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1.
 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   

2.
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 K300, 1*4.88 (4)*5.36 (16) Temperature derivative*–0.020 (2)*–0.043 (3)  (∂K T,1 /∂T) P (GPa/K) Molar volume V300,1*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  相似文献   

3.
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  相似文献   

4.
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 .  相似文献   

5.
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 α0, T  = 4.09(6) × 10−5 K−1. The α0, 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  相似文献   

6.
The thermo-elastic behavior of a natural epidote [Ca1.925 Fe0.745Al2.265Ti0.004Si3.037O12(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)Å3, 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, βP(°) = βP0 −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 K1/2 for the unit-cell volume, α0(a) = 1.21(7) × 10−5 K−1 and α1(a) = −1.2(2) × 10−4 K1/2 for the a-axis, α0(b) = 1.88(7) × 10−5 K−1 and α1(b) = −1.7(2) × 10−4 K1/2 for the b-axis, and α0(c) = 2.14(9) × 10−5 K−1 and α1(c) = −2.0(2) × 10−4 K1/2 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 βT(°) = βT0 + 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.  相似文献   

7.
The unit cell parameters, extracted from Rietveld analysis of neutron powder diffraction data collected between 4.2 K and 320 K, have been used to calculate the temperature evolution of the thermal expansion tensor for gypsum for 50 ≤ T ≤ 320 K. At 300 K the magnitudes of the principal axes are α 11  = 1.2(6) × 10−6 K−1, α 22  = 36.82(1) × 10−6 K−1 and α 33  = 25.1(5) × 10−6 K−1. The maximum axis, α 22 , is parallel to b, and using Institution of Radio Engineers (IRE) convention for the tensor orthonormal basis, the axes α 11 and α 33 have directions equal to (−0.979, 0, 0.201) and (0.201, 0, 0.979) respectively. The orientation and temperature dependent behaviour of the thermal expansion tensor is related to the crystal structure in the I2/a setting. Received 12 February 1998 / Revised, accepted 19 October 1998  相似文献   

8.
 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   

9.
Low- and high-temperature heat capacities were measured for a series of synthetic high-structural state (K,Ca)-feldspars (Or–An) using both a relaxation and a differential scanning calorimeter. The data were collected at temperatures between 5 and 800 K on polycrystalline samples that had been synthesised and characterised in a previous study. Below T = 300 K, Or90An10, and Or80An20 showed excess heat capacities of mixing with maximum values of ~3 J mol−1 K−1. The other members of this binary (An > 20 mol%) had lower excess heat capacity values of up to ~1 J mol−1 K−1. Above T = 300 K, some compositions exhibited negative excess heat capacities of mixing (with maximum values of −2 J mol−1 K−1). The vibrational entropy at 298.15 K for Or90An10 and Or80An20 deviated strongly from the behaviour of a mechanical mixture, with excess entropy values of ~3.5 J mol−1 K−1. More An-rich members had only small excess vibrational entropies at T = 298.15 K. The difference in behaviour between members with An > 20 mol% and those with An ≤ 20 mol% is probably a consequence of the structural state of the (K,Ca)-feldspars, i.e., (K,Ca)-feldspars with An ≤ 20 mol% have monoclinic symmetry, whereas those with An > 20 mol% are triclinic. At T = 800 K, the vibrational entropy values were found to scatter around the values expected for a mechanical mixture and, thus, correspond to a quasi-ideal behaviour. The solvus for the (K,Ca)-feldspar binary was calculated based on the entropy data from this study in combination with enthalpy and volume of mixing data from a previous study.  相似文献   

10.
 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  high102.54 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  相似文献   

11.
The accepted standard state entropy of titanite (sphene) has been questioned in several recent studies, which suggested a revision from the literature value 129.3 ± 0.8 J/mol K to values in the range of 110–120 J/mol K. The heat capacity of titanite was therefore re-measured with a PPMS in the range 5 to 300 K and the standard entropy of titanite was calculated as 127.2 ± 0.2 J/mol K, much closer to the original data than the suggested revisions. Volume parameters for a modified Murgnahan equation of state: V P,T  = V 298° × [1 + a°(T − 298) − 20a°(T − 298)] × [1 – 4P/(K 298 × (1 – 1.5 × 10−4 [T − 298]) + 4P)]1/4 were fit to recent unit cell determinations at elevated pressures and temperatures, yielding the constants V 298° = 5.568 J/bar, a° = 3.1 × 10−5 K−1, and K = 1,100 kbar. The standard Gibbs free energy of formation of titanite, −2456.2 kJ/mol (∆H°f = −2598.4 kJ/mol) was calculated from the new entropy and volume data combined with data from experimental reversals on the reaction, titanite + kyanite = anorthite + rutile. This value is 4–11 kJ/mol less negative than that obtained from experimental determinations of the enthalpy of formation, and it is slightly more negative than values given in internally consistent databases. The displacement of most calculated phase equilibria involving titanite is not large except for reactions with small ∆S. Re-calculated baric estimates for several metamorphic suites yield pressure differences on the order of 2 kbar in eclogites and 10 kbar for ultra-high pressure titanite-bearing assemblages.  相似文献   

12.
The thermoelastic behaviour of anthophyllite has been determined for a natural crystal with crystal-chemical formula ANa0.01 B(Mg1.30Mn0.57Ca0.09Na0.04) C(Mg4.95Fe0.02Al0.03) T(Si8.00)O22 W(OH)2 using single-crystal X-ray diffraction to 973 K. The best model for fitting the thermal expansion data is that of Berman (J Petrol 29:445–522, 1988) in which the coefficient of volume thermal expansion varies linearly with T as α V,T  = a 1 + 2a 2 (T − T 0): α298 = a 1 = 3.40(6) × 10−5 K−1, a 2 = 5.1(1.0) × 10−9 K−2. The corresponding axial thermal expansion coefficients for this linear model are: α a ,298 = 1.21(2) × 10−5 K−1, a 2,a  = 5.2(4) × 10−9 K−2; α b ,298 = 9.2(1) × 10−6 K−1, a 2,b  = 7(2) × 10−10 K−2. α c ,298 = 1.26(3) × 10−5 K−1, a 2,c  = 1.3(6) × 10−9 K−2. The thermoelastic behaviour of anthophyllite differs from that of most monoclinic (C2/m) amphiboles: (a) the ε 1 − ε 2 plane of the unit-strain ellipsoid, which is normal to b in anthophyllite but usually at a high angle to c in monoclinic amphiboles; (b) the strain components are ε 1 ≫ ε 2 > ε 3 in anthophyllite, but ε 1 ~ ε 2 ≫ ε 3 in monoclinic amphiboles. The strain behaviour of anthophyllite is similar to that of synthetic C2/m ANa B(LiMg) CMg5 TSi8 O22 W(OH)2, suggesting that high contents of small cations at the B-site may be primarily responsible for the much higher thermal expansion ⊥(100). Refined values for site-scattering at M4 decrease from 31.64 epfu at 298 K to 30.81 epfu at 973 K, which couples with similar increases of those of M1 and M2 sites. These changes in site scattering are interpreted in terms of Mn ↔ Mg exchange involving M1,2 ↔ M4, which was first detected at 673 K.  相似文献   

13.
The high-temperature cell parameters of lime (CaO), periclase (MgO), corundum (Al2O3), and spinel (MgAl2O4) have been determined from 300 up to 3000 K through X-ray diffraction experiments with synchrotron radiation. The good agreement found with dilatometric results suggests that vacancy-type defects do not make a large contribution to thermal expansion for these oxides, even near the melting point, justifying the use of X-ray diffraction for determining volume properties up to very high temperatures. Thermal expansion coefficients were determined from the measured cell volumes with equations of the form α=α0 + α1 T + α2/T 2. Along with available isobaric heat capacity and compressibility data, these derived coefficients clearly show that anharmonic effects contribute little to the isochoric heat capacities (C v ) of CaO, MgO, and Al2O3, which do not depart appreciably from the 3nR Dulong and Petit limit. Received: 31 March 1999 / Revised, accepted: 23 June 1999  相似文献   

14.
 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   

15.
 Single crystals of synthetic vanadium-, chromium- and cobalt-bearing garnets, Pyr:V0.06, Pyr:V0.13, Pyr:Cr0.04, Pyr:Co0.10, and Gt:Co3.00, and a natural vanadium-bearing grossular, Gross:V0.07 (Cr3+ < 0.005), were studied by electronic absorption spectroscopy in the wavenumber range 35 000–5000 cm−1 under ambient conditions and at temperatures up to 600 K and pressures up to 8 GPa. The T and P behavior of the absorption band energies and intensities shows the following for the different transition metal-bearing garnets: Cr: The thermal expansion of chromium octahedra are similar to and the Racah parameter the same in synthetic Cr-doped pyrope, αpoly≅ 1.3 × 10−5 K−1, and in natural pyrope, αpoly≅ 1.5 × 10−5 K−1, and B=655 cm−1, respectively. Ca2+[8]-free garnets have a slightly stronger crystal field at the Y[6] site and, therefore, the energies of the two spin-allowed Cr3+ dd bands are ca. 300 cm−1 higher in Mg-pyrope than in natural Ca-bearing pyrope. Co: Increasing temperature causes only a small thermal expansion of the cobalt dodecahedra. Increasing pressure gives rise to appreciable compression, which is similar to that of the Fe2+-dodecahedra in almandine, where k=125 ± 25 GPa. T and P dependence of the Co band intensities may be caused by strong spin-orbit coupling. V: Occurs in at least two valence states and structural sites: (1) V3+ in octahedral sites gives rise to two spin-allowed bands, at 17 220 cm−1 and 24 600 cm−1, whose temperature dependence is typical for spin-allowed dd transitions in centrosymmetric sites. (2) V4+, which causes a set of dd absorption bands similar to those observed in the spectrum of V4+-doped Zr[SiO4]. The P behavior of the V absorption bands indicates an interaction between V3+ and V4+ species. Received: 27 June 2001 / Accepted: 19 December 2001  相似文献   

16.
 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   

17.
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  相似文献   

18.
 Dehydroxylation of muscovite in the form of small lamellae at 923 <T <1173 K was studied by Electron Spin Resonance (ESR) on Fe3+. The kinetics of the process has been established to be described by the model of continuous nucleation on the large surface planes of the small plates. Determined by experimental data the rate constant of the process k is shown to be that of dehydroxylation itself. The activation energy obtained by data at T<1100 K is 97.5 KJ·mol−1. The nonlinear dependence of ln(k) on 1/T is explained by the theory of transitions induced by the fluctuative preparation of a potential barrier as a result of thermal oscillations of ions in the lattice. At high temperatures the potential curve of the hydroxyl's proton is transformed so that it can overcome the barrier from one potential well to the other (from one hydroxyl site to the adjacent one). Such transformations of the curve can be caused by the oscillations of large structural clusters (∼1·10−22 kg) with the frequency ∼4.5·1012 s−1. Received: 3 August 1995 / Accepted: 13 April 1997  相似文献   

19.
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 Of–Ok, and Ob–Om 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 Cr3+ 4A2g→4T2g(F)(I), →4T1g(F)(II), and →4T1g(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  相似文献   

20.
 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 [Jdpx*Caliq*FmliqDiHdpx*Naliq*Alliq] −0.86* ln [MgliqMgliq+Feliq]+0.52*ln [Caliq] 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 [Jdpx[Siliq]2*Naliq*Alliq] +367*[Naliq*Alliq] which estimates pressure to ± 1.4 kbar. Pressure is in kbar, T is in Kelvin. Quantities such as Naliq represent the cation fraction of the given oxide (NaO0.5) 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 AlVI 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 VJd 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  相似文献   

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