Thermodynamics of (Fe2+, Mn2+, Mg, Ca)3− Al2Si3O12 garnet: a review and analysis

Summary The thermodynamic properties of garnets in the system (Fe²⁺, Mn²⁺, Mg, Ca)₃A1₂Si₃O₁₂ are reviewed. The thermodynamic properties of the three end-member garnets pyrope, almandine and grossular, including their volume, enthalpy of formation, entropy, compressibility and thermal expansion have been well determined. For spessartine enthalpy of formation and heat capacity at low temperatures are needed. Pyrope's unusual behavior in some of its properties is probably related to the presence of the small, light Mg cation, which has a large anisotropic thermal vibration. The thermodynamic mixing properties of the six binaries are also discussed. Good volume of mixing data exist now for all of the binaries, but much work is still required to determine the enthalpies and third-law vibrational entropies of mixing. It is shown that the magnitude of the positive deviations in the volumes of mixing is related to the volume difference between the two end-member components. It is probable that excess entropies, if present, originate at low temperatures below 200 K. Recent²⁹Si NMR experiments have demonstrated the presence of short-range ordering (SRO) of Ca and Mg in pyrope-grossular solid solutions. Short-range order will have to be considered in new models describing the entropies of mixing. Its possible presence in all garnet solid solutions needs to be examined. The mixing properties of pyrope-grossular garnets, which are the best known for any garnet binary, can, in part, be described by the Quasi-Chemical approximation, which gives insight into the microscopic interactions which determine the macroscopic thermodynamic mixing properties. Microscopic properties are best investigated by spectroscopic and computational approaches. Hard mode IR measurements on binary solid solutions show that the range of local microscopic structural distortion is reflected in the macroscopic volumes of mixing. The nature of The contents of this contribution was presented at the IMA Meeting in Toronto in August, 1998. It precedes issues of Mineralogy and Petrology containing thematic sets of IMApapers strain tiields and site relaxation needs to be studied in order to obtain a better understanding of the solid-solution process and energetics in garnet. Critical areas for future experimentation are also addressed.[/p]

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Eine kritische Zusammenstellung und Analyse der thermodynamischen Daten der (Fe²⁺, Mn²⁺, Mg, Ca)₃Al₂Si₃O₁₂ granate

Zusammenfassung In dieser Studie werden die thermodynamischen Eigenschaften der Granate im System (Fe²⁺,Mn²⁺, Mg, Ca)₃Al₂Si₃O₁₂ kritisch zusammengestellt. Die thermodynamischen Eigenschaften der drei Endglied-Granate Pyrop, Almandin und Grossular, einschließlich ihrer Volumina, Bildungswärmen, Entropien, Kompressibilitäten und thermischen Ausdehnungen wurden bereits hinreichend gut bestimmt. Dagegen müssen die Bildungswärme und Tieftemperatur-Wärmekapazität von Spessartin noch gemessen werden. Die Eigenschaften des Pyrops sind wahrscheinlich mit den großen anisotropen Schwingungen des kleinen, leichten Mg-Kations verbunden. Die thermodynamischen Mischungseigenschaften der sechs binären Mischkristallreihen werden ebenfalls diskutiert. Während die Mischungs-Volumendaten der binären Mischreihen gut bekannt sind, müssen ihre Mischungs-Enthalpien und Standard-Mischungsentropien noch ermittelt werden. Es wurde gezeigt, daß die Größe der positiven Exzeß-Volumina mit dem Volumen-Unterschied der zwei Endglied-Komponenten der jeweiligen Mischreihe verknüpft ist. Es ist wahrscheinlich, daß Exzeß-Entropien, wenn vorhanden, erst bei Tieftemperaturen unter 200 K auftreten. Neue²⁹Si NMR-Experimente belegen, daß in Pyrop-Grossular-Mischkristallen Nahordnung von Mg und Ca vorliegt. Der Effekt der Nahordnung muß in künftigen thermodynamischen Modellen berücksichtigt werden. Hieraus ergibt sich die Notwendigkeit, alle Granat-Mischreihen auf mögliche Nahordnung hin zu untersuchen. Die Mischungseigenschaften der Pyrop-Grossular-Mischreihe, die von sämtlichen Granat-Mischreihen am besten bestimmt wurden, können teilweise mit dem Quasi-Chemical-Model beschrieben werden. Dieses Modell ermöglicht die Beschreibung der mikroskopischen Wechselwirkungen, die die makroskopischen thermodynamischen Eigenschaften bestimmen. Mikroskopische Eigenschaften werden am besten mit spektroskopischen Messungen und theoretischen Berechnungen untersucht. Hard-mode IR-Spektroskopie-Messungen an binären Mischreihen zeigen, daß die lokalen mikroskopischen strukturellen Verzerrungen in den makroskopischen Mischungs-Volumina widergespiegelt werden. Die Art der Spannungsfelder und Platz-Relaxationen muß detaillierter untersucht werden, um ein besseres Verständnis des Mischkristall-Bildungsprozsses und der Energetik der Granate zu erreichen. Darüber hinaus werden wichtige künftige Forschungsgebiete diskutiert.

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With 11 Figures     

Mineralogy, Mössbauer spectroscopy and electrical conductivity of heterosite (Fe3+, Mn3+)PO4

Mineralogical analysis, electrical conductivity and thermopower are reported for monocrystalline heterosite (Fe³⁺, Mn³⁺)PO₄ with the orthorhombic olivine-type structure. The ⁵⁷Fe Mössbauer spectrum could be adequately described using two Fe³⁺ doublets. By impedance spectroscopy (20 Hz–1 MHz) the electrical DC conductivity σ_DC and AC conductivity σ_AC were determined parallel (∥) and perpendicular to the [001] direction (space group Pnma) in the range ～160–440 K. The graph log σ_DC?1/T shows a slightly bent curve in both directions with activation energies of E _A ～0.30 and ～0.15 eV in the high and low temperature ranges, respectively. The reduced E _A is associated with electronic conduction; σ_DC ∥ [001] follows Mott’s T ^1/4 variable range hopping law at lower temperatures with hopping between localized levels. The values of σ_AC are increased relative to σ_DC at high frequencies and low temperatures, obeying Jonscher’s universal dynamic response law; for σ_AC ∥ [001], the variation with temperature of the frequency exponent is in fair agreement with the model of small polaron hopping. The absolute thermopower Θ is negative and low between ～295 and ～440 K, Θ does hardly vary with temperatures in both directions; the temperature independency of Θ ∥ [001] is consistent with the small polaron hopping model.     

The adsorption characteristics of δ-manganese dioxide: a collection of diffuse double layer constants for the adsorption of H+, Cu2+, Ni2+, Zn2+, Cd2+ and Pb2+

Thermodynamic data for all fate-determining processes are needed in order to predict the fate and transport of metals in natural systems. The surface complexation properties of a synthetic MnO₂, δ-MnO₂, have accordingly been investigated using glass electrode potentiometry. Experimental data were interpreted according to the surface complexation model in conjunction with the diffuse double layer model of the solid/solution interface. Adsorption constants were determined using the non-linear optimisation program FITEQL. Surface complexation parameters determined in this way were validated against results obtained from the literature. Best fits of alkalimetric titration data were obtained with a 2-site, 3 surface-species model of the δ-MnO₂ surface. Site concentrations of 2.23×10⁻³ mol g⁻¹ and 7.66×10⁻⁴ mol g⁻¹ were obtained. Corresponding logarithms of formation constants for the postulated surface species are −1.27 (≡XO⁻), −5.99 (≡YO⁻) and 3.52 (≡YOH₂⁺) at I=0.1 M. The surface speciation of δ-MnO₂ is dominated by ≡XO⁻ over the pH range investigated. Metal adsorption was modelled with surface species of the type ≡XOM⁺, ≡XOMOH, ≡YOM⁺, ≡YOMOH (M=Cu, Ni, Zn, Cd and Pb) and ≡XOM₂OH²⁺ (M=Pb). For Cu, Ni and Zn, titration data could be modelled with ≡XOM⁺, ≡XOMOH, ≡YOM⁺ and ≡YOMOH, whereas for Cd, ≡XOM⁺ and ≡YOM⁺ were sufficient. Lead data were best modelled by assuming the dinuclear species ≡XOM₂OH²⁺ to be the only surface species to form. Adsorption constants determined for Ni, Cu and Zn follow the Irving-Williams sequence. The model suggests an adsorption order of (Pb, Cu) > (Ni, Zn) > Cd. The discrepancy between model predictions and published adsorption results is similar to the variability observed in experimental results from different laboratories.     

Mössbauer effect study of anapaite, Ca2Fe2+(PO4)2 · 4H2O, and of its oxidation products

Mössbauer spectra (MS) of anapaite (Ca₂ Fe²⁺(PO₄)₂?·?4H₂O) and of a sample after being immersed in a 4% H₂O₂ solution at room temperature (RT) over 12 days (hereafter an4ox) were collected at temperatures in the range 4.2 to 420?K and 11 to 300?K respectively. All MS consist of symmetrical doublets, hence magnetic ordering was not observed. The temperature dependencies of the Fe²⁺ centre shifts of anapaite and an4ox were analysed with the Debye model for the lattice vibrations. The characteristic Mössbauer temperatures were found as 370?K?±?25?K and 340?K?±?25?K, and the intrinsic isomer shifts as 1.427?±?0.005?mm/s and 1.418?±?0.005?mm/s respectively. From the external-field (60?kOe) MS recorded at 4.2 and 189?K for the non-treated sample, the principal component V _zz of the electric field gradient (EFG) is determined to be positive and the asymmetry parameter η?≈?0.2 and 0.4 respectively. The temperature variations of the quadrupole splittings, ΔE _Q(T), cannot be interpreted on the basis of the thermal population of the ⁵ D electronic levels resulting from the tetragonal compression of the O₆ co-ordination. The low-temperature linear behaviour of ΔE _Q(T) is attributed to a strong orbit-lattice coupling. A field of 60 kOe applied to anapaite at 4.2?K produces magnetic hyperfine splitting with effective hyperfine fields of ?136, ?254 and ?171?kOe along the principal axes Ox, Oy and Oz of the EFG tensor respectively. Additional oxidation treatments in solutions with various H₂O₂ concentrations up to 20% and subsequent Mössbauer experiments at room temperature, have revealed that the anapaite structure is not sensitive to oxidation since eventually only a small amount of Fe²⁺ (～6.5%) is converted into Fe³⁺.     

57Fe Mössbauer spectroscopy of tektites

Tektite glasses are investigated using ⁵⁷Fe Mössbauer spectroscopy. Room temperature spectra analysis is performed using two complementary analytical methods based on two-dimensional distributions of both isomer shift and quadrupole splitting. No a priori correlation between the two hyperfine parameters is considered. The first method, based on a shape independent distribution, provides the justification for the Gaussian distribution shape used in the second method. No ferric iron contribution is evidenced by Mössbauer spectra analysis in these samples, although several criteria are used. Ferrous iron sites are shown to be continuously distributed between four- and five-fold co-ordinated sites.     

Mineralogy, 57Fe Mössbauer spectra and magnetization of chalcolithic pottery

Three chalcolithic pottery sherds, paint removed from the surface of each sherd, and an unheated red pigment (Tell-Halaf culture, Turkey) were analysed within the frame of archaeometric studies using mineralogical methods, ⁵⁷Fe Mössbauer spectroscopy, magnetization and rotational hysteresis data. From mineralogical results, the individual minerals forming the cores of the sherds were determined. It was found that the sherds are lime-rich. High temperature X-ray analysis on comparable Ca-rich material showed that the established composition is consistent with a firing temperature of 750-950°C. Apart from the pigment, each Mössbauer spectrum of Fe-bearing components consists of dominating paramagnetic doublets, arising mostly from silicate phases, and of a six-line pattern with reduced intensity, due to ferri- and/or antiferromagnetic Fe-oxide phases. For three samples, an Fe³⁺ silicate component of the spectra is clearly dominating, which points to oxidizing conditions during firing. For the others Fe²⁺ and Fe³⁺ components occur in about equal intensities. For the pigment, the magnetic sextet is of similar intensity to the Fe³⁺ silicate component. From magnetic analysis of ferrimagnetic phases it follows that a low percentage of particles of solid solutions -Fe₂O₃ – Fe₃O₄ exist, probably in part 0.1 m in diameter. The ferrimagnetic particles of at least one paint are probably covered by a thin layer of hematite as found from rotational hysteresis data. An attempt is made to draw conclusions from the experimental results, regarding the firing conditions of the sherds and paints.     

Advanced analyses of 57Fe Mössbauer data of alumino-silicate glasses

⁵⁷Fe Mössbauer spectra of iron bearing alumino-silicate glasses are analysed by two complementary methods (SID and x-VBF) especially adapted for the analysis of disordered systems by taking into account distributions of hyperfine Mössbauer parameters. Qualitative and quantitative information about the oxidation state of iron are obtained as well as information about the distribution of local environments of iron. The possibility to separate the signal of ferric iron from that of ferrous iron allows to derive precise redox ratio in favourable cases but also to analyse more sharply the different contributions to Mössbauer spectra. Using two different glass series (feldspar composition, haplo-tonalitic composition), the characteristics of the two methods are described and employed to study the effect of composition, water incorporation and oxidation state on the glass structure. Optical absorption spectroscopy is used to support the interpretation of the Mössbauer spectra in case of the feldspar glasses.     

Intracrystalline fractionation of Fe in synthetic (Fe, Mg, Zn) - bearing staurolite: a Mössbauer spectroscopic study

⁵⁷Fe-Mössbauer spectra of eleven Fe-Mg-bearing staurolite samples, synthesized at 5, 20 and 25 kbar and 680°C, ranging in composition from x_Fe?=1.00 to x_Fe?=0.15, and of two Zn-Fe-bearing staurolite samples, synthesized at 20 kbar and 700°C with x_Fe?=0.10 and x_Fe?=0.32 were collected at room temperature. The spectra reveal that about 80% of Fe_tot (in case of Fe-Mg-bearing staurolite) and about 70% of Fe_tot (in case of Fe-Zn-bearing staurolite) are located as Fe²⁺ at the three subsites Fe1, Fe2 and Fe3 of the tetrahedral T2-site. The refinement of the spectra results in almost identical values for the isomer shift (IS) (±1.0 mm/s) but significantly different values for the quadropole splitting (QS) for the three subsites which is in accordance with the different distortions of these sites. About 8% of Fe_tot (in case of Fe-Mg-bearing staurolite) and 13% of Fe_tot (in case of Fe-Zn-bearing staurolite) are located as Fe²⁺ at the octahedral M4 site, while the remainder percents of Fe_tot indistinguishably occur as Fe²⁺ at the octahedral M1 and M2 sites of the kyanite-like part of the structure. Within the whole Fe-Mg-staurolite solid solution series the Mössbauer parameters QS of the sites M4 and (M1, M2) vary systematically with composition whereas IS remains constant. There is a high negative correlation of the total Mg-content with Fe-occupation of all the Fe-bearing sites indicating a continuous substitution of Fe²⁺ by Mg on all these sites. Synthetic Fe-staurolites show no increasing occupation of the octahedral sites by two-valent cations with pressure, as was assumed by several authors.