27Al, 29Si,and 23Na MAS NMR study of an Al,Si ordered alkali feldspar solid solution series

Solid-state ²⁷Al, ²⁹Si and ²³Na MAS NMR spectra have been obtained for an Al,Si ordered low albite to low microcline ion exchange series for which unit-cell parameters and ²⁹Si NMR data have previously been reported. ²⁷Al δ_i vary continuously with composition from 63.4 (±0.5) ppm for albite to 58.9 (±0.5) ppm for microcline, and parallel the ²⁹Si chemical shifts assigned to the T2m-site. The ²⁷Al and ²⁹Si chemical shifts for this series correlate well with composition-dependent lattice parameters, most notably cell volume and the angle [201]¹b. The linewidths of the ²⁹Si and ²⁷Al resonances indicate a significant amount of structural disorder in the intermediate compositions due to Na, K substitution. The 1 σ width of the distribution of average Si-O-T angles for each T-site is estimated to be about 1° for the Or33 sample. The average ²³Na δ_i varies monotonically from -8.5 (±1) ppm for albite to -24.3 (±1)ppm for Or83. Similarly, the average ²³Na nuclear quadrupole coupling constant decreases from 2.60 to 1.15 (±0.05) MHz and the asymmetry parameter of the electric field gradient increases from 0.25 to 0.6 with increasing K-content from albite to Or83. The observed variations in the quadrupole coupling parameters are consistent with simple electrostatic calculations. Higher resolution ²³Na spectra of the intermediate compositions obtained at 11.7 T indicate the presence of an inhomogeneous linebroadening which is related to the distribution of Na-environments. A model based on a random distribution of local compositions does not simulate the spectra, suggesting that the distribution of Na is skewed toward Na-rich clusters. Observation of the ²³Na NMR lineshape of Or49 after short periods of heat treatment indicate that ²³Na NMR is very sensitive to the changes in the Na, K distribution accompanying the early stages of exsolution. Reversible changes occur after heating at 530° C for 3 h, whereas heating at 600° C produces no changes, possibly bracketing the position of the coherent spinodal for Al, Si ordered alkali feldspars at this composition.     

Si,Al ordering in leucite by high-resolution 27Al MAS NMR spectroscopy

High-resolution ²⁷Al MAS NMR spectra of natural leucite recorded at H ₀=11.7T contain three resolvable resonances at ²⁷Al δ _i = 69.2, 64.7, and 61.0±0.5 ppm. These three resonances are assigned to the three inequivalent framework positions of leucite: T3, T2, and T1, respectively. Fitting the observed spectra yields a Si,Al distribution for leucite in which approximately one-half of the Al is in T1 and one-quarter in each of T2 and T3. This Si,Al distribution differs substantially from those obtained by previous workers using ²⁹Si NMR spectroscopy and X-ray diffraction. New ²⁹Si NMR spectra and revision of previously reported ²⁹Si NMR peak assignments, however, make the ²⁷Al and ²⁹Si NMR results consistent. The ²⁷Al δ _i correlate linearly with the mean T-O-T′ bond angles of the average structure, which allows the peak assignments to be made. However, this correlation lies distinctly toward higher frequency and larger bond angles than correlations for Si,Al ordered aluminosilicates, suggesting that the mean T(Al)-O-T′(Si) bond angle for each site in leucite is smaller than the mean bond angle of the average structure, which is averaged over T(Al)-O-T′(Si) and T(Si)-OT′(Si,Al) angles.     

Structural studies of imogolite and allophanes by aluminum-27 and silicon-29 nuclear magnetic resonance spectroscopy

High-resolution aluminum-27 and silicon-29 nuclear magnetic resonance spectra of natural and synthetic imogolites and allophanes obtained using high-field“magic-angle” sample-spinning (MASS) techniques indicate that the imogolite and protoimogolite components of allophanes are characterized by sharp (≈3 ppm) silicon-29 resonances at ?78±1 ppm from tetramethylsilane (in accord with Barron et al. 1982), and quite narrow (≈10 ppm at 11.7 Tesla) aluminum-27 resonances, at 5.2±1 ppm from Al(H₂O) ₆ ³⁺ (in accord with Wilson et al. 1984). However, the spectra of natural allophanes usually contain significant intensity arising from a less well defined material, characterized by a broad (≈20 ppm) silicon-29 resonance centered at ?90±2 ppm from tetramethylsilane, and a second relatively narrow (≈15 ppm at 11.7 Tesla) aluminum-27 resonance at 58.5±2 ppm from Al(H₂O) ₆ ³⁺ . Similar characteristic spectral features are exhibited by a synthetic amorphous Si:Al (1:1) gel, and presumably indicate the presence of framework aluminosilicate materials in the gel, and in most allophanes.     

Thermodynamics and crystal chemistry of the hematite–corundum solid solution and the FeAlO3 phase

High-temperature oxide-melt calorimetry and Rietveld refinement of powder X-ray diffraction patterns were used to investigate the energetics and structure of the hematite–corundum solid solution and ternary phase FeAlO₃ (with FeGaO₃ structure). The mixing enthalpies in the solid solution can be described by a polynomial ΔH_mix=WX _hem(1?X _hem) with W=116 ± 10 kJ mol^?1. The excess mixing enthalpies are too positive to reproduce the experimental phase diagram, and excess entropies in the solid solution should be considered. The hematite–corundum solvus can be approximately reproduced by a symmetric, regular-like solution model with ΔG _excess=(W _H ?TW _S )X _hem X _cor, where W _H= 116 ± 10 kJ mol^?1 and W _S =32 ± 4 J mol^?1 K^?1. In this model, short-range order (SRO) of Fe/Al is neglected because SRO probably becomes important only at intermediate compositions close to Fe:Al=1:1 but these compositions cannot be synthesized. The volume of mixing is positive for Al-hematite but almost ideal for Fe-corundum. Moreover, the degree of deviation from Vegard's law for Al-hematite depends on the history of the samples. Introduction of Al into the hematite structure causes varying distortion of the hexagonal network of oxygen ions while the position of the metal ions remains intact. Distortion of the hexagonal network of oxygen ions attains a minimum at the composition (Fe_0.95Al_0.05)₂O₃. The enthalpy of formation of FeAlO₃ from oxides at 298 K is 27.9 ± 1.8 kJ mol^?1. Its estimated standard entropy (including configurational entropy due to disorder of Fe/Al) is 98.9 J mol^?1 K^?1, giving the standard free energy of formation at 298 K from oxides and elements as +19.1 ± 1.8 and ?1144.2 ± 2.0 kJ mol^?1, respectively. The heat capacity of FeAlO₃ is approximated as C _p (T in K)= 175.8 ? 0.002472T ? (1.958 × 10⁶)/T ²? 917.3/T ^0.5+(7.546 × 10^?6) T ² between 298 and 1550 K, based on differential scanning calorimetric measurements. No ferrous iron was detected in FeAlO₃ by Mössbauer spectroscopy. The ternary phase is entropy stabilized and is predicted to be stable above about 1730 ± 70 K, in good agreement with the experiment. Static lattice calculations show that the LiNbO₃-, FeGaO₃-, FeTiO₃-, and disordered corundum-like FeAlO₃ structures are less stable (in the order in which they are listed) than a mechanical mixture of corundum and hematite. At high temperatures, the FeGaO₃-like structure is favored by its entropy, and its stability field appears on the phase diagram.     

Constraints on the structure and dynamics of the β-cristobalite polymorphs of SiO2 and AlPO4 from 31P, 27Al and 29Si NMR spectroscopy to 770 K

Nuclear magnetic resonance spectroscopic data are presented for the cristobalite polymorphs of AlPO₄ and SiO₂ from RT to 770 K, through their respective α-β transitions. The nuclear magnetic resonance (NMR) data include chemical shifts for ³¹P, ²⁷Al, and ²⁹Si, ²⁷Al quadrupole coupling parameters, and ³¹P and ²⁷Al spin-lattice relaxation rates. Also presented are electron diffraction patterns of β-cristobalite AlPO₄ that show diffuse scattering similar to that reported previously for SiO₂. For the α-phases of both AlPO₄ and SiO₂, the chemical shifts decrease approximately linearly with increasing temperature from RT to T_c and discontinuously by -2 to -3 ppm from α to β. This result is consistent with a small, continuous increase in the mean T-O-T angle (〈θ〉) of the α-phases with increasing T and an increase of 〈θ〉 by about 4° across the α-β transition for both cristobalite and its AlPO₄ analogue. Based on the ²⁹Si chemical shifts, the mean Si-O-Si angle for β-cristobalite is 152.7±1° near T_c. For AlPO₄-cristobalite, the ²⁷Al nuclear quadrupole coupling constant (C_Q) decreases approximately linearly from 1.2 MHz at RT to 0.94 MHz near T_c (493±10 K). At the α-β transition the ²⁷Al C_Q approaches zero, in agreement with the cubic average structure observed by diffraction. The satellite transitions retain a small frequency distribution above the α-β transition from electric field gradients attributed to defects. The short-range cubic symmetry of the Al-site and non-linear Al-O-P angle support a dynamically disordered model of the β-cristobalite structure. Complete averaging of the ²⁷Al quadrupole coupling in the β-phase indicates that the lifetime of any short-range ordered domains must be shorter than about 1 μs.     

δ98/95Mo values and Molybdenum Concentration Data for NIST SRM 610, 612 and 3134: Towards a Common Protocol for Reporting Mo Data

Molybdenum concentration and δ^98/95Mo values for NIST SRM 610 and 612 (solid glass), NIST SRM 3134 (lot 891307; liquid) and IAPSO seawater reference material are presented based on comparative measurements by MC‐ICP‐MS performed in laboratories at the Universities of Bern and Oxford. NIST SRM 3134 and NIST SRM 610 and 612 were found to have identical and homogeneous ⁹⁸Mo/⁹⁵Mo ratios at a test portion mass of 0.02 g. We suggest, therefore, that NIST SRM 3134 should be used as reference for the δ–Mo notation and to employ NIST SRM 610 or 612 as solid silicate secondary measurement standards, in the absence of an isotopically homogeneous solid geological reference material for Mo. The δ^98/95Mo_{JMC Bern} composition (Johnson Matthey ICP standard solution, lot 602332B as reference) of NIST SRM 3134 was 0.25 ± 0.09‰ (2s). Based on five new values, we determined more precisely the mean open ocean δ^98/95Mo_{SRM 3134} value of 2.09 ± 0.07‰, which equals the value of δ^98/95Mo_{JMC Bern} of 2.34 ± 0.07‰. We also refined the Mo concentration data for NIST SRM 610 to 412 ± 9 μg g^?1 (2s) and NIST SRM 612 to 6.4 ± 0.7 μg g^?1 by isotope dilution. We propose these concentration data as new working values, which allow for more accurate in situ Mo determination using laser ablation ICP‐MS or SIMS.     

Bonding and dynamical phenomena in MgO: A high temperature 17O and 25Mg NMR study

We have measured the isotropic chemical shifts (δ_iso) and the spin-lattice relaxation times (T₁) for ¹⁷O and ²⁵Mg in MgO from room temperature up to 1300° C. The ¹⁷O chemical shifts increase linearly from 47 ppm at room temperature to 57 ppm at 1300° C, and over the same temperature range the ²⁵Mg chemical shift increases linearly from 25 to 27 ppm. These changes are not the result of changes in the bulk magnetic susceptibility of the samples, but may be due to increased orbital overlap which is the result of the increase in thermal vibration of the ions with temperature. In the case of ²⁵Mg, the shift to lower shielding with increasing temperature is opposite to that expected from simple bond length versus chemical shift trends established for the oxides at room temperature. If this is a general phenomenon, high-temperature NMR data may be biased to lower shielding. Spin-lattice relaxation times (T₁) were measured in order to study the energetics of defect motion. T₁'s for ¹⁷O and ²⁵Mg exhibit similar behavior over the range of temperatures studied. Up to 800° C, T₁'s decrease gradually, but above 800° C, T₁'s drop rapidly, with slopes corresponding to apparent activation energies of 192±9 kJ/mol (2.0±0.1 eV) for ¹⁷O and 151±6 kJ/mol (1.56±0.06 eV) for ²⁵Mg. While direct comparison of these activation energies to those derived from diffusion or conductivity measurements is complicated, the similar behavior for both nuclei suggests their relaxation phenomena are related.     

Effects of cation substitutions in garnet and pyroxene on equilibrium oxygen isotope fractionations

High-grade metamorphic rocks were used to explore oxygen isotope fractionations between pyroxene and garnet, and to investigate the effects on fractionation factors of the cation substitutions Fe³⁺Al_?1 and Ca(Fe,Mg)_?1. Recrystallized, granulite facies (725 °C) wollastonite ores from the northern Adirondack highlands contain essentially only the minerals clinopyroxene (a Di–Hd solid solution)+garnet (a Grs–Adr solid solution)±wollastonite, and exhibit a systematic dependence of measured fractionations on the Fe³⁺ content of calcic garnet: Δ(Cpx–CaGrt)=(0.14±0.12)+(0.78±0.20)X_Adr and Δ(Wo–CaGrt)=(0.15±0.22)+(0.57±0.33)X_Adr. In eclogites formed at T ≤650 °C, measured compositions of Ca-poor garnet and omphacite combined with experimental data indicate that Ca-poor, Fe-rich garnet is enriched in ¹⁸O compared to both diopside and grossular: extrapolating to 1000 K, Δ(Alm–Di)≈c. 0.2 and Δ(Alm–Grs)≈c. 0.5. Orthopyroxene and clinopyroxene from Gore Mountain, New York, show a constant fractionation that is independent of rock type, as expected if they have the same closure temperature. These data imply Δ(Opx-Cpx)≈c. 0.7 at 1000 K. Measured fractionations among Ca-poor garnet, orthopyroxene, clinopyroxene and hornblende in the Gore Mountain rocks further indicate an ¹⁸O enrichment in Ca-poor garnet over Grs (≈c. 0.5 at 1000 K). The new measurements are indistinguishable from expected equilibrium values based on experiments for the minerals enstatite, diopside, grossular, wollastonite and feldspar, but consistently indicate a significant isotope effect for the simple octahedral cation substitutions Fe³⁺Al_?1 (Grs vs. Adr) and Ca(Fe,Mg)_?1 (Ca-poor garnet vs. Grs; Opx vs. Cpx). Neither cation substitution has been directly investigated for its effect on ¹⁸O/¹⁶O fractionation with experiments in silicates. Chemical characterization of minerals is required prior to petrological interpretation of oxygen isotope trends.     

Partitioning of Fe and Mn between ilmenite and olivine at 1100 °C: constraints on the thermodynamic mixing properties of (Fe, Mn)TiO3 ilmenite solid solutions

The partitioning of Fe²⁺ and Mn²⁺ between (Fe, Mn)TiO₃ and (Fe, Mn)₂SiO₄ solid solutions in the system FeO-MnO-TiO₂-SiO₂ has been experimentally investigated at 1100 ^∘C and pressures of 1 bar and 25 kbar, over a wide range of Fe/Mn ratios, using electron microprobe analysis of quenched run products. The ilmenite solid solution in this system is within analytical uncertainty a simple binary between FeTiO₃ and MnTiO₃, but the olivine solid solution appears to contain up to 2.5 wt% TiO₂. The Fe-Mn partitioning results constrain precisely the difference in the thermodynamic mixing properties of the two solid solutions. If the mixing properties of (Fe, Mn)₂SiO₄ solid solutions are assumed to be ideal, as experimentally determined by Schwerdtfeger and Muan (1966), then the ilmenite is a regular, symmetric solution with W ^ilm _Fe-Mn=1.8±0.1 kJ mol⁻¹. The quoted uncertainty does not include the contribution from the uncertainty in the mixing properties of the olivine solution, which is estimated to be ±1.8 kJ mol⁻¹, and which therefore dominates the uncertainty in the present results. Nevertheless, this result is in good agreement with the previous experimental study of O'Neill et al. (1989), who obtained W ^ilm _Fe-Mn=2.2±0.3 kJ mol⁻¹ from an independent method. The results provide another item of empirical evidence supporting the proposition that solid solutions between isostructural end-members, in which order-disorder effects are not important, generally have simple thermodynamic mixing properties, with little asymmetry, modest excess entropies, and excess enthalpies approximately proportional to the difference in the molar volumes of the end-members. Received: 11 February 1998 / Accepted: 29 June 1998     

Cr and Al diffusion in chromite spinel: experimental determination and its implication for diffusion creep

Diffusion coefficients of Cr and Al in chromite spinel have been determined at pressures ranging from 3 to 7 GPa and temperatures ranging from 1,400 to 1,700°C by using the diffusion couple of natural single crystals of MgAl₂O₄ spinel and chromite. The interdiffusion coefficient of Cr–Al as a function of Cr# (=Cr/(Cr + Al)) was determined as D _Cr–Al = D ₀ exp {−(Q′ + PV*)/RT}, where D ₀ = exp{(10.3 ± 0.08) × Cr#^0.54±0.02} + (1170 ± 31.2) cm²/s, Q′ = 520 ± 81 kJ/mol at 3 GPa, and V* = 1.36 ± 0.25 cm³/mol at 1,600°C, which is applicable up to Cr# = 0.8. The estimation of the self-diffusion coefficients of Cr and Al from Cr–Al interdiffusion shows that the diffusivity of Cr is more than one order of magnitude smaller than that of Al. These results are in agreement with patterns of multipolar Cr–Al zoning observed in natural chromite spinel samples deformed by diffusion creep.     

29Si and 27Al magic-angle-spinning NMR studies of the thermal transformation of kaolinite

Thermal transformations of kaolinite of different degree of crystallinity have been monitored by ²⁷Al and ²⁹Si high-resolution NMR with magic-angle spinning (MAS NMR), X-ray diffraction, Fourier transform infrared, atomic absorption spectrophotometry and thermogravimetric analysis. NMR shows differences in the dehydroxylation process of kaolinites with different degree of crystallinity and reveals the presence of short-range order in metakaolinite. ²⁹Si NMR spectra acquired with a 30 s recycle delay of poorly and highly crystalline samples heated at 480 and 500° C, respectively, contain three distinct signals; we discuss their assignment in the light of experiments involving leaching of the samples with aqueous KOH. Ca. 40% of Si sites retain their original Q ³ symmetry just above the onset of dehydroxylation and the Q ⁴ environment is present showing that a small amount of amorphous silica has already segregated. The spectrum of samples treated at 1000° C contains a signal at -110ppm (from Q ⁴ silicons) and a faint resonance, from mullite, at ca. -87 ppm. ²⁹Si NMR also shows that cristobalite germs are already present at 950–1000° C. The ²⁷Al MAS NMR spectra of metakaolinite reveal the presence of 4-, 5-and 6-coordinated Al. Changes in the three Al populations as a function of temperature have been monitored quantitatively. Below 800° C, 4-and 5-coordinated Al appears at the expense of 6-coordinated Al, but above 800° C the amount of 6-coordinated Al increases again. We suggest a dehydroxylation scheme which accounts for the presence of 4-and 5 coordinated Al. Above 900–950° C the latter signal is no longer present in the ²⁷Al NMR spectra and new 4-and 6-coordinated Al species (mullite and γ-alumina) appear. We propose new ideas for the structure of metakaolinite.     

Thermodynamic mixing behavior of synthetic Ca-Tschermak–diopside pyroxene solid solutions: II. Heat of mixing and activity–composition relationships

The heat of mixing for the binary solid solution diopside–Ca-Tschermak was investigated at T = 980 K by lead borate solution calorimetry. A new statistical technique was applied to overcome the problem of using experimental data of various precisions. A two-parameter Margules model was fitted to the calorimetric data leading to W _CaTs–Di^H = 31.3 ± 3.4 kJ mol⁻¹ and W ^H _Di–CaTs = 2.4 ± 4.3 kJ mol⁻¹. The results are in good agreement with calorimetric data given in the literature. They agree also with enthalpy data that were extracted from phase equilibrium experiments. With configurational entropy values taken from the literature, the volume and the vibrational entropy, presented in Part I of this work, and the enthalpy data of this study, the activity–composition relationships of the diopside–Ca-Tschermak binary were calculated.     

Electron Probe Microanalysis of Bromine in Minerals and Glasses with Correction for Spectral Interference from Aluminium,and Comparison with Microbeam Synchrotron X‐Ray Fluorescence Spectrometry

The strong spectral interference between Br‐ and Al‐induced X‐ray lines hampers the utilisation of electron probe microanalysis (EPMA) for measuring Br mass fractions in Al‐bearing minerals and glasses. Through measuring Br‐free Al‐bearing materials, we established an EPMA method to quantify the overlap from AlKα on BrLβ, which can be expressed as a linear function of the Al₂O₃ content. The count rate of the BrLβ peak signal was enhanced by high beam currents and long measurement times. Application of this EPMA method to Al‐ and Br‐bearing materials, such as sodalite and scapolite, and to five experimental glasses yielded Br mass fractions (in the range of 250–4000 μg g^?1) that are consistent with those measured by microbeam synchrotron X‐ray fluorescence (μ‐SXRF) spectrometry. The EPMA method has an estimated detection limit of ~ 100–300 μg g^?1. We propose that this method is useful for measuring Br mass fractions (hundreds to thousands of μg g^?1) in Al‐bearing minerals and glasses, including those produced in Br‐doped experiments. In addition, the natural marialitic scapolite (ON70) from Mpwapwa (Tanzania) containing homogeneously distributed high mass fractions of Br (2058 ± 56 μg g^?1) and Cl (1.98 ± 0.03% m/m) is an ideal reference material for future in situ analyses.     

Growth of multilayered polycrystalline reaction rims in the MgO–SiO<Subscript>2</Subscript> system,part II: modelling

Part I of this contribution (Gardés et al. in Contrib Mineral Petrol, 2010) reported time- and temperature-dependent experimental growth of polycrystalline forsterite-enstatite double layers between single crystals of periclase and quartz, and enstatite single layers between forsterite and quartz. Both double and single layers displayed growth rates decreasing with time and pronounced grain coarsening. Here, a model is presented for the growth of the layers that couples grain boundary diffusion and grain coarsening to interpret the drop of the growth rates. It results that the growth of the layers is such that (Δx)² ∝ t ^1−1/n , where Δx is the layer thickness and n the grain coarsening exponent, as experimentally observed. It is shown that component transport occurs mainly by grain boundary diffusion and that the contribution of volume diffusion is negligible. Assuming a value of 1 nm for the effective grain boundary width, the following Arrhenius laws for MgO grain boundary diffusion are derived: log D _gb,0^Fo (m²/s) = −2.71 ± 1.03 and E _gb^Fo = 329 ± 30 kJ/mol in forsterite and log D _gb,0^En (m²/s) = 0.13 ± 1.31 and E _gb^En = 417 ± 38 kJ/mol in enstatite. The different activation energies are responsible for the changes in the enstatite/forsterite thickness ratio with varying temperature. We show that significant biases are introduced if grain boundary diffusion-controlled rim growth is modelled assuming constant bulk diffusivities so that differences in activation energies of more than 100 kJ/mol may arise. It is thus important to consider grain coarsening when modelling layered reaction zones because they are usually polycrystalline and controlled by grain boundary transport.     

Structural change and mineralogical transformation mechanism of aluminum hydroxide gels from forced hydrolysis Al（Ⅲ） solutions containing AlO4Al12（OH）24（H2O）12^7＋ polyoxycation during aging

The structural change and mineralogy of Al gel during aging time were investigated by using spectroscopy techniques. The results indicated that: 1) the aggregation extent of solution-gel system increases with aging time, and the structure of amorphous gel becomes more short-ordered; 2) after six months, the gel formats nordstrandite and little gibbsite; 3) a marked decrease in the number of (Al-OH)_oh bands occurring at 610 cm⁻¹ and increase in the number of (Al-OH₂)_oh bands occurring at 555 cm⁻¹ indicate that the gel undergoes rearrangement-like process during aging; 4) the gel constantly contains Al-O tetrahedron of Keggin structure, but the signal peak occurring at ≈61×10⁻⁶ of ²⁷Al MAS NMR have a slight shift to downfield with aging time. A mineralogical transformation mechanism for hydrolysis Al(III) solution was proposed.     

Low-temperature thermodynamic properties of disordered zeolites of the natrolite group

 The heat capacity of paranatrolite and tetranatrolite with a disordered distribution of Al and Si atoms has been measured in the temperature range of 6–309 K using the adiabatic calorimetry technique. The composition of the samples is represented with the formula (Na_1.90K_0.22Ca_0.06)[Al_2.24Si_2.76O₁₀]·nH₂O, where n=3.10 for paranatrolite and n=2.31 for tetranatrolite. For both zeolites, thermodynamic functions (vibrational entropy, enthalpy, and free energy function) have been calculated. At T=298.15 K, the values of the heat capacity and entropy are 425.1 ± 0.8 and 419.1 ±0.8 J K⁻¹ mol⁻¹ for paranatrolite and 381.0 ± 0.7 and 383.2 ± 0.7 J K⁻¹ mol⁻¹ for tetranatrolite. Thermodynamic functions for tetranatrolite and paranatrolite with compositions corrected for the amount of extraframework cations and water molecules have also been calculated. The calculation for tetranatrolite with two water molecules and two extraframework cations per formula yields: C _p (298.15)=359.1 J K⁻¹ mol⁻¹, S(298.15) −S(0)=362.8 J K⁻¹ mol⁻¹. Comparing these values with the literature data for the (Al,Si)-ordered natrolite, we can conclude that the order in tetrahedral atoms does not affect the heat capacity. The analysis of derivatives dC/dT for natrolite, paranatrolite, and tetranatrolite has indicated that the water- cations subsystem within the highly hydrated zeolite may become unstable at temperatures above 200 K. Received: 30 July 2001 / Accepted: 15 November 2001     

Internally consistent recalibrations of mineral equilibria for geothermobarometry involving garnet–orthopyroxene–plagioclase–quartz assemblages and their application to the South Indian granulites

Abstract Three reactions are calibrated as geothermobarometers for garnet–orthopyroxene–plagioclase–quartz assemblages, namely: 1/2 ferrosilite + 1/3 pyrope ± 1/2 enstatite + 1/3 almandine (A): ferrosilite + anorthite ± 2/3 almandine + 1/3 grossularite + quartz (B); and enstatite + anorthite ± 2/3 pyrope + 1/3 grossularite + quartz (C). The internally consistent geothermobarometers based on reactions (A), (B) and (C) are calibrated from experimental data only. The thermodynamic parameters of reaction (A) are derived from published experimental data in the FMAS system (n= 104) in the range 700–1400°C and 5–50 kbar, while those for reaction (B) are derived by summation of the existing reversed experimental data of the mineral equilibria: ferrosilite ± fayalite + quartz (D) and anorthite + fayalite ± 2/3 almandine + 1/3 grossularite (E). The retrieved thermodynamic parameters for reactions (A), (B) and (C) are, respectively: (ΔH⁰, cal) -3367 ± 209, -2749 ± 350 and +3985 ± 545; (ΔS⁰, cal K^?1) -1.634 ± 0.163, -8.644 ± 0.298 and -5.376 ± 0.391; and (ΔV⁰_1,298, cal bar^?1) -0.024, -0.60946 and -0.5614. On a one-cation basis, the derived Margules parameters of the ternary Ca–Fe–Mg in garnet are: W_Fe–Mg= -1256 + 1.0 (～0.23) T(K), W_Mg–Fe= 2880 -1.7 (～0.13) T(K), W_Ca–Mg= 4047 (～77) -1.5 T(K), W_Mg–Ca= 1000 (～77) -1.5 T(K), W_Ca–Fe= -723 + 0.332 (～0.02) T(K), W_Fe–Ca= 1090, (cal) and the ternary constant C₁₂₃= -4498 + 1.516 (～0.265) T(K) cal (subregular solution model of non-ideal mixing); and Fe–Mg–Al in orthopyroxene: W_Fe–Mg= 948 (～200) -0.34 (～0.10) T(K), W_Fe–Al= -1950 (～500) and W_Mg–Al= 0 (cal) (regular solution model of non-ideal mixing). The anorthite activity in plagioclase is calculated by the ‘Al-avoidance’model of subregular Ca–Na mixing commonly used for geobarometry based on reactions (B) and (C). When the geothermobarometers are applied to garnet–orthopyroxene–plagioclase–quartz assemblages (n= 45) of wide compositional range from the Precambrian South Indian granulites, temperature ranges of 690–860°C (X= 760 ± 45°C) and pressure ranges of 5–10 kbar were obtained. The P–T values were estimated simultaneously and there is no difference in the pressure calculated from P_Mg (reaction C) and P_Fe (reaction B). In the existing calibrations this difference is 1 kbar or more. Furthermore, there is no compositional dependence of the ln K of the experimental data in the FMAS (n= 104) and the CFMAS (n= 78) systems at different temperatures and the estimated temperatures of the South Indian granulites.     

Water dissolution in albite melts:: Constraints from ab initio NMR calculations

Hartree-Fock and B3LYP NMR calculations were performed at the 6-311+G(2df,p) level on cluster models representing albite glasses using B3LYP/6 to 31G* optimized geometries. Calculation results on several well-known crystalline materials, such as low albite and KHSi₂O_5, were used to check the accuracy of the calculation methods.Calculated ²⁹Si-NMR results on clusters that model protonation of Al-O-Si linkages and the replacement of Na⁺ by H⁺ indicate a major increase in Si-O(H) bond length and a 5 ppm difference in δ_iso for ²⁹Si compared to that for anhydrous albite glass. The calculated δ_iso of ²⁷Al in such linkages agrees with the experimental data, but shows an increase in C_q that cannot be fully diminished by H-bonding to additional water molecules. This protonation model is consistent with both experimental ¹⁷O NMR data and the major peak of ¹H-NMR spectra. It cannot readily explain the existence of the small peak in the experimental ¹H spectra around 1.5 ppm. Production of the depolymerized units Al [Q³]-O-H upon the dissolution of water is not consistent with ²⁷Al, ¹H, or ¹⁷O NMR experimental results. Production of Si [Q³]-O-H is consistent with all of the experimental ¹⁷O and ¹H-NMR data; such units can produce both the major peak at 3.5 ppm and the small peak at 1.5 ppm in ¹H spectra, either with or without hydrogen bonding. This species, however, cannot produce the main features of ²⁹Si spectra.It is concluded that although neither protonation nor the production of Si [Q³]-O-H alone is consistent with the available experimental data, the combination of these two processes is consistent with available experimental NMR data.     

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     

Location and quantitative analysis of OH in coesite

 The incorporation of hydrogen (deuterium) into the coesite structure was investigated at pressures from 3.1 to 7.5 GPa and temperatures of 700, 800, and 1100 °C. Hydrogen could only be incorporated into the coesite structure at pressures greater 5.0 GPa and 1100 °C . No correlation between the concentration of trace elements such as Al and B and the hydrogen content was observed based on ion probe analysis (1335 ± 16 H ppm and 17 ± 1 Al ppm at 7.5 GPa, 1100 °C). The FTIR spectra show three relatively intense bands at 3575, 3516, and 3459 cm⁻¹ (ν₁ to ν₃, respectively) and two very weak bands at 3296 and 3210 cm⁻¹ (ν₄ and ν₅, respectively). The band at 3516 cm⁻¹ is strongly asymmetric and can be resolved into two bands, 3528 (ν_2a) and 3508 (ν_2b) cm⁻¹, with nearly identical areas. Polarized infrared absorption spectra of coesite single-crystal slabs, cut parallel to (0 1 0) and (1 0 0), were collected to locate the OH dipoles in the structure and to calibrate the IR spectroscopy for quantitative analysis of OH in coesite (ɛ _{i ,tot}=190 000 ± 30 000 l mol⁻¹ _H2O cm⁻²). The polarized spectra revealed a strong pleochroism of the OH bands. High-pressure FTIR spectra at pressures up to 8 GPa were performed in a diamond-anvil cell to gain further insight into incorporation mechanism of OH in coesite. The peak positions of the ν₁, ν₂, and ν₃ bands decrease linearly with pressure. The mode Grüneisen parameters for ν₁, ν₂, and ν₃ are −0.074, −0.144 and −0.398, respectively. There is a linear increase of the pressure derivatives with band position which follows the trend proposed by Hofmeister et al. (1999). The full widths at half maximum (FWHM) of the ν₁, ν₂, and ν₃ bands increase from 35, 21, and 28 cm⁻¹ in the spectra at ambient conditions to 71, 68, and 105 in the 8 GPa spectra, respectively. On the basis of these results, a model for the incorporation of hydrogen in coesite was developed: the OH defects are introduced into the structure by the substitution Si^4+(Si2)+4O²⁻= ^[4]□^(Si2) + 4OH⁻, which gives rise to four vibrations, ν₁, ν_2a, ν_2b, and ν₃. Because the OH(D)-bearing samples do contain traces of Al and B, the bands ν₄ and ν₅ may be coupled to Al and/or B substitution. Received: 19 December 2000 / Accepted: 23 April 2001