Thermodynamic properties and hydrogen speciation from vibrational spectra of dense hydrous magnesium silicates

Infrared absorption measurements were taken from 100 to 5000 cm^?1 of a natural chondrodite and three dense hydrous magnesium silicates: phase A, phase B, and superhydrous phase B (shy-B). Raman spectra were also acquired from phase B and the chondrodite. Roughly half of the lattice modes are represented and our data are the first report of the low frequency modes. Comparison of our new spectra to symmetry analyses suggests that multiple sites for hydrogen exist for all the phases. The shy-B we examined crystallizes in P2₁ nm with two OH sites. Models for the density of states are constructed based on band assignments for the lattice modes and for the OH stretching vibrations. Heat capacity C_P and entropy S calculated using Kieffer's formulation should be accurate within 3% from 200 to 800 K. Model values for C_P at 298 K are 299.6 J/mol-K for chondrodite, 421.5 J/mol-K for phase A, 529.4 J/mol-K for shy-B, and 618.9 J/mol-K for phase B. Model values for S₂₉₈ ⁰ are 234.2 J/mol-K for chondrodite, 303.5 J/ mol-K for phase A, 377.9 J/mol-K for shy-B, and 473.3 J/mol-K for phase B. Debye temperatures are near 1000 K.     

Thermodynamic properties of MgSiO3 ilmenite from vibrational spectra

Unpolarized infrared (IR) reflectance spectra for MgSiO₃ ilmenite taken from a single-crystal and from a densly packed polycrystalline sample possessed all eight peaks mandated by symmetry between 337 and 850 cm^?1. Polarizations were inferred from intensity differences between the two samples. IR peak positions differ by up to 250 cm^?1 from recent calculations, but on average are within 11%. Heat capacity C _p calculated from these data by using a Kieffer-type model are within the experimental uncertainty of calorimetric measurements from 170 to 700 K. Outside this range, calculated C _p is probably accurate within a few percent, based on recent results for garnets. Calculated entropy is only slightly less accurate, giving S ⁰ (298.15 K) as 54.1 ±0.5 J/ mol-K, which is 10% lower than recent estimates based on phase equilibria. The slope of the phase boundary between ilmenite and perovskite is used to predict S ⁰ (298.15 K) of perovskite as 58.7 ±1.4 J/mol-K, which is 10% lower than previous values.     

Aluminum speciation, vibrational entropy and short-range order in calcium aluminosilicate glasses

The heat capacity and vibrational entropy of a calcium aluminate and three peraluminous calcium aluminosilicate glasses have been determined from 2 to 300 K by heat-pulse relaxation calorimetry. Together with previous adiabatic data for six other glasses in the system CaO-Al₂O₃-SiO₂, these results have been used to determine partial molar heat capacities and entropies for five species namely, SiO₂, CaO and three different sorts of Al₂O₃ in which Al is 4-, 5- and 6-fold coordinated by oxygen. Given the determining role of oxygen coordination on low-temperature heat capacity, the composition independent entropies found for SiO₂ and CaO indicate that short-range order around Si and Ca is not sensitive to aluminum speciation up to the highest fraction of 25% observed for ^VAl by NMR spectroscopy. Because of the higher room-temperature vibrational entropy of ^IVAl₂O₃ (72.8 J/mol K) compared to ^VAl₂O₃ (48.5 J/mol K), temperature-induced changes from ^IVAl to ^VAl give rise to a small negative contribution of the order of 1 J/mol K to the partial molar configurational heat capacity of Al₂O₃ in melts. Near 0 K, pure SiO₂ glass distinguishes itself by the importance of the calorimetric boson peak. On a g atom basis, the maximum of this peak varies with the composition of calcium aluminosilicate glasses by a factor of about 2. It does not show smooth variations, however, either as a function of SiO₂ content, at constant CaO/Al₂O₃ ratio, or as a function of Al₂O₃ content, at constant SiO₂ content.     

Raman spectroscopy and heat capacity measurement of calcium ferrite type MgAl2O4 and CaAl2O4

Raman spectroscopy of calcium ferrite type MgAl₂O₄ and CaAl₂O₄ and heat capacity measurement of CaAl₂O₄ calcium ferrite were performed. The heat-capacity of CaAl₂O₄ calcium ferrite measured by a differential scanning calorimeter (DSC) was represented as C_P(T)=190.6–1.116 × 10⁷T^–2 + 1.491 × 10⁹T^–3 above 250 K (T in K). The obtained Raman spectra were applied to lattice dynamics calculation of heat capacity using the Kieffer model. The calculated heat capacity for CaAl₂O₄ calcium ferrite showed good agreement with that by the DSC measurement. A Kieffer model calculation for MgAl₂O₄ calcium ferrite similar to that for CaAl₂O₄ calcium ferrite was made to estimate the heat capacity of the former. The heat capacity of MgAl₂O₄ calcium ferrite was represented as C_P(T)=223.4–1352T ^–0.5 – 4.181 × 10⁶T ^–2 + 4.300 × 10⁸T ^–3 above 250 K. The calculation also gave approximated vibrational entropies at 298 K of calcium ferrite type MgAl₂O₄ and CaAl₂O₄ as 97.6 and 114.9 J mol^–1 K^–1, respectively.     

A revised model for the density and thermal expansivity of K2O-Na2O-CaO-MgO-Al2O3-SiO2 liquids from 700 to 1900 K: extension to crustal magmatic temperatures

A revised model for the volume and thermal expansivity of K₂O-Na₂O-CaO-MgO-Al₂O₃-SiO₂ liquids, which can be applied at crustal magmatic temperatures, has been derived from new low temperature (701–1092 K) density measurements on sixteen supercooled liquids, for which high temperature (1421–1896 K) liquid density data are available. These data were combined with similar measurements previously performed by the present author on eight sodium aluminosilicate samples, for which high temperature density measurements are also available. Compositions (in mol%) range from 37 to 75% SiO₂, 0 to 27% Al₂O₃, 0 to 38% MgO, 0 to 43% CaO, 0 to 33% Na₂O and 0 to 29% K₂O. The strategy employed for the low temperature density measurements is based on the assumption that the volume of a glass is equal to that of the liquid at the limiting fictive temperature, T _f ^′. The volume of the glass and liquid at T _f ^′ was obtained from the glass density at 298 K and the glass thermal expansion coefficient from 298 K to T _f ^′. The low temperature volume data were combined with the existing high temperature measurements to derive a constant thermal expansivity of each liquid over a wide temperature interval (767–1127 degrees) with a fitted 1 error of 0.5 to 5.7%. Calibration of a linear model equation leads to fitted values of Vˉ _i ±1 (cc/mol) at 1373 K for SiO₂ (26.86 ± 0.03), Al₂O₃ (37.42±0.09), MgO (10.71±0.08), CaO (15.41±0.06), Na₂O (26.57±0.06), K₂O (42.45 ± 0.09), and fitted values of dVˉ _i /dT (10⁻³ cc/mol-K) for MgO (3.27±0.17), CaO (3.74±0.12), Na₂O (7.68±0.10) and K₂O (12.08±0.20). The results indicate that neither SiO₂ nor Al₂O₃ contribute to the thermal expansivity of the liquids, and that dV/dT ^liq is independent of temperature between 701 and 1896 K over a wide range of composition. Between 59 and 78% of the thermal expansivity of the experimental liquids is derived from configurational (vs vibrational) contributions. Measured volumes and thermal expansivities can be recovered with this model with a standard deviation of 0.25% and 5.7%, respectively. Received: 2 August 1996 / Accepted: 12 June 1997     

Mode of formation of hibonite (CaAl12O19) within the U-Th skarns from the granulites of S-E Madagascar

 In Madagascar, hibonite occurs as a rather frequent mineral within thorianite-bearing skarns which are widespread in the Pan African granulitic formations constituting the S-E part of the Island (Tranomaro area). In these skarns, leucocratic segregations made up of CO₃-scapolite to meionite (An_equivalent=89–95% which implies T≥850° C), spinel and corundum were formed at stage 1 of metasomatism in a titanite-bearing matrix consisting of scapolite (An_eq=77–88) and aluminous diopside. During stage 2 of metasomatism, scapolite from the lenses were altered to anorthite+calcite while the less calcic scapolite remained stable which indicates T≈800° C. Hibonite crystallized at the expense of corundum and spinel. Expressed as mol% of the CaAl₁₂O₁₉/Ca(Al₁₀TiR²⁺)O₁₉/REE(Al₁₁R²⁺)O₁₉ [+Th (Al₁₀R²⁺ ₂)O₁₉] end-members (R ²⁺=Mg, Fe²⁺, Zn²⁺; Al=Al, Fe³⁺; Ti=Ti, Si), its composition varies from 26/72/2 to 50/23/27. The ideal activity of the CaAl₁₂O₁₉ component is about 0.25. Fluid inclusions in corundum, hibonite and anorthite are composed of nearly pure CO₂. In corundum, the isochores for primary inclusions are in agreement with the P-T estimates for regional metamorphism and stage 1 metasomatism (T≈850° C, P≈5 kbar). Inclusions with the highest density in hibonite and anorthite constrain P to about 3–3.5 kbar for T=800° C. Thermodynamic calculations indicate that, in addition to a low activity of CaAl₁₂O₁₉, stability of hibonite in equilibrium with anorthite and calcite implies an extremely low activity of silica (below the zircon-baddeleyite buffer). By contrast the activity of CO₂ may be high, in agreement with the observed fluid compositions. These results are corroborated by a short comparison with the other granulite occurrences of hibonite in Tanzania and South India. Received: 18 August 1994 / Accepted: 12 October 1995     

Recent developments and the future of low‐T calorimetric investigations in the Earth sciences: Consequences for thermodynamic calculations and databases

Low‐T calorimetry is an experimental science that measures the thermodynamic function heat capacity, C_p(T), from which the standard third‐law entropy (298.15 K), S°, is calculated. The recent technological development of relaxation calorimetry allows both new experimental strategies and types of C_p investigations to be made, which were previously not possible. The C_p measurements are fast and automated and can be made on mg‐sized mineralogical samples between 2 and 400 K. These advantages, when careful measurement procedures are used, permit better determinations of C_p(T) behaviour. The C_p of synthetic single‐crystal MgO was measured between 5 and 302 K, and S° calculated using relaxation calorimetry to further investigate the method's precision and accuracy. A number of synthetic and natural end‐member or nearly end‐member compositions of silicate garnet were investigated in the past via adiabatic calorimetry, an old and established technique, and more recently and extensively with the relaxation method. First C_p(T) and S° results, using relaxation calorimetry, have been obtained on spessartine (Mn₃Al₂Si₃O₁₂) and knorringite (Mg₃Cr₂Si₃O₁₂). Furthermore, reinvestigations on pyrope (Mg₃Al₂Si₃O₁₂), almandine (Fe₃Al₂Si₃O₁₂), grossular (Ca₃Al₂Si₃O₁₂) and andradite (Ca₃Al₂Si₃O₁₂), often on multiple samples, have resolved uncertainties and certain problems with published thermodynamic data. S° can be affected by various low‐T physical phenomena, such as cooperative magnetic phase transitions or Schottky anomalies at temperatures of <15 K, which were not described fully in some older adiabatic calorimetric studies. New C_p results show that small differences in the thermodynamic behaviour between some natural and synthetic silicates may exist as demonstrated by extensive work on grossular. Important and “new” research questions on the thermodynamic behaviour of minerals are coming to light and are being investigated. The C_p behaviour and S° values for six silicate garnet end‐members are analysed and the latter are compared to the “best fit or optimized” S° values given in various internally consistent thermodynamic databases. Conclusions are drawn on what types and directions of calorimetric study are required in order to obtain better thermodynamic property determinations of minerals, as well as achieving a better understanding of the underlying microscopic physical behaviour that determines the macroscopic C_p and S° functions.     

Evaluation of thermochemical data on Fe-Mg olivine,orthopyroxene, spinel and Ca-Fe-Mg-Al garnet

Thermochemical data on Fe-Mg olivine, orthopyroxene, spinel and Ca-Fe-Mg garnet have been tested and reevaluated in reproducing experimental equilibrium data. All data (except of spinel) adjusted in this process lie within the error limits of original calorimetric experiments. For spinel, an enthalpy of −2307.2 kJ/mol and an entropy of 81.5 J/mol-K has been recommended. Recommended interaction parameters for the spinel-hercynite and forsterite-fayalite solutions are as follows:Spinel: W_{spinel-hercynite} = 9124.0 J/mol. W_{hercynite-spinel} = 0.0 J/molOlivine: W = 4500.0 J/mol for 1 cation.Excess entropies (on 1 cation basis) necessary to reproduce phase equilibria for the pyrope-almandine and almandine-grossular solutions are as follows:Mg-Fegarnet: W^s_{pyrope-almandine} = 11.760 − 0.00167 J/mol-K. W^s_{almandine-pyrope} = −10.146 +0.0037T J/mol-K.Fe-Ca garnet: W^s = −16.07 + 0.0126T J/mol-K.     

Molecular H2O in armenite, BaCa2Al6Si9O30·2H2O, and epididymite, Na2Be2Si6O15·H2O: Heat capacity, entropy and local-bonding behavior of confined H2O in microporous silicates

Armenite, ideal formula BaCa₂Al₆Si₉O₃₀·2H₂O, and its dehydrated analog BaCa₂Al₆Si₉O₃₀ and epididymite, ideal formula Na₂Be₂Si₆O₁₅·H₂O, and its dehydrated analog Na₂Be₂Si₆O₁₅ were studied by low-temperature relaxation calorimetry between 5 and 300 K to determine the heat capacity, C_p, behavior of their confined H₂O. Differential thermal analysis and thermogravimetry measurements, FTIR spectroscopy, electron microprobe analysis and powder Rietveld refinements were undertaken to characterize the phases and the local environment around the H₂O molecule.The determined structural formula for armenite is Ba_0.88(0.01)Ca_1.99(0.02)Na_0.04(0.01)Al_5.89(0.03)Si_9.12(0.02)O₃₀·2H₂O and for epididymite Na_1.88(0.03)K_0.05(0.004)Na_0.01(0.004)Be_2.02(0.008)Si_6.00(0.01)O₁₅·H₂O. The infrared (IR) spectra give information on the nature of the H₂O molecules in the natural phases via their H₂O stretching and bending vibrations, which in the case of epididymite only could be assigned. The powder X-ray diffraction data show that armenite and its dehydrated analog have similar structures, whereas in the case of epididymite there are structural differences between the natural and dehydrated phases. This is also reflected in the lattice IR mode behavior, as observed for the natural phases and the H₂O-free phases. The standard entropy at 298 K for armenite is S° = 795.7 ± 6.2 J/mol K and its dehydrated analog is S° = 737.0 ± 6.2 J/mol K. For epididymite S° = 425.7 ± 4.1 J/mol K was obtained and its dehydrated analog has S° = 372.5 ± 5.0 J/mol K. The heat capacity and entropy of dehydration at 298 K are Δ = 3.4 J/mol K and ΔS^rxn = 319.1 J/mol K and Δ = −14.3 J/mol K and ΔS^rxn = 135.7 J/mol K for armenite and epididymite, respectively. The H₂O molecules in both phases appear to be ordered. They are held in place via an ion-dipole interaction between the H₂O molecule and a Ca cation in the case of armenite and a Na cation in epididymite and through hydrogen-bonding between the H₂O molecule and oxygen atoms of the respective silicate frameworks. Of the three different H₂O phases ice, liquid water and steam, the C_p behavior of confined H₂O in both armenite and epididymite is most similar to that of ice, but there are differences between the two silicates and from the C_p behavior of ice. Hydrogen-bonding behavior and its relation to the entropy of confined H₂O at 298 K is analyzed for various microporous silicates.The entropy of confined H₂O at 298 K in various silicates increases approximately linearly with increasing average wavenumber of the OH-stretching vibrations. The interpretation is that decreased hydrogen-bonding strength between a H₂O molecule and the silicate framework, as well as weak ion-dipole interactions, results in increased entropy of H₂O. This results in increased amplitudes of external H₂O vibrations, especially translations of the molecule, and they contribute strongly to the entropy of confined H₂O at T < 298 K.     

Role of basicity and tetrahedral speciation in controlling the thermodynamic properties of silicate liquids, part 1: the system CaO-MgO-Al2O3-SiO2

Activity coefficients of oxide components in the system CaO-MgO-Al2O3-SiO2 (CMAS) were calculated with the model of Berman (Berman R. G., “A thermodynamic model for multicomponent melts with application to the system CaO-MgO-Al2O3-SiO2,” Ph.D. dissertation, University of British Columbia, 1983) and used to explore large-scale relationships among these variables and between them and the liquid composition. On the basis of Berman’s model, the natural logarithm of the activity coefficient of MgO, ln(γMgOLiq), and ln(γMgOLiq/γSiO2Liq) are nearly linear functions of ln(γCaOLiq). All three of these variables are simple functions of the optical basicity Λ with which they display minima near Λ ∼ 0.54 that are generated by liquids with low ratios of nonbridging to tetrahedral oxygens (NBO/T) (<0.3) and a mole fraction ratio, XSiO2Liq/XAl2O3Liq, in the range 4 to 20. Variations in ln(γCaOLiq) at constant Λ near the minimum are due mostly to liquids with (XCaOLiq + XMgOLiq)/XAl2O3Liq < 1. The correlations with optical basicity imply that the electron donor power is an important factor in determining the thermodynamic properties of aluminosilicate liquids.For a constant NBO/T, ln(γCaOLiq/γAl2O3Liq) and ln(γMgOLiqγAl2O3Liq) form curves in terms of XSiO2Liq/XAl2O3Liq. The same liquids that generate minima in the Λ plots are also associated with minima in ln(γCaOLiqγAl2O3Liq) and ln(γMgOLiqγAl2O3Liq) as a function of XSiO2Liq/XAl2O3Liq. In addition, there are maxima or sharp changes in slope for NBO/T > 0.3, which occur for XSiO2Liq/XAl2O3Liq ranging from ∼0 to ∼6 and increase with increasing NBO/T. The systematic variations in activity coefficients as a function of composition and optical basicity reflect underlying shifts in speciation as the composition of the liquid is changed. On the basis of correlations among the activity coefficients, it is likely that the use of CaO, an exchange component such as SiMg−1 and two of MgO, CaAl2O4, or MgAl2O4 would yield significant savings in the number of parameters required to model the excess free energy surface of liquids over large portions of CMAS relative to the use of oxide end members.Systematic behavior of thermodynamic properties extends to small amounts of other elements dissolved in otherwise CMAS liquids. For example, ln(XFe2+Liq/XFe3+Liq) at constant oxygen fugacity is linearly correlated with ln(γCaOLiq). Similarly, ln(CS), where CS is the sulfide capacity is linearly correlated at constant temperature with each of the optical basicity, ln(aCaOLiq) and ln(γCaOLiq), although the correlation for the latter breaks down for low values of Λ. The well-known systematic behavior of sulfide capacity as a function of optical basicity for systems inside as well as outside CMAS suggests that ln(γCaSLiq) is also a simple function of optical basicity and that the relationships observed among the activity coefficients in CMAS may hold for more complex systems.     

Heat capacity of ferrosilite, Fe2Si2O6

The heat capacity of synthetic ferrosilite, Fe₂Si₂O₆, was measured between 2 and 820 K. The physical properties measurement system (PPMS, Quantum Design^®) was used in the low-temperature region between 2 and 303 K. In the temperature region between 340 and 820 K measurements were performed using differential scanning calorimetry (DSC). The C _p data show two transitions, a sharp λ-type at 38.7 K and a small shoulder near 9 K. The λ-type transition can be related to collinear antiferromagnetic ordering of the Fe²⁺ spin moments and the shoulder at 10 K to a change from a collinear to a canted-spin structure or to a Schottky anomaly related to an electronic transition. The C _p data in the temperature region between 145 and 830 K are described by the polynomial $C_{p} {\left[ {\hbox{J\,mol}^{{ - 1}}\,{\hbox{K}}^{{ - 1}} } \right]} = 371.75 - 3219.2T^{{ - 1/2}} - 15.199 \times 10^{5} T^{{ - 2}} + 2.070 \times 10^{7} T^{{ - 3}} $ The heat content [H ₂₉₈ – H ₀] and the standard molar entropy [S ₂₉₈ – S ₀] are 28.6 ± 0.1 kJ mol^?1 and 186.5 ± 0.5 J mol^?1 K^?1, respectively. The vibrational part of the heat capacitiy was calculated using an elastic Debye temperature of 541 K. The results of the calculations are in good agreement with the maximum theoretical magnetic entropy of 26.8 J mol^?1 K^?1 as calculated from the relationship 2*Rln5.     

Modeling the thermodynamic parameters of six endmember garnets at ambient and high pressures from vibrational data

Raman and infrared spectroscopic data at ambient and high pressures were used to compute the lattice contribution to the heat capacities and entropies of six endmember garnets: pyrope, almandine, spessartine, grossular, andradite and uvarovite. Electronic, configurational and magnetic contributions are obtained from comparing available calorimetric data to the computed lattice contributions. For garnets with entropy in excess of the computed lattice contribution, the overwhelming majority is found in the subambient temperature regime. At room temperature, the non-lattice entropy is approximately 11.5 J/mol-K for pyrope, 49 J/mol-K for almandine, and 19 J/mol-K for andradite. The non-lattice entropy for pyrope and some for almandine cannot be accounted for by magnetic or electronic contributions and is likely to be configurational in nature. Estimates of low temperature non-lattice entropies for both spessartine and uvarovite are made in absence of calorimetric measurements and are based on low temperature calorimetry of other minerals containing the Mn²⁺ and Cr³⁺ cations as well as on solid solution garnets containing these cations. The estimate for uvarovite non-lattice entropy is approximately 18 J/mol-K, while for spessartine, approximately 45 J/mol-K. Neither of these cations is expected to provide electronic contributions to the entropy. For both iron-bearing garnets, a small electronic or magnetic entropy contribution continues above ambient temperatures. High pressure data on pyrope, grossular and andradite permit calculation of the thermodynamic parameters at high pressures, which are important for computation of processes in the Earth’s mantle. Thermal expansion coefficients of these materials were found to be 1.6, 1.5, 1.6×10⁻⁵ K⁻¹ at 298 K, respectively, using a Maxwell relation. These closely match the literature values at ambient conditions.     

Vibrational mode analysis and heat capacity calculation of K2SiSi3O9-wadeite

The phonon dispersions and vibrational density of state (VDoS) of the K₂SiSi₃O₉-wadeite (Wd) have been calculated by the first-principles method using density functional perturbation theory. The vibrational frequencies at the Brillouin zone center are in good correspondence with the Raman and infrared experimental data. The calculated VDoS was then used in conjunction with a quasi-harmonic approximation to compute the isobaric heat capacity (C _P ) and vibrational entropy ( $S_{298}^{0}$ ), yielding C _P (T) = 469.4(6) ? 2.90(2) × 10³  T ^?0.5 ? 9.5(2) × 10⁶  T ^?2 + 1.36(3) × 10⁹  T ^?3 for the T range of 298–1,000 K and $S_{298}^{0}$  = 250.4 J mol^?1 K^?1. In comparison, these thermodynamic properties were calculated by a second method, the classic Kieffer’s lattice vibrational model. On the basis of the vibrational mode analysis facilitated by the first-principles simulation result, we developed a new Kieffer’s model for the Wd phase. This new Kieffer’s model yielded C _P (T) = 475.9(6) ? 3.15(2) × 10³  T ^?0.5 – 8.8(2) × 10⁶  T ^?2 + 1.31(3) × 10⁹  T ^?3 for the T range of 298–1,000 K and $S_{298}^{0}$  = 249.5(40) J mol^?1 K^?1, which are in good agreement both with the results from our first method containing the component of the first-principles calculation and with some calorimetric measurements in the literature.     

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.     

The heat capacity of a natural monticellite and phase equilibria in the system CaO-MgO-SiO2-CO2

The heat capacity of a natural monticellite (Ca_1.00Mg_.09Fe_.91Mn_.01Si_0.99O_3.99) measured between 9.6 and 343 K using intermittent-heating, adiabatic calorimetry yields C_p⁰(298) and S₂₉₈⁰ of 123.64 ± 0.18 and 109.44 ± 0.16 J · mol⁻¹K⁻¹ respectively. Extrapolation of this entropy value to end-member monticellite results in an S⁰₂₉₈ = 108.1 ± 0.2 J · mol⁻¹K⁻¹. High-temperature heat-capacity data were measured between 340–1000 K with a differential scanning calorimeter. The high-temperature data were combined with the 290–350 K adiabatic values, extrapolated to 1700 K, and integrated to yield the following entropy equation for end-member monticellite (298–1700 K): S_T⁰(J · mol⁻¹K⁻¹) = S₂₉₈⁰ + 164.79 In T + 15.337 · 10⁻³T + 22.791 · 10⁵T⁻² − 968.94. Phase equilibria in the CaO-MgO-SiO₂ system were calculated from 973 to 1673 K and 0 to 12 kbar with these new data combined with existing data for akermanite (Ak), diopside (Di), forsterite (Fo), merwinite (Me) and wollastonite (Wo). The location of the calculated reactions involving the phases Mo and Fo is affected by their mutual solid solution. A best fit of the thermodynamically generated curves to all experiments is made when the S⁰₂₉₈ of Me is 250.2 J · mol⁻¹ K⁻¹ less than the measured value of 253.2 J · mol⁻¹ K⁻¹.A best fit to the reversals for the solid-solid and decarbonation reactions in the CaO-MgO-SiO₂-CO₂ system was obtained with the ΔG⁰₂₉₈ (kJ · mole⁻¹) for the phases Ak(−3667), Di(−3025), Fo(−2051), Me(−4317) and Mo(−2133). The two invariant points − Wo and −Fo for the solid-solid reactions are located at 1008 ± 5 K and 6.3 ± 0.1 kbar, and 1361 ± 10 K and 10.2 ± 0.2 kbar respectively. The location of the thermodynamically generated curves is in excellent agreement with most experimental data on decarbonation equilibria involving these phases.     

Entropy and structure of oxidized and reduced iron-bearing silicate glasses

The influence of ferrous and ferric iron on the low-temperature heat capacity and vibrational entropy of silicate glasses has been determined by adiabatic calorimetry. Two pairs of samples based on sodium disilicate and calcium Tschermak molecule compositions have been studied. Along with previous data for another Fe-bearing glass, these results have been used to complement the available set of composition independent partial molar relative entropies of oxides in silicate glasses with S₂₉₈ − S₀ values of 56.7 and 116 J/mol for FeO and Fe₂O₃, respectively. The calorimetric data indicate that the fraction of fivefold coordinated Al is significant in the CaO-“FeO”-Al₂O₃-SiO₂ system and that association of Ca²⁺ and Na⁺ with Fe³⁺ in tetrahedral coordination for charge compensation does not entail significant changes in coordination for these two cations. At very low temperatures, however, the heat capacity is no longer an additive function of composition because of unexpectedly high positive deviations from Debye laws. These anomalies are stronger for the reduced than the oxidized glasses and considerably larger than for iron-free glasses, but their origin cannot be established from the present measurements.     

Thermodynamic data of lawsonite and zoisite in the system CaO–Al2O3–SiO2–H2O based on experimental phase equilibria and calorimetric work

The enthalpy of drop-solution in molten 2PbO·B₂O₃ of synthetic and natural lawsonite, CaAl₂(Si₂O₇)(OH)₂·H₂O, was measured by high-temperature oxide melt calorimetry. The enthalpy of formation determined for the synthetic material is (_fH^Oxides=-168.7Dž.4 kJ mol^-1, or (_fH⁰₂₉₈=-4,872.5dž.0 kJ mol^-1. These values are in reasonable agreement with previously published data, although previous calorimetric work yielded slightly more exothermic data and optimisation methods resulted in slightly less exothermic values. The equilibrium conditions for the dehydration of lawsonite to zoisite, kyanite and quartz/coesite at pressures and temperatures up to 5 GPa and 850 °C were determined by piston cylinder experiments. These results, other recent phase equilibrium data, and new calorimetric and thermophysical data for lawsonite and zoisite, Ca₂Al₃(SiO₄)(Si₂O₇)O(OH), were used to constrain a mathematical programming analysis of the thermodynamic data for these two minerals in the chemical system CaO-Al₂O₃-SiO₂-H₂O (CASH). The following data for lawsonite and zoisite were obtained: (_fH⁰₂₉₈ (lawsonite)=-4,865.68 kJ mol^-1 , S⁰₂₉₈ (lawsonite)=229.27 J K^-1 mol^-1 , (_fH⁰₂₉₈ (zoisite)=-6,888.99 kJ mol^-1 , S⁰₂₉₈ (zoisite)=297.71 J K^-1 mol^-1 . Additionally, a recalculation of the bulk modulus of lawsonite yielded K=120.7 GPa, which is in good agreement with recent experimental work.     

Some binary and ternary silicate solution models

Four different solution models, the two-parameter Margules, the quasi-chemical (QC), the Wilson and the non-random two-liquid (NRTL) model, have been used for fitting the calorimetric excess enthalpy of solution for the following four binary silicate systems: anorthite-albite, pyrope-grossular, diopside-enstatite and diopside-Ca-Tschermak. All models except the Wilson model yield a satisfactory fit to the data but the NRTL model generally results in the lowest residuals. The use of NRTL and QC facilitates the study of the configurational and non-configurational parts of the excess entropy of mixing.Three different methods, namely those of Kohler, Wohl, and Hillert, have been used to combine binary solution properties to predict ternary solution properties. Comparison of computed excess free energy of mixing in a hypothetical solution shows that all the three methods are viable but the Kohler and Wohl methods are similar to each other and are significantly different from the Hillert method. The Kohler method with one or a combination of different binary models is recommended for predicting multicomponent solution properties.Abbreviations G ^ex excess free energy of mixing - H ^ex excess enthalpy of mixing - S ^ex total excess entropy of mixing - S _ex ^c configurational excess entropy of mixing - W _ij interaction energy parameter between speciesi andj - X _i mole fraction of speciesi - QC quasi-chemical - NRTL non-random two-liquid - M Margules formulation - W Wohl's formulation - RK Redlich-Kister - K Bertrand-Kohler - H Hillert - Di diopside (CaMgSi₂O₆) - En enstatite (Mg₂Si₂O₆) - Py pyrope (MgAl_2/3SiO₄) - Gr grossular (CaAl_2/3SiO₄) - CaTs Ca-Tschermak (CaAl₂SiO₆) - Ab albite (NaAlSi₃O₈) - An anorthite (CaAl₂Si₂O₈)     

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

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

On the entropy of glaucophane Na2Mg3Al2Si8O22(OH)2

The heat capacity of glaucophane from the Sesia-Lanza region of Italy having the approximate composition (Na_1.93Ca_0.05Fe_0.02) (Mg_2.60Fe_0.41) (Al_1.83Fe_0.15Cr_0.01) (Si_7.92Al_0.08)O₂₂(OH)₂ was measured by adiabatic calorimetry between 4.6 and 359.4 K. After correcting the C _p ⁰ data to values for ideal glaucophane, Na₂Mg₃Al₂Si₈O₂₂(OH)₂ the third-law entropy S ₂₉₈ ⁰ -S ₀ ⁰ was calculated to be 541.2±3.0 J·mol^-1·K^-1. Our value for S ₂₉₈ ⁰ -S ₀ ⁰ is 12.0 J·mol^-1·K^-1 (2.2%) smaller than the value of Likhoydov et al. (1982), 553.2±3.0, is within 6.2 J·mol^-1·K^-1 of the value estimated by Holland (1988), and agrees remarkably well with the value calculated by Gillet et al. (1989) from spectroscopic data, 539 J·mol^-1·K^-1.