Melting of portlandite up to 6 GPa

 Using the high-pressure differential thermal analysis (HP-DTA) system in a cubic multianvil high-pressure apparatus, we measured the melting points of portlandite, Ca(OH)₂, up to 6 GPa and 1000 °C. We detected endothermic behavior at the temperature and pressure conditions of 800 °C and 2.5 GPa, 769 °C and 3.5 GPa, 752 °C and 4.0 GPa, 686 °C and 5.0 GPa, and 596 °C and 6.0 GPa, respectively, due to melting of portlandite. By in situ X-ray studies under pressure, the melting of portlandite was observed at 730 °C and 4.32 GPa and at 640 °C and 5.81 GPa, respectively. Results of both HP-DTA and X-ray studies were consistent within experimental error. The melting is congruent and has a negative Clapeyron slope, indicating that liquid Ca(OH)₂ has higher densities than crystalline portlandite in this pressure range. Received: 19 June 1999 / Revised, accepted: 11 September 1999     

The low-pressure stability of phase A,Mg7Si2O8(OH)6

 Phase A, Mg₇Si₂O₈(OH)₆, is a dense hydrous magnesium silicate whose importance as a host of H₂O in the Earth’s mantle is a subject of debate. We have investigated the low-pressure stability of phase A in experiments on the reaction phase A=brucite+forsterite. Experiments were conducted in piston-cylinder and multi-anvil apparatus, using mixtures of synthetic phase A, brucite and forsterite. The reaction was bracketed between 2.60 and 2.75 GPa at 500° C, between 3.25 and 3.48 GPa at 600° C and between 3.75 and 3.95 GPa at 650^° C. These pressures are much lower than observed in the synthesis experiments of Yamamoto and Akimoto (1977). At 750^° C the stability field of brucite + chondrodite was entered. The enthalpy of formation and entropy of phase A at 1 bar (10⁵ Pa), 298 K, were derived from the experimental brackets on the reaction phase A=brucite+forsterite using a modified version of the thermodynamic dataset THERMOCALC of Holland and Powell (1990), which includes a new equation of state of H₂O derived from the molecular dynamics simulations of Brodholt and Wood (1993). The data for phase A are: ΔH ^o _f =−7126±8 kJ mol^-1, S ^o=351 J K^-1 mol^-1. Incorporating these data into THERMOCALC allows the positions of other reactions involving phase A to be calculated, for example the reaction phase A + enstatite=forsterite+vapour, which limits the stability of phase A in equilibrium with enstatite. The calculated position of this reaction (753° C at 7 GPa to 937° C at 10 GPa) is in excellent agreement with the experimental brackets of Luth (1995) between 7 and 10 GPa, supporting the choice of equation of state of H₂O used in THERMOCALC. Comparison of our results with calculated P-T paths of subducting slabs (Peacock et al. 1994) suggests that, in the system MgO–SiO₂–H₂O, phase A could crystallise in compositions with Mg/Si>2 at pressures as low as 3 GPa. In less Mg rich compositions phase A could crystallise at pressures above approximately 6 GPa. Received: 3 July 1995/Accepted: 14 December 1995     

Pressure–volume–temperature equation of state of andradite and grossular, by high-pressure and -temperature powder diffraction

 The thermoelastic parameters of natural andradite and grossular have been investigated by high-pressure and -temperature synchrotron X-ray powder diffraction, at ESRF, on the ID30 beamline. The P–V–T data have been fitted by Birch-Murnaghan-like EOSs, using both the approximated and the general form. We have obtained for andradite K ₀=158.0(±1.5) GPa, (dK/dT )₀=−0.020(3) GPa K⁻¹ and α₀=31.6(2) 10⁻⁶ K⁻¹, and for grossular K ₀=168.2(±1.7) GPa, (dK/dT)₀=−0.016(3) GPa K⁻¹ and α₀=27.8(2) 10⁻⁶ K⁻¹. Comparisons between the present issues and thermoelastic properties of garnets earlier determined are carried out. Received: 7 July 2000 / Accepted: 20 October 2000     

Computer modelling of a pressure induced phase change in clinoenstatite pyroxenes

 Using lattice dynamic modelling of pure MgSiO₃ clinopyroxenes, we have be able to simulate the properties of both the low-clino (P2₁/c) and a high-density-clino (C2/c) phases and our results are comparable with the high pressure (HP) X-ray study of these phases (Angel et al. 1992). The transition between the two phases is predicted to occur at 6GPa. The volume variation with pressure for both phases is described by a third-order Birch-Murnaghan equation of state with the parameters V _{0  low}=31.122 cm³·mol⁻¹, K _{T0  low}= 107.42 GPa, K′ _{T0  low}=5.96, V _{0  high}=30.142 cm³·mol^–1, K _{T0  high}102.54 GPa and K′ _{T0  high}=8.21. The change in entropy between the two modelled phases at 6GPa is ΔS _{6 Gpa}=−1.335 J·mol⁻¹·K⁻¹ and the equivalent change in volume is ΔV _{6 GPa}=−0.92 cm³·mol⁻¹, from which the gradient of the phase boundary δP/δT is 0.0014 GPa·K⁻¹. The variation of the bulk modulus with pressure was also determined from the modelled elastic constants and compares very well with the EOS data. The reported Lehmann discontinuity, ∼220 km depth and pressure of 7.11Gpa, has an increase in the seismic compressional wave velocity, v _p , of 7.14% using the data given for PREM (Anderson 1989). At a pressure of 7GPa any phase transition of MgSiO₃ pyroxene would be between ortho (Pbca) and high-clino. We find the value of v _p at 7GPa, for modelled orthoenstatite (Pbca), is 8.41 km·sec⁻¹ and that for the modelled high-clino phase at 7GPa is 8.93 km·sec⁻¹, giving a dv _p /v _p of 6.18%. Received: July 26, 1996 / Revised, accepted: September 27, 1996     

Synchrotron X-ray powder diffraction study of natural P2 /n-omphacites at high-pressure conditions

 Synchrotron X-ray powder diffraction experiments at high pressure conditions (0.0001–13 GPa) were performed at ESRF (Grenoble-F), on the beamline ID9, to investigate the bulk elastic properties of natural P2/n-omphacites, with quasi-ideal composition. The monoclinic cell parameters a, b, c and β were determined as a function of pressure, and their compressibility coefficients are 0.00277(7), 0.00313(8), 0.00292(5) and 0.00116(4) GPa⁻¹, respectively. The third-order Birch-Murnaghan equation of state was used to interpolate the experimental P−V data, obtaining K ₀=116.6(±2.5) GPa and K′₀=6.03(±0.60). K ₀ was also determined by means of the axial and angular compressibilities [122.5(±1.7) GPa], and of the finite Lagrangian strain theory [121.5(±1.0) GPa]. The discrepancies on K ₀ are discussed in the light of a comparison between techniques to determine the bulk modulus of crystalline materials from static compression diffraction data. Received: 22 February 2000 / Accepted: 10 July 2000     

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     

X-ray diffraction study of magnesite at high pressure and high temperature

 P–V–T measurements on magnesite MgCO₃ have been carried out at high pressure and high temperature up to 8.6 GPa and 1285 K, using a DIA-type, cubic-anvil apparatus (SAM-85) in conjunction with in situ synchrotron X-ray powder diffraction. Precise volumes are obtained by the use of data collected above 873 K on heating and in the entire cooling cycle to minimize non-hydrostatic stress. From these data, the equation-of-state parameters are derived from various approaches based on the Birch-Murnaghan equation of state and on the relevant thermodynamic relations. With K′₀ fixed at 4, we obtain K₀=103(1) GPa, α(K⁻¹)=3.15(17)×10⁻⁵ +2.32(28)×10⁻⁸ T, (∂K_T/∂T)_P=−0.021(2) GPaK⁻¹, (dα/∂P)_T=−1.81×10⁻⁶ GPa⁻¹K⁻¹ and (∂K_T/∂T)_V= −0.007(1) GPaK⁻¹; whereas the third-order Birch-Murnaghan equation of state with K′₀ as an adjustable parameter yields the following values: K₀=108(3) GPa, K′₀=2.33(94), α(K⁻¹)=3.08(16)×10⁻⁵+2.05(27) ×10⁻⁸ T, (∂K_T/∂T)_P=−0.017(1) GPaK⁻¹, (dα/∂P)_T= −1.41×10⁻⁶ GPa⁻¹K⁻¹ and (∂K_T/∂T)_V=−0.008(1) GPaK⁻¹. Within the investigated P–T range, thermal pressure for magnesite increases linearly with temperature and is pressure (or volume) dependent. The present measurements of room-temperature bulk modulus, of its pressure derivative, and of the extrapolated zero-pressure volumes at high temperatures, are in agreement with previous single-crystal study and ultrasonic measurements, whereas (∂K_T/∂T)_P, (∂α/∂P)_T and (∂K_T/∂T)_V are determined for the first time in this compound. Using this new equation of state, thermodynamic calculations for the reactions (1) magnesite=periclase+CO₂ and (2) magnesite+enstatite=forsterite+CO₂ are consistent with existing experimental phase equilibrium data. Received September 28, 1995/Revised, accepted May 22, 1996     

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     

P-V-T equation of state of lawsonite

A pressure-volume-temperature data set has been obtained for lawsonite [CaAl₂Si₂O₇(OH)₂.H₂O], using synchrotron X-ray diffraction and an externally heated diamond anvil cell. Unit-cell volumes were measured to 9.4 GPa and 767 K by angle dispersive X-ray diffraction using imaging plates. Phase changes were not observed within this pressure-temperature range, and lawsonite compressed almost isotropically at constant temperature. The P-V-T data have been analyzed using a Birch- Murnaghan equation of state and a linear equation of state expressed as β=–1/V₀ (∂V/∂P) _T . At room temperature, the derived equation of state parameters are: K ₀=124.1 (18) GPa K'₀ set to 4) and β^–1=142.0(24) GPa, respectively. Our results are intermediate between previously reported measurements. The high-temperature data show that the incompressibility of lawsonite decreases with increasing temperature to ∼500 K and then increases above. Hence, the second order temperature derivative of the bulk modulus is taken into account in the equation of state; a fit of the volume data yields K ₀=123.9(18) GPa, (∂K/∂T)_P=–0.111(3) GPa K^–1, (∂² K/∂T ²)_P=0.28(6) 10^–3 GPa K^–2, α₀=3.1(2) 10^–5 K^–1, assuming K'₀=4. Received: 2 June 1998 / Revised, accepted: 12 Ocotber 1998     

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.     

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     

Phase transition of synthetic zinc ferrite spinel (ZnFe2O4) at high pressure, from synchrotron X-ray powder diffraction

 Synthetic Zn-ferrite (ideally ZnFe₂O₄; mineral name: franklinite) was studied up to 37 GPa, by X-ray powder diffraction at ESRF (Grenoble, France), on the ID9 beamline; high pressure was achieved by means of a DAC. The P-V equation of state of franklinite was investigated using the Birch-Murnaghan function, and the elastic properties thus inferred [K₀ = 166.4(±3.0) GPa K₀ ^′ = 9.3(±0.6) K₀ ^″ = −0.22 GPa⁻¹] are compared with earlier determinations for MgAl-spinel and magnetite. The structural behaviour of Zn-ferrite as a function of pressure was studied by Rietveld refinements, and interpreted in the light of a phase transition from spinel to either CaTi₂O₄- or MnFe₂O₄-like structure; this transformation occurs above 24 GPa. Received: 15 March 1999 / Accepted: 22 April 2000     

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.     

Ion tracks in apatite at high pressures: the effect of crystallographic track orientation on the elastic properties of fluorapatite under hydrostatic compression

Static elasticity measurements at high pressures were carried out on oriented fluorapatite single crystals, some of which contained oriented amorphous ion tracks (ITs) implanted with relativistic Au ions (2.2 GeV) from the UNILAC linear accelerator at GSI, Darmstadt. High-pressure experiments on irradiated and non-irradiated crystal sections were carried out in diamond-anvil high-pressure cells under hydrostatic conditions. In situ single-crystal diffraction was performed to determine the high-precision lattice parameters, simultaneously monitoring the widths of X-ray diffraction Bragg peaks. High-pressure Raman spectra were analyzed with respect to the frequency shift and widths of bands, which correspond to the Raman-active vibrational modes of the phosphate tetrahedra. Swift heavy ion irradiation was found to induce anisotropic lattice expansion and tensile strain within the host lattice dependent on the ion-track orientation. The relatively low Grüneisen parameter for the ν _1b(A _g) mode, which has been assigned to originate from the volume fraction of the amorphous tracks, and the γ(ν _1a)/γ(ν _1b) ratio reveals compressive strain on the amorphous ITs. The comparative compressibilities for the host lattice reveal approximately equivalent bulk moduli, but significantly different pressure derivatives (K _T = 88.4 ± 0.7 GPa, ∂K/∂P = 6.3 ± 0.3 for non-irradiated, K _T = 90.0 ± 1.7 GPa, ∂K/∂P = 3.8 ± 0.5 for irradiated samples). The axial compressibility moduli β ⁻¹ reveal significant differences, which correlate with the ion-track orientation [b_a ^{- 1} \beta_{a}^{ - 1}  = 240 ± 5 GPa, b_c ^{- 1} \beta_{c}^{ - 1}  = 361 ± 14 GPa, ∂( b_a ^{- 1} ) \left( {\beta_{a}^{ - 1} } \right) /∂P = 11.3 ± 1.2, ∂( b_c ^{- 1} ) \left( {\beta_{c}^{ - 1} } \right) /∂P = 11.6 ± 3.4 for irradiation ⊥(100); 246 ± 9 GPa, 364 ± 57 GPa, 9.5 ± 2.9, 14.7 ± 14.1 for irradiation ⊥(001), 230.7 ± 3.6 GPa, 373.5 ± 5.1 GPa, 19.2 ± 1.4, 20.1 ± 1.8 for no irradiation]. Line widths of XRD Bragg peaks in irradiated apatites confirm the strain of the host lattice, which appears to decrease with increasing pressure. By contrast, the bandwidths of Raman modes increase with pressure, and this is attributed to increasing strain gradients on the length scale of the short-range order. The investigations reveal considerable deviatoric stress on the [100]-oriented tracks due to the anisotropic elasticity, while the compression is uniform for the directions perpendicular to the tracks, which are aligned parallel to the c-axis. This difference might be considered to control the diffusion properties related to the annealing kinetics and its observed anisotropy, and hence to cause potential pressure effects on track-fading rates.     

Hydrostatic compression and crystal structure of pyrope to 33 GPa

The equation of state and crystal structure of pyrope were determined by single crystal X-ray diffraction under hydrostatic conditions to 33 GPa, a pressure that corresponds to a depth of about 900 km in the lower mantle. The bulk modulus K _T0 and its pressure derivative K ^' _T0 were determined simultaneously from an unweighted fit of the volume data at different pressures to a third order Birch-Murnaghan equation of state. They are 171(2) GPa and 4.4(2), respectively. Over the whole pressure range, MgO₈ polyhedra showed the largest compression of 18.10(8)%, followed by AlO₆ and SiO₄ polyhedra, with compression of 11.7(1)% and 4.6(1)%, respectively. The polyhedral bulk moduli for MgO₈, AlO₆ and SiO₄ are 107(1), 211(11) and 580(24) GPa, respectively, with K ^' _T0 fixed to 4. Significant compression of up to 1.8(1)% in the very rigid Si−O bonding in pyrope could be detected to 33 GPa. Changes in the degree of polyhedral distortion for all three types of polyhedra could also be observed. These changes could be found for the first time for AlO₆ and SiO₄ in pyrope. It seems that the compression of pyrope crystal structure is governed by the kinking of the Al−O−Si angle between the octahedra and tetrahedra. No phase transition could be detected to 33 GPa. Received: 24 March 1997 / Revised, accepted: 29 July 1997     

Behavior of epidote at high pressure and high temperature: a powder diffraction study up to 10 GPa and 1,200 K

The thermo-elastic behavior of a natural epidote [Ca_1.925 Fe_0.745Al_2.265Ti_0.004Si_3.037O₁₂(OH)] has been investigated up to 1,200 K (at 0.0001 GPa) and 10 GPa (at 298 K) by means of in situ synchrotron powder diffraction. No phase transition has been observed within the temperature and pressure range investigated. P–V data fitted with a third-order Birch–Murnaghan equation of state (BM-EoS) give V ₀ = 458.8(1)ų, K _T0 = 111(3) GPa, and K′ = 7.6(7). The confidence ellipse from the variance–covariance matrix of K _T0 and K′ from the least-square procedure is strongly elongated with negative slope. The evolution of the “Eulerian finite strain” vs “normalized stress” yields Fe(0) = 114(1) GPa as intercept values, and the slope of the regression line gives K′ = 7.0(4). The evolution of the lattice parameters with pressure is slightly anisotropic. The elastic parameters calculated with a linearized BM-EoS are: a ₀ = 8.8877(7) Å, K _T0(a) = 117(2) GPa, and K′(a) = 3.7(4) for the a-axis; b ₀ = 5.6271(7) Å, K _T0(b) = 126(3) GPa, and K′(b) = 12(1) for the b-axis; and c ₀ = 10.1527(7) Å, K _T0(c) = 90(1) GPa, and K’(c) = 8.1(4) for the c-axis [K _T0(a):K _T0(b):K _T0(c) = 1.30:1.40:1]. The β angle decreases with pressure, β_P(°) = β_P0 −0.0286(9)P +0.00134(9)P ² (P in GPa). The evolution of axial and volume thermal expansion coefficient, α, with T was described by the polynomial function: α(T) = α₀ + α₁ T ^−1/2. The refined parameters for epidote are: α₀ = 5.1(2) × 10⁻⁵ K⁻¹ and α₁ = −5.1(6) × 10⁻⁴ K^1/2 for the unit-cell volume, α₀(a) = 1.21(7) × 10⁻⁵ K⁻¹ and α₁(a) = −1.2(2) × 10⁻⁴ K^1/2 for the a-axis, α₀(b) = 1.88(7) × 10⁻⁵ K⁻¹ and α₁(b) = −1.7(2) × 10⁻⁴ K^1/2 for the b-axis, and α₀(c) = 2.14(9) × 10⁻⁵ K⁻¹ and α₁(c) = −2.0(2) × 10⁻⁴ K^1/2 for the c-axis. The thermo-elastic anisotropy can be described, at a first approximation, by α₀(a): α₀(b): α₀(c) = 1 : 1.55 : 1.77. The β angle increases continuously with T, with β_T(°) = β_T0 + 2.5(1) × 10⁻⁴ T + 1.3(7) × 10⁻⁸ T ². A comparison between the thermo-elastic parameters of epidote and clinozoisite is carried out.     

(Na,Ca)(Ti3+,Mg)Si2O6-clinopyroxenes at high pressure: influence of cation substitution on elastic behavior and phase transition

A compressional study of (Na,Ca)(Ti³⁺,Mg)Si₂O₆-clinopyroxenes was carried out at high pressures between 10⁻⁴ and 10.2 GPa using in situ single-crystal X-ray diffraction, Raman spectroscopy and optical absorption spectroscopy. Compressional discontinuities accompanied by structural changes, in particular, the appearance of two distinct Ti³⁺–Ti³⁺ distances within the octahedral chains at 4.37 GPa, provide evidence for the occurrence of a phase transition in NaTi³⁺Si₂O₆. Equation-of-state parameters are K ₀ = 115.9(7) GPa with K′ = −0.9(3) and K ₀ = 102.7(8) GPa with K′ = 4.08(5) for the low- and high-pressure range, respectively. The transition involves a C2/c–P [`1] \overline{1} symmetry change, which can be confirmed by the occurrence of new modes in Raman spectra. Since no significant discontinuity in the evolution of the unit-cell volume with pressure has been observed, the transition appears to be second-order in character. The influence of the coupled substitution Na⁺Ti³⁺↔Ca²⁺Mg²⁺ on the static compression behavior and the structural stability has been investigated using a sample of the intermediate composition (Na_0.54Ca_0.46)(Mg_0.46Ti_0.54)Si₂O₆. No evidence for a deviation from continuous compression behavior has been found, neither in lattice parameter nor in structural data and the fit of a third-order Birch–Murnaghan equation-of-state to the pressure–volume data yields a bulk modulus of K ₀ = 109.1(5) GPa and K′ = 5.02(13). Raman and polarized absorption spectra have been compared to NaTiSi₂O₆ and reveal major similarities. The main driving force for the phase transition in NaTi³⁺Si₂O₆ is the localization of the Ti³⁺ d-electron and the accompanying distortion, which is suppressed in the (Na,Ca)(Ti³⁺,Mg)Si₂O₆-clinopyroxene.     

The effect of oxygen vacancies and aluminium substitution on the high-pressure properties of brownmillerite-structured Ca2Fe2?xAlxO5

The structural evolution with pressure and the equations of state of three members of the brownmillerite solid solution, Ca₂(Fe_2−x Al _x )O₅, have been determined by single-crystal X-ray diffraction up to a maximum pressure of 9.73 GPa. The compositions of the samples were x = 0.00 and x = 0.37 (with Pnma symmetry) and x = 0.55 (with I2mb symmetry). No phase transitions were observed in the experiments. The equation of state parameters determined from the pressure-volume data are K _0T = 128.0 (7) GPa, K′₀ = 5.8 (3) for the sample with x = 0.00, K _0T = 131 (2) GPa, K′₀ = 5.5 (4) for x = 0.37, and K _0T = 137.5 (6) GPa, K′₀ = 4 for x = 0.55. The bulk modulus therefore increases with Al content, being 11% higher in the x = 0.55 sample than in the Al-free sample. The unit-cell compression is anisotropic, with the c-axis being stiffer than a or b, and the anisotropy increases with increasing Al content of the structure. The structural response to pressure of all samples is similar. The (Al,Fe)O₄ tetrahedra and the (Al,Fe)O₆ octahedra undergo approximately isotropic compression. There is an increase in the twists of the chains of corner-sharing (Al,Fe)O₄ tetrahedra, and an increase in the tilts of the (Al,Fe)O₆ octahedra, because these framework polyhedra are stiffer than the Ca–O bonds to the extra-framework Ca site. The alignment of the two shortest Ca–O bonds sub-parallel to [001] accounts for the relative stiffness of the c-axis and thus the elastic anisotropy. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Thermoelastic properties of the high-pressure phase of SnO2 determined by in situ X-ray observations up to 30 GPa and 1400 K

 In situ synchrotron X-ray experiments in the system SnO₂ were made at pressures of 4–29 GPa and temperatures of 300–1400 K using sintered diamond anvils in a 6–8 type high-pressure apparatus. Orthorhombic phase (α-PbO₂ structure) underwent a transition to a cubic phase (Pa3ˉ structure) at 18 GPa. This transition was observed at significantly lower pressures in DAC experiments. We obtained the isothermal bulk modulus of cubic phase K ₀= 252(28) GPa and its pressure derivative K ^′=3.5(2.2). The thermal expansion coefficient of cubic phase at 25 GPa up to 1300 K was determined from interpolation of the P-V-T data obtained, and is 1.7(±0.7) × 10⁻⁵ K⁻¹ at 25 GPa. Received: 7 December 1999 / Accepted: 27 April 2000     

The high-pressure and temperature equation of state of a majorite solid solution in the system of Mg4Si4O12-Mg3Al2Si3O12

The high-pressure and temperature equation of state of majorite solid solution, Mj_0.8Py_0.2, was determined up to 23 GPa and 773 K with energy-dispersive synchrotron X-ray diffraction at high pressure and high temperature using the single- and double-stage configurations of the multianvil apparatuses, MAX80 and 90. The X-ray diffraction data of the majorite sample were analyzed using the WPPD (whole-powder-pattern decomposition) method to obtain the lattice parameters. A least-squares fitting using the third-order Birch-Murnaghan equation of state yields the isothermal bulk modulus, K _T0  = 156 GPa, its pressure derivative, K′ = 4.4(±0.3), and temperature derivative (∂K _T /∂T) _P = −1.9(±0.3)× 10⁻² GPa/K, assuming that the thermal expansion coefficient is similar to that of pyrope-almandine solid solution. Received: 5 October 1998 / Revised, accepted: 24 June 1999