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     

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     

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     

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     

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     

High-temperature elasticity of magnesioferrite spinel

The elastic moduli of magnesioferrite spinel, MgFe₂O₄, and their temperature dependence have been determined for the first time by ultrasonic measurements on a polycrystalline specimen. The measurements were carried out at 300 MPa and to 700°C in a gas-medium high-pressure apparatus. On heating, both the elastic bulk (K _S) and shear (G) moduli decrease linearly to 350°C. By combining with extant thermal-expansion data, the values for the room-temperature K _S and G, and their temperature derivatives are as follows: K ₀ = 176.3(7) GPa, G ₀ = 80.1(2) GPa, (∂K _S/∂T) _P = −0.032(3) GPa K⁻¹ and (∂G/∂T) _P = −0.012(1) GPa K⁻¹. Between 350 and 400°C, there are abrupt increases of 1.4% in both of the elastic moduli; these closely coincide with the magnetic Curie transition that was observed by thermal analyses at about 360°C.     

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%.     

Thermobarometry of mafic igneous rocks based on clinopyroxene-liquid equilibria, 0–30 kbar

 Models for estimating the pressure and temperature of igneous rocks from co-existing clino-pyroxene and liquid compositions are calibrated from existing data and from new data obtained from experiments performed on several mafic bulk compositions (from 8–30 kbar and 1100–1475° C). The resulting geothermobarometers involve thermodynamic expressions that relate temperature and pressure to equilibrium constants. Specifically, the jadeite (Jd; NaAlSi₂O₆)–diopside/hedenbergite (DiHd; Ca(Mg, Fe) Si₂O₆) exchange equilibrium between clinopyroxene and liquid is temperature sensitive. When compositional corrections are made to the calibrated equilibrium constant the resulting geothermometer is (i) 10⁴ T=6.73−0.26^* ln [Jd^px*Ca^liq*Fm^liqDiHd^px*Na^liq*Al^liq] −0.86^* ln [Mg^liqMg^liq+Fe^liq]+0.52^*ln [Ca^liq] an expression which estimates temperature to ±27 K. Compared to (i), the equilibrium constant for jadeite formation is more sensitive to pressure resulting in a thermobarometer (ii) P=−54.3+299^* T10⁴+36.4^* T10⁴ ln [Jd^px[Si^liq]^2*Na^liq*Al^liq] +367^*[Na^liq*Al^liq] which estimates pressure to ± 1.4 kbar. Pressure is in kbar, T is in Kelvin. Quantities such as Na^liq represent the cation fraction of the given oxide (NaO_0.5) in the liquid and Fm=MgO+FeO. The mole fractions of Jd and diopside+hedenbergite (DiHd) components are calculated from a normative scheme which assigns the lesser of Na or octahedral Al to form Jd; any excess Al^VI forms Calcium Tschermak’s component (CaTs; CaAlAlSiO₆); Ca remaining after forming CaTs and CaTiAl₂O₆ is taken as DiHd. Experimental data not included in the regressions were used to test models (i) and (ii). Error on predictions of T using model (i) is ±40 K. A pressure-dependent form of (i) reduces this error to ±30 K. Using model (ii) to predict pressures, the error on mean values of 10 isobaric data sets (0–25 kbar, 118 data) is ±0.3 kbar. Calculating thermodynamic properties from regression coefficients in (ii) gives V^Jd _f of 23.4 ±1.3 cm³/mol, close to the value anticipated from bar molar volume data (23.5 cm³/mol). Applied to clinopyroxene phenocrysts from Mauna Kea, Hawaii lavas, the expressions estimate equilibration depths as great as 40 km. This result indicates that transport was sufficiently rapid that at least some phenocrysts had insufficient time to re-equilibrate at lower pressures. Received: 16 May 1994/Accepted: 15 June 1995     

Thermal equation of state of iron and Fe0.91Si0.09

We have carried out an in situ synchrotron X-ray diffraction study on iron and an iron-silicon alloy Fe_0.91Si_0.09 at simultaneously high pressure and temperature. Unit-cell volumes, measured up to 8.9 GPa and 773 K on the bcc phases of iron and Fe_0.91Si_0.09, are analyzed using the Birch-Murnaghan equation of state and thermal pressure approach of Anderson. Equation of state parameters on iron are found to be in agreement with results of previous studies. For both iron and Fe_0.91Si_0.09, thermal pressures show strong dependence on volume; the (∂K_T/∂T)_V values are considerably larger than those previously reported for other solids. The present results, in combination with our previous results on ɛ-FeSi, suggest a small dependency of the room-temperature bulk modulus upon the silicon content, less than 0.3 GPa for 1 wt.% silicon. We also find that substitution of silicon in iron would not appreciably change the thermoelastic properties of iron-rich Fe−Si alloys. If this behavior persists over large pressure and temperature ranges, the relative density contrast between iron and iron-rich Fe−Si alloys at conditions of the outer core of the Earth could be close to that measured at ambient conditions, i.e., 0.6% for 1 wt.% Si. Received: 13 January 1998 / Revised, accepted: 8 May 1998     

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     

Mode of formation of hibonite (CaAl12O19) within the U-Th skarns from the granulites of S-E Madagascar

 In Madagascar, hibonite occurs as a rather frequent mineral within thorianite-bearing skarns which are widespread in the Pan African granulitic formations constituting the S-E part of the Island (Tranomaro area). In these skarns, leucocratic segregations made up of CO₃-scapolite to meionite (An_equivalent=89–95% which implies T≥850° C), spinel and corundum were formed at stage 1 of metasomatism in a titanite-bearing matrix consisting of scapolite (An_eq=77–88) and aluminous diopside. During stage 2 of metasomatism, scapolite from the lenses were altered to anorthite+calcite while the less calcic scapolite remained stable which indicates T≈800° C. Hibonite crystallized at the expense of corundum and spinel. Expressed as mol% of the CaAl₁₂O₁₉/Ca(Al₁₀TiR²⁺)O₁₉/REE(Al₁₁R²⁺)O₁₉ [+Th (Al₁₀R²⁺ ₂)O₁₉] end-members (R ²⁺=Mg, Fe²⁺, Zn²⁺; Al=Al, Fe³⁺; Ti=Ti, Si), its composition varies from 26/72/2 to 50/23/27. The ideal activity of the CaAl₁₂O₁₉ component is about 0.25. Fluid inclusions in corundum, hibonite and anorthite are composed of nearly pure CO₂. In corundum, the isochores for primary inclusions are in agreement with the P-T estimates for regional metamorphism and stage 1 metasomatism (T≈850° C, P≈5 kbar). Inclusions with the highest density in hibonite and anorthite constrain P to about 3–3.5 kbar for T=800° C. Thermodynamic calculations indicate that, in addition to a low activity of CaAl₁₂O₁₉, stability of hibonite in equilibrium with anorthite and calcite implies an extremely low activity of silica (below the zircon-baddeleyite buffer). By contrast the activity of CO₂ may be high, in agreement with the observed fluid compositions. These results are corroborated by a short comparison with the other granulite occurrences of hibonite in Tanzania and South India. Received: 18 August 1994 / Accepted: 12 October 1995     

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     

P–V–T equation of state of Ca3Al2Si3O12 grossular garnet

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.     

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

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

Oxide perovskites: pressure derivatives of the bulk and shear moduli

The pressure derivatives of elastic moduli (∂M/∂P; M=K_S and G) for a suite of polycrystalline oxide perovskites (2 titanates, 1 stannate and 2 aluminates) have been measured up to 3 GPa using the ultrasonic interferometry method combined with a buffer rod technique. Two empirical systematic relationships (∂G/∂P vs K_S/G and ∂K_S/∂P vs K_S (/ρ)^1/3) have been used to investigate the elasticity systematics of this suite of perovskites and to estimate ∂M/∂P of MgSiO₃ perovskite. The pressure derivatives ∂G/∂P and ∂K_S/∂P for this suite of perovskites scatter between well-defined linear trends for the rutile, rocksalt and spinel structures. The more diffuse trends observed for the perovskites might reflect greater flexibility in the response of its corner-connected octahedral framework structure to changing pressure. The pressure derivatives of the elastic moduli for MgSiO₃ perovskite estimated by the “perovskite bands” are ∂G/∂P=1.6–2.2 and ∂K_S/∂P=3.9–4.2. Received: 13 November 1997 / Revised, accepted: 31 August 1998     

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     

Electronic absorption and luminescence spectroscopic studies of kyanite single crystals: differentiation between excitation of FeTi charge transfer and Cr3+ dd transitions

A selected set of five different kyanite samples was analysed by electron microprobe and found to contain chromium between <0.001 and 0.055 per formula unit (pfu). Polarized electronic absorption spectroscopy on oriented single crystals, R₁, R₂-sharp line luminescence and spectra of excitation of λ₃- and λ₄-components of R₁-line of Cr³⁺-emission had the following results: (1) The Fe²⁺–Ti⁴⁺ charge transfer in c-parallel chains of edge connected M(1) and M(2) octahedra shows up in the electronic absorption spectra as an almost exclusively c(||Z′)-polarized, very strong and broad band at 16000 cm⁻¹ if <, in this case the only band in the spectrum, and at an invariably lower energy of 15400 cm⁻¹ in crystals with  ≥ . The energy difference is explained by an expansion of the O_f–O_k, and O_b–O_m edges, by which the M(1) and M(2) octahedra are interconnected (Burnham 1963), when Cr³⁺ substitutes for Al compared to the chromium-free case. (2) The Cr³⁺ is proven in two greatly differing crystal fields a and b, giving rise to two sets of bands, derived from the well known dd transitions of Cr^{3+ 4}A_2g→⁴T_2g(F)(I), →⁴T_1g(F)(II), and →⁴T_1g(P)(III). Band energies in the two sets a and b, as obtained by absorption, A, and excitation, E, agree well: I: 17300(a, A), 17200(a, E), 16000(b, A), 16200(b, E); II: 24800(a, A), 24400(a, E); 22300(b, A), 22200(b, E); III: 28800(b,A) cm⁻¹. Evaluation of crystal field parameters from the bands in the electronic spectra yield Dq(a)=1730 cm⁻¹, Dq(b)=1600 cm⁻¹, B(a)=790 cm⁻¹, B(b)=620 cm⁻¹ (errors ca. ±10 cm⁻¹), again in agreement with values extracted from the λ³, λ⁴ excitation spectra. The CF-values of set a are close to those typical of Cr³⁺ substituting for Al in octahedra of other silicate minerals without constitutional OH⁻ as for sapphirine, mantle garnets or beryl, and are, therefore, interpreted as caused by Cr³⁺ substituting for Al in some or all of the M(1) to M(4) octaheda of the kyanite structure, which are crystallographically different but close in their mean Al–O distances, ranging from 1.896 to 1.919 A (Burnham 1963), and slight degrees of distortion. Hence, band set a originates from substitutive Cr³⁺ in the kyanite structural matrix. The CF-data of Cr³⁺ type b, expecially B, resemble those of Cr³⁺ in oxides, especially of corundum type solid solutions or eskolaite. This may be interpreted by the assumption that a fraction of the total chromium contents might be allocated in a precursor of a corundum type exsolution. Received: 3 January 1997 / Revised, accepted: 2 May 1997     

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     

Heat capacity and phase equilibria of hollandite polymorph of KAlSi3O8

The low-temperature heat capacity (C _p ) of KAlSi₃O₈ with a hollandite structure was measured over the range of 5–303 K with a physical properties measurement system. The standard entropy of KAlSi₃O₈ hollandite is 166.2±0.2 J mol⁻¹ K⁻¹, including an 18.7 J mol⁻¹ K⁻¹ contribution from the configurational entropy due to disorder of Al and Si in the octahedral sites. The entropy of K₂Si₄O₉ with a wadeite structure (Si-wadeite) was also estimated to facilitate calculation of phase equilibria in the system K₂O–Al₂O₃–SiO₂. The calculated phase equilibria obtained using Perple_x are in general agreement with experimental studies. Calculated phase relations in the system K₂O–Al₂O₃–SiO₂ confirm a substantial stability field for kyanite–stishovite/coesite–Si-wadeite intervening between KAlSi₃O₈ hollandite and sanidine. The upper stability of kyanite is bounded by the reaction kyanite (Al₂SiO₅) = corundum (Al₂O₃) + stishovite (SiO₂), which is located at 13–14 GPa for 1,100–1,400 K. The entropy and enthalpy of formation for K-cymrite (KAlSi₃O₈·H₂O) were modified to better fit global best-fit compilations of thermodynamic data and experimental studies. Thermodynamic calculations were undertaken on the reaction of K-cymrite to KAlSi₃O₈ hollandite + H₂O, which is located at 8.3–10.0 GPa for the temperature range 800–1,600 K, well inside the stability field of stishovite. The reaction of muscovite to KAlSi₃O₈ hollandite + corundum + H₂O is placed at 10.0–10.6 GPa for the temperature range 900–1,500 K, in reasonable agreement with some but not all experiments on this reaction.