that in the Fe–S binary system. The oxygen content in the Fe–O–S eutectic liquid drops when the coexisting solid phases changes from FeS to Fe₃S₂. The cotectic lines in the ternary phase diagram lie close to the Fe–FeS binary axis. The isothermal sections indicate that oxygen solubility in the Fe–O–S liquid increases with increasing temperature, and with increasing sulfur content. The solubility of sulfur in the solid Fe has a maximum value at the eutectic temperature, and decreases with increasing temperature. Our results could have important implications for formation and composition of the Martian core.     

The stability and compressibility of MgAl2O4 high-pressure polymorphs

High-pressure and high-temperature experiments using a laser-heated diamond anvil cell (LHDAC) and synchrotron X-ray diffraction have revealed a phase transition in MgAl₂O₄. CaTi₂O₄-type MgAl₂O₄ was found to be stable at pressures between 45 and at least 117 GPa. The transition pressure of CaTi₂O₄-type phase in MgAl₂O₄ is much lower than that in the natural N-type mid-oceanic ridge basalt composition. The Birch–Murnaghan equation of state for CaTi₂O₄-type MgAl₂O₄ was determined from the experimental unit cell parameters with K ₀=219(±6) GPa, K ₀′=4(constrained value), and V ₀=238.9(±9) ų. The observed compressibility was in agreement with the theoretical compressibility calculated in a previous study. ε-MgAl₂O₄ was observed at pressures between 40 and 45 GPa, which has not been reported in natural rock compositions. The gradient (dP/dT slope) of the transition from the ε-type to CaTi₂O₄-type MgAl₂O₄ had a positive value. These results should resolve the dispute regarding the stable high-pressure phase of MgAl₂O₄, which has been reported in earlier studies using both the multi-anvil press and the diamond anvil cell.