Transport properties of high albite crystals,near-endmember feldspar and pyroxene glasses,and their melts to high temperature

Thermal diffusivity (D) was measured using laser-flash analysis (LFA) from oriented single-crystal albite and glasses near LiAlSi₃O₈, NaAlSi₃O₈, CaAl₂Si₂O₈, LiAlSi₂O₆ and CaMgSi₂O₆ compositions. Viscosity measurements of the supercooled liquids, over 2.6 × 10⁸ to 8.9 × 10¹² Pa s, confirm strongly non-Arrhenian behavior for CaAl₂Si₂O₈, and CaMgSi₂O₆, and near-Arrhenian behavior for the others. As T increases, D _glass decreases, approaching a constant near 1,000 K. Upon crossing the glass transition, D decreases rapidly. For feldspars, D for the melt is ~15% below D of the bulk crystal, whereas for pyroxenes, this difference is ~40%. Thermal conductivity (k _lat = ρC _P D) of crystals decreases with increasing T, but k _lat of glasses increases with T because heat capacity (C _P ) increases with T more strongly than density (ρ) and D decrease. For feldspars, k _lat for the melt is ~10% below that of the bulk crystal or glass, whereas this decrease for pyroxene is ~50%. Therefore, melting substantially impedes heat transport, providing positive thermal feedback that could promote further melting.     

The study of the kinetics and the mechanism of dehydroxylation in muscovite by ESR on Fe3+

 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     

Thermal diffusivity of garnets at high temperature

Thermal diffusivity (D) of garnets with diverse chemical compositions was measured using the laser-flash technique, which is accurate (±2%) and isolates the lattice component from direct radiative transfer. Temperatures ranged from ~290 to ~1,600 K (unless limited by melting). Seven synthetic (e.g., YAG, GGG) and 15 natural garnets with two types of ionic substitution [Ca₃(Fe,Al)₂Si₃O₁₂ and (Mg,Fe,Ca)₃Al₂Si₃O₁₂] and varying amounts of OH^- were examined. Cation substitution or hydroxyl incorporation lowers D from end-member values. Thermal diffusivity is constant once the temperature (T) exceeds a critical value (T _sat) of ~1,100 to 1,500 K. From ~290 K to T _sat, the measurements are best represented by 1/D=A+BT+CT ² where A, B, and C are constants. These constants vary little among diverse chemical compositions, suggesting that the oxygen sublattice controls heat transport. Higher order terms are needed only when T _sat is low, such as Ant Hill garnet wherein 1/D=0.049403+0.0032299T−2.3992T ²×10⁻⁶+6.0168T ³×10⁻¹⁰(1/D in s/mm²; T in K). The mean free path (λ, computed from D and sound velocities) is slightly larger than the lattice parameter above T _sat, in accord with phonon–phonon interactions requiring non-localized modes. At most temperatures, λ is nm-sized. Large values of λ are obtained by extrapolation to a few Kelvins, suggesting that boundary scattering can only be important at extremely cold temperatures. The observed behavior with T and chemical composition is consistent with the damped harmonic oscillator model. Phonon transport is best represented by inverse thermal diffusivity wherein 1/D goes as T ⁿ where n is between 1 and 3 up to ~200 K, depends on a quadratic or cubic polynomial at moderate T, but is constant above T _sat. The predicted and observed temperature response of 1/D mimics the well-known form for heat capacity, in that acoustic modes control heat transport near cryogenic temperatures, optic phonons dominate above ambient temperature, and a limit analogous to that of Dulong and Petit is reached at very high temperature, due to full population of discrete phonon states.     

Viscoelastic behaviour of mica-based glass-ceramic aggregate

The present study deals with the small strain torsion deformation of MACOR glass-ceramic samples at high temperatures (450–850 °C) and over a range of low frequencies (20 Hz–5 mHz). The samples of MACOR ceramic consist of 55 vol% randomly oriented, sheet-like fluorophlogopite mica crystals (∼100–20 μm in planar size, 1–2 μm in thickness) and 45 vol% of isotropic alumino-borosilicate glass matrix. Measurements of the complex shear modulus show that the sample does not possess the relaxed shear viscosity even at temperatures above the glass transition temperature of the glass matrix. The maximum of the imaginary component G ^′′() of the shear modulus is ∼0.15 of the unrelaxed value G _∞, the relaxation strength Δ≈0.9. The activation energy of the peak of G ^′′() is ∼245 kJ mol⁻¹. Using this value of E _a , the data obtained at various frequencies and temperatures have been reduced to a master curve using the dimensionless variable ωτ, where ∼₀ exp(−E _a /RT). The internal friction Q⁻¹(ωτ) is ∝1/()^0.35−0.4 in the low-temperature high-frequency range (1); passes through a maximum at ∼1 and trends asymptotically to a value Q⁻¹∼0.25–0.30 at ≪1. The behaviour of Q ⁻¹(ωτ) differs from that of a Caputo body by the presence of the resolved peak which may be attributed to the slow mechanical relaxation of mica crystals due to rotation as well as flexing and bending modes of crystal deformation. Received: 26 June 1998 / Revised, accepted: 13 January 1999     

An SF<Subscript>6</Subscript> Tracer Study of the Flow Dynamics in the Stockton Deep Water Ship Channel: Implications for Dissolved Oxygen Dynamics

A sulfur hexafluoride (SF₆) tracer release experiment was conducted in the Stockton Deep Water Ship Channel (DWSC) to quantify mixing and transport rates. SF₆ was injected in the San Joaquin River upstream of the DWSC and mapped for 8 days. From the temporal change in SF₆ distributions, the longitudinal dispersion coefficient (K _x ) was determined to be 32.7 ± 3.6 m² s⁻¹ and the net velocity was 1.75 ± 0.03 km day⁻¹. Based on the decrease in SF₆ inventory during the experiment, the pulsed residence time for waters in the DWSC was estimated at ∼17 days. Within the DWSC from Stockton downstream to Turner Cut, dissolved oxygen concentrations maintained a steady state value of 4 mg l⁻¹. These values are below water quality objectives for the time of year. The low flow rates observed in the DWSC and the inability of oxygen-rich waters from downstream to mix into the DWSC upstream of Turner Cut contribute to the low dissolved oxygen concentration.     

Interaction of Freshly Precipitated Silica Gel with Aqueous Silicic Acid Solutions under Ambient and Near Neutral pH-conditions: A Detailed Analysis of Linear Rate Law

Interaction of freshly precipitated silica gel with aqueous solutions was studied at laboratory batch experiments under ambient and near neutral pH-conditions. The overall process showed excellent reversibility: gel growth could be considered as an opposite process to dissolution and a linear rate law could be applied to experimental data. Depending on the used rate law form, the resulting rate constants were sensitive to errors in parameters/variables such as gel surface area, equilibrium constants, Si-fluxes, and reaction quotients. The application of an Integrated Exponential Model appeared to be the best approach for dissolution data evaluation. It yielded the rate constants k _dissol ∼ (4.50 ± 0.68) × 10⁻¹² and k _growth ∼ (2.58 ± 0.39) × 10⁻⁹ mol m⁻² s⁻¹ for zero ionic strength. In contrast, a Differential Model gave best results for growth data modeling. It yielded the rate constants k _dissol ∼ (1.14 ± 0.44) × 10⁻¹¹ and k _growth ∼ (6.08 ± 2.37) × 10⁻⁹ mol m⁻² s⁻¹ for higher ionic strength (I ∼ 0.04 to 0.11 mol L⁻¹). The found silica gel solubility at zero ionic strength was somewhat lower than the generally accepted value. Based on the and standard Gibbs free energy of silica gel formation was calculated as and −850,318 ± 20 J mol⁻¹, respectively. Activation energies for silica gel dissolution and growth were determined as and respectively. An universal value for growth of any silica polymorph, is not consistent with the value for silica gel growth, which questions the hypothesis about one unique activated complex controlling the silica polymorph growth.     

Si diffusion in zircon

Self-diffusion of Si under anhydrous conditions at 1 atm has been measured in natural zircon. The source of diffusant for experiments was a mixture of ZrO₂ and ³⁰Si-enriched SiO₂ in 1:1 molar proportions; experiments were run in crimped Pt capsules in 1-atm furnaces. ³⁰Si profiles were measured with both Rutherford backscattering spectrometry (RBS) and nuclear reaction analysis with the resonant nuclear reaction ³⁰Si(p,γ)³¹P. For Si diffusion normal to c over the temperature range 1,350–1,550°C, we obtain an Arrhenius relation D = 5.8 exp(−702 ± 54 kJ mol⁻¹/RT) m² s⁻¹ for the NRA measurements, which agrees within uncertainty with an Arrhenius relation determined from the RBS measurements [62 exp(−738 ± 61 kJ mol⁻¹/RT) m² s⁻¹]. Diffusion of Si parallel to c appears slightly faster, but agrees within experimental uncertainty at most temperatures with diffusivities for Si normal to c. Diffusion of Si in zircon is similar to that of Ti, but about an order of magnitude faster than diffusion of Hf and two orders of magnitude faster than diffusion of U and Th. Si diffusion is, however, many orders of magnitude slower than oxygen diffusion under both dry and hydrothermal conditions, with the difference increasing with decreasing temperature because of the larger activation energy for Si diffusion. If we consider Hf as a proxy for Zr, given its similar charge and size, we can rank the diffusivities of the major constituents in zircon as follows: D _Zr < D _Si << D _{O, dry} < D _{O, ‘wet’}.     

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     

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     

Diffusion of tetravalent cations in zircon

Diffusion rates for the three tetravalent cations U, Th and Hf have been measured in synthetic zircon. Diffusant sources included oxide powders and ground pre-synthesized silicates. Rutherford backscattering spectrometry (RBS) was used to measure depth profiles. Over the temperature range 1400–1650 °C, the following Arrhenius relations were obtained (diffusion coefficients in m²sec⁻¹): log D _Th = (1.936 ± 0.9820) + (− 792 ± 34 kJ mol⁻¹ /2.303 RT) log D _U = (0.212 ± 2.440) + (− 726 ± 83 kJ mol⁻¹ /2.303 RT) log D _Hf = (3.206 ± 1.592) + (− 812 ± 54 kJ mol⁻¹ /2.303 RT) The data show a systematic increase in diffusivity with decreasing ionic radius (i.e., faster diffusion rates for Hf than for U or Th), a trend also observed in our earlier study of rare earth diffusion in zircon. Diffusive fractionation may be a factor in the Lu-Hf system given the much slower diffusion rates of tetravalent cations when compared with the trivalent rare earths. The very slow diffusion rates measured for these tetravalent cations suggest that they are essentially immobile under most geologic conditions, permitting the preservation of fine-scale chemical zoning and isotopic signatures of inherited cores. Received: 12 July 1996 / Accepted: 2 December 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=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 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 .     

Trace element partitioning between orthopyroxene and anhydrous silicate melt on the lherzolite solidus from 1.1 to 3.2 GPa and 1,230 to 1,535°C in the model system Na<Subscript>2</Subscript>O–CaO–MgO–Al<Subscript>2</Subscript>O<Subscript>3</Subscript>–SiO<Subscript>2</Subscript>

We determined experimentally the Nernst distribution coefficient between orthopyroxene and anhydrous silicate melt for trace elements i in the system Na₂O–CaO–MgO–Al₂O₃–SiO₂ (NCMAS) along the dry model lherzolite solidus from 1.1 GPa/1,230°C up to 3.2 GPa/1,535°C in a piston cylinder apparatus. Major and trace element composition of melt and orthopyroxene were determined with a combination of electron microprobe and ion probe analyses. We provide partitioning data for trace elements Li, Be, B, K, Sc, Ti, V, Cr, Co, Ni, Rb, Sr, Y, Zr, Nb, Cs, Ba, La, Ce, Sm, Nd, Yb, Lu, Hf, Ta, Pb, U, and Th. The melts were chosen to be boninitic at 1.1 and 2.0 GPa, picritic at 2.3 GPa and komatiitic at 2.7 and 3.2 GPa. Orthopyroxene is Tschermakitic with 8 mol% Mg-Tschermaks MgAl[AlSiO₆] at 1.1 GPa while at higher pressure it has 18–20 mol%. The rare earth elements show a continuous, significant increase in compatibility with decreasing ionic radius from D _La^opx−melt ∼ 0.0008 to D _Lu^opx−melt ∼ 0.15. For the high-field-strength elements compatibility increases from D _Th^opx−melt ∼ 0.001 through D _Nb^opx−melt ∼ 0.0015, D _U^opx−melt ∼ 0.002, D _Ta^opx−melt ∼ 0.005, D _Zr^opx−melt ∼ 0.02 and D _Hf^opx−melt ∼ 0.04 to D _Ti^opx−melt ∼ 0.14. From mathematical and graphical fits we determined best-fit values for D ₀^M1, D ₀^M2, r ₀^M1, r ₀^M2, E ₀^M1, and E ₀^M2 for the two different M sites in orthopyroxene according to the lattice strain model and calculated the intracrystalline distribution between M1 and M2. Our data indicate extreme intracrystalline fractionation for most elements in orthopyroxene; for the divalent cations D _i ^M2−M1 varies by three orders of magnitude between D _Co^M2−M1 = 0.00098–0.00919 and D _Ba^M2−M1 = 2.3–28. Trivalent cations Al and Cr almost exclusively substitute on M1 while the other trivalent cations substitute on M2; D _La^M2−M1 reaches extreme values between 6.5 × 10⁷ and 1.4 × 10¹⁶. Tetravalent cations Ti, Hf, and Zr almost exclusively substitute on M1 while U and Th exclusively substitute on M2. Our new comprehensive data set can be used for polybaric-polythermal melting models along the Earth’s mantle solidus. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Optical spectroscopic study of synthetic NaScSi<Subscript>2</Subscript>O<Subscript>6</Subscript>–CaNiSi<Subscript>2</Subscript>O<Subscript>6</Subscript> pyroxenes at normal and high pressures

Six synthetic NaScSi₂O₆–CaNiSi₂O₆ pyroxenes were studied by optical absorption spectroscopy. Five of them of intermediate (Na_1−x , Ca _x )(Sc_1−x , Ni _x )Si₂O₆ compositions show spectra typical of Ni²⁺ in octahedral coordination, more precise Ni²⁺ at the M1 site of the pyroxene structure. The common feature of all spectra is three broad absorption bands with maxima around 8,000, 13,000 and 24,000 cm⁻¹ assigned to ³ A _2g → ³ T _2g, ³ A _2g → ³ T _1g and →³ T _1g (³ P) electronic spin-allowed transitions of ^VINi²⁺. A weak narrow peak at ∼14,400 cm⁻¹ is assigned to the spin-forbidden ³ A _2g → ¹ T _2g (¹ D) transition of Ni²⁺. Under pressure the spin-allowed bands shift to higher energies and change in intensity. The octahedral compression modulus, calculated from the shift of the ³ A _2g → ³ T _2g band in the (Na_0.7Ca_0.3)(Sc_0.7Ni_0.3)Si₂O₆ pyroxene is evaluated as 85±20 GPa. The Racah parameter B of Ni²⁺(M1) is found gradually changing from ∼919 cm⁻¹ at ambient pressure to ∼890 cm⁻¹ at 6.18 GPa. The Ni end-member pyroxene [(Ca_0.93 Ni_0.07)NiSi₂O₆] has a spectrum different from all others. In addition to the above mentioned bands of Ni²⁺(M1) it displays several new relatively intense and broad extra bands, which were attributed to electronic transitions of Ni²⁺ at the M2 site. In difference to CaO₈ polyhedron geometry of an eightfold coordination, Ni²⁺(M2)O₈ polyhedra are assumed to be relatively large distorted octahedra. Due to different distortions and different compressibilities of the M1 and M2 sites the Ni²⁺(M1)- and Ni²⁺(M2)-bands display rather different pressure-induced behaviors, becoming more resolved in the high-pressure spectra than in that measured at atmospheric pressure. The octahedral compression modulus of Ni²⁺(M1) in this end-member pyroxene is evaluated as 150 ± 25 GPa, which is noticeably larger than in Ni_0.3 pyroxene. This is due to a smaller size and, thus, a stiffer character of Ni²⁺(M1)O₆ octahedron in the (Ca_0.93Ni_0.07)NiSi₂O₆ pyroxene compared to (Na_0.7Ca_0.3)(Sc_0.7Ni_0.3)Si₂O₆.

The cosmic vacuum and the rotation of galaxies

The rotational effect of the cosmic vacuum is investigated. The induced rotation of elliptical galaxies due to the anti-gravity of the vacuum is found to be 10⁻²¹ s⁻¹ for real elliptical galaxies. The effect of the vacuum rotation of the entire Universe is discussed, and can be described by the invariant ω _ν = ω ₀ ∼ $ \sqrt {G\rho v} $ \sqrt {G\rho v} . The corresponding numerical angular velocity of the Universe is 10⁻¹⁹ s⁻¹, in good agreement with modern data on the temperature fluctuations of the cosmic background radiation.     

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     

Comparison of soil organic carbon content,hydraulic conductivity,and particle size fractions between a grassland and a nearby black pine plantation of 40 years in two surface depths

In highlands of semiarid Turkey, ecosystems have been significantly transformed through human actions, and today changes are taking place very rapidly, causing harmful consequences such as soil degradation. This paper examines two neighboring land use types in Indagi Mountain Pass, Cankiri, Turkey, to determine effects of the conversion of Blackpine (Pinus nigra Arn. subsp. pallasiana) plantation from grassland 40 years ago on soil organic carbon (SOC) and soil erodibility (USLE-K). For this purpose, a total of 302 disturbed and undisturbed soil samples were taken at irregular intervals from two sites and from two soil depths of 0–10 cm (D₁) and 10–20 cm (D₂). In terms of SOC, conversion did not make any statistical difference between grassland and plantation; however, there were statistically significant differences with soil depth within each land use, and SOC contents significantly decreased with the soil depth (P < 0.05) and mostly accumulated in D₁. SOC values were 2.4 and 1.8% for grassland and 2.8 and 1.6% for plantation, respectively, at D₁ and D₂. USLE-K values also statistically differed significantly with the land use, and in contrast to the statistics of SOC, there was no change in USLE-K with the soil depth. Since USLE-K was estimated using SOC, hydraulic conductivity (HC) and soil textural composition––sand (S), silt (Si), and clay (C) contents of soils––as well as SOC did not change with the land use, we ascribed the changes of USLE-K with the land uses to the differences in the HC as strongly affected by the interactions between SOC and contents of S, Si, and C. On an average, the soil of the grassland (USLE-K = 0.161 t ha h ha⁻¹ MJ⁻¹ mm⁻¹) was more erodible than those of the plantation (USLE-K = 0.126 t ha h ha⁻¹ MJ⁻¹ mm⁻¹). Additionally, topographic factors, such as aspect and slope, were statistically effective on spatial distribution of the USLE-K and SOC.     

Heat capacities of Tschermak substituted Fe-biotite

Six members of the annite–siderophyllite join were synthesized in a three step process – crystallization of biotite from gels, decomposition of the fine-grained biotite under oxidizing conditions and resynthesis of Fe-Al biotite with planned compositions from these products – producing biotite crystals with thicknesses of up to 10 μm. The biotite was characterized by microprobe, electron microscopy and X-ray diffraction. Heat capacities of these biotites were measured with a DSC (differential scanning calorimeter) over the temperature range 143 to 623 K. Using a least-squares technique, the data were fitted to a c_p-polynomial, c _p =k ₀+k ₁ T ^−0.5+ k ₂ T ⁻²+k ₃ T ⁻³. In the temperature range 143 to 250 K, heat capacities of the different annite–siderophyllite members decrease linearly with increasing Al content. At higher temperatures, however, the c_p-polynomial of biotites with intermediate composition (except Ann₇₉Sid₂₁) exhibit a steeper slope than those of other biotites. This produces positive excess heat capacities in the annite–siderophyllite join at higher temperatures. The activity-composition data of the same binary derived from phase equilibrium experiments (Benisek et al. 1996) and the data of this study suggest two compositional regions along this join, with different extent of deviation from ideality. One at X _Sid < 0.3, characterized by a small deviation, one at X _Sid > 0.3 showing a higher nonideality, resulting in a discontinuity visible at this composition. Powder IR-spectra of these solid solutions were measured with a FTIR-spectrometer and used to calculate heat capacities according to the vibrational model of Kieffer (1979). The comparison of the vibrational function with the c_p-polynomials shows that the vibrational function reproduces well the DSC-data of the siderophyllite-poor and -rich members, but deviates for intermediate compositions, where the excess heats of mixing occur. With increasing Tschermak vector, the tetrahedral rotation angle α increases from 0 to 13° for annite to siderophyllite, respectively. At the composition of the discontinuity, this rotation angle α reaches a value of ∼8^∘. The processing of ∼300 chemical data of natural biotites indicates that over 90% of them have a tetrahedral rotation angle that lies between 7 and 9°. It would appear that biotites with these structural characteristics are most stable. Received: 27 August 1998 / Accepted: 10 November 1998     

HTP21/c–C2/c phase transition and kinetics of Fe2+–Mg order–disorder of an Fe-poor pigeonite: implications for the cooling history of ureilites

A natural Ca-poor pigeonite (Wo₆En₇₆Fs₁₈) from the ureilite meteorite sample PCA82506-3, free of exsolved augite, was studied by in situ high-temperature single-crystal X-ray diffraction. The sample, monoclinic P2₁/c, was annealed up to 1,093°C to induce a phase transition from P2₁/c to C2/c symmetry. The variation with increasing temperature of the lattice parameters and of the intensity of the b-type reflections (h + k = 2n + 1, present only in the P2₁/c phase) showed a displacive phase transition P2₁/c to C2/c at a transition temperature T _Tr = 944°C, first order in character. The Fe–Mg exchange kinetics was studied by ex situ single-crystal X-ray diffraction in a range of temperatures between the closure temperature of the Fe–Mg exchange reaction and the transition temperature. Isothermal disordering annealing experiments, using the IW buffer, were performed on three crystals at 790, 840 and 865°C. Linear regression of ln k _D versus 1/T yielded the following equation: ln k_\textD = - 3717( ±416)/T(K) + 1.290( ±0.378);    (R² = 0.988) \ln \,k_{\text{D}} = - 3717( \pm 416)/T(K) + 1.290( \pm 0.378);\quad (R^{2} = 0.988) . The closure temperature (T _c) calculated using this equation was ∼740(±30)°C. Analysis of the kinetic data carried out taking into account the e.s.d.'s of the atomic fractions used to define the Fe–Mg degree of order, performed according to Mueller’s model, allowed us to retrieve the disordering rate constants C ₀ K _dis⁺ for all three temperatures yielding the following Arrhenius relation: ln( C₀ K_\textdis ⁺ ) = ln K₀ - Q/(RT) = 20.99( ±3.74) - 26406( ±4165)/T(K);    (R² = 0.988) \ln \left( {C_{0} K_{\text{dis}}^{ + } } \right) = \ln \,K_{0} - Q/(RT) = 20.99( \pm 3.74) - 26406( \pm 4165)/T(K);\quad (R^{2} = 0.988) . An activation energy of 52.5(±4) kcal/mol for the Fe–Mg exchange process was obtained. The above relation was used to calculate the following Arrhenius relation modified as a function of X _Fe (in the range of X _Fe = 0.20–0.50): ln( C₀ K_\textdis ⁺ ) = (21.185 - 1.47X_\textFe ) - \frac(27267 - 4170X_\textFe )T(K) \ln \left( {C_{0} K_{\text{dis}}^{ + } } \right) = (21.185 - 1.47X_{\text{Fe}} ) - {\frac{{(27267 - 4170X_{\text{Fe}} )}}{T(K)}} . The cooling time constant, η = 6 × 10⁻¹ K⁻¹ year⁻¹ calculated on the PCA82506-3 sample, provided a cooling rate of the order of 1°C/min consistent with the extremely fast late cooling history of the ureilite parent body after impact excavation.