Cordierite IV: structural heterogeneity and energetics of Mg–Fe solid solutions

The local structural heterogeneity and energetic properties of 22 natural Mg–Fe cordierites, ideal formula (Mg,Fe)₂Al₄Si₅O₁₈·x(H₂O,CO₂), were investigated at length scales given by powder infrared spectroscopy (IR) and also by published electronic absorption spectra. The studied samples have iron mole fractions from X_Fe = 0.06 to 0.82 and cover most of the Mg–Fe cordierite binary. Variations in wavenumbers and line widths of the IR bands were determined as a function of composition. Most modes shift linearly to lower wavenumbers with increasing X_Fe, except those at high wavenumbers located between 900 and 1,200 cm^-1. They are vibrations that have a large internal (Si,Al)O₄ character and are not greatly affected by Mg–Fe exchange on the octahedral site. The lower wavenumber modes can be best characterized as lattice vibrations having mixed character. The systematics of the wavenumber shifts suggest small continuous variations in the "average" cordierite structure with Mg–Fe exchange and are consistent with an ideal volume of mixing, V^mix= 0, behavior (Boberski and Schreyer 1990). IR line broadening was measured using the autocorrelation function for three wavenumber regions in order to determine the range of structural heterogeneity between roughly 2 and 100 Å (0.2–10.0 nm) in the solid solution. In order to do this, an empirical correction was first made to account for the effect that small amounts of channel Na have on the phonon systematics. The results show that between 1,200 and 540 cm^-1 the line widths of the IR bands broaden slightly and linearly with increasing X_Fe. Between 350 and 125 cm^-1 nonlinear behavior was observed and it may be related to dynamic effects. These results suggest minimal excess elastic enthalpies of mixing for Mg–Fe cordierite solid solutions. Channel Na should affect measurably the thermodynamic properties of natural cordierites as evidenced by variations in the IR spectra of Na-containing samples. Occluded H₂O (Class I) and CO₂ should have little interaction with the framework and can be considered nearly "free" molecules. They should not give rise to measurable structural heterogeneity in the framework. The contribution of the crystal field stabilization energy (CFSE) of octahedral Fe²⁺ to the energetics of Mg–Fe cordierites was also investigated using published electronic absorption spectra (Khomenko et al. 2001). Two bands are observed between 8,000 and 10,500 cm^-1 and they represent electronic dd-excitations of octahedral Fe²⁺ derived from the ⁵T_2g ⁵E_g transition. They shift to higher wavenumbers with increasing X_Mg in cordierite. An analysis gives slightly asymmetric excess -CFSE across the Mg–Fe cordierite join with a maximum of about –550 J/mole towards iron-rich compositions.Editorial responsibility: J. Hoefs     

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.     

Thermodynamic properties of hematite — ilmenite — geikielite solid solutions

A solution model is developed for rhombohedral oxide solid solutions having compositions within the ternary system ilmenite [(Fe ₂₊ ^s Ti ₄₊ ^1–s ) ^A (Fe ₂₊ ^1–s Ti ₄₊ ^s ) ^B O₃]-geikielite [(Mg ₂₊ ^t Ti ₄₊ ^1–t ) ^A (Mg ₂₊ ^1–t Ti ₄₊ ^t ) ^B O₃]-hematite [(Fe³⁺) ^A (Fe³⁺) ^B O₃]. The model incorporates an expression for the configurational entropy of solution, which accounts for varying degrees of structural long-range order (0s, t1) and utilizes simple regular solution theory to characterize the excess Gibbs free energy of mixing within the five-dimensional composition-ordering space. The 13 model parameters are calibrated from available data on: (1) the degree of long-range order and the composition-temperature dependence of the transition along the ilmenite-hematite binary join; (2) the compositions of coexisting olivine and rhombohedral oxide solid solutions close to the Mg–Fe²⁺ join; (3) the shape of the miscibility gap along the ilmenite-hematite join; (4) the compositions of coexisting spinel and rhombohedral oxide solid solutions along the Fe²⁺–Fe³⁺ join. In the course of calibration, estimates are obtained for the reference state enthalpy of formation of ulvöspinel and stoichiometric hematite (–1488.5 and –822.0 kJ/mol at 298 K and 1 bar, respectively). The model involves no excess entropies of mixing nor does it incorporate ternary interaction parameters. The formulation fits the available data and represents an internally consistent energetic model when used in conjuction with the standard state thermodynamic data set of Berman (1988) and the solution theory for orthopyroxenes, olivines and Fe–Mg titanomagnetite-aluminate-chromate spinels developed by Sack and Ghiorso (1989, 1990a, b). Calculated activity-composition relations for the end-members of the series, demonstrate the substantial degree of nonideality associated with interactions between the ordered and disordered structures and the dominant influence of the miscibility gap across much of the ternary system. The predicted shape of the miscibility gap, and the orientation of tie-lines relating the compositions of coexisting phases, display the effects of coupling between the excess enthalpy of solution and the degree of long-range order. One limb of the miscibility gap follows the composititiontemperature surface corresponding to the ternary second-order transition.     

A thermodynamic model of Fe–Cr spinels

A new thermodynamic model for multi-component spinel solid solutions has been developed which takes into account thermodynamic consequences of cation mixing in spinel sublattices. It has been applied to the evaluation of thermodynamic functions of cation mixing and thermodynamic properties of Fe₃O₄–FeCr₂O₄ spinels using intracrystalline cation distribution in magnetite, lattice parameters and activity-composition relations of magnetite–chromite solid solutions. According to the model, cation distribution in binary spinels, (Fe_1-x²⁺ Fe_x³⁺)[Fe_x²⁺Fe_2-2y-x³⁺Cr_2y]O₄, and their thermodynamic properties depend strongly on Fe²⁺–Cr³⁺ cation mixing. Mixing of Fe²⁺–Fe³⁺ and Fe³⁺–Cr³⁺ can be accepted as ideal. If Fe²⁺, Fe³⁺ and Cr are denoted as 1, 3 and 4 respectively, the equation of cation distribution is –RT ln(x²/((1–x)(2–2y–x)))= G₁₃^* + (1–2x)W₁₃+y(W₁₄–W₁₃–W₃₄) where G₁₃^* is the difference between the Gibbs energy of inverse and normal magnetite, W_ij is a Margules parameter of cation mixing and G₁₃^*, J/mol =–23,000+13.4 T, W₁₄=36 kJ/mol, W₁₃=W₃₄=0. The positive nonconfigurational Gibbs energy of mixing is the main reason for changing activity–composition relations with temperature. According to the model, the solvus in Fe₃O₄–FeCr₂O₄ spinel has a critical temperature close to 500°C, which is consistent with mineralogical data.     

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.     

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     

Activities of components in omphacitic solid solutions

Available experimental data on mixing of disordered C2/c clinopyroxenes in the system diopside-jadeite-hedenbergite-acmite are reviewed and evaluated. Because the methods used to determine jadeite activity suffer from severe uncertainty at high jadeite mol fractions, these data cannot be used to infer asymmetry in the jadeite-diopside or the jadeite-hedenbergite solid solutions. If the measurement uncertainties are taken into account, a single parameter (regular, or reciprocal energy) suffices to describe the mixing properties of these two solid solutions. It is argued that a two-site entropy of mixing satisfies the experiments and is consistent with the C2/c disordered nature of the solid solutions; the data in the range 600–1300° C are consistent with a temperature-independent interaction energy, implying no discernible excess entropy. The available experimental data imply W=26±2 kJ mol^–1 for jd-di, and W=25±3 kJ mol^–1 for jd-hd, solid-solutions. Landau theory for a tricritical phase transformation (C2/c-P2/n) is in good agreement with the calorimetrically determined disordering enthalpy, and may be used to derive a simple expression for the activities in ordered omphacite solid solutions. The derived activities of jadeite at 600° C in ordered omphacites are remarkably close to those reported previously for short-range ordered pyroxenes. A simple model is presented for determining the activities of end-members in the system jadeite-diopside-hedenbergite-acmite.     

A temperature-dependent single-crystal Raman spectroscopic study of fayalite: evidence for phonon-magnetic excitation coupling

The polarized single-crystal Raman spectrum of synthetic fayalite, Fe₂SiO₄, was recorded between 5 and 773 K in order to investigate its lattice dynamic behavior. A broad absorption envelope is observed at wavenumbers between 800 and 960 cm^–1 and it contains two intense bands at 816 and 840 cm^–1 at 293 K in the (cc) spectrum. The integral area of the envelope decreases upon cooling from 293 K and reaches a minimum around 55 K. It then increases again with a further decrease in temperature down to 5 K. It is proposed that the envelope in the (cc) spectra consists of seven different modes, some of which are symmetry-forbidden, that arise from combination scattering of nonsymmetric internal SiO₄-stretching modes of B_ig symmetry (i = 1, 2, 3) and low-energy excitations. The individual modes can be observed under different polarizations and agree in number and wavenumber with those obtained by fitting the broad envelope with Lorentzians. An analysis of the Raman spectrum as a function of temperature, using the known magnetic properties of fayalite, allows the assignment of the low-energy excitations to short-range magnetic interactions. Modulation of the Fe²⁺(1)–Fe²⁺(2) exchange energy leads to phonon-magnetic excitation coupling and the main role in the Fe²⁺(1)–Fe²⁺(2) magnetic interaction occurs via superexchange through the oxygens. The magnetic excitations are not magnons in the usual sense, that is as quasiparticles having a long wavelength in an ordered system. The degree of observed broadening of the SiO₄-stretching modes is consonant with a Fe²⁺(1)–Fe²⁺(2) exchange energy of 4.7 cm^–1 presented by Schmidt et al. (1992). At temperatures above 300 K the line width of the mode at 840 cm^–1 decreases slightly, whereas those of low energy lattice modes increase. This suggests that a decrease in mode broadening due to weakened magnetic interactions compensates any thermally related broadening. Complete Fe²⁺ spin disorder may not be reached until at least 530 K. Results from this study show that estimates of third-law entropies for silicates using simple crystal-chemical considerations that do not account for magnetic properties cannot give accurate values for many transition-metal-containing phases.     

A crystallographic and m?ssbauer spectroscopy study of Fe

The crystal chemistry of garnet solid solutions on the Fe ₃ ²⁺ Al₂Si₃O₁₂-Fe ₃ ²⁺ Fe ₂ ³⁺ Si₃O₁₂ (almandine-“skiagite”) and Ca₃Fe ₂ ³⁺ Si₃O₁₂-Fe ₃ ²⁺ Fe ₂ ³⁺ Si₃O₁₂ (andradite-“skiagite”) joins have been investigated by single-crystal X-ray structure refinements and M?ssbauer spectroscopy. Together, these two solid solution series encompass the complete range in Fe³⁺/ΣFe from 0.0 to 1.0. All garnets are isotropic and were re0fined in the Ia d space group. Small excess volumes of mixing are observed in andradite-“skiagite” solid solutions (W _v =1.0±0.2 cm³ mol^-1) and along the almandine-“skiagite” join (W _v =-0.77±0.17cm³ mol^-1). The octahedral (Al, Fe³⁺)-O bond lengths show a much greater variation across the almandine-skiagite join compared to the andradite-skiagite garnets. The dodecahedral (X)-O bond lengths show the opposite behaviour. In andradite-“skiagite” solid solutions, the octahedral site passes from being flattened to elongated parallel to the 3 axis of symmetry with increasing “skiagite” content. A perfect octahedron occurs in a composition of ≈35 mol% “skiagite”. The occupancy of the neighboring dodecahedral sites has the greatest effect on octahedral distortion and vice versa. The M?ssbauer hyperfine parameters of Fe²⁺remain constant in both solid solutions. The hyperfine parameters of Fe³⁺ (at room temperature: centre shift=0.32–0.40 mm/sec, quadrupole splitting (QS)≈0.21–0.55 mm/ sec) indicate that all Fe³⁺ is in octahedral coordination. The Fe³⁺ parameters are nearly constant in almandine-“skiagite” solid solutions, but vary significantly across the andradite-“skiagite” join. The structural unit that contributes to the electric field gradient of the octahedral site is different from that of the coordinating oxygen polyhedron, probably involving the neighboring dodeca-hedral sites.     

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.     

Characterization of vivianite from Catavi,Llallagua Bolivia

Summary Vivianite from Catavi Mine, Llallagua, Bolivia, has a near ideal composition with traces of Mg, Zn and Mn. Total rare-earth elements are < 1,gmg/g. Mössbauer spectroscopy shows Fe^III/(Fe^II + Fe^III) is approximately 0.04.a = 10.030Å,b = 13.434Å,c = 4.714Å, = 102.73dg. The middle-infrared powder spectrum shows H₂O-related bands at 3490, 3290, 3130 cm^–1 (stretch), 1618 cm^–1 (bend), 825 cm^–1 (rock), and at 665 cm^–1 a possible M-OH₂ twist. P0₄ bands occur at 1045-940 cm^–1 (stretch) and 570-450 cm^–1 (bend). Corresponding laser Raman microprobe bands occur at 1051 (ms), 986 (m), 948 (vs), 867 (mw), 828 (w), 568, 532, 453 (m), 442 (mw). Weak Raman bands at about 342, 303, 270 (w), 235 (ms), 227 (sh, ms), 196 (ms), 187 (sh, m), 162 (mw), and 126 (m) may arise from lattice vibrations. Differential thermal responses include a major endotherm from 115–235°C with a shoulder at 170°C and a maximum at 210°C resulting from loss of structural water combined with oxidation of Fe²⁺, and two small exotherms with maxima at 605 and 780°C related to structural transformations.

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Charakterisierung des Vivianits von Catavi, Llallagua, Bolivien

Zusammenfassung Vivianit von der Catavi Mine, Llallagua, Bolivien zeigt annähernd ideale Zusammensetzung mit Spuren von Mg, Zn und Mn. Der gesamte Gehalt an seltenen EvolElementen ist < 1 ppm. Die Mössbauer Spektroskopie liefert ein Fe³⁺/(Fe²⁺ + Fe³⁺) Verhältnis von ungefähr 0.04.a = 10.030,b = 13.434,c = 4.714 Å, = 102.73°. Das Infrarot-Pulverspektrum zeigt dem H₂0 zuzuordnende Banden bei 3490, 3290, 3130 cm^–1 (Streckschwingungen), 1618 cm^–1 (Deformationsschwingung), 825 cm^–1 (Schaukelschwingung) und eine mögliche M-OH₂ Torsionsschwingung bei 665 cm^–1. PO₄ Banden liegen bei 1045-940 cm^–1 (Streckschwingung) und 570-450 cm^–1 (Deformations-schwingung). Entsprechende Banden der Laser Raman Mikrosonde liegen bei 1051 (mst), 986 (m), 948 (sst) 867 (mschw), 828 (schw), 568, 532, 453 (m), 442 (mschw). Raman Banden bei etwa 342, 303, 270 (schw), 235 (mst), 227 (Schulter, mst), 196 (mst), 187 (Schulter, m), 162 (mschw) und 126 (m) können auf Gitterschwingungen zurückgeführt werden. Differential-thermoanalytische Untersuchungen zeigen einen endothermen Bereich von 115–235°C mit einer Schulter bei 170 und einem Maximum bei 210°C, was auf den Verlust von strukturellem Wasser, das an eine Oxidation des Fe²⁺ gebunden ist, zurückzuführen ist; zwei auf strukturelle Transformationen zurückzuführende exotherme Maxima liegen bei 605 und 780°C.

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With 4 Figures     

Thermodynamic data from redox reactions at high temperatures. III. Activity-composition relations in Ni-Pd alloys from EMF measurements at 850–1250 K,and calibration of the NiO+Ni-Pd assemblage as a redox sensor

The assemblage NiO+Ni-Pd alloy has been calibrated as a precise oxygen fugacity sensor in the temperature range 850–1250 K at 1 bar, using an electrochemical technique with oxygen-specific CSZ electrolytes, and Ni+NiO and Cu+Cu₂O as the reference electrodes. Nine compositions were studied, ranging from 0.12 to 0.83 X _Ni ^alloy . Steady EMFs, implying equilibrium, were rapidly achieved in all cells, and were found to be reversible on increasing and decreasing temperature with a precision approaching 0.1 mV. The estimated accuracy of the measurements on each cell is ±0.2 mV (1, corresponding to ±0.003 log-bar units in fo₂ at 1273 K). Compositions of the Ni-Pd alloys were measured after each run by electron microprobe, and these compositions were then checked for internal consistency by measuring the lattice parameter by X-ray diffraction. Nickel-rich alloys show positive deviations from ideality and endothermic enthalpies of mixing, but palladium-rich compositions have exothermic enthalpies of mixing and strong negative deviations from ideality. The excess entropies of mixing are positive for all compositions, and correlate approximately with the excess volumes of mixing. The highly asymmetrical deviations from ideality are well described by a polynomial expression of the Redlich-Kister form, with three terms for the enthalpies, and two for the excess entropies and volumes of mixing. The experimental data from this study have been used to re-formulate the Ni-Pd oxygen fugacity sensor to give an expression; _O2 ^ss = _O2 ^NNO – 2RT ln X _Ni ^alloy – [2 · (1 – X _Ni ^alloy )² · [(–2165–7.958 · T) + (9409 – 0.888 · T) · (4 X _Ni ^alloy – 1) + 2089 · (6 X _Ni ^alloy – 1) · (2 X _Ni ^alloy – 1)]](850<T<1300) where _O2 ^ss is in J mol^-1, T is in kelvins, and the expression for _O2 ^NNO is that given by O'Neill and Pownceby (1993). Values in terms of log fo₂ may be obtained from the above by dividing by RT ln 10. The estimated standard error in _O2 ^ss is on the order of ±200 J mol^-1, which is approximately ±0.01 log-bar units in fo₂ at 1273 K.     

An internally consistent model for the thermodynamic properties of Fe−Mg-titanomagnetite-aluminate spinels

A model is developed for the thermodynamic properties of Fe²⁺–Mg²⁺-aluminate-titanate-ferrite spinels of space group Fd3m. The model incorporates an expression for the configurational entropy of mixing which accounts for long-range order over tetrahedral and octahedral sites. Short-range order or departures from cubic symmetry are not considered. The non-configurational Gibbs energy is formulated as a second degree Taylor expansion in six linearly independent composition and ordering variables. The model parameters are calibrated to reproduce miscibility gap constraints, order-disorder phenomena in MgAl₂O₄ and MgFe₂O₄, and Fe²⁺–Mg²⁺ partitioning data between olivine and: (1) aluminate spinels; (2) ferrite spinels; (3) titanate spinels; (4) mixed aluminate-ferrite spinels. This calibration is achieved without invoking non-configurational excess entropies of mixing. The model predicts that the ordering state of FeAl₂O₄ is more normal than that of MgAl₂O₄. It also successfully accounts for heat of solution measurements and activity-composition relations in the constituent binaries. Phase equilibrium constraints require that the structure of Fe₃O₄ is more inverse than random at all temperatures and that Mg²⁺ has a strong tetrahedral site preference with respect to that of Fe²⁺. The analysis suggests that in the titanates short range order on octahedral sites may be significant at temperatures as high as 1300° C. Constraints developed from calibrating the thermodynamic properties of Fe²⁺–Mg²⁺-aluminatetitanate-ferrite spinel solid solutions permit extension of the database of Berman (1988) to include estimates of the end-member properties of hercynite (FeAl₂O₄), ulvöspinel (Fe₂TiO₄), MgFe₂O₄ and cubic Mg₂TiO₄. In constructing these estimates, provision is made for low-temperature magnetic entropy contributions and the energetic consequences of disordering the aluminates and the ferrites. These estimates are consistent with all of the available low-temperature adiabatic calorimetry, high-temperature heat content, and heat of solution measurements on the end-members. The analysis implies that there is a substantial heat capacity anomaly in the range 300°–900° C associated with disordering of the MgAl₂O₄ structure while that in FeAl₂O₄ becomes significant at temperatures above 700° C. The same heat capacity response in the ferrites indicates that the order/disorder transformation is coupled to the antiferromagnetic-paramagnetic transition in MgFe₂O₄ but takes place well above the ferrimagnetic-paramagnetic transition in magnetite. The proposed model is internally consistent with solution theory reported elsewhere for Fe²⁺–Mg²⁺ olivines and orthopyroxenes (Sack and Ghiorso 1989), rhombohedral oxides (Ghiorso 1990a) and the remaining end-member properties of Berman (1988).     

Characterization of synthetic hedenbergite (CaFeSi<Subscript>2</Subscript>O<Subscript>6</Subscript>)–petedunnite (CaZnSi<Subscript>2</Subscript>O<Subscript>6</Subscript>) solid solution series by X-ray powder diffraction and <Superscript>57</Superscript>Fe Mössbauer spectroscopy

Clinopyroxenes along the solid solution series hedenbergite (CaFeSi₂O₆)–petedunnite (CaZnSi₂O₆) were synthesized under hydrothermal conditions and different oxygen fugacities at temperatures of 700 to 1200 °C and pressures of 0.2 to 2.5 GPa. Properties were determined by means of X-ray diffraction, electron microprobe analysis and ⁵⁷Fe Mössbauer spectroscopy at 298 K. Unit-cell parameters display a linear dependency with changing composition. Parameters a₀ and b₀ exhibit a linear decrease with increasing Zn content while the monoclinic angle increases linearly. Parameter c₀ is not affected by composition and remains constant at a value of 5.248 Å. The molar volume can be described according to the equation V_mol (ccm mol^–1)=33.963(16)–0.544(31)*Zn pfu. The isomer shifts of ferrous iron on the octahedral M1 site in hedenbergite are not affected by composition along the hedenbergite–petedunnite solid solution series and remain constant at an average value of 1.18 mm s^–1. Quadrupole splittings of Fe²⁺ on the M1 are, however, strongly affected by composition, and they decrease linearly with increasing petedunnite component in hedenbergite, ranging from 2.25 mm s^–1 for pure hedenbergite end member to 1.99 mm s^–1 for a solid solution containing 84 mole% petedunnite. The half-widths of intermediate solid solutions vary between 0.26 and 0.33 mm s^–1, indicating, in accordance with the microprobe analyses and X-ray diffraction, that samples are homogeneous and well-crystallized. The data from this study demonstrate that the crystallinity of hedenbergitic clinopyroxenes can be improved by using oxide mixtures as starting materials. Crystal sizes for intermediate compositions range up to 70 m, suitable for standard single-crystal X-ray analysis.This paper is dedicated to Prof. Dr. Georg Amthauer, Salzburg, on occasion of his 60th birthday     

Crystal field and charge transfer spectrum of (Mg, Fe)SiO3 majorite

Majorite of bulk composition Mg_0.86Fe_0.15SiO₃ was synthesized at 19 GPa and 1900 °C at an oxygen fugacity close to the Re/ReO₂ buffer. Optical absorption spectra of polycrystalline samples were measured from 4000 to 25000cm^?1. The following features were observed: (1) Three bands at 4554, 6005 and 8093 cm^?1 due to the ⁵E_g → ⁵T_2g transition of Fe²⁺ in a distorted dodecahedral site. (2) A band at 9340 cm^?1 due to the transition ⁵T_2g → ⁵E_g of octahedral Fe²⁺. (3) A band at 22784 cm^?1 resulting from Fe³⁺, probably in an octahedral site (⁶A_1g → ⁴A_1g, ⁴E_g). (4) A very intense system of Fe²⁺ → Fe³⁺ intervalence charge transfer bands which can be modelled by two Gaussian components centered at 16542 and 20128 cm^?1. The existence of two components in the charge transfer spectrum could be related to the fact that the tetragonal majorite structure may contain Fe³⁺ in two different octahedral sites. The crystal field splitting Δ of Fe²⁺ in dodecahedral coordination is 5717 cm^?1. If a splitting of the ground state in the order of 1000 cm^?1 is assumed, this yields a crystal field stabilization energy (CFSE) of 3930 cm^?1, comparable to the CFSE of Fe²⁺ in pyrope-rich garnet. However, the splitting of ⁵T_2g is significantly higher than in pyrope. This would be consistent with Fe²⁺ preferentially occupying the more distorted one of the two dodecahedral sites in the majorite structure. For octahedral Fe²⁺, Δ= 9340 cm^?1 and CFSE=3736 cm^?1, assuming negligible splitting of the ground state.     

Simulation of thermodynamic mixing properties of garnet solid solutions at high temperatures and pressures

We present results of high temperature, high pressure atomistic simulations aimed at determining the thermodynamic mixing properties of key binary garnet solid solutions. Computations cover the pressure range 0–15 GPa and the temperature range 0–2000 K. Through a combination of Monte-Carlo and lattice-dynamics calculations, we derive thermodynamic mixing properties for garnets with compositions along the pyrope–almandine and pyrope–grossular joins, and compare these with existing experimental data. Across the pressure–temperature range considered, simulations show virtually ideal mixing behaviour in garnet on the pyrope–almandine join, while large excess volumes and enthalpies of mixing are predicted for garnet along the pyrope–grossular join. Excess heat capacities and entropies are also examined. These simulations shed additional light on the link between the behaviour at the atomic level and macroscopic thermodynamic properties: we illustrate the importance of certain atomistic Ca–Mg contacts in the pyrope–grossular solid solutions. For simulation techniques of this type to become sufficiently accurate for direct use in geological applications such as geothermobarometry, there is an urgent need for improved experimental determinations of several key quantities, such as the enthalpies of mixing along both joins.     

Thermochemistry of forsterite-fayalite olivine solutions

The enthalpies of solution of synthetic Mg₂SiO₄-Fe₂SiO₄ olivine solid solutions have been measured in Pb₂B₂O₅ melt at 970 K. The heat of solution of forsterite was found to be 15.62 ± 0.3 kcal mol^?1 and that of fayalite 9.39 ± 0.14 kcal mol^?1. Solid solutions between these end-members exhibit small positive deviations from mixing ideality, asymmetric towards the Fe end-member. In terms of the sub-regular solution model, excess enthalpies of intermediate olivine are adequately represented by the equation H^xs = 2(1000 + 1000X_Fe) X_FeX_MgThe enthalpies of solution at 970 K are consistent with high temperature phase equilibrium measurements of activity-composition relationships in the olivine series. Excess entropy terms are not needed to relate the phase equilibrium data to the calorimetric data presented here.The enthalpy of solution of FeSiO₃ ferrosilite at 970 K was found to be 4.36 ± 0.10 kcal mol^?1. This value, when taken together with calorimetric measurements on fayalite and quartz, is consistent with phase equilibrium investigations of the reaction: 2FeSiO₃ = Fe₂SiO₄ + SiO₂ Ferrosilite Fayalite QuartzThese provide a check on the internal consistency of the calorimetric data presented here.     

Scaling of thermodynamic mixing properties in garnet solid solutions

 The volumes and enthalpies of mixing, ΔV ^Mix and ΔH ^Mix, of binary solid-solution aluminosilicate garnets have been studied by computer simulation. The use of “average atoms” to simulate solid solution was found to give results that are considerably different from those obtained by calculating and averaging over many configurations of cations at a given composition. Although we expect mineral properties calculated from model calculations to be correct only on a qualitative rather than a quantitative scale, fair agreement with experiment was obtained where carefully tested potential parameters were used. The results show that mixing behaviour in these materials is controlled by local strain and relaxation effects resulting from the atomic size mismatch of the mixing divalent cations. In particular, ΔV ^Mix and ΔH ^Mix are shown to scale quadratically with the volume difference between the end members, and to vary essentially symmetrically with composition, with a moderate dependence on the degree and nature of cation order. We conclude that computer modelling should be useful in providing detailed qualitative information about the mixing properties of solid solutions, which can help to better constrain and interpret experimental results. Received: 8 March 2000 / Accepted: 1 October 2000     

Experimental study on the phase equilibria in the join CaMgSi2O6-CaCrCrSiO6 with special reference to the blue diopside

The behaviour of tetrahedrally coordinated and octahedrally coordinated Cr³⁺ ions in diopside is discussed from the study on the join CaMg-Si₂O₆-CaCrCrSiO₆. The molecule CaCrCrSiO₆ decomposes into uvarovite+eskolaite and its maximum solubility in diopside is 6.7 wt percent at 940 ° C. Crystalline phases are diopside ss (ss is abbreviation of solid solution), uvarovite ss, wollastonite ss, spinel and eskolaite. The diopside ss is blue in colour. Its optical spectra were measured in the wavelenght range of 325–2600 nm, and assigned after tetrahedral configuration Td and octahedral configuration Oh. It is estimated that octahedral Cr³⁺ ions are in high spin state, while tetrahedral Cr³⁺ ions may be probably in low spin state. The _t and B are 10,300–10,370 cm^–1 and 429–432 cm^–1. The CFSE for tetrahedral low spin Cr³⁺ ions is nearly the same as that for octahedral high spin Cr³⁺ ions. The ionic radii of tetrahedral low spin Cr³⁺ ions calculated are 0.47–0.53 Å, shrinked from the radius of octahedral high spin Cr³⁺ ion (0.615 Å) as much as 14–24 percent. Petrologic implications of the result are also discussed.The first half of the D. Sc. dissertation of K. Ikeda presented to Hokkaido University in June, 1976     

Importance of considerations of mixing properties in establishing an internally consistent thermodynamic database: thermochemistry of minerals in the system Mg2SiO4-Fe2SiO4-SiO2

A thermodynamic solution model is developed for minerals whose compositions lie in the two binary systems Mg₂SiO₄-Fe₂SiO₄ and Mg₂Si₂O₆-Fe₂Si₂O₆. The formulation makes explicit provision for nonconvergent ordering of Fe²⁺ and Mg²⁺ between M1 and M2 sites in orthopyroxenes and non-zero Gibbs energies of reciprocal ordering reactions in both olivine and orthopyroxene. The calibration is consistent with (1) constraints provided by available experimental and natural data on the Fe-Mg exchange reaction between olivine and orthopyroxene ± quartz, (2) site occupancy data on orthopyroxenes including both crystallographic refinements and Mössbauer spectroscopy, (3) enthalpy of solution data on olivines and orthopyroxenes and enthalpy of disordering data on orthopyroxene, (4) available data on the temperature and ordering dependence of the excess volume of orthopyroxene solid solutions, and (5) direct activity-composition determinations of orthopyroxene and olivine solid solutions at elevated temperatures. Our analysis suggests that the entropies of the exchange [Mg(M2)Fe(M1)Fe(M2)Mg(M1)] and reciprocal ordering reactions [Mg(M2)Mg(M1)+ Fe(M2)Fe(M1)Fe(M2)Mg(M1)+Mg(M2)Fe(M1)] cannot differ significantly (± 1 cal/K) from zero over the temperature range of calibration (400°–1300° C). Consideration of the mixing properties of olivine-orthopyroxene solid solutions places tight constraints on the standard state thermodynamic quantities describing Fe-Mg exchange reactions involving olivine, orthopyroxene, pyralspite garnets, aluminate spinels, ferrite spinels and biotite. These constraints are entirely consistent with the standard state properties for the phases-quartz,-quartz, orthoenstatite, clinoenstatite, protoenstatite, fayalite, ferrosilite and forsterite which were deduced by Berman (1988) from an independent analysis of phase equilibria and calorimetric data. In conjunction with these standard state properties, the solution model presented in this paper provides a means of evaluating an internally consistent set of Gibbs energies of mineral solid solutions in the system Mg₂SiO₄-Fe₂SiO₄-SiO₂ over the temperature range 0–1300° C and pressure interval 0.001–50 kbars. As a consequence of our analysis, we find that the excess Gibbs energies associated with mixing of Fe and Mg in (Fe, Mg)₂SiO₄ olivines, (Fe, Mg)₃Al₂Si₃O₁₂ garnets, (Fe, Mg)Al₂O₄ and (Fe, Mg)Fe₂O₄ spinels, and K(Mg, Fe)₃AlSi₃O₁₀(OH)₂ biotites may be satisfactory described, on a macroscopic basis, with symmetric regular solution type parameters having values of 4.86±0.12 (olivine), 3.85±0.09 (garnet), 1.96±0.13 (spinel), and 3.21±0.29 kcals/gfw (biotite). Applications of the proposed solution model demonstrate the sensitivity of petrologic modeling to activity-composition relations of olivine-orthopyroxene solutions. We explore the consequences of estimating the activity of silica in melts forming in the mantle and we develop a graphical geothermometer/geobarometer for metamorphic assemblages of olivine+orthopyroxene+quartz. Quantitative evaluation of these results suggests that accurate and realistic estimates of silica activity in melts derived from mantle source regions,P-T paths of metamorphism and other intensive variables of petrologic interest await further refinements involving the addition of trace elements (Al³⁺ and Fe³⁺) to the thermodynamic formulation for orthopyroxenes.