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     

An infrared spectroscopic study of lawsonite to 20 GPa

The infrared spectrum of CaAl₂Si₂O₇ · H₂O-lawsonite, has been characterized to pressures of 20 GPa at 300 K. Our results constrain the response to compression of the silicate tetrahedra, hydroxyl units, and water molecules in this material. The asymmetric and symmetric stretching and bending vibrations of the Si₂O₇ groups (at zero pressure frequencies between 600 and 1000 cm⁻¹) increase in frequency with pressure at rates between 3.6 and 5.9 cm⁻¹/GPa. All silicate modes appear to shift continuously with pressure to 20 GPa, although the lowest frequency stretching vibration becomes unresolvable above 18 GPa, and a splitting of the main bending vibration is observed near this pressure. The O-H stretches of the hydroxyl units exhibit a discontinuity in their mode shifts at ∼8–9 GPa, which we interpret to be produced by a pressure-induced change in hydrogen bonding. The stretching and bending vibrations of the water molecule are relatively unaffected by compression to 20 GPa, thus demonstrating that the structural cavities in which water molecules reside are relatively rigid. Significant changes in the amplitude of the O-H stretches of the hydroxyl and water units are observed at this pressure as well; nevertheless, our results demonstrate that the dominant structural units in lawsonite persist metastably at 300 K with only modest structural modifications well beyond the known stability field of this phase. Received: 10 July 1998 / Revised, accepted: 23 October 1998     

Structural and vibrational behaviour of fluorapatite with pressure. Part II: in situ micro-Raman spectroscopic investigation

 High-pressure Raman investigations were carried out on a synthetic fluorapatite up to about 7 GPa to analyse the behaviour of the phosphate group's internal modes and of its lattice modes. The Raman frequencies of all modes increased with pressure and a trend toward reduced splitting was observed for the PO₄-stretching modes [(ν_3a(A_g) and ν_3b(A_g); ν_3a(E_2g) and ν_3b(E_2g)] and the PO₄ out-of-plane bending modes [ν_4a(A_g) and ν_4b(A_g)]. The pressure coefficients of phosphate modes ranged from 0.0047 to 0.0052 GPa⁻¹ for ν₃, from 0.0025 to 0.0044 GPa⁻¹ for ν₄, from 0.0056 to 0.0086 GPa⁻¹ for ν₂ and 0.0046 for ν₁ GPa⁻¹, while the pressure coefficients of lattice modes ranged from 0.0106 to 0.0278 GPa⁻¹. The corresponding Grüneisen parameters varied from 0.437 to 0.474, 0.428, 0.232 to 0.409 and 0.521 to 0.800 for phosphate modes ν₃, ν₁, ν₄, ν₂, respectively, and from 0.99 to 2.59 for lattice modes. The vibrational behaviour was interpreted in view of the high-pressure structural refinement performed on the same crystal under the same experimental conditions. The reduced splitting may thus be linked to the reduced distortion of the environment around the phosphate tetrahedron rather than to the decrease of the tetrahedral distortion itself. Moreover, the amount of calcium polyhedral compression, which is about three times the compression of phosphate tetrahedra, may explain the different Grüneisen parameters. Received: 25 April 2000 / Accepted: 20 December 2000     

A high-temperature and high-pressure Raman spectroscopic study of CaGeO3 garnet

 High-pressure and high-temperature Raman spectra of CaGeO₃ tetragonal garnet have been collected to 11.5 GPa and 1225 K, respectively, in order to investigate possible intrinsic anharmonic behaviour in this phase. The Raman peak positions were observed to vary linearly with pressure and temperature within the ranges studied, with the higher-energy peaks showing larger P- and T-induced shifts than the low energy modes. The observed T-induced shifts are similar to those reported for grossular and andradite, while the observed P-induced shifts are generally larger than those of aluminosilicate and MgSiO₃ majorite garnets (Gillet et al. 1992; Rauch et al. 1996) due to the larger bulk modulus of CaGeO₃ garnet. The observed mode shifts of CaGeO₃ garnet were used to determine the isothermal and isobaric mode Grüneisen parameters for this phase. These parameters are similar in value to those reported previously for grossular and andradite (Gillet et al. 1992). The calculated intrinsic anharmonic parameters, a _i , for CaGeO₃ garnet were determined to be nonzero, indicating significant anharmonic behaviour for this phase. These values, which range from −3.8 × 10⁻⁵ K⁻¹ to −1.3 × 10⁻⁵ K⁻¹, are also similar to those reported for andradite and grossular, but smaller than those determined for pyrope (Gillet et al. 1992). Hence, we expect MgSiO₃ majorite to show greater anharmonicity than the germanate analogue studied by us. The anharmonic parameters determined for CaGeO₃ tetragonal garnet may now be introduced into quasiharmonic vibrational heat capacity models to account for the observed anharmonic behaviour. Received: 21 April 1999 / Revised, accepted: 11 September 1999     

High-pressure phase transition and behavior of protons in brucite Mg(OH)2: a high-pressure–temperature study using IR synchrotron radiation

 Infrared absorption spectra of brucite Mg (OH)₂ were measured under high pressure and high temperature from 0.1 MPa 25 °C to 16 GPa 360 °C using infrared synchrotron radiation at BL43IR of Spring-8 and a high-temperature diamond-anvil cell. Brucite originally has an absorption peak at 3700 cm⁻¹, which is due to the OH dipole at ambient pressure. Over 3 GPa, brucite shows a pressure-induced absorption peak at 3650 cm⁻¹. The pressure-induced peak can be assigned to a new OH dipole under pressure. The new peak indicates that brucite has a new proton site under pressure and undergoes a high-pressure phase transition. From observations of the pressure-induced peak under various P–T condition, a stable region of the high-pressure phase was determined. The original peak shifts to lower wavenumber at −0.25 cm⁻¹ GPa⁻¹, while the pressure-induced peak shifts at −5.1 cm⁻¹ GPa⁻¹. These negative dependences of original and pressure-induced peak shifts against pressure result from enhanced hydrogen bond by shortened O–H···O distance, and the two dependences must result from the differences of hydrogen bond types of the original and pressure-induced peaks, most likely from trifurcated and bent types, respectively. Under high pressure and high temperature, the pressure-induced peak disappears, but a broad absorption band between 3300 and 3500 cm⁻¹ was observed. The broad absorption band may suggest free proton, and the possibility of proton conduction in brucite under high pressure and temperature. Received: 16 July 2001 / Accepted: 25 December 2001     

Pressure dependence of hydroxyl solubility in coesite

 The solubility of hydroxyl in coesite was investigated in multianvil experiments performed at 1200 °C over the nominal pressure range 5–10 GPa, at an f _O2 close to the Ni-NiO buffer. The starting material for each experiment was a cylinder of pure silica glass plus talc, which dehydrates at high P and T to provide a source of water and hydrogen (plus enstatite and excess SiO₂). Fourier-transform infrared (FTIR) spectra of the recovered coesite crystals show five sharp bands at 3606, 3573, 3523, 3459, and 3299 cm⁻¹, indicative of structurally bonded hydrogen (hydroxyl). The concentration of hydrogen increases with pressure from 285 H/10⁶ Si (at 5 GPa) to 1415 H/10⁶ Si (at 10 GPa). Assuming a model of incorporation by (4H)_Si defects, the data are fit well by the equation C _OH=Af ² _H2<\INF>Oexp(−PΔV/RT), with A=4.38 H/10⁶ Si/GPa, and ΔV=20.6 × 10⁻⁶ m³ mol⁻¹. An alternative model entailing association of hydrogen with cation substitution can also be used to fit the data. These results show that the solubility of hydroxyl in coesite is approximately an order of magnitude lower than in olivines and pyroxenes, but comparable to that in pyropic garnet. However, FTIR investigations on a variety of ultrahigh pressure metamorphic rocks have failed in all cases to detect the presence of water or hydrogen in coesite, indicating either that it grew in dry environments or lost its hydrogen during partial transformation to quartz. On the other hand, micro-FTIR investigations of quartz crystals replacing coesite show that they contain varying amounts of H₂O. These results support the hypothesis that preservation of coesite is not necessarily linked to fast exhumation rates but is crucially dependent on limited fluid infiltration during exhumation. Received: 23 August 1999 / Accepted: 10 April 2000     

Hydrous olivine (Mg1? y? Fe2+y)2? x ?v x ? SiO4H2 x – a new DHMS phase of variable composition observed as nanometer-sized precipitations in mantle olivine

 An olivine grain from a peridotite nodule 9206 (Udachnaya kimberlite, Siberia) was investigated by TEM methods including AEM, HRTEM, SAED and EELS techniques. A previous study of the 9206 olivine sample revealed OH absorption bands in the IR spectrum and abundant nanometer-sized OH-bearing inclusions, of hexagonal-like or lamellar shape. Inclusions, which are several hundred nm in size, consist of 10 ? phase, talc and serpentine (chrysotile and lizardite). The lamellar (LI) and hexagon-like small inclusions of several ten nm in size (SI) are the topic of the present paper. AEM investigations of the inclusions reveal Mg, Fe and Si as cations only. The Mg/Si and Fe/Si atomic ratios are lower in the inclusions than in the host olivine. The Si concentration in the olivine host and both lamellar inclusions and small inclusions is the same. A pre-peak at 528eV was observed in EEL spectra of LI and SI, which is attributed to OH⁻ or Fe³⁺. From these data it is concluded that there is a OH⁻- or Fe³⁺-bearing cation-deficient olivine-like phase present. HRTEM lattice fringe images of LI and SI exhibit modulated band-like contrasts, which are superimposed onto the olivine lattice. Diffraction patterns (Fourier-transforms) of the HREM images as well as SAED patterns show that the band-like contrasts in HRTEM images of the inclusions are caused by periodic modulations of the olivine lattice. Three kinds of superperiodicity in the olivine structure such as 2a, 3a and 3c, were observed in SAED patterns. The corresponding olivine supercells labelled here as Hy-2a, Hy-3a and Hy-3c were derived. The M1-vacancies located in the (100) and (001) octahedral layers of the olivine lattice are suggested to form ordered arrays of planar defects (PD), which cause the band-like contrasts in HRTEM patterns as well as the superperiodicity in the SAED patterns. The vacancy concentrations as well as the chemical composition of Hy-2a, Hy-3a and Hy-3c olivine supercells were calculated using crystal chemical approaches, assuming either {(OH)^< _O−V^" _Me−(OH)^< _O}^↔, or {F e ^< _Fe −H _Me ^′}^↔ or {2F e ^< _Fe −V _Me ^"}^↔ point defect associates. The calculated theoretical compositions Mg_1.615Fe⁺² _0.135v_0.25SiO₄H_0.5 (Hy-2a) and Mg_1.54Fe²⁺ _0.12v_0.33SiO₄H_0.66 (Hy-3a and Hy-3c) are in a good agreement with the AEM data on inclusions. Hy-2a, Hy-3a and Hy-3c are considered to be a hydrous olivine with the extended chemical formula (Mg_1-yFe²⁺ _y)_2−xv_xSiO₄H_2x. The crystal structure of hydrous olivine is proposed to be a modular olivine structure with Mg-vacant modules. The crystal chemical formula of hydrous olivines in terms of a modular structure can be written as [MgSiO₄H₂] · 3[Mg_1.82Fe_0.18SiO₄] for Hy-2a, [MgSiO₄H₂] · 2[Mg_1.82Fe_0.18SiO₄] for Hy-3a and Hy-3c. Hydrous olivine is suggested to be exsolved from the olivine 9206, which has been initially saturated by OH-bearing point defects. The olivine 9206 hydration as well as the following exsolution of hydrous olivine inclusions is suggested to occur at high pressure-high temperature conditions of the upper mantle. Received: 15 January 2001 / Accepted: 2 July 2001     

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     

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     

Crystal orbital contributions to the pyrrhotite valence band with XPS evidence for weak Fe–Fe π bond formation

 Synchrotron excited X-ray photoelectron spectra (SXPS) of hexagonal pyrrhotite reveal three distinct Fe 3d-derived photopeaks within its outer valence band. The t _2gα band (majority spin) is centered at about 2.5 eV, the e _g α band at about 1.0 eV and the t _2gβ (minority spin) contribution at about 0.25 eV. From these data the ligand field splitting energy is 1.5 (±0.2) eV and the majority spin pairing energy is 2.25 (±0.2) eV. These are the first such XPS measurements for this mineral. S 3p-derived bonding and non-bonding bands are identified, with the former centred at about 6.5 eV and the latter near 4.5 eV. The XPS results are remarkably consistent with SCF-Xα scattered wave molecular orbital calculations. Although the calculations and the collected spectra are consistent, they differ from a recent interpretation of the pyrrhotite valence band. An explanation for the discrepant results is provided. Auger resonant enhancement of Fe 3d photopeaks at 60 eV photon energy results in the t _2gα emission (at 2.5 eV) being strongly enhanced and broader than the t _2gβ emission (0.25 eV). The explanation of these observations requires the presence of weak Fe–Fe π and π^* crystal (molecular) orbitals located near 2.5 eV, and separated by no more than about 0.5 eV. The π-bonded crystal orbitals are derived from weak mixing of adjacent Fe t _2g atomic orbitals along the c crystallographic axis. Received: 15 June 2000 / Accepted: 11 June 2001     

Location and quantitative analysis of OH in coesite

 The incorporation of hydrogen (deuterium) into the coesite structure was investigated at pressures from 3.1 to 7.5 GPa and temperatures of 700, 800, and 1100 °C. Hydrogen could only be incorporated into the coesite structure at pressures greater 5.0 GPa and 1100 °C . No correlation between the concentration of trace elements such as Al and B and the hydrogen content was observed based on ion probe analysis (1335 ± 16 H ppm and 17 ± 1 Al ppm at 7.5 GPa, 1100 °C). The FTIR spectra show three relatively intense bands at 3575, 3516, and 3459 cm⁻¹ (ν₁ to ν₃, respectively) and two very weak bands at 3296 and 3210 cm⁻¹ (ν₄ and ν₅, respectively). The band at 3516 cm⁻¹ is strongly asymmetric and can be resolved into two bands, 3528 (ν_2a) and 3508 (ν_2b) cm⁻¹, with nearly identical areas. Polarized infrared absorption spectra of coesite single-crystal slabs, cut parallel to (0 1 0) and (1 0 0), were collected to locate the OH dipoles in the structure and to calibrate the IR spectroscopy for quantitative analysis of OH in coesite (ɛ _{i ,tot}=190 000 ± 30 000 l mol⁻¹ _H2O cm⁻²). The polarized spectra revealed a strong pleochroism of the OH bands. High-pressure FTIR spectra at pressures up to 8 GPa were performed in a diamond-anvil cell to gain further insight into incorporation mechanism of OH in coesite. The peak positions of the ν₁, ν₂, and ν₃ bands decrease linearly with pressure. The mode Grüneisen parameters for ν₁, ν₂, and ν₃ are −0.074, −0.144 and −0.398, respectively. There is a linear increase of the pressure derivatives with band position which follows the trend proposed by Hofmeister et al. (1999). The full widths at half maximum (FWHM) of the ν₁, ν₂, and ν₃ bands increase from 35, 21, and 28 cm⁻¹ in the spectra at ambient conditions to 71, 68, and 105 in the 8 GPa spectra, respectively. On the basis of these results, a model for the incorporation of hydrogen in coesite was developed: the OH defects are introduced into the structure by the substitution Si^4+(Si2)+4O²⁻= ^[4]□^(Si2) + 4OH⁻, which gives rise to four vibrations, ν₁, ν_2a, ν_2b, and ν₃. Because the OH(D)-bearing samples do contain traces of Al and B, the bands ν₄ and ν₅ may be coupled to Al and/or B substitution. Received: 19 December 2000 / Accepted: 23 April 2001     

Raman spectroscopic study of hydrous wadsleyite (β-Mg2SiO4) to 50 GPa

 Raman spectra of hydrous β-Mg₂SiO₄ (1.65 wt% H₂O) have been measured in a diamond-anvil cell with helium as a pressure-transmitting medium at room temperature to 50 GPa. We observe three OH-stretching modes, a doublet with components at 3329 and 3373 cm⁻¹, which decrease linearly with pressure, and a single mode at 3586 cm⁻¹, which remains nearly constant up to 24 GPa before decreasing at higher pressures. Assessment of the mode frequencies and their pressure dependence, together with previous results from X-ray and IR data, are consistent with protonation of the O1 site in agreement with previous studies. Strict assignment of Raman activity awaits detailed structural models. The nature of the protonation in wadsleyite may require more specific experimental probes for full solution of the hydrogen-site problem. Received: 18 July 2000 / Accepted: 22 November 2000     

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     

Thermodynamic data of the high-pressure phase Mg5Al5Si6O21(OH)7 (Mg-sursassite)

 Calorimetric and P–V–T data for the high-pressure phase Mg₅Al₅Si₆O₂₁(OH)₇ (Mg-sursassite) have been obtained. The enthalpy of drop solution of three different samples was measured by high-temperature oxide melt calorimetry in two laboratories (UC Davis, California, and Ruhr University Bochum, Germany) using lead borate (2PbO·B₂O₃) at T=700 ^∘C as solvent. The resulting values were used to calculate the enthalpy of formation from different thermodynamic datasets; they range from −221.1 to −259.4 kJ mol⁻¹ (formation from the oxides) respectively −13892.2 to −13927.9 kJ mol⁻¹ (formation from the elements). The heat capacity of Mg₅Al₅Si₆O₂₁(OH)₇ has been measured from T=50 ^∘C to T=500 ^∘C by differential scanning calorimetry in step-scanning mode. A Berman and Brown (1985)-type four-term equation represents the heat capacity over the entire temperature range to within the experimental uncertainty: C _P (Mg-sursassite) =(1571.104 −10560.89×T ^−0.5−26217890.0 ×T ⁻²+1798861000.0×T ⁻³) J K⁻¹ mol⁻¹ (T in K). The P V T behaviour of Mg-sursassite has been determined under high pressures and high temperatures up to 8 GPa and 800 ^∘C using a MAX 80 cubic anvil high-pressure apparatus. The samples were mixed with Vaseline to ensure hydrostatic pressure-transmitting conditions, NaCl served as an internal standard for pressure calibration. By fitting a Birch-Murnaghan EOS to the data, the bulk modulus was determined as 116.0±1.3 GPa, (K ^′=4), V _T,0 =446.49 ³ exp[∫(0.33±0.05) × 10⁻⁴ + (0.65±0.85)×10⁻⁸ T dT], (K _T/T) _P  = −0.011± 0.004 GPa K⁻¹. The thermodynamic data obtained for Mg-sursassite are consistent with phase equilibrium data reported recently (Fockenberg 1998); the best agreement was obtained with Δ_f H ⁰ ₂₉₈ (Mg-sursassite) = −13901.33 kJ mol⁻¹, and S ⁰ ₂₉₈ (Mg-sursassite) = 614.61 J K⁻¹ mol⁻¹. Received: 21 September 2000 / Accepted: 26 February 2001     

Raman spectra of hydrous γ -Mg2SiO4 at various pressures and temperatures

 One well-defined OH Raman band at 3651 ± 1 cm⁻¹ and one weak feature near 3700 ± 5 cm⁻¹ are recognized for the hydrous γ-phase of Mg₂SiO₄. Like the hydrous β-phase, the H₂O content in the γ-phase shifts most of the corresponding silicate modes towards lower frequencies. Variations in Raman spectra of the hydrous γ-phase were investigated up to about 200 kbar at room temperature and in the range 81–873 K at atmospheric pressure. Unlike the anhydrous γ-phase, which remains intact up to at least 873 K, the hydrous γ-phase sometimes converts to a defective forsterite structure above 800 K. Although the hydrous γ-phase remains intact up to at least 800 K, Raman signals of the OH bands disappear completely above 423 K. The Raman frequency of the well-defined OH band decreases linearly with increasing temperature between 81 and 423 K. In the region of the silicate vibrations, the Raman frequencies of the two most intense bands increase nonlinearly with increasing pressure, and decrease with increasing temperature. The frequencies for all other weak bands, however, decreased linearly with increasing temperature. The latter most likely reflects the larger scatter of the data for the weak bands. Received: 27 April 2001 / Accepted: 12 September 2001     

High-temperature viscoelasticity of fine-grained polycrystalline olivine

 Torsional forced-oscillation and microcreep methods have been employed in a study of the viscoelastic behaviour of fine-grained polycrystalline olivine at high temperatures (to 1300 °C), seismic frequencies and low strain amplitudes. The Fo₉₀ specimens are of low porosity and low dislocation density. They vary in mean grain size from 8 to 150 μm and contain only trace amounts (≪0.1 vol%) of quenched melt glass. For T ≤ 900 °C, their behaviour is essentially elastic and the shear modulus G closely approaches that expected for a dense polycrystal from single-crystal elasticity data – confirming the suppression of thermal microcracking in␣this study. At higher temperatures, pronounced absorption-band dissipation and associated dispersion␣of the shear modulus provide evidence of linear viscoelastic behaviour. Both recoverable (anelastic) and permanent (viscous) strains are involved and the proportion of the latter increases with increasing temperature and decreasing frequency. Comparison of the results for the three specimens provides a clear indication that the viscoelastic behaviour, attributed to diffusional processes, is grain-size-sensitive with the dissipation and associated dispersion increasing with decreasing grain size. Both elastically accommodated and diffusionally accommodated grain-boundary sliding appear to be implicated. Received: 29 September 2000 / Accepted: 7 May 2001     

Molecular dynamics simulations of the phase transition between low-temperature and high-temperature clinoenstatites

 Phase transition between low-temperature clinoenstatite (LT-CEn) and high-temperature clinoenstatite (HT-CEn) was studied by using molecular dynamics (MD) simulations, based on empirical potential parameters. Starting from LT-CEn, the MD calculations were carried out at atmospheric pressure and at elevated pressures (1–6 GPa). At elevated temperatures the transformation from the starting LT-CEn to HT-CEn occurred at any pressure. It was confirmed that the HT-CEn has the same space group C2/c as diopside but the M2 site is six-coordinated, unlike diopside. A significant difference in the MD-simulated cell volumes between LT-CEn and HT-CEn was also observed, showing a first-order transition. In addition, there were some temperature ranges where LT-CEN and HT-CEn would be coexistent and very small thermal hystereses between increasing and decreasing temperatures during the transition. These behaviors are consistent with the characteristic of a thermoelastic-martensitic transformation. The phase boundary between LT-CEn and HT-CEn was determined for the first time. Its positive dT/dP slope strongly shows that the high-pressure clinoenstatite is a significantly distinct phase from HT-CEn although the both phases have the same space group, C2/c. Received: 8 November 2000 / Accepted: 28 April 2001     

Thermal expansion and crystal structure of FeSi between 4 and 1173 K determined by time-of-flight neutron powder diffraction

The thermal expansion and crystal structure of FeSi has been determined by neutron powder diffraction between 4 and 1173?K. No evidence was seen of any structural or magnetic transitions at low temperatures. The average volumetric thermal expansion coefficient above room temperature was found to be 4.85(5)?×?10^?5?K^?1. The cell volume was fitted over the complete temperature range using Grüneisen approximations to the zero pressure equation of state, with the internal energy calculated via a Debye model; a Grüneisen second-order approximation gave the following parameters: θ_D=445(11)?K, V ₀=89.596(8)?ų, K ₀′=4.4(4) and γ′=2.33(3), where θ_D is the Debye temperature, V ₀ is V at T=0?K, K ₀′ is the first derivative with respect to pressure of the incompressibility and γ′ is a Grüneisen parameter. The thermodynamic Grüneisen parameter, γ_th, has been calculated from experimental data in the range 4–400?K. The crystal structure was found to be almost invariant with temperature. The thermal vibrations of the Fe atoms are almost isotropic at all temperatures; those of the Si atoms become more anisotropic as the temperature increases.     

The Gibbs energy formulation of the α, β, and γ forms of Mg2SiO4 using Grover, Getting and Kennedy's empirical relation between volume and bulk modulus

 The empirical linear relation between volume and logarithm of bulk modulus of a material, discovered by Grover, Getting and Kennedy is taken as the basis for our equation of state. Using the latest experimental information on the adiabatic bulk modulus, the equation of state is applied to the three polymorphs of Mg₂SiO₄ to develop a consistent dataset of their thermodynamic properties in the temperature range of 200–2273 K and a pressure range of 0.1 MPa–30 GPa. The results imply that the bulk sound velocity contrast (v ^β−v ^α)/v ^α increases with temperature along the α–β phase boundary and reaches the value 8.9% at 13.5 GPa, a pressure equivalent to 410 km depth in the Earth. The bulk sound velocity contrast (v ^γ−v ^β)/v ^β decreases with temperature along the β–γ phase boundary and becomes less than 0.7% at temperatures and pressures equivalent to those associated with the 520-km seismic discontinuity in the Earth. Received: 1 August 2000 / Accepted: 1 March 2001     

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