Local structural heterogeneity,mixing behaviour and saturation effects in the grossular–spessartine solid solution

Local structural heterogeneities in crystals of the binary grossular–spessartine solid solution have been analyzed using powder IR absorption spectroscopy. Wavenumber shifts of the highest energy Si–O stretching mode in spectra collected at room temperature are consistent with variations in Si–O bond length from structural data. They show a smaller positive deviation from linearity across the join than is seen for the grossular–pyrope and grossular–almandine binaries. The effective line widths, corr, of three selected wavenumber regions all deviate positively from linear behaviour. An empirical calibration of this excess spectroscopic property, obtained by comparison with calorimetric enthalpy of mixing data, gives an estimate for the symmetric Margules parameter of W^H_spec = 14.4(7) kJ mol^–1 in H^mix = W^H_specX_GrX_Sp. W^H_spec values derived on the same basis for four aluminosilicate garnet solid solutions analyzed by IR spectroscopy vary with V², where V represents the difference in molar volume between the end members of each binary system. Measurements of lattice parameters and IR spectra were made over a range of temperatures for seven samples with different compositions. Positive excess molar volumes of mixing at low temperature (30 K) may be larger than the excess molar volumes at room temperature. The saturation temperatures of the molar volumes show no correlation with composition, however, in contrast with what had been expected on the basis of data for the grossular–pyrope binary. Saturation temperatures for spectroscopic parameters and lattice parameters of samples with compositions Gr15Sp85 and Gr60Sp40 seem to be outliers in all experiments. It is concluded that the data hint at systematic changes in saturation temperatures across the solid solution, with implications for both the excess entropy of mixing and the excess volume of mixing, but more precise data or further sample characterization are needed to prove that this composition dependence is real in garnet solid solutions.     

Crystal chemistry of tremolite–tschermakite solid solutions

Tremolite–tschermakite solid solutions have been synthesized between 700 and 850 °C and 200 and 2000 MPa. The starting materials were oxide–hydroxide mixtures and an additional 0.1–1.8 molal CaBr₂ solution. The run products were characterized using SEM, HRTEM, EMP, XRD and FTIR. The synthesized Al tremolites formed needles and lath-shaped crystals of up to 300 × 20 μm. HRTEM investigations showed that the majority of the amphiboles were well ordered. The EMP analysis revealed that the Al tremolites were solid solutions in the ternary tremolite–tschermakite–cummingtonite. The highest observed Al content was close to the composition of magnesiohornblende (X_ts=0.54). Different cummingtonite concentrations (X_cum=0.00–0.18) were observed, which generally increased with Al content. Rietveld refinements of the lattice constants showed a linear decrease of the cell parameters a and b with increasing Al content, whereas c and β increased. Small deviations from the linear behaviour were caused by variable amounts of the cummingtonite component. For pure tschermakite lattice parameters of a=9.7438(11) Å, b=17.936(14) Å, c=5.2995(3) Å, β=105.68(9)° and V=891.7 ± 1.4 ų were extrapolated by least-squares regression. Using the a and β lattice parameters for tremolite, tschermakite and cummingtonite, it was possible to derive amphibole compositions using powder XRD. IR spectra of the Al tremolites showed a total of 12 individual bands. The FWHMs of all bands increased with increasing Al content. According to their FWHMs, these bands were grouped into three band systems at 3664–3676 cm^?1 (I), 3633–3664 cm^?1 (II) and 3526–3633 cm^?1 (III). Assuming ^[6]Al substitution at M2 and/or M3 and ^[4]Al at T1, three principal different configurational groups could be assigned as local environments for the proton. I: only Si⁴⁺ at T1 and one or two Al³⁺ at M2 and/or M3_far, II: one Al³⁺ at T1 and one to three Al³⁺ at M2 and/or at M3_far, III: either Al³⁺ on M3_near and/or two Al³⁺ on T1 and additional one to four Al³⁺ at M2. It is assumed that these three configurational groups correspond to the three groups of observed bands. This was quantitativly supported by Monte-Carlo simulations. A model with random distribution at M2 and M3 including Al avoidance at tetrahedral and octahedral sites yielded the best agreement with the spectroscopical results.     

Multistage growth of Fe–Mg–carpholite and Fe–Mg–chloritoid,from field evidence to thermodynamic modelling

We provide new insights into the prograde evolution of HP/LT metasedimentary rocks on the basis of detailed petrologic examination, element-partitioning analysis, and thermodynamic modelling of well-preserved Fe–Mg–carpholite- and Fe–Mg–chloritoid-bearing rocks from the Afyon Zone (Anatolia). We document continuous and discontinuous compositional (ferromagnesian substitution) zoning of carpholite (overall X _Mg = 0.27–0.73) and chloritoid (overall X _Mg = 0.07–0.30), as well as clear equilibrium and disequilibrium (i.e., reaction-related) textures involving carpholite and chloritoid, which consistently account for the consistent enrichment in Mg of both minerals through time, and the progressive replacement of carpholite by chloritoid. Mg/Fe distribution coefficients calculated between carpholite and chloritoid vary widely within samples (2.2–20.0). Among this range, only values of 7–11 correlate with equilibrium textures, in agreement with data from the literature. Equilibrium phase diagrams for metapelitic compositions are calculated using a newly modified thermodynamic dataset, including most recent data for carpholite, chloritoid, chlorite, and white mica, as well as further refinements for Fe–carpholite, and both chloritoid end-members, as required to reproduce accurately petrologic observations (phase relations, experimental constraints, Mg/Fe partitioning). Modelling reveals that Mg/Fe partitioning between carpholite and chloritoid is greatly sensitive to temperature and calls for a future evaluation of possible use as a thermometer. In addition, calculations show significant effective bulk composition changes during prograde metamorphism due to the fractionation of chloritoid formed at the expense of carpholite. We retrieve P–T conditions for several carpholite and chloritoid growth stages (1) during prograde stages using unfractionated, bulk-rock XRF analyses, and (2) at peak conditions using compositions fractionated for chloritoid. The P–T paths reconstructed for the Kütahya and Afyon areas shed light on contrasting temperature conditions for these areas during prograde and peak stages.     

Fe–Mg interdiffusion rates in clinopyroxene: experimental data and implications for Fe–Mg exchange geothermometers

Chemical interdiffusion of Fe–Mg along the c-axis [001] in natural diopside crystals (X _Di = 0.93) was experimentally studied at ambient pressure, at temperatures ranging from 800 to 1,200 °C and oxygen fugacities from 10^?11 to 10^?17 bar. Diffusion couples were prepared by ablating an olivine (X _Fo = 0.3) target to deposit a thin film (20–100 nm) onto a polished surface of a natural, oriented diopside crystal using the pulsed laser deposition technique. After diffusion anneals, compositional depth profiles at the near surface region (~400 nm) were measured using Rutherford backscattering spectroscopy. In the experimental temperature and compositional range, no strong dependence of D ^Fe–Mg on composition of clinopyroxene (Fe/Mg ratio between Di₉₃–Di₆₅) or oxygen fugacity could be detected within the resolution of the study. The lack of fO₂-dependence may be related to the relatively high Al content of the crystals used in this study. Diffusion coefficients, D ^Fe–Mg, can be described by a single Arrhenius relation with $$D^{{{\text{Fe}} - {\text{Mg}}}} = 2. 7 7\pm 4. 2 7\times 10^{ - 7} {\text{exp(}}-3 20. 7\pm 1 6.0{\text{ kJ}}/{\text{mol}}/{\text{RT)m}}^{ 2} /{\text{s}}.$$ D ^Fe–Mg in clinopyroxene appears to be faster than diffusion involving Ca-species (e.g., D ^Ca–Mg) while it is slower than D ^Fe–Mg in other common mafic minerals (spinel, olivine, garnet, and orthopyroxene). As a consequence, diffusion in clinopyroxene may be the rate-limiting process for the freezing of many geothermometers, and compositional zoning in clinopyroxene may preserve records of a higher (compared to that preserved in other coexisting mafic minerals) temperature segment of the thermal history of a rock. In the absence of pervasive recrystallization, clinopyroxene grains will retain compositions from peak temperatures at their cores in most geological and planetary settings where peak temperatures did not exceed ~1,100 °C (e.g., resetting may be expected in slowly cooled mantle rocks, many plutonic mafic rocks, or ultra-high temperature metamorphic rocks).     

The influence on Fe content on Raman spectra and unit cell parameters of magnesite–siderite solid solutions

Characterization of a set of iron–magnesium carbonate mineral samples was done by Raman spectroscopy, X-ray diffraction and electron microprobe. The evolution of unit cell parameters and of the Raman peak positions of the three vibrations modes T, L and 2ν₂ are reported as a function of the Fe content. Fourteen samples spanning the compositional range from FeCO₃ siderite to MgCO₃ magnesite were used for this calibration. Such a calibration provides a non-destructive and rapid method for extracting mineral chemistry, suitable for samples that cannot be moved and need immediate analysis or for samples that cannot be destructed or that are in small quantities.     

Thermochemical study of Mg–Fe chlorites

The thermochemical study of two natural trioctahedral Mg–Fe chlorites—clinochlores was carried out using high-temperature melt solution calorimetry with a Tian–Calvet microcalorimeter. The enthalpies of formation of clinochlores of compositions (Mg_4.9Fe _0.3 ²⁺ Al_0.8)[Si_3.2Al_0.8O₁₀](OH)₈ (–8811 ± 12 kJ/mol) and (Mg_4.3Fe _0.7 ²⁺ Al_1.0)[Si_3.0Al_1.0O₁₀](OH)₈ (–8696 ± 13 kJ/mol) from elements were determined. The values of the standard entropies and the Gibbs energies of formation of the studied natural minerals as well as thermodynamic properties of Mg–Fe chlorites of theoretical composition were estimated.     

Strain and local heterogeneity in the forsterite–fayalite solid solution

Infrared powder-absorption spectra of nine natural and five synthetic olivine samples across the forsterite–fayalite join have been investigated at room temperature in the range 70–1400 cm^–1. Variations of peak positions as a function of Fe content are close to linear for those vibrational bands whose trend could be followed across the solid solution. Line-broadening has been quantified by autocorrelation analysis. Positive deviations from linearity of the line-broadening parameter, _corr, for groups of bands at low energies are consistent with the existence of local elastic strain heterogeneities at intermediate compositions in the solid solution. It also appears that the structure of forsterite is more homogeneous than Fe-rich olivines in relation to local elastic strain effects. Positive deviations from linearity of the line-broadening parameter for the low-energy regions scale linearly with calorimetric data for the enthalpy of mixing. This close correlation between line-broadening in IR spectra and calorimetric enthalpies of mixing has now been observed for four different binary solid solutions, and there is a further, qualitative correlation with bulk modulus.     

Preparation and Characterization of a New Layered Double Hydroxide, Mg–Fe–Ce

正1 Introduction In the present paper,MgCl2·6H2O,FeCl3·6H2O,and CeCl3·6H2O were used as raw materials in the precipitationhydrothermal method to synthesize MgF eC e hydrotalcite.The effects of the Fe:Ce molar ratio on the composition,crystal structure,and thermal stability of hydrotalcite are examined.Energy-dispersive X-ray spectroscopy(EDS),X-     

A Raman spectroscopic study of Fe–Mg olivines

End-member synthetic fayalite and forsterite and a natural solid-solution crystal of composition (Mg_1.80,Fe_0.20)SiO₄ were investigated using Raman spectroscopy. Polarized single-crystal spectra were measured as a function of temperature. In addition, polycrystalline forsterite and fayalite, isotopically enriched in ²⁶Mg and ⁵⁷Fe, respectively, were synthesized and their powder spectra measured. The high-wavenumber modes in olivine consist of internal SiO₄ vibrations that show little variation upon isotopic substitution. This confirms conclusions from previous spectroscopic studies that showed that the internal SiO₄ vibrations have minimal coupling with the lower-wavenumber lattice modes. The lowest wavenumber modes in both forsterite and fayalite shift in energy following isotopic substitution, but with energies less than that which would be associated with pure Mg and Fe translations. The low-wavenumber Raman modes in olivine are best described as lattice modes consisting to a large degree of mixed vibrations of M(2) cation translations and external vibrations of the SiO₄ tetrahedra. The single-crystal spectra of forsterite and Fo₉₀Fa₁₀ were recorded at a number of temperatures from room temperature to about 1200 °C. From these data the microscopic Grüneisen parameters for three different A_g modes for both compositions were calculated, and also the structural state of the solid solution crystal was investigated. Small discontinuities observed in the wavenumber behavior of a low-energy mixed Mg/T(SiO₄) mode between 700 and 1000 °C may be related to minor variations in the Fe–Mg intracrystalline partitioning state in the Fo₉₀Fa₁₀ crystal, but further spectroscopic work is needed to clarify and quantify this issue. The mode wavenumber and intensity behavior of internal SiO₄ vibrations as a function of temperature are discussed in terms of crystal field and dynamic splitting and also ₁ and ₃ coupling. Crystal-field splitting increases only very slightly with temperature, whereas dynamical-field splitting is temperature dependent. The degree of ₁–₃ coupling decreases with increasing temperature.     

Fe–Mg Interdiffusion in (Mg,Fe)O

We have performed a series of interdiffusion experiments on magnesiowüstite samples at room pressure, temperatures from 1,320° to 1,400°C, and oxygen fugacities from 10^?1.0 Pa to 10^?4.3 Pa, using mixed CO/CO₂ or H₂/CO₂ gases. The interdiffusion couples were composed of a single-crystal of MgO lightly pressed against a single-crystal of (Mg_1-x Fe _x )_1-δO with 0.07<x<0.27. The interdiffusion coefficient was calculated using the Boltzmann–Matano analysis as a function of iron content, oxygen fugacity, temperature, and water fugacity. For the entire range of conditions tested and for compositions with 0.01<x<0.27, the interdiffusion coefficient varies as $$\tilde D\, =\,2.9\times10^{ - 6}\,f_{{\text{O}}_2 }^{0.19}\,x^{0.73}\,{\text{e}}^{ - (209,000\, -\,96,000\,x)/RT}\,\,{\text{m}}^{\text{2}} {\text{s}}^{ -1} $$ These dependencies on oxygen fugacity and composition are reasonably consistent with interdiffusion mediated by unassociated cation vacancies. For the limited range of water activity that could be investigated using mixed gases at room pressure, no effect of water on interdiffusion could be observed. The dependence of the interdiffusion coefficient on iron content decreased with increasing iron concentration at constant oxygen fugacity and temperature. There is a close agreement between our activation energy for interdiffusion extrapolated to zero iron content (x=0) and that of previous researchers who used electrical conductivity experiments to determine vacancy diffusivities in lightly doped MgO.     

Natural polycomponent solid solutions of the Ru–Os–Ir–Pt–Fe system from the eastern Witwatersrand (South Africa)

This study presents compositional features of platinum-group element mineralization derived from the Late Archaean placers in the eastern part of the Witwatersrand basin. The significant presence of platinum-group minerals, formed by polycomponent solid-solution series in the system Ru–Os–Ir–Pt(±Fe), was determined using an electron microprobe analysis. Compositional data indicate that the source for polycomponent solid solutions of the Ru–Os–Ir–Pt–Fe system was the Archaean mantle of the Earth, slightly differentiated with respect to platinum-group elements.     

Thermochemical study Mg–Fe amphiboles

The paper presents data on the thermochemical study (high-temperature melt calorimetry in a Tian–Calvet microcalorometer) of two natural Mg–Fe amphiboles: anthophyllite Mg_2.0(Mg_4.8Fe_0.2 ²⁺)[Si_8.0O₂₂](OH)₂ from Kukh-i-Lal, southwestern Pamirs, Tajikistan, and gedrite Na_0.4Mg_2.0(Mg_1.7Fe_0.2 ²⁺Al_1.3)[Si_6.3Al_1.7O₂₂](OH)₂ from the Kola Peninsula, Russia. The enthalpy of formation from elements is obtained as–12021 ± 20 kJ/mol for anthophyllite and as–11545 ± 12 kJ/mol for gedrite. The standard entropy, enthalpy, and Gibbs energy of formation are evaluated for Mg–Fe amphiboles of theoretical composition.     

Thermochemistry of sulfide liquids IV: density measurements and the thermodynamics of O–S–Fe–Ni–Cu liquids at low to moderate pressures

We present the results of a series of density experiments in the system O–S–Fe–Ni–Cu. These experiments were designed to extend our understanding of the physical properties of sulfide liquids, and to extend one-bar thermochemical models for sulfide liquids to apply to low to moderate pressures. Density measurements indicate both positive and negative deviations from linear mixing of partial molar volumes across this five-dimensional composition space. In terms of the homogeneous speciation model of Kress (in Contrib Mineral Petrol 154:191–204, 2007), the best fit to experimental data can be achieved by starting with a model where the volume of formation reaction for associated species initially is set to zero. Further refinement of this first-order fit yields a volume mixing model which reproduces experimental data to within nearly the estimated experimental uncertainty. Experimental ultrasonic and X-ray absorption data from the literature, along with the bulk modulus–volume relation of Anderson and Nafe (J Geophys Res 16:3951–3963, 1965), allow the estimation of the pressure dependence of partial molar volumes for sulfide liquid species. The resulting combined thermochemical model should be valid to about 2,000 K and 3 GPa. Application of this thermochemical model in a simple adiabatic magma ascent scenario confirms earlier work suggesting that the pressure dependence of sulfur solubility in sulfide-saturated magma will decrease with increasing pressure along geologically reasonable paths in P–T–– space.     

Ternary Ca–Fe–Mg carbonates: subsolidus phase relations at 3.5 GPa and a thermodynamic solid solution model including order/disorder

Subduction carries atmospheric and crustal carbon hosted in the altered oceanic crystalline basement and in pelagic sediments back into the mantle. Reactions involving complex carbonate solid solutions(s) lead to the transfer of carbon into the mantle, where it may be stored as graphite/diamond, in fluids or melts, or in carbonates. To constrain the thermodynamics and thus reactions of the ternary Ca–Mg–Fe carbonate solid solution, piston cylinder experiments have been performed in the system CaCO₃–MgCO₃–FeCO₃ at a pressure of 3.5 GPa and temperatures of 900–1,100°C. At 900°C, the system has two miscibility gaps: the solvus dolomite–calcite, which closes at X _MgCO3 ~0.7, and the solvus dolomite–magnesite, which ranges from the Mg to the Fe side of the ternary. With increasing temperature, the two miscibility gaps become narrower until complete solid solutions between CaCO₃–Ca_0.5Mg_0.5CO₃ is reached at 1,100°C and between CaCO₃–FeCO₃ at 1,000°C. The solvi are characterized by strong compositional asymmetry and by an order–disorder mechanism. To deal with these features, a solid solution model based on the van Laar macroscopic formalism has been calculated for ternary carbonates. This thermodynamic solid solution model is able to reproduce the experimentally constrained phase relations in the system CaCO₃–MgCO₃–FeCO₃ in a broad P–T range. To test our model, calculated phase equilibria were compared with experiments performed in carbonated mafic protolithes, demonstrating the reliability of our solid solution model at pressures up to 6 GPa in complex systems.     

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     

Anomalous birefringence in andradite–grossular solid solutions: a quantum-mechanical approach

The static linear optical properties (refractive indices, birefringence and axial angle) of andradite–grossular (Ca₃Fe₂Si₃O₁₂–Ca₃Al₂Si₃O₁₂) solid solutions have been computed at the ab initio quantum-mechanical level through the Coupled Perturbed Kohn–Sham scheme, using an all-electron Gaussian-type basis set. Geometry relaxation after substitution of 1–8 Al for Fe atoms in the primitive cell of andradite yields 23 non-equivalent configurations ranging from cubic to triclinic symmetry. Refractive indices vary quite regularly between the andradite (1.860) and grossular (1.671) end-members; the birefringence δ and the axial angle 2V at intermediate compositions can be as large as 0.02° and 89°, respectively. Comparison with experiments suffers from inhomogeneities and impurities of natural samples; however, semi-quantitative agreement is observed.     

Influence of hydrogen on Fe–Mg interdiffusion in (Mg,Fe)O and implications for Earth’s lower mantle

Interdiffusion of Fe and Mg in (Mg,Fe)O has been investigated experimentally under hydrous conditions. Single crystals of MgO in contact with (Mg_0.73Fe_0.27)O were annealed hydrothermally at 300 MPa between 1,000 and 1,250°C and using a Ni–NiO buffer. After electron microprobe analyses, the dependence of the interdiffusivity on Fe concentration was determined using a Boltzmann–Matano analysis. For a water fugacity of ∼300 MPa, the Fe–Mg interdiffusion coefficient in Fe _x Mg_1−x O with 0.01 ≤ x ≤ 0.25 can be described by with and C = −80 ± 10 kJ mol⁻¹. For x = 0.1 and at 1,000°C, Fe–Mg interdiffusion is a factor of ∼4 faster under hydrous than under anhydrous conditions. This enhanced rate of interdiffusion is attributed to an increased concentration of metal vacancies resulting from the incorporation of hydrogen. Such water-induced enhancement of kinetics may have important implications for the rheological properties of the lower mantle.

Thermodynamic mixing behavior of synthetic Ca-Tschermak–diopside pyroxene solid solutions: III. An analysis of IR line broadening and heat of mixing behavior

A series of synthetic Ca-Tschermak–diopside (CaAlAlSiO₆–CaMgSi₂O₆) clinopyroxenes were investigated by powder infrared spectroscopy at room temperature in the wavenumber range 80–2,000 cm⁻¹. Measurable local structural heterogeneities in the crystals are suggested by the line broadening parameter, Δcorr that are observed for intermediate solid-solution compositions. The broadening is most pronounced in the high wavenumber region of the IR spectra that contains stretching modes involving the TO₄ polyhedra. The effective line widths for three selected wavenumber regions deviate positively from linear behavior. This is also observed for the enthalpy of mixing of this solid solution. The relationship between “excess Δcorr”, δΔcorr, and heat of mixing, ΔH _mix, behavior was investigated for this clinopyroxene series and for several other binary silicate solid solutions. The ΔH _mix versus δΔcorr slope values show a linear relationship with respect to the integrated excess volume of the various solid solutions.