Effect of pressure on the thermal expansion of MgO up to 8.2 GPa

Isobaric volume measurements for MgO were carried out at 2.6, 5.4, and 8.2 GPa in the temperature range 300–1073 K using a DIA-type, large-volume apparatus in conjunction with synchrotron X-ray powder diffraction. Linear fit of the thermal expansion data over the experimental pressure range yields the pressure derivative, (∂α/∂P) _T , of −1.04(8) × 10⁻⁶ GPa⁻¹ K⁻¹ and the mean zero-pressure thermal expansion α_{0, T}  = 4.09(6) × 10⁻⁵ K⁻¹. The α_{0, T} value is in good agreement with results of Suzuki (1975) and Utsumi et al. (1998) over the same temperature range, whereas (∂α/∂P) _T is determined for the first time on MgO by direct measurements. The cross-derivative (∂α²/∂P∂T) cannot be resolved because of large uncertainties associated with the temperature derivative of α at all pressures. The temperature derivative of the bulk modulus, (∂K _T/∂T) _P , of −0.025(3) GPa K⁻¹, obtained from the measured (∂α/∂P) _T value, is in accord with previous findings. Received: 2 April 1999 / Revised, accepted: 22 June 1999     

Thermal equations of state of dioctahedral micas on the join muscovite–paragonite

 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     

Elasticity of TiO2 rutile to 1800 K

The ambient pressure elastic properties of single-crystal TiO₂ rutile are reported from room temperature (RT) to 1800 K, extending by more than 1200 oK the maximum temperature for which rutile elasticity data are available. The magnitudes of the temperature derivatives decrease with increasing temperature for five of the six adiabatic elastic moduli (C _ij ). At RT, we find (units, GPa): C ₁₁=268(1); C ₃₃=484(2); C ₄₄=123.8(2); C ₆₆=190.2(5); C ₂₃=147(1); and C ₁₂=175(1). The temperature derivatives (units, GPa K⁻¹) at RT are: (∂C ₁₁/∂T) _P =−0.042(5); (∂C ₃₃/∂T) _P =−0.087(6); (∂C ₄₄/∂T) _P =−0.0187(2); (∂C ₆₆/∂T) _P =−0.067(2); (∂C ₂₃/∂T) _P =−0.025; and (∂C ₁₂/∂T) _P −0.048(5). The values for K _S (adiabatic bulk modulus) and μ (isotropic shear modulus) and their temperature derivatives are K _S =212(1) GPa; μ=113(1) GPa; (∂K _S /∂T) _P =−0.040(4) GPa K⁻¹; and (∂μ/∂T) _P =−0.018(1) GPa K⁻¹. We calculate several dimensionless parameters over a large temperature range using our new data. The unusually high values for the Anderson-Gròneisen parameters at room temperature decrease with increasing temperature. At high T, however, these parameters are still well above those for most other oxides. We also find that for TiO₂, anharmonicity, as evidenced by a non-zero value of [∂ln (K _T )/∂lnV] _T , is insignificant at high T, implying that for the TiO₂ analogue of stishovite, thermal pressure is independent of volume (or pressure). Systematic relations indicate that ∂² K _S /∂T∂P is as high as 7×10⁻⁴ K⁻¹ for rutile, whereas ∂²μ/∂T∂P is an order of magnitude less. Received: 19 September 1997 / Revised, accepted: 27 February 1998     

High pressure study of ScAlO3 perovskite

The crystal structure of orthorhombic (Pbnm) ScAlO₃ perovskite has been refined to 5 GPa using single-crystal X-ray diffraction. The compression of the structure if anisotropic with β _a =1.39(3)×10⁻³ GPa⁻¹, β _b =1.14(3)×10⁻³ GPa⁻¹ and β _c =1.84(3)×10⁻³ GPa⁻¹. The isothermal bulk modulus of ScAlO₃, K _T , determined from fitting a Birch-Murnaghan equation of state (K ^′ _T =4) to the volume compression data is 218(1) GPa. The interoctahedral angles to not vary significantly with pressure, and the compression of the structure is entirely attributable to compression of the AlO₆ octahedra. The compressibilities of the constituent AlO₆ and ScO₁₂ are well matched: β_Al−O=1.6×10⁻³ GPa⁻¹ and β_Sc−O=1.5×10⁻³ GPa⁻¹. Therefore the distortion of the structure shows no significant change with increasing pressure. Received: 18 August 1997 / Revised, accepted: 11 November 1997     

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     

Thermal Expansion of Periclase (MgO) and Tungsten (W) to Melting Temperatures

 In situ x-ray data on molar volumes of periclase and tungsten have been collected over the temperature range from 300 K to melting. We determine the temperature by combining the technique of spectroradiometry and electrical resistance wire heating. The thermal expansion (α) of periclase between 300 and 3100 K is given by α=2.6025 10⁻⁵+1.3535 10⁻⁸ T+6.5687 10⁻³ T⁻¹−1.8281 T⁻². For tungsten, we have (300 to 3600 K) α=7.862 10⁻⁶+6.392 10⁻⁹ T. The data at 298 K for periclase is: molar volume 11.246 (0.031) cm³, α=3.15 (0.07) 10⁻⁵ K⁻¹, and for tungsten: molar volume 9.55 cm³, α=9.77 (10.08) 10⁻⁶ K⁻¹. Received: July 18, 1996 / Revised, accepted: February 14, 1997     

The thermoelastic behavior of clintonite up to 10?GPa and 1,000°C

The thermoelastic behavior of a natural clintonite-1M [with composition: Ca_1.01(Mg_2.29Al_0.59Fe_0.12)_Σ3.00(Si_1.20Al_2.80)_Σ4.00O₁₀(OH)₂] has been investigated up to 10 GPa (at room temperature) and up to 960°C (at room pressure) by means of in situ synchrotron single-crystal and powder diffraction, respectively. No evidence of phase transition has been observed within the pressure and temperature range investigated. P–V data fitted with an isothermal third-order Birch–Murnaghan equation of state (BM-EoS) give V ₀ = 457.1(2) ?³, K _T0 = 76(3)GPa, and K′ = 10.6(15). The evolution of the “Eulerian finite strain” versus “normalized stress” shows a linear positive trend. The linear regression yields Fe(0) = 76(3) GPa as intercept value, and the slope of the regression line leads to a K′ value of 10.6(8). The evolution of the lattice parameters with pressure is significantly anisotropic [β(a) = 1/3K _T0(a) = 0.0023(1) GPa⁻¹; β(b) = 1/3K _T0(b) = 0.0018(1) GPa⁻¹; β(c) = 1/K _T0(c) = 0.0072(3) GPa⁻¹]. The β-angle increases in response to the applied P, with: β_P = β₀ + 0.033(4)P (P in GPa). The structure refinements of clintonite up to 10.1 GPa show that, under hydrostatic pressure, the structure rearranges by compressing mainly isotropically the inter-layer Ca-polyhedron. The bulk modulus of the Ca-polyhedron, described using a second-order BM-EoS, is K _T0(Ca-polyhedron) = 41(2) GPa. The compression of the bond distances between calcium and the basal oxygens of the tetrahedral sheet leads, in turn, to an increase in the ditrigonal distortion of the tetrahedral ring, with ∂α/∂P ≈ 0.1°/GPa within the P-range investigated. The Mg-rich octahedra appear to compress in response to the applied pressure, whereas the tetrahedron appears to behave as a rigid unit. The evolution of axial and volume thermal expansion coefficient α with temperature was described by the polynomial α(T) = α₀ + α₁ T ^−1/2. The refined parameters for clintonite are as follows: α₀ = 2.78(4) 10⁻⁵°C⁻¹ and α₁ = −4.4(6) 10⁻⁵°C^1/2 for the unit-cell volume; α₀(a) = 1.01(2) 10⁻⁵°C⁻¹ and α₁(a) = −1.8(3) 10⁻⁵°C^1/2 for the a-axis; α₀(b) = 1.07(1) 10⁻⁵°C⁻¹ and α₁(b) = −2.3(2) 10⁻⁵°C^1/2 for the b-axis; and α₀(c) = 0.64(2) 10⁻⁵°C⁻¹ and α₁(c) = −7.3(30) 10⁻⁶°C^1/2for the c-axis. The β-angle appears to be almost constant within the given T-range. No structure collapsing in response to the T-induced dehydroxylation was found up to 960°C. The HP- and HT-data of this study show that in clintonite, the most and the less expandable directions do not correspond to the most and the less compressible directions, respectively. A comparison between the thermoelastic parameters of clintonite and those of true micas was carried out.     

Thermal expansion of gehlenite, Ca2Al[AlSiO7], and the related aluminates LnCaAl[Al2O7] with Ln = Tb, Sm

The thermal expansion of gehlenite, Ca₂Al[AlSiO₇], (up to T=830 K), TbCaAl[Al₂O₇] (up to T=1100 K) and SmCaAl[Al₂O₇] (up to T=1024 K) has been determined. All compounds are of the melilite structure type with space group Thermal expansion data were obtained from in situ X-ray powder diffraction experiments in-house and at HASYLAB at the Deutsches Elektronen Synchrotron (DESY) in Hamburg (Germany). The thermal expansion coefficients for gehlenite were found to be: α₁=7.2(4)×10⁻⁶×K⁻¹+3.6(7)×10⁻⁹ΔT×K⁻² and α₃=15.0(1)×10⁻⁶×K⁻¹. For TbCaAl[Al₂O₇] the respective values are: α₁=7.0(2)×10⁻⁶×K⁻¹+2.0(2)×10⁻⁹ΔT×K⁻² and α₃=8.5(2)×10⁻⁶×K⁻¹+2.0(3)×10⁻⁹ΔT×K⁻², and the thermal expansion coefficients for SmCaAl[Al₂O₇] are: α₁=6.9(2)×10⁻⁶×K⁻¹+1.7(2)×10⁻⁹ΔT×K⁻² and α₃=9.344(5)×10⁻⁶×K⁻¹. The expansion mechanisms of the three compounds are explained in terms of structural trends obtained from Rietveld refinements of the crystal structures of the compounds against the powder diffraction patterns. No structural phase transitions have been observed. While gehlenite behaves like a ‘proper’ layer structure, the aluminates show increased framework structure behavior. This is most probably explained by stronger coulombic interactions between the tetrahedral conformation and the layer-bridging cations due to the coupled substitution (Ca²⁺+Si⁴⁺)–(Ln ³⁺+Al³⁺) in the melilite-type structure. This article has been mistakenly published twice. The first and original version of it is available at .     

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.     

Thermal expansion of gehlenite, Ca2Al[AlSiO7], and the related aluminates LnCaAl[Al2O7] with Ln=Tb, Sm

The thermal expansion of gehlenite, Ca₂Al[AlSiO₇], (up to T=830 K), TbCaAl[Al₂O₇] (up to T=1,100 K) and SmCaAl[Al₂O₇] (up to T=1,024 K) has been determined. All compounds are of the melilite structure type with space group Thermal expansion data was obtained from in situ X-ray powder diffraction experiments in-house and at HASYLAB at the Deutsches Elektronen Synchrotron (DESY) in Hamburg (Germany). The thermal expansion coefficients for gehlenite were found to be: α₁=7.2(4)×10⁻⁶ K⁻¹+3.6(7)×10⁻⁹ΔT K⁻² and α₃=15.0(1)×10⁻⁶ K⁻¹. For TbCaAl[Al₂O₇] the respective values are: α₁=7.0(2)×10⁻⁶ K⁻¹+2.0(2)×10⁻⁹ΔT K⁻² and α₃=8.5(2)×10⁻⁶ K⁻¹+2.0(3)×10⁻⁹ΔT K⁻², and the thermal expansion coefficients for SmCaAl[Al₂O₇] are: α₁=6.9(2)× 10⁻⁶ K⁻¹+1.7(2)×10⁻⁹ΔT K⁻² and α₃=9.344(5)×10⁻⁶ K⁻¹. The expansion-mechanisms of the three compounds are explained in terms of structural trends obtained from Rietveld refinements of the crystal structures of the compounds against the powder diffraction patterns. No structural phase transitions have been observed. While gehlenite behaves like a ’proper’ layer structure, the aluminates show increased framework structure behaviour. This is most probably explained by stronger coulombic interactions between the tetrahedral conformation and the layer-bridging cations due to the coupled substitution (Ca²⁺+Si⁴⁺)-(Ln ³⁺+Al³⁺) in the melilite-type structure. Electronic Supplementary Material Supplementary material is available for this article at     

X-ray diffraction study of arsenopyrite at high pressure

The high-pressure X-ray diffraction study of a natural arsenopyrite was investigated up to 28.2 GPa using in situ angle-dispersive X-ray diffraction and a diamond anvil cell at National Synchrotron Light Source, Brookhaven National Laboratory. The 16:3:1 methanol–ethanol–water mixture was used as a pressure-transmitting medium. Pressures were measured using the ruby-fluorescence method. No phase change has been observed up to 28.2 GPa. The isothermal equation of state (EOS) was determined. The values of K ₀, and K′ ₀ refined with a third-order Birch–Murnaghan EOS are K ₀ = 123(9) GPa, and K′ ₀ = 5.2(8). Furthermore, we confirm that the linear compressibilities (β) along a, b and c directions of arsenopyrite is elastically isotropic (β _a  = 6.82 × 10⁻⁴, β _b  = 6.17 × 10⁻⁴ and β _c  = 6.57 × 10⁻⁴ GPa⁻¹).     

High-pressure and high-temperature in situ X-ray diffraction study of iron and corundum to 68 GPa using an internally heated diamond anvil cell

Using powder X-ray diffraction of heated solids to pressures reaching 68 GPa, the pressure-volume-temperature (PVT) data on corundum Al₂O₃ and ɛ-Fe were determined with the following results: *Corundum,*Iron, *Al₂O₃*ɛ-Fe Isothermal bulk*258 (2)*164 (3)  modulus K'_{300, 1} (GPa) Pressure derivative K_{300, 1}*4.88 (4)*5.36 (16) Temperature derivative*–0.020 (2)*–0.043 (3)  (∂K _T,1 /∂T) _P (GPa/K) Molar volume V_300,1*25.59 (2)*6.76 (2)  (cm³/mol) Isobaric thermal expansion at 1 atm (0.101 MPa) is given by (K^–1): α _T =2.6 (2) 10^–5+1.81 (9) 10^–9 T–0.67 (6)/T ² for corundum, and α _T =5.7 (4) 10^–5+4.2 (4) 10^–9 T–0.17 (7)/T ² for iron ɛ-Fe. Received: 1 March 1997 / Revised, accepted: 21 August 1997     

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     

High-pressure X-ray diffraction study of ε-FeOOH

An in situ synchrotron X-ray diffraction study was carried out on ε-FeOOH at room temperature up to a pressure of 8.6 GPa using the energy-dispersive method. The linear compressibility was determined to be β _a  = 1.69(3) × 10⁻³ GPa⁻¹, β _b  = 2.86(6) × 10⁻³ GPa⁻¹, and β _c  = 1.73(5) × 10⁻³ GPa⁻¹. The b-axis of the unit cell is more compressible than the a and c axes. The pressure–volume data were fitted to a third-order Birch–Murnaghan equation of state. The best fit was found using a room temperature isothermal bulk modulus of K ₀ = 126(3) GPa and its pressure derivative K′ = 10(1).     

In search of the mixed derivative ?2 M /? P ? T ( M = G , K ): joint analysis of ultrasonic data for polycrystalline pyrope from gas- and solid-medium apparatus

Elastic wave velocities for dense (99.8% of theoretical density) isotropic polycrystalline specimens of synthetic pyrope (Mg₃Al₂Si₃O₁₂) were measured to 1,000 K at 300 MPa by the phase comparison method of ultrasonic interferometry in an internally heated gas-medium apparatus. The temperature derivatives of the elastic moduli [(∂Ks/∂T) _P = −19.3(4); (∂G/∂T) _P = −10.4(2) MPa K⁻¹] measured in this study are consistent with previous acoustic measurements on both synthetic polycrystalline pyrope in a DIA-type cubic anvil apparatus (Gwanmesia et al. in Phys Earth Planet Inter 155:179–190, 2006) and on a natural single crystal by the rectangular parallelepiped resonance (RPR; Suzuki and Anderson in J Phys Earth 31:125–138, 1983) method but |(∂Ks/∂T) _P | is significantly larger than from a Brillouin spectroscopy study of single-crystal pyrope (Sinogeikin and Bass in Phys Earth Planet Inter 203:549–555, 2002). Alternative approaches to the retrieval of mixed derivatives of the elastic moduli from joint analysis of data from this study and from the solid-medium data of Gwanmesia et al. in Phys Earth Planet Inter 155:179–190 (2006) yield ∂² G/∂P∂T = [0.07(12), 0.20(14)] × 10⁻³ K⁻¹ and ∂² K _S /∂P∂T = [−0.20(24), 0.22(26)] × 10⁻³ K⁻¹, both of order 10⁻⁴ K⁻¹ and not significantly different from zero. More robust inference of the mixed derivatives will require solid-medium acoustic measurements of precision significantly better than 1%.     

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     

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     

A high P-T single-crystal X-ray diffraction study of thermoelasticity of MgSiO3 orthoenstatite

P-V-T data of MgSiO₃ orthoenstatite have been measured by single-crystal X-ray diffraction at simultaneous high pressures (in excess of 4.5 GPa) and temperatures (up to 1000 K). The new P-V-T data of the orthoenstatite, together with previous compression data and thermal expansion data, are described by a modified Birch-Murnaghan equation of state for diverse temperatures. The fitted thermoelastic parameters for MgSiO₃ orthoenstatite are: thermal expansion ?α/?P with values of a=2.86(29)×10^-5 K^-1 and b=0.72(16)×10^-8 K^-2; isothermal bulk modulus K _{T o} =102.8(2) GPa; pressure derivative of bulk modulus K′=?K/?P=10.2(1.2); and temperature derivative of bulk modulus K=?K/?T=-0.037(5) GPa/K. The derived thermal Grüneisen parameter is γ _th=1.05 for ambient conditions; Anderson-Grüneisen parameter is δ _{T o} =11.6, and the pressure derivative of thermal expansion is ?α/?P=-3.5×10^-6K^-1 GPa^-1. From the P-V-T data and the thermoelastic equation of state, thermal expansions at two constant pressures of 1.5 GPa and 4.0 GPa are calculated. The resulting pressure dependence of thermal expansion is Δα/ΔP=-3.2(1)× 10^-6 K^-1 GPa^-1. The significantly large values of K′, K, δ _T and ?α/?P indicate that compression/expansion of MgSiO₃ orthoenstatite is very sensitive to changes of pressure and temperature.     

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     

The elastic constants of monoclinic single-crystal chrome-diopside to 1,300 K

Values of the complete adiabatic elastic tensor for single-crystal chrome-diopside (a monoclinic pyroxene mineral) are presented from 298 to 1,300 K. The data were obtained using resonant ultrasound spectroscopy (RUS). They are the first published results for the temperature T dependences of the 13 individual elastic constants C _ij of any clinopyroxene mineral. Each C _ij is appropriately described by a linear function in T throughout the range of T. Values for each (∂C _ij /∂T) _P in GPa K⁻¹ are as follows: C ₁₁, −0.0291; C ₂₂, −0.0248; C ₃₃, −0.0179; C ₄₄, −0.0103; C ₅₅, −0.0077; C ₆₆, −0.0152; C ₁₂, −0.0119; C ₁₃, −0.0064; C ₂₃, 0.0000; C ₁₅, 0.0025; C ₂₅, 0.0022; C ₃₅, −0.0046; and C ₄₆, 0.0026. Values of (∂M/∂T) _P in GPa K⁻¹, where M represents an isotropic bulk property calculated from the C _ij data, are as follows: adiabatic bulk modulus K _S , −0.0123; isothermal bulk modulus K _T , −0.0178; and shear modulus G, −0.00998. Some diopside derivatives, notably (∂K _S /∂T) _P , (∂K _T /∂T) _P , and (∂V _P /∂T) _P , where V _P is the compressional wave velocity, have smaller magnitudes than all other minerals of importance in Earth’s mantle, thus, confirming predictions from systematics studies. We find several dimensionless quantities for this monoclinic mineral have normal values compared to other mantle minerals. Further, αK _T (α is the volume coefficient of thermal expansion) for diopside is approximately independent of both T and volume V at elevated temperature, so its equation of state is accurately expressed in simplified form.