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1.
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) Å3. 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.  相似文献   

2.
 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  相似文献   

3.
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  相似文献   

4.
 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  相似文献   

5.
Fe-bearing dense hydrous magnesium silicate Phase A, Mg6.85Fe0.14Si2.00O8(OH)6 has been studied by single-crystal X-ray diffraction at ambient conditions and by high-pressure powder diffraction using synchrotron radiation to 33 GPa. Unit cell parameters at room temperature and pressure from single crystal diffraction are a=7.8678 (4) Å, c=9.5771 (5) Å, and V=513.43 (4) Å3. Fitting of the P–V data to a third-order Birch-Murnaghan isothermal equation of state yields V 0=512.3 (3) Å3, K T,0=102.9 (28) GPa and K′=6.4 (3). Compression is strongly anisotropic with the a-axes, which lie in the plane of the distorted close-packed layers, approximately 26% more compressible than the c-axis, which is normal to the plane. Structure refinement from single-crystal X-ray intensity data reveals expansion of the structure with Fe substitution, mainly by expansion of M-site octahedra. The short Si2–O6 distance becomes nearly 1% shorter with ~2% Fe substitution for Mg, possibly providing additional rigidity in the c-direction over the Mg end member. K T obtained for the Fe-bearing sample is ~5.5% greater than reported previously for Fe-free Phase A, despite the larger unit cell volume. This study represents a direct comparison of structure and K T–ρ relations between two compositions of a F-free dense hydrous magnesium silicate (DHMS) phase, and may help to characterize the effect of Fe substitution on the properties of other DHMS phases from studies of the Fe-free end-members.  相似文献   

6.
 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  相似文献   

7.
 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  相似文献   

8.
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9.
The behaviour of synthetic Mg-ferrite (MgFe2O4) has been investigated at high pressure (in situ high-pressure synchrotron radiation powder diffraction at ESRF) and at high temperature (in situ high-temperature X-ray powder diffraction) conditions. The elastic properties determined by the third-order Birch–Murnaghan equation of state result in K0=181.5(± 1.3) GPa, K=6.32(± 0.14) and K= –0.0638 GPa–1. The symmetry-independent coordinate of oxygen does not show significant sensitivity to pressure, and the structure shrinking is mainly attributable to the shortening of the cell edge (homogeneous strain). The lattice parameter thermal expansion is described by a0+a1*(T–298)+a2/(T–298)2, where a0=9.1(1) 10–6 K–1, a1=4.9(2) 10–9 K–2 and a2= 5.1(5) 10–2 K. The high-temperature cation-ordering reaction which MgFe-spinel undergoes has been interpreted by the ONeill model, whose parameters are = 22.2(± 1.8) kJ mol–1 and =–17.6(± 1.2) kJ mol–1. The elastic and thermal properties measured have then been used to model the phase diagram of MgFe2O4, which shows that the high-pressure transition from spinel to orthorombic CaMn2O4-like structure at T < 1700 K is preceded by a decomposition into MgO and Fe2O3.  相似文献   

10.
The elastic behaviour and the high-pressure structural evolution of a natural topaz, Al2.00Si1.05O4.00(OH0.26F1.75), have been investigated by means of in situ single-crystal X-ray diffraction up to 10.55(5) GPa. No phase transition has been observed within the pressure range investigated. Unit-cell volume data were fitted with a third-order Birch-Murnaghan Equation of State (III-BM-EoS). The III-BM-EoS parameters, simultaneously refined using the data weighted by the uncertainties in P and V, are: V 0=345.57(7) Å3, K T0=164(2) GPa and K′=2.9(4). The axial-EoS parameters are: a 0=4.6634(3) Å, K T0(a)=152(2) GPa, K′(a)=2.8(4) for the a-axis; b 0=8.8349(5) Å, K T0(b)=224(3) GPa, K′(b)=2.6(6) for the b-axis; c 0=8.3875(7) Å, K T0(c)=137(2) GPa, K′(c)=2.9(4) for the c-axis. The magnitude and the orientation of the principal Lagrangian unit-strain ellipsoid were determined. At P−P 0=10.55 GPa, the ratios ε1:ε2:ε3 are 1.00:1.42:1.56 (with ε1||b, ε2||a, ε3||c and |ε3| > |ε2| > |ε1|). Four structural refinements, performed at 0.0001, 3.14(5), 5.79(5) and 8.39(5) GPa describe the structural evolution in terms of polyhedral distortions.  相似文献   

11.
 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 Δf 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  相似文献   

12.
 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  相似文献   

13.
The compression of synthetic pyrope Mg3Al2 (SiO4)3, almandine Fe3Al2(SiO4)3, spessartine Mn3Al2 (SiO4)3 grossular Ca3Al2(SiO4)3 and andradite Ca3Fe2 (SiO4)3 was studied by loading the crystals together in a diamond anvil cell. The unit-cell parameters were determined as a function of pressure by X-ray diffraction up to 15 GPa using neon as a pressure transmitting medium. The unit-cell parameters of pyrope and almandine were measured up to 33 and 21 GPa, respectively, using helium as a pressure medium. The bulk moduli, K T 0, and their first pressure derivatives, K T 0 ′, were simultaneously determined for all five garnets by fitting the volume data to a third order Birch-Murnaghan equation of state. Both parameters can be further constrained through a comparison of volume compressions between pairs of garnets, giving for K T 0 and K T 0 ′ 171(2) GPa and 4.4(2) for pyrope, 185(3) GPa and 4.2(3) for almandine, 189(1) GPa and 4.2 for spessartine, 175(1) GPa and 4.4 for grossular and 157(1) GPa and 5.1 for andradite, where the K T 0 ′ are fixed in the case of spessartine, grossular and andradite. Direct comparisons of the unit-cell volumes determined at high pressures between pairs of garnets reveal anomalous compression behavior for Mg2+ in the 8-fold coordinated triangular dodecahedron in pyrope. This agrees with previous studies concerning the compression behaviors of Mg2+ in 6-fold coordinated polyhedra at high pressures. The results show that simple bulk modulus–volume systematics are not obeyed by garnets. Received: 29 July 1998 / Revised, accepted: 7 April 1999  相似文献   

14.
High-pressure single-crystal X-ray diffraction measurements of lattice parameters of the compound Li2VOSiO4, which crystallises with a natisite-type structure, has been carried out to a pressure of 8.54(5) GPa at room temperature. Unit-cell volume data were fitted with a second-order Birch-Murnaghan EoS (BM-EoS), simultaneously refining V 0 and K 0 using the data weighted by the uncertainties in V. The bulk modulus is K 0 = 99(1) GPa, with K′ fixed to 4. Refinements of third order equations-of-state yielded values of K′ that did not differ significantly from 4. The compressibility of the unit-cell is strongly anisotropic with the c axis (K 0(c) = 49.7 ± 0.5 GPa) approximately four times more compressible than the a axis (K 0(a) = 195 ± 3 GPa).  相似文献   

15.
 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, (∂KT/∂T)P=−0.021(2) GPaK−1, (dα/∂P)T=−1.81×10−6 GPa−1K−1 and (∂KT/∂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, (∂KT/∂T)P=−0.017(1) GPaK−1, (dα/∂P)T= −1.41×10−6 GPa−1K−1 and (∂KT/∂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 (∂KT/∂T)P, (∂α/∂P)T and (∂KT/∂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  相似文献   

16.
 Powder diffraction measurements at simultaneous high pressure and temperature on samples of 2M1 polytype of muscovite (Ms) and paragonite (Pg) were performed at the beamline ID30 of ESRF (Grenoble), using the Paris-Edinburgh cell. The bulk moduli of Ms, calculated from the least-squares fitting of V–P data on each isotherm using a second-order Birch–Murnaghan EoS, were: 57.0(6), 55.1(7), 51.1(7) and 48.9(5) GPa on the isotherms at 298, 573, 723 and 873 K, respectively. The value of (∂K T /∂T) was −0.0146(2) GPa K−1. The thermal expansion coefficient α varied from 35.7(3) × 10−6 K−1 at P ambient to 20.1(3) × 10−6 K−1 at P = 4 GPa [(∂α/∂P) T = −3.9(1) × 10−6 GPa−1 K−1]. The corresponding values for Pg on the isotherms at 298, 723 and 823 K were: bulk moduli 59.9(5), 55.7(6) and 53.8(7) GPa, (∂K T /∂T) −0.0109(1) GPa K−1. The thermal expansion coefficient α varied from 44.1(2) × 10−6 K−1 at P ambient to 32.5(2) × 10−6 K−1 at P = 4 GPa [(∂α/∂P) T = −2.9(1) × 10−6 GPa−1 K−1]. Thermoelastic coefficients showed that Pg is stiffer than Ms; Ms softens more rapidly than Pg upon heating; thermal expansion is greater and its variation with pressure is smaller in Pg than in Ms. Received: 28 January 2002 / Accepted: 5 April 2002  相似文献   

17.
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) Å3. 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) Å3 and K 0 = 275 (24) GPa, K′ = 4.0 (fixed), V 0 = 10.42 (2) Å3, 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.  相似文献   

18.
The high-pressure (HP) behaviour of a natural orthorhombic and tetragonal edingtonite from Ice River, Canada, has been investigated using in situ single-crystal X-ray diffraction. The two isothermal equations of state up to 6.74(5) GPa were determined. V0, KT0 and K refined with a third-order Birch–Murnaghan equation of state (BM-EoS) are: V0 = 598.70(7) Å3, KT0 = 59(1) GPa and K=3.9(4) for orthorhombic edingtonite and V0 = 600.9(2) Å3, KT0 = 59(1) GPa and K=4.2(5) for tetragonal edingtonite. The experiments were conducted with nominally hydrous pressure penetrating transmitting medium. No overhydration effect was observed within the pressure range investigated. At high-pressures the main deformation mechanism is represented by cooperative rotation of the secondary building unit (SBU).Si/Al distribution slightly influences the elastic behaviour of the tetrahedral framework: the SBU bulk moduli are 125(8) GPa and 111(4) GPa for orthorhombic and tetragonal edingtonite, respectively. Extra-framework contents of both zeolites show an interesting behaviour under HP conditions: the split Ba2 site at P >2.85 GPa is completely empty; only the position Ba1 is occupied. Electronic Supplementary Material. Supplementary material to this paper (Observed and calculated structure factors) is available in electronic form at Electronic Supplementary Material Supplementary material is available in the online version of this article at  相似文献   

19.
The high-pressure elastic behaviour of a synthetic zeolite mordenite, Na6Al6.02Si42.02O96·19H2O [a=18.131(2), b=20.507(2), c=7.5221(5) Å, space group Cmc21], has been investigated by means of in situ synchrotron X-ray powder diffraction up to 5.68 GPa. No phase transition has been observed within the pressure range investigated. Axial and volume bulk moduli have been calculated using a truncated second-order Birch–Murnaghan equation-of-state (II-BM-EoS). The refined elastic parameters are: V 0=2801(11) Å3, K T0= 41(2) GPa for the unit-cell volume; a 0=18.138(32) Å, K T0(a)=70(8) GPa for the a-axis; b 0=20.517(35) Å, K T0(b)=29(2) GPa for the b-axis and c 0=7.531(5) Å, K T0(c)=38(1) GPa for the c-axis [K T0(a): K T0(b): K T0(c)=2.41:1.00:1.31]. Axial and volume Eulerian finite strain versus “normalized stress” plots (fe–Fe plot) show an almost linear trend and the weighted linear regression through the data points yields the following intercept values: Fe(0)=39(4) GPa for V; Fe a (0)=65(18) GPa for a; Fe b (0)=28(3) GPa for b; Fe c (0)=38(2) GPa for c. The magnitudes of the principal Lagrangian unit-strain coefficients, between 0.47 GPa (the lowest HP-data point) and each measured P>0.47 GPa, were calculated. The unit-strain ellipsoid is oriented with ε1 || b, ε2 || c, ε3 || a and |ε1|> |ε2|> |ε3|. Between 0.47 and 5.68 GPa the relationship between the unit-strain coefficient is ε1: ε2: ε3=2.16:1.81:1.00. The reasons of the elastic anisotropy are discussed.An erratum to this article can be found at  相似文献   

20.
The thermoelastic parameters of synthetic Ca3Al2Si3O12 grossular garnet were examined in situ at high-pressure and high-temperature by energy dispersive X-ray diffraction, using a Kawai-type multi-anvil press apparatus coupled with synchrotron radiation. Measurements have been conducted at pressures up to 20 GPa and temperatures up to 1,650 K: this P, T range covered the entire high-P, T stability field of grossular garnet. The analysis of room temperature data yielded V 0,300 = 1,664 ± 2 ?3 and K 0 = 166 ± 3 GPa for K￠0 K^{\prime}_{0} fixed to 4.0. Fitting of our P–V–T data by means of the high-temperature third order Birch–Murnaghan or the Mie–Grüneisen–Debye thermal equations of state, gives the thermoelastic parameters: (∂K 0,T /∂T) P  = −0.019 ± 0.001 GPa K−1 and α 0,T  = 2.62 ± 0.23 × 10−5 K−1, or γ 0 = 1.21 for fixed values q 0 = 1.0 and θ 0 = 823 (Isaak et al. Phys Chem Min19:106–120, 1992). From the comparison of fits from two different approaches, we propose to constrain the bulk modulus of grossular garnet and its pressure derivative to K T0 = 166 GPa and K￠T0 K^{\prime}_{T0}  = 4.03–4.35. Present results are compared with previously determined thermoelastic properties of grossular-rich garnets.  相似文献   

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