High-temperature study and thermal expansion of phlogopite

 Unit-cell dimensions of a natural phlogopite from Pargas, Finland, have been determined in the temperature interval of 27–1050 °C by X-ray powder diffraction technique. Expansion rates vary discontinuously with temperature with a break at 412 °C. Below this temperature, the linear expansions (α) for a, b and c axis lengths are 3.74 × 10⁻⁵ K⁻¹, 1.09 × 10⁻⁵ K⁻¹, and 1.19 × 10⁻⁵ K⁻¹, respectively, and above that they are 0.86 × 10⁻⁵ K⁻¹, 0.80 × 10⁻⁵ K⁻¹, and 1.93 × 10⁻⁵ K⁻¹. The volume thermal expansion coefficients are 6.26 × 10⁻⁵ K⁻¹ and 3.71 × 10⁻⁵ K⁻¹ for low-temperature and high-temperature intervals, respectively. The observed kink in the rate of thermal expansions with temperature could be due to the different mode of structural changes. Thermogravimetric analysis of the sample indicates the oxidation of iron in the temperature range of 500–600 °C and dehydroxylation as well as decomposition of phlogopite in the temperature range of 900–1200 °C. Received: 8 September 1998 / Accepted: 28 February 2000     

Temperature evolution between 50 K and 320 K of the thermal expansion tensor of gypsum derived from neutron powder diffraction data

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     

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 and decomposition of jarosite: a high-temperature neutron diffraction study

The structure of deuterated jarosite, KFe₃(SO₄)₂(OD)₆, was investigated using time-of-flight neutron diffraction up to its dehydroxylation temperature. Rietveld analysis reveals that with increasing temperature, its c dimension expands at a rate ~10 times greater than that for a. This anisotropy of thermal expansion is due to rapid increase in the thickness of the (001) sheet of [Fe(O,OH)₆] octahedra and [SO₄] tetrahedra with increasing temperature. Fitting of the measured cell volumes yields a coefficient of thermal expansion, α = α₀ + α₁ T, where α₀ = 1.01 × 10⁻⁴ K⁻¹ and α₁ = −1.15 × 10⁻⁷ K⁻². On heating, the hydrogen bonds, O1···D–O3, through which the (001) octahedral–tetrahedral sheets are held together, become weakened, as reflected by an increase in the D···O1 distance and a concomitant decrease in the O3–D distance with increasing temperature. On further heating to 575 K, jarosite starts to decompose into nanocrystalline yavapaiite and hematite (as well as water vapor), a direct result of the breaking of the hydrogen bonds that hold the jarosite structure together.     

Retrograde fluids in the Archean Shawmere anorthosite, Kapuskasing Structural Zone, Ontario, Canada

The Archean Shawmere anorthosite lies within the granulite facies portion of the Kapuskasing Structural Zone (KSZ), Ontario, and is crosscut by numerous linear alteration veins containing calcite + quartz ± dolomite ± zoisite ± clinozoisite ± margarite ±paragonite ± chlorite. These veins roughly parallel the trend of the Ivanhoe Lake Cataclastic Zone. Equilibria involving clinozoisite + margarite + quartz ± calcite ± plagioclase show that the vein minerals were stable at T < 600 °C, XCO₂ < 0.4 at P ≈ 6 kbar. The stabilities of margarite and paragonite in equilibrium with quartz are also consistent with T < 600 °C and XCO₂ < 0.4 at 6 kbar. Additional assemblages consisting of calcite + clinochlore + quartz + talc + margarite indicate T < 500 °C with XCO₂ > 0.9. Thus, vein formation, while clearly retrograde, spanned a range of temperatures, and fluid compositions evolved from H₂O-rich to CO₂-rich. The calcite in the retrograde veins has δ¹⁸O values that range from 8.4 to 11.2‰ (average = +9.7 ± 0.9‰) and δ¹³C values that range from −3.9 to −1.6‰ (average = −3.1 ± 0.6‰). These values indicate that the fluids from which calcite precipitated underwent extensive exchange with the anorthosite and other crustal lithologies. The fluids may have been initially derived either from devolatilization of metamorphic rocks or crystallization of igneous rocks in the adjacent Abitibi subprovince. Vein quartz contains CO₂-rich fluid inclusions (final melting T = −57.0 to −58.7 °C) that range in size from 5 to 17 μm. Measured homogenization temperatures (T h) range from −44.0 to 14.5 °C, however for most inclusions (46 of S1), T h = −44.0 to −21.1 °C (ρCO₂ ≈ 1.13 to 1.05 g/cm³). At 400 to 600 °C, these densities correspond to pressures of 3.5 to 7 kbar, which is the best estimate of pressures of vein formation. It has been argued that some high density CO₂-rich fluid inclusions found in the KSZ were formed during peak metamorphism and thus document the presence of a CO₂-rich fluid during peak granulite facies metamorphism (Rudnick et al. 1984). The association of high density CO₂-rich fluid inclusions with clearly retrograde veins documents the formation of similar composition and density inclusions after the peak of metamorphism. Thus, the coincidence of entrapment pressures calculated from fluid inclusion density measurements with peak metamorphic pressures alone should not be considered strong evidence for peak metamorphic inclusion entrapment. All fluid inclusion results are consistent with an initially semi-isobaric retrograde P–T path. Received: 2 April 1996 / Accepted: 15 November 1996     

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 .     

Octahedral cation ordering in olivine at high temperature. II: an in situ neutron powder diffraction study on synthetic MgFeSiO4 (Fa50)

 The partitioning of Fe and Mg between the M1 and M2 octahedral sites of olivine has been investigated by in situ time-of-flight neutron powder diffraction. The degree of M-cation order was determined from direct measurements of site occupancies in a synthetic sample of Fo50Fa50 heated to 1250 °C at the Fe-FeO oxygen buffer. Fe shows slight preference for M1 at temperatures below about 600 °C, progressively disordering on heating to this temperature. Above 630 °C, the temperature at which site preferences cross over (T _cr), Fe preferentially occupies M2, becoming progressively more ordered into M2 on increasing temperature. The cation-ordering behaviour is discussed in relation to the temperature dependence of the M1 and M2 site geometries, and it is suggested that vibrational entropy, crystal field effects and changes in bond characteristics play a part in the cross-over of partitioning behaviour. The temperature dependence of site ordering is modelled using a Landau expansion of the free energy of ordering of the type ΔG = −hQ + gTQ +  (T − T _c)Q ² +  Q ⁴, with a/h = 0.00406 K⁻¹, b/h = 2.3, T _c = 572 K and g/h = 0.00106 K⁻¹. These results suggest that the high-temperature ordering behaviour across the forsterite-fayalite join will have a bearing on the activity-composition relations of this important rock-forming mineral, and indicate that Fe-Mg olivine solid solutions become less ideal as temperature increases. Received: 12 August 1999 / Accepted: 25 April 2000     

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

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

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.     

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     

Pb diffusion in rutile

Diffusion of Pb was measured in natural and synthetic rutile under dry, 1 atmosphere conditions, using mixtures of Pb titanate or Pb sulfide and TiO₂ as the sources of diffusant. Pb depth profiles were then measured with Rutherford Backscattering Spectrometry (RBS). Over the temperature range 700–1100 °C, the following Arrhenius relation was obtained for the synthetic rutile: D=3.9 × 10⁻¹⁰exp(−250 ± 12 kJ mol⁻¹/RT) m²s⁻¹. Results for diffusion in natural and synthetic rutile were quite similar, despite significant differences in trace element compositions. Mean closure temperatures calculated from the diffusion parameters are around 600 °C for rutile grains of ∼100 μm size. This is about 100 °C higher than rutile closure temperature determinations from past field-based studies, suggesting that rutile is more resistant to Pb loss through volume diffusion than previously thought. Received: 28 June 1999 / Accepted: 29 December 1999     

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     

Thermal expansion of new arsenate minerals,bradaczekite, NaCu<Subscript>4</Subscript>(AsO<Subscript>4</Subscript>)<Subscript>3</Subscript>, and urusovite,Cu(AsAlO<Subscript>5</Subscript>)

Thermal behavior of two new exhalation copper-bearing minerals, bradaczekite and urusovite, from the Great Tolbachik Fissure Eruption (1975–1976, Kamchatka Peninsula, Russia) has been studied by X-ray thermal analysis within the range 20–700°C in air. The following major values of the thermal expansion tensor have been calculated for urusovite: α₁₁ = 10, α₂₂ = α_b = 7, α₃₃ = 4, α_V = 21 × 10⁻⁶°C⁻¹, μ = c∧α₃₃ = 49° and bradaczekite: α_11aver = 23, α₂₂ = 8, α_33aver = 6 × 10⁻⁶°C⁻¹, μ(c∧α₃₃) = 73°. The sharp anisotropy of thermal deformations of these minerals, absences of phase transitions, and stability of the minerals in the selected temperature range corresponding to conditions of their formation and alteration during the posteruption period of the volcanic activity are established.     

Magnesium self-diffusion in orthoenstatite

Magnesium self-diffusion coefficients were determined experimentally for diffusion parallel to each of the three crystallographic directions in natural orthoenstatite (En₈₈Fs₁₂). Experiments were conducted at 1 atm in CO-CO₂ gas mixing furnaces, which provided oxygen fugacities equivalent to the iron-wüstite buffer. Diffusion of ²⁵Mg was induced in polished samples of oriented orthoenstatite using a film of isotopically enriched ²⁵MgO as the source material. Very short (<0.15 μm) diffusional penetration profiles were measured by ion microprobe depth profiling. The diffusion coefficients determined for four temperatures (900, 850, 800, 750 °C) provide the activation energies, E _a , and frequency factors, D _o, where D = D _o exp (−E _a /RT) for Mg self-diffusion parallel to each crystallographic direction: a-axis, E _a  = 360 ± 52 kJ/mole and D _o = 1.10 × 10⁻⁴ m²/s; b-axis, E _a  = 339 ± 77 kJ/mole and D _o = 6.93 × 10⁻⁶ m²/s and c-axis, E _a  = 265 ± 66 kJ/mole and D _o = 4.34 × 10⁻⁹ m²/s. In this temperature range, any possible anisotropy of cation diffusion is very small, however the activation energy for diffusion parallel to the c-axis (001) is the lowest and the activation energies for diffusion parallel to the a-axis (100) and b-axis (010) are higher. Application of these diffusion results to the silicate phases of the Lowicz mesosiderite meteorite provides cooling rates for the silicate portion of the meteorite (4–11 °C/100 years) that are similar, although slower, to previous estimates. These silicate cooling rates are still several orders of magnitude faster than the cooling rates (0.1 °C/10⁶ years) for the metal portions. Received: 22 January 1997 / Accepted: 2 October 1997     

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     

X-ray powder diffraction study on the modulated high temperature forms of SiO2 tridymite between 110 and 220 °C

 The crystal structure of intermediate incommensurate tridymite was refined at 150 °C from powder data. Upon cooling from above 220 °C, the basic structure with space group symmetry C222₁ is gradually distorted from orthorhombic to monoclinic symmetry. With decreasing temperature, the monoclinic angle γ smoothly opens up to 90.3°, while a displacive modulation with temperature-dependent wavelength develops. The 3 + 1 dimensional superspace group of the incommensurate phase is C112₁(αβ0). The modulation mainly consists of two sinusoidal transverse displacement waves for the silicon atoms coupled to rotations of the rigid SiO_4/2 tetrahedra. The wave vector is r=0.1192(1)a* − 0.0043(1)b* at 150 °C. Below 150 °C tridymite discontinuously transforms to another orthorhombic phase and the modulation partially locks in at the wave vector r ₁=1/3a*. Simultaneously, an additional incommensurate modulation with r ₂= 0.0395(1)b* − 0.3882(1)c* is formed. The two-dimensional modulation does not vary significantly with the temperature. Received: 13 September 2000 / Accepted: 29 January 2001     

Synthesis of Ca-tourmaline in the system CaO-MgO-Al2O3-SiO2-B2O3-H2O-HCl

Summary. ?Ca-tourmaline has been synthesized hydrothermally in the presence of Ca(OH)₂ and CaCl₂-bearing solutions of different concentration at T = 300–700 °C at a constant fluid pressure of 200 MPa in the system CaO-MgO-Al₂O₃-SiO₂-B₂O₃-H₂O-HCl. Synthesis of tourmaline was possible at 400 °C, but only above 500 °C considerable amounts of tourmaline formed. Electron microprobe analysis and X-ray powder data indicate that the synthetic tourmalines are essentially solid solutions between oxy-uvite, CaMg₃- Al₆(Si₆O₁₈)(BO₃)₃(OH)₃O, and oxy-Mg-foitite, □(MgAl₂)Al₆(Si₆O₁₈)(BO₃)₃(OH)₃O. The amount of Ca ranges from 0.36 to 0.88 Ca pfu and increases with synthesis temperature as well as with bulk Ca-concentration in the starting mixture. No hydroxy-uvite, CaMg₃(MgAl₅)(Si₆O₁₈)(BO₃)₃(OH)₃(OH), could be synthesized. All tourmalines have < 3 Mg and > 6 Al pfu. The Al/(Al + Mg)-ratio decreases from 0.80 to 0.70 with increasing Ca content. Al is coupled with Mg and Ca via the substitutions Al₂□Mg₋₂Ca₋₁ and AlMg₋₁H₋₁. No single phase tourmaline could be synthesized. Anorthite ( + quartz in most runs) has been found coexisting with tourmaline. Other phases are chlorite, tremolite, enstatite or cordierite. Between solid and fluid, Ca is strongly fractionated into tourmaline ( + anorthite). The concentration ratio D = Ca(fluid)/Ca(tur) increases from 0.20 at 500 °C up to 0.31 at 700 °C. For the assemblage turmaline + anorthite + quartz + chlorite or tremolite or cordierite, the relationship between Ca content in tourmaline and in fluid with temperature can be described by the equation (whereby T = temperature in °C, Ca(tur) = amount of Ca on the X-site in tourmaline, Ca( fluid) = concentration of Ca²⁺ in the fluid in mol/l). The investigations may serve as a first guideline to evaluate the possibility to use tourmaline as an indicator for the fluid composition.

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Zusammenfassung. ?Synthese von Ca-Turmelin im System CaO-MgO-Al ₂ O ₃ -SiO ₂ -B ₂ O ₃ -H ₂ O-HCl Im System CaO-MgO-Al₂O₃-SiO₂-B₂O₃-H₂O-HCl wurde Ca-Turmalin hydrothermal aus Ca(OH)₂ and CaCl₂-haltigen L?sungen bei T = 300–700 °C und einem konstanten Fluiddruck von 200 MPa synthetisiert. Die Synthese von Turmalin war m?glich ab 400 °C, aber nur oberhalb von 500 °C bildeten sich deutliche Mengen an Turmalin. Elektronenstrahl-Mikrosondenanalysen und R?ntgenpulveraufnahmen zeigen, da? Mischkristalle der Reihe Oxy-Uvit, CaMg₃Al₆(Si₆O₁₈)(BO₃)₃(OH)₃O, und Oxy-Mg-Foitit, □(MgAl₂)Al₆(Si₆O₁₈)(BO₃)₃(OH)₃O gebildet wurden. Der Anteil an Ca variiert zwischen 0.36 und 0.88 Ca pfu und nimmt mit zunehmender Synthesetemperatur und zunehmender Ca-Konzentration im System zu. Hydroxy-Uvit, CaMg₃(MgAl₅) (Si₆O₁₈)(BO₃)₃(OH)₃(OH), konnte nicht synthetisiert werden. Alle Turmaline haben < 3 Mg und > 6 Al pfu. Dabei nimmt das Al/(Al + Mg)- Verh?ltnis mit zunehmendem Ca-Gehalt von 0.80 auf 0.70 ab. Al ist gekoppelt mit Mg und Ca über die Substitutionen Al₂□Mg₋₂Ca₋₁ und AlMg₋₁H₋₁. Einphasiger Turmalin konnte nicht synthetisiert werden. Anorthit (+ Quarz in den meisten F?llen) koexistiert mit Turmalin. Andere Phasen sind Chlorit, Tremolit, Enstatit oder Cordierit. Ca zeigt eine deutliche Fraktionierung in den Festk?rpern Turmalin (+ Anorthit). Das Konzentrationsverh?ltnis D = Ca(fluid)/Ca(tur) nimmt von 0.20 bei 500 °C auf 0.31 bei 700 °C zu. Für die Paragenese Turmalin + Anorthit + Quarz mit Chlorit oder Tremolit oder Cordierit gilt folgende Beziehung zwischen Ca-Gehalt in Turmalin und Fluid und der Temperatur: (wobei T = Temperatur in °C, Ca(tur) = Anteil an Ca auf der X-Position in Turmalin, Ca(fluid) = Konzentration von Ca²⁺ im Fluid in mol/l). Die Untersuchungen dienen zur ersten Absch?tzung, ob Turmalin als Fluidindikator petrologisch nutzbar ist.

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Received July 24, 1998;/revised version accepted October 21, 1999     

Thermoelastic properties of the high-pressure phase of SnO2 determined by in situ X-ray observations up to 30 GPa and 1400 K

 In situ synchrotron X-ray experiments in the system SnO₂ were made at pressures of 4–29 GPa and temperatures of 300–1400 K using sintered diamond anvils in a 6–8 type high-pressure apparatus. Orthorhombic phase (α-PbO₂ structure) underwent a transition to a cubic phase (Pa3ˉ structure) at 18 GPa. This transition was observed at significantly lower pressures in DAC experiments. We obtained the isothermal bulk modulus of cubic phase K ₀= 252(28) GPa and its pressure derivative K ^′=3.5(2.2). The thermal expansion coefficient of cubic phase at 25 GPa up to 1300 K was determined from interpolation of the P-V-T data obtained, and is 1.7(±0.7) × 10⁻⁵ K⁻¹ at 25 GPa. Received: 7 December 1999 / Accepted: 27 April 2000     

Iron Diffusion in Single-Crystal Diopside

 Iron tracer diffusion experiments in diopside have been performed using natural and synthetic single crystals of diopside, and stable iron tracers enriched in ⁵⁴Fe, at temperatures in the range 950–1100 °C, total pressure 1 atm, for times up to 29 days. Iron isotope diffusion profiles were determined with an ion microprobe. For experiments performed at log pO₂ = −13, in directions parallel to the c axis and the b axis of two natural, low iron (Fe ∼ 1.8 at %) diopsides, the data obey a single Arrhenius relationship of the form D = 6.22_−5.9 ^+49.6×10⁻¹⁵ exp(−161.5 ± 35.0 kJ mol⁻¹/RT) m² s⁻¹. A single datum for iron diffusion in iron-free, single-crystal diopside at 1050 °C, is approximately 1 order of magnitude slower than in the natural crystals. The pO₂ dependence of iron diffusion in natural crystals at 1050 °C (power exponent = 0.229 ± 0.036) indicates a vacancy mechanism; this is consistent with the results of unpublished atomistic simulation studies. There is no evidence of anisotropy for iron diffusion in diopside. Received: 16 March 1999 / Accepted: 10 April 2000     

H2O activity in concentrated KCl and KCl-NaCl solutions at high temperatures and pressures measured by the brucite-periclase equilibrium

H₂O activities in supercritical fluids in the system KCl-H₂O-(MgO) were measured at pressures of 1, 2, 4, 7, 10 and 15  kbar by numerous reversals of vapor compositions in equilibrium with brucite and periclase. Measurements spanned the range 550–900 °C. A change of state of solute KCl occurs as pressures increase above 2 kbar, by which H₂O activity becomes very low and, at pressures of 4 kbar and above, nearly coincident with the square of the mole fraction (x _H2O). The effect undoubtedly results primarily from ionic dissociation as H₂O density (ρ_H2O) approaches 1 gm/cm³, and is more pronounced than in the NaCl-H₂O system at the same P-T-X conditions. Six values of solute KCl activity were yielded by terminal points of the isobaric brucite-periclase T-x _H2O curves where sylvite saturation occurs. The H₂O mole fraction of the isobaric invariant assemblage brucite-periclase-sylvite-fluid is near 0.52 at all pressures, and the corresponding temperatures span only 100 °C between 1 and 15 kbar. This remarkable convergence of the isobaric equilibrium curves reflects the great influence of pressure on lowering of both KCl and H₂O activities. The H₂O and KCl activities can be expressed by the formulas: a _H2O = γ_H2O[x _H2O+(1 + (1 + α)x _KCl)], and a _KCL = γ_KCl[(1 + α)x _KCl/(x _H2O +(1 + α)x _KCl)]^(1 + α), where α is a degree of dissociation parameter which increases from zero at the lowest pressures to near one at high pressures and the γ's are activity coefficients based on an empirical regular solution parameter W: ln γ_i = (1 − x_i)²W. Least squares fitting of our H₂O and KCl activity data evaluates the parameters: α = exp(4.166 −2.709/ρ_H2O) − 212.1P/T, and W = (−589.6 − 23.10P) /T, with ρ_H2O in gm/cm³, P in kbar and T in K. The standard deviation from the measured activities is only ± 0.014. The equations define isobaric liquidus curves, which are in perfect agreement with previous DTA liquidus measurements at 0.5–2 kbar, but which depart progressively from their extrapolation to higher pressures because of the pressure-induced dissociation effect. The great similarity of the NaCl-H₂O and KCl-H₂O systems suggests that H₂O activities in the ternary NaCl-KCl-H₂O system can be described with reasonable accuracy by assuming proportionality between the binary systems. This assumption was verified by a few reconnaissance measurements at 10 kbar of the brucite-periclase equilibrium with a Na/(Na + K) ratio of 0.5 and of the saturation temperature for Na/(Na + K) of 0.35 and 0.50. At that pressure the brucite-periclase curves reach a lowest x _H2O of 0.45 and a temperature of 587 °C before salt saturation occurs, values considerably lower than in either binary. This double-salt eutectic effect may have a significant application to natural polyionic hypersaline solutions in the deep crust and upper mantle in that higher solute concentrations and very low H₂O activities may be realized in complex solutions before salt saturation occurs. Concentrated salt solutions seem, from this standpoint, and also because of high mechanical mobility and alkali-exchanging potential, feasible as metasomatic fluids for a variety of deep-crust and upper mantle processes. Received: 9 August 1996 / Accepted: 15 November 1996