Synthesis, characterization and thermochemistry of a Pb-jarosite

The enthalpy of formation from the elements of a well-characterized synthetic Pb-jarosite sample corresponding to the chemical formula (H₃O)_0.74Pb_0.13Fe_2.92(SO₄)₂(OH)_5.76(H₂O)_0.24 was measured by high temperature oxide melt solution calorimetry. This value ( = −3695.9 ± 9.7 kJ/mol) is the first direct measurement of the heat of formation for a lead-containing jarosite. Comparison to the thermochemical properties of hydronium jarosite and plumbojarosite end-members strongly suggests the existence of a negative enthalpy of mixing possibly related to the nonrandom distribution of Pb²⁺ ions within the jarosite structure. Based on these considerations, the following thermodynamic data are proposed as the recommended values for the enthalpy of formation from the elements of the ideal stoichiometric plumbojarosite Pb_0.5Fe₃(SO₄)₂(OH)₆:  = −3118.1 ± 4.6 kJ/mol,  = −3603.6 ± 4.6 kJ/mol and S° = 376.6 ± 4.5 J/(mol K). These data should prove helpful for the calculation of phase diagrams of the Pb-Fe-SO₄-H₂O system and for estimating the solubility product of pure plumbojarosite. For illustration, the evolution of the estimated solubility product of ideal plumbojarosite as a function of temperature in the range 5-45 °C was computed (Log(K_sp) ranging from −24.3 to −26.2). An Eh-pH diagram is also presented.     

Hydration-dehydration behavior and thermodynamics of chabazite

Equilibrium in the chabazite-H₂O system was investigated by isothermal thermogravimetric analysis over a large range of temperatures (from 23 to 315°C) and H₂O-vapor pressures (from 0.03 to 28 mbar). Thermodynamic analysis of the phase-equilibrium data revealed the existence of three energetically distinct types of H₂O, referred to as S-1, S-2, and S-3. At 23°C and 26 mbar of H₂O-vapor pressure, chabazite has maximum H₂O occupancies of 8.2, 11.1, and 3.1 wt.% for S-1, S-2, and S-3, respectively. During dehydration, S-1 H₂O is lost first, followed by S-2 H₂O and then S-3 H₂O, with significant overlap for S-1 and S-2 as well as S-2 and S-3. The thermodynamics of chabazite-H₂O were modeled using three independent equilibrium formulations for S-1, S-2, and S-3. These formulations yielded standard-state molar Gibbs free energy of hydration of −21.8 ± 0.6, −52.1 ± 1.8, and −111.7 ± 6.7 kJ/mol for S-1, S-2, and S-3. Standard-state molar enthalpies of hydration for each type of H₂O are −65.6 ± 0.5, −100.1 ± 1.6, and −156.9 ± 6.2 kJ/mol, respectively. Integral molar values for the Gibbs free energy of hydration for each type of H₂O are −19.0 ± 0.7, −40.1 ± 2.1, and −76.9 ± 9.6 kJ/mol, respectively. Integral molar values for the enthalpy of hydration for each type of H₂O are −62.8 ± 0.6, −88.1 ± 1.9, and −122.2 ± 9.3 kJ/mol, respectively. Integration of the predicted total partial molar enthalpy of hydration for all three types of H₂O over the full H₂O content of chabazite gave an integral molar enthalpy of −39.65 ± 9.3 kJ/mol relative to liquid water. The thermodynamic data obtained for the hydration of natural chabazite were used to predict the hydration state of chemically similar chabazites under various temperatures and P_H2O, ranging from 25 to 400°C and from 10⁻⁵ to 10⁴ bars.     

Thermodynamics of iron oxides: Part III. Enthalpies of formation and stability of ferrihydrite (∼Fe(OH)3), schwertmannite (∼FeO(OH)3/4(SO4)1/8), and ε-Fe2O3

Enthalpies of formation of ferrihydrite and schwertmannite were measured by acid solution calorimetry in 5 N HCl at 298 K. The published thermodynamic data for these two phases and ε-Fe₂O₃ were evaluated, and the best thermodynamic data for the studied compounds were selected.Ferrihydrite is metastable in enthalpy with respect to α-Fe₂O₃ and liquid water by 11.5 to 14.7 kJ•mol⁻¹ at 298.15 K. The less positive enthalpy corresponds to 6-line ferrihydrite, and the higher one, indicating lesser stability, to 2-line ferrihydrite. In other words, ferrihydrite samples become more stable with increasing crystallinity. The best thermodynamic data set for ferrihydrite of composition Fe(OH)₃ was selected by using the measured enthalpies and (1) requiring ferrihydrite to be metastable with respect to fine-grained lepidocrocite; (2) requiring ferrihydrite to have entropy higher than the entropy of hypothetical, well-crystalline Fe(OH)₃; and (3) considering published estimates of solubility products of ferrihydrite. The ΔG°_f for 2-line ferrihydrite is best described by a range of −708.5±2.0 to −705.2±2.0 kJ•mol⁻¹, and ΔG°_f for 6-line ferrihydrite by −711.0±2.0 to −708.5±2.0 kJ•mol⁻¹.A published enthalpy measurement by acid calorimetry of ε-Fe₂O₃ was re-evaluated, arriving at ΔH°_f (ε-Fe₂O₃) = −798.0±6.6 kJ•mol⁻¹. The standard entropy (S°) of ε-Fe₂O₃ was considered to be equal to S° (γ-Fe₂O₃) (93.0±0.2 J•K⁻¹•mol⁻¹), giving ΔG°_f (ε-Fe₂O₃) = −717.8±6.6 kJ•mol⁻¹. ε-Fe₂O₃ thus appears to have no stability field, and it is metastable with respect to most phases in the Fe₂O₃-H₂O system which is probably the reason why this phase is rare in nature.Enthalpies of formation of two schwertmannite samples are: ΔH°_f (FeO(OH)_0.686(SO₄)_0.157•0.972H₂O) = −884.0±1.3 kJ•mol⁻¹, ΔH°_f (FeO(OH)_0.664(SO₄)_0.168•1.226H₂O) = −960.7±1.2 kJ•mol⁻¹. When combined with an entropy estimate, these data give Gibbs free energies of formation of −761.3 ± 1.3 and −823.3 ± 1.2 kJ•mol⁻¹ for the two samples, respectively. These ΔG_f° values imply that schwertmannite is thermodynamically favored over ferrihydrite over a wide range of pH (2-8) when the system contains even small concentration of sulfate. The stability relations of the two investigated samples can be replicated by schwertmannite of the “ideal” composition FeO(OH)_3/4(SO₄)_1/8 with ΔG°_f = −518.0±2.0 kJ•mol⁻¹.     

Formation enthalpy of ThSiO4 and enthalpy of the thorite → huttonite phase transition

The standard enthalpy of formation of thorite and huttonite and the enthalpy of the phase transition between these polymorphs were determined using high-temperature oxide melt solution calorimetry and transposed temperature drop calorimetry. Standard enthalpies of formation of thorite and huttonite are reported for the first time and are −2117.6 ± 4.2 kJ/mol and −2110.9 ± 4.7 kJ/mol, respectively. Based on our measurements, thorite and huttonite are metastable relative to SiO₂ (quartz) and ThO₂ (thorianite) at standard conditions, but are presumably stabilized at high temperature by the entropy contribution. Based on the measured enthalpy of the thorite-huttonite phase transition of 6.7 ± 2.5 kJ/mol, a dP/dT slope for the transformation was calculated as −1.21 ± 0.45 MPa/K.     

An experimental investigation of heulandite-laumontite equilibrium at 1000 to 2000 bar P fluid

The univariant reaction governing the upper stability of heulandite (CaAl₂Si₇O₁₈·6H₂O), heulandite=laumontite+3 quartz+2H₂O (1), has been bracketed through reversal experiments at: 155±6° C, 1000 bar; 175±6° C, 1500 bar; and 180±8° C, 2000 bar. Reversals were established by determining the growth of one assemblage at the expense of the other, using both XRD and SEM studies. The standard molal entropy of heulandite is estimated to be 783.7±16 J mol^–1 K^–1 from the experimental brackets. Predicted standard molal Gibbs free energy and enthalpy of formation of heulandite are –9722.3±6.3 kJ mol^–1 and –10524.3±9.6 kJ mol^–1, respectively. The reaction (1), together with the reaction, stilbite=laumontite+3 quartz+3 H₂O, defines an invariant point at which a third reaction, stilbite=heulandite+ H₂O, meets. By combining the present experimental data with past work, this invariant point is located at approximately 600 bar and 140° C. Heulandite, which is stable between the stability fields of stilbite and laumontite, can occur only at pressures higher than that of the invariant point, for = P _total.These results are consistent with natural parageneses in low-grade metamorphic rocks recrystallized in equilibrium with an aqueous phase in which is very close to unity.     

Thermodynamic properties of strontianite-witherite solid solution (Sr,Ba)CO3

Structural parameters and thermodynamic properties of strontianite — witherite solid solutions have been studied by X-ray powder diffraction, heat flux Calvet calorimetry and cation-exchange equilibria technique. X-ray study of the synthetic samples have shown linear and quadratic (for c-parameter) composition dependencies of the lattice constants in the carbonate solid solution. The thermodynamic energy parameters demonstrate the non-ideal character of strontianite — witherite solid solutions. Enthalpies of solution of the samples have been measured in 2PbO*B₂O₃ at 973 K. The new data on the enthalpy of formation H _f,298.15 ⁰ of SrCO₃ and BaCO₃ were obtained: -1231.4±3.2 and -1209.9±5.8 kJ*mol^-1 respectively. The enthalpy of mixing of the solid solution was found to be positive and asymmetric with maximum at X_Ba (carbonate)=0.35. The composition dependence of the enthalpy of mixing may be described by two — parametric Margules model equation: H _mix=X _BaX _Sr[(4.40±3.91)X _Ba+(28.13±3.91)X _Sr] kJmol^–1 Cation-exchange reactions between carbonates and aqueous SrCl₂-BaCl₂ supercritical solutions (fluids) were carried out at 973 and 1073 K and 2 kbar. Calculated Margules model parameters of the excess free energy are: for orthorhombic carbonate solid solutions W _Sr=W _Ba=11.51±0.40 kJmol^–1 (973 K) and W _Sr=W _Ba=12.09±0.95 kJmol^– (1073 K) for trigonal carbonate solid solutions W _Sr=W _Ba=13.55±0.40 kJmol^– (1073 K).     

Thermochemistry of carbonate-pyroxene equilibria

The enthalpies of drop solution of calcite, magnesite, dolomite, wollastonite and diopside have been measured in a lead borate solvent at 977 K in a Calvettype microcalorimeter. The carbonate calorimetry was done under flowing gas atmosphere. Both natural and synthetic samples were used. From these calorimetric data, the enthalpies of several reactions of carbonate with quartz were calculated. The enthalpies of these reactions (kJ/mol) at 298 K are: calcite+quartzwollastonite+CO₂, 92.3±1.0; magnesite+quartzenstatite+CO₂, 82.9±2.8; dolomite+quartzdiopside+CO₂, 163.0±1.9. These values generally are in agreement with those calculated from Robie et al., Helgeson et al., Berman and Holland and Powell. The enthalpy of dolomite-quartz reaction overlaps marginally with those from Berman and Holland and Powell. The enthalpy of formation of dolomite from magnesite and calcite (-11.1±2.5 kJ/mol) was also derived from the measured enthalpies, and this value is consistent with that from acid solution calorimetric measurements as shown by Navrotsky and Capobianco, but different from values in the earlier literature. These results support the premise that drop-solution of carbonates into molten lead borate results in a well-defined final state consisting of dissolved oxide and evolved CO₂. This was also confirmed by weight change experiments. Thus, oxide melt calorimetry is applicable to carbonates.     

High-temperature heat capacity of Co3O4 spinel: thermally induced spin unpairing transition

A strong anomaly was found in the heat capacity of Co₃O₄ between 1000 K and the decomposition temperature. This anomaly is not related to the decomposition of Co₃O₄ to CoO. The measured entropy of transition, S=46±4 J mol^-1 K^-1 of Co₃O₄, supports the interpretation that this anomaly reflects a spin unpairing transition in octahedrally coordinated Co³⁺ cations. Experimental values of heat capacity, heat content and entropy of Co₃O₄ in the high temperature region are provided. The enthalpy of the spin unpairing transition is 53±4 kJ mol^-1 of Co₃O₄.     

Thermochemistry of yavapaiite KFe(SO4)2: Formation and decomposition

Yavapaiite, KFe(SO₄)₂, is a rare mineral in nature, but its structure is considered as a reference for many synthetic compounds in the alum supergroup. Several authors mention the formation of yavapaiite by heating potassium jarosite above ca. 400°C. To understand the thermal decomposition of jarosite, thermodynamic data for phases in the K-Fe-S-O-(H) system, including yavapaiite, are needed. A synthetic sample of yavapaiite was characterized in this work by X-ray diffraction (XRD), scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR), and thermal analysis. Based on X-ray diffraction pattern refinement, the unit cell dimensions for this sample were found to be a = 8.152 ± 0.001 Å, b = 5.151 ± 0.001 Å, c = 7.875 ± 0.001 Å, and β = 94.80°. Thermal decomposition indicates that the final breakdown of the yavapaiite structure takes place at 700°C (first major endothermic peak), but the decomposition starts earlier, around 500°C. The enthalpy of formation from the elements of yavapaiite, KFe(SO₄)₂, ΔH°_f = −2042.8 ± 6.2 kJ/mol, was determined by high-temperature oxide melt solution calorimetry. Using literature data for hematite, corundum, and Fe/Al sulfates, the standard entropy and Gibbs free energy of formation of yavapaiite at 25°C (298 K) were calculated as S°(yavapaiite) = 224.7 ± 2.0 J.mol⁻¹.K⁻¹ and ΔG°_f = −1818.8 ± 6.4 kJ/mol. The equilibrium decomposition curve for the reaction jarosite = yavapaiite + Fe₂O₃ + H₂O has been calculated, at pH₂O = 1 atm, the phase boundary lies at 219 ± 2°C.     

MgSiO3 ilmenite: Heat capacity,thermal expansivity,and enthalpy of transformation

A new determination, using high temperature drop-solution calorimetry, of the enthalpy of transformation of MgSiO₃ pyroxene to ilmenite gives H ₂₉₈ = 59.03 ±4.26 kJ/mol. The heat capacity of the ilmenite and orthopyroxene phases has been measured by differential scanning calorimetry at 170–700 K; C_p of MgSiO₃ ilmenite is 4–10 percent less than that of MgSiO₃ pyroxene throughout the range studied. The heat capacity differences are consistent with lattice vibrational models proposed by McMillan and Ross (1987) and suggest an entropy change of -18 ± 3 J-K^-1 ·mol^-1, approximately independent of temperature, for the pyroxene-ilmenite transition. The unit cell parameters of MgSiO₃ ilmenite were measured at 298–876 K and yield an average volume thermal expansion coefficient of 2.44 × 10^-5 K^-1. The thermochemical data are used to calculate phase relations involving pyroxene, -Mg₂SiO₄ plus stishovite, Mg₂SiO₄ spinel plus stishovite, and ilmenite in good agreement with the results of high pressure studies.     

Experimental determination of Mn-Mg mixing properties in garnet,olivine and oxide

We have measured the mixing properties of Mn-Mg olivine and Mn-Mg garnet at 1300° C from a combination of interphase partitioning experiments involving these phases, Pt-Mn alloys and Mn-Mg oxide solid solutions. Activity coefficients of Mn dilute in Pt-Mn alloys at 1300° C/1 atm were measured by equilibrating the alloy with MnO at known f _{O 2}. Assuming that the log f _{O 2} of the Mn-MnO equilibrium under these conditions is-17.80 (Robie et al. 1978), we obtain for _Mn: log_Mn = –5.25 + 3.67 X_Mn + 11.41X² _Mn Mixing properties of (Mn,Mg)O were determined by reversing the Mn contents of the alloys in equilibrium with oxide at known f _{O 2}. Additional constraints were obtained by measuring the maximum extent of immiscibility in (Mn,Mg)O at 800 and 750° C. The data are adequately described by an asymmetric (Mn,Mg)O solution with the following upper and lower limits on nonideality: (a) W_Mn = 19.9kj/Mol; W_Mg = 13.7kj/Mol; (b) W_Mn = 19.9kj/Mol; W_Mg = 8.2kj/Mol; Olivine-oxide partitioning was tightly bracketed at 1300° C and oxide properties used to obtain activity-composition relations for Mn-Mg olivine. Despite strong M2 ordering of Mn in olivine, the macroscopic properties are adequately described by a symmetric model with: W^ol = 5.5 ± 2.5 kj/mol (1-site basis) Using these values for olivine, garnet-olivine partitioning at 27 kbar/1300° C leads to an Mn-Mg interaction parameter in garnet given by: W^gt = 1.5 ± 2.5kJ/mol (1-site basis) Garnet-olivine partitioning at 9 kbar/1000° C is consistent with the same extent of garnet nonideality and the apparent absence of excess volume on the pyrope-spessartine join indicates that any pressure-dependence of W^Gt must be small. If olivine and garnet properties are both treated as unknown and the garnet-olivine partitioning data alone used to derive W^Ol and W^Gt, by multiple linear regression, best-fit values of 6.16 and 1.44 kJ/mol. are obtained. These are in excellent agreement with the values derived from metal-oxide, oxide-olivine and olivine-garnet equilibria.     

Energy associated with dislocations: A calorimetric study using synthetic quartz

High temperature oxide melt solution calorimetry was used to study the energy associated with dislocations in quartz by comparing undeformed and deformed single crystals of synthetic quartz. Samples were deformed at 698 K, 1000–1500 MPa at a strain rate of 10^–5 sec^–1. Two sets of calorimetric measurements were made: (i) using a Pt capsule as a container for powdered sample, and (ii) using pellets made from sample powder without any container. For the first set of measurements, the undeformed sample with a dislocation density of enthalpy is sum of heat content H ₉₇₃-H ₂₉₅ and enthalpy of solution in molten lead borate at 973 K of 39.22 ± 1.00 kJ mol^–1, while the sample deformed in the dislocation creep regime with a dislocation density of 6 × 10¹⁰ to 1 × 10¹¹ cm^–2 gave an enthalpy of 38.59 ± 0.78 kJ mol^–1. For the second set of measurements the measured enthalpy of the undeformed sample was 38.87 ± 0.31 kJ mol^–1, and that of a deformed sample with a dislocation density of 3 × 10¹⁰ to 1 × 10¹¹ cm^–2 was 38.24 ± 0.58 kJ mol^–1.The present study and previous theoretical calculations and estimates are consistent and suggest that the energy associated with dislocations in quartz is 0.6 ± 0.6 kJ mol^–1 for a dislocation density of 10¹¹ cm^–2; a precise value is difficult to determine because of the overlapping errors. These results indicate that for geologically realistic dislocation densities, the maximum excess energy due to dislocations would be 0.5 kJ mol^–1 for most minerals; the exact value would depend on the Burgers vector as well as the shear modulus.     

Experimental determination of the activity of chromite in multicomponent spinels

We determined activity-composition relationships in Pt-Cr and Pt-Fe-Cr alloys at 1300°C experimentally and used the results to constrain the thermodynamic properties of chromite-picrochromite spinels. The Pt-Cr binary is characterized by strong negative deviations from ideality throughout the investigated composition range and the activity-composition relationship can be fit by a four-suffix asymmetric regular solution with three binary interaction parameters. The ternary alloy was modeled as a four-suffix asymmetric regular solution; the three ternary interaction parameters in this model were constrained by combining interaction parameters for the three bounding binaries taken from this and previous work with results for a set of experiments in which the activity of Cr in Pt-Fe-Cr-alloys was fixed by coexisting Cr₂O₃ at known f_O2.The free energy of formation of FeCr₂O₄ at 1300°C was determined using the activities of Fe and Cr in Pt-alloys in equilibrium with oxide mixes of FeCr₂O₄ and Cr₂O₃. The free energy of formation of chromite from Fe+Cr₂O₃+O₂ is −202.7 ± 0.4 kJ/mol (1σ), indistinguishable from literature values. The corresponding free energy of formation of FeCr₂O₄ from the elements is −923.5 ± 2.1 kJ/mol (1σ), and the enthalpy of formation at 298 K is −1438 kJ/mol. The activity-composition relationship for the chromite component in (Fe,Mg)Cr₂O₄ solid solutions was determined from a set of experiments in which Pt-alloys were equilibrated with spinel + Cr₂O₃. (Fe,Mg)Cr₂O₄ spinels are nearly ideal at 1300°C; modeling our data with a one-site symmetric regular solution yields an interaction parameter of +2.14 ± 0.62 kJ/mol (1σ), similar to values based on data from the literature.     

Energetics of water dissolution in trachyte glasses and liquids

Enthalpies of dissolution in HF solutions have been measured at 323 K for a series of hydrous trachyte glasses. Enthalpies of mixing between water and molten trachyte have then been calculated from heat capacity data for the same set of samples and available enthalpy for pure water. The moderately negative enthalpies of mixing suggested at 1 bar by the measurements made on glasses almost disappear when trachyte liquids and water are referred to the same temperature, and particularly so when enthalpies of mixing are calculated for a few kbars pressure. As found for albite and phonolite liquids, trachyte melts thus appear to mix nearly ideally as far as enthalpy is concerned. These results imply that the enthalpy of exsolution of water from magmas is very small or negligible under the P-T-X conditions relevant to trachytic volcanism, even for complete degassing of up to 5 wt% H₂O. Furthermore, the viscosity increase associated with exsolution-driven cooling is negligible compared to the decrease caused directly by water exsolution.     

Diffusion of lead in plagioclase and K-feldspar: an investigation using Rutherford Backscattering and Resonant Nuclear Reaction Analysis

Chemical diffusion of Pb has been measured in K-feldspar (Or₉₃) and plagioclase of 4 compositions ranging from An₂₃ to An₉₃ under anhydrous, 0.101 MPa conditions. The source of diffusant for the experiments was a mixture of PbS powder and ground feldspar of the same composition as the sample. Rutherford Backscattering (RBS) was used to measure Pb diffusion profiles. Over the temperature range 700–1050°C, the following Arrhenius relations were obtained (diffusivities in m²s^-1):Oligoclase (An₂₃): Diffusion normal to (001): log D = ( – 6.84 ± 0.59) – [(261 ± 13 kJ mol ^–1)/2.303RT]Diffusion normal to (010): log D = ( – 3.40 ± 0.50) – [(335 ± 11 kJ mol ^–1)/2.303RT]Andesine (An₄₃): Diffusion normal to (001): log D = ( – 6.73 ± 0.54) – [(266 ± 12 kJ mol ^–1)/2.303RT] Diffusion normal to (010) appears to be only slightly slower than diffusion normal to (001) in andesine.Labradorite (An₆₇): Diffusion normal to (001): log D = ( – 7.16 ± 0.61) – [(267 ± 13 kJ mol ^–1)/2.303RT] Diffusion normal to (010) is slower by 0.7 log units on average.Anorthite Diffusion normal to (010): log D = ( – 5.43 ± 0.48) – [(327 ± 11 kJ mol ^–1)/2.303RT]K-feldspar (Or₉₃): Diffusion normal to (001): log D = ( – 4.74 ± 0.52) – [(309 ± 16 kJ mol ^–1)/2.303RT] Diffusion normal to (010): log D = ( – 5.99 ± 0.51) – [(302 ± 11 kJ mol ^–1)/2.303RT]In calcic plagioclase, Pb uptake is correlated with a reduction of Ca, indicating the involvement of PbCa exchange in chemical diffusion. Decreases of Na and K concentrations in sodic plagioclase and K-feldspar, respectively, are correlated with Pb uptake and increase in Al concentration (measured by resonant nuclear reaction analysis), suggesting a coupled process for Pb exchange in these feldspars. These results have important implications for common Pb corrections and Pb isotope systematics. Pb diffusion in apatite is faster than in the investigated feldspar compositions, and Pb diffusion rates in titanite are comparable to both K-feldspar and labradorite. Given these diffusion data and typical effective diffusion radii for feldspars and accessory minerals, we may conclude that feldspars used in common Pb corrections are in general less inclined to experience diffusion-controlled Pb isotope exchange than minerals used in U-Pb dating that require a common Pb correction.     

The enthalpy of fusion of anorthite

The high-temperature enthalpies of liquid and glassy CaAl₂Si₂O₈ were measured by drop calorimetry using a diphenyl ether drop calorimeter. These data are combined with published values of the high-temperature enthalpy of crystalline anorthite and the enthalpy of vitrification of anorthite to obtain the enthalpy of fusion of anorthite. Analysis of the data yields the following preferred values (enthalpy in kcal/mol, uncertainty limits correspond to two standard deviations):enthalpy of vitrification at 985 K, _v H _{v 985}=18.6±0.6; enthalpy of the liquid at 1,830 K, H ₁₈₃₀ ^l ₃₀₀ ^g =130.4±1.2; enthalpy of the glass at 985 K, H ₉₈₅ ^g -H ₃₀₀ ^g =46.7±0.4; enthalpy of crystalline anorthite between 985 and 1,830 K, H ₁₈₃₀ ^c -H ₉₈₅ ^c =69.9±1.4; calculated enthalpy of fusion of anorthite at 1,830 K, _f H ₁₈₃₀= 32.4±2.1.The average heat capacity of supercooled liquid CaAl₂Si₂O₈ between the glass transition (T _g 1,086 K) and the melting point (T _f7=1,830 K) is 102 ± 2 cal/mol/K. The large difference between the enthalpy of fusion and the enthalpy of vitrification for the minerals anorthite and diopside is emphasized. The practice of assuming _fH _vH should be discontinued for silicate compounds for which T _f T _g.     

Calorimetry of silicate melts at 1773 K: measurement of enthalpies of fusion and of mixing in the systems diopside-anorthite-albite and anorthite-forsterite

Transposed-temperature-drop calorimetry, using a Setaram HT 1500 calorimeter, was used to study directly the melting at 1773 K of mixtures of crystalline albite, anorthite, and diopside and of anorthite and forsterite. The enthalpy of albite at 1000–1773 K, starting with both crystalline and glassy samples, was also measured. The results confirm previously measured enthalpies of fusion of albite, diopside and anorthite (Stebbins et al. 1982, 1983; Richet and Bottinga 1984,1986). The new results use thermochemical cycles which completely avoid the glassy state by transforming crystals directly to melts. The enthalpy of fusion of forsterite is estimated to be 89±12 kJ/mol at 1773 K and 114±20 kJ/mol at its melting point of 2163 K. The data allow semiquantitative evaluation of heats of mixing in the molten silicates. Along the Ab-An join, enthalpies of mixing in the liquid at 773 K are the same or somewhat more negative than those in the glass at 986 K, whereas along Ab-Di and An-Di, enthalpies of mixing in the liquid are distinctly more positive than in the glass. These differences correlate with excess heat capacities in the liquids suggested by Stebbins et al. (1984).     

Thermodynamics of open networks: Ordering and entropy in NaAlSiO4 glass,liquid, and polymorphs

The thermodynamic properties of carnegieite and NaAlSiO₄ glass and liquid have been investigated through C _p determinations from 10 to 1800 K and solution-calorimetry measurements. The relative entropies S ₂₉₈-S₀ of carnegieite and NaAlSiO₄ glass are 118.7 and 124.8 J/mol K, respectively. The low-high carnegieite transition has been observed at 966 K with an enthalpy of transition of 8.1±0.3 kJ/mol, and the enthalpy of fusion of carnegieite at the congruent melting point of 1799 K is 21.7±3 kJ/mol. These results are consistent with the reported temperature of the nepheline-carnegieite transition and available thermodynamic data for nepheline. The entropy of quenched NaAlSiO₄ glass at 0 K is 9.7±2 J/mol K and indicates considerable ordering among AlO₄ and SiO₄ tetrahedra. In the liquid state, progressive, temperature-induced Si, Al disordering could account for the high configurational heat capacity. Finally, the differences between the entropies and heat capacities of nepheline and carnegieite do not seem to conform to current polyhedral modeling of these properties     

The Blosseville Coast basalts of East Greenland: Their occurrence,composition and temporal variations

In the system CaO-MgO-A1₂O₃-SiO₂ the tie lines connecting anorthite with other phases are sequentially broken down with increasing pressure according to the following univariant reactions: anorthite+ enstatite_ss+sillimanite pyrope-grossular_ss+quartz (3), anorthite+enstatite_ss pyrope-grossular_ss+diopside_ss+quartz (2), anorthite+pyrope-grossular_ss+ quartz diopside_ss+kyanite (4) and anorthite+diopside_ss grossular-pyrope_ss +kyanite+quartz (8). At 1,200 ° C these reactions occur at 14.5± 0.5, 15.5±0.5, 19.5±0.5 and 26.4±1 kilobar and have positive slopes (dP/dT) of 1±0.5, 2.8±0.5, 13.3±0.5 and 24±2bars/°C respectively. An invariant point involving kyanite rather than sillimanite, occurs at 850 °C±25 °C and 14.5±0.5kbar at the intersection of reactions (3), (2) and (4). Reaction(4) exhibits significant curvature with an increase in dP/dT from 13.3±0.5 to 18.5± 0.5 bars/°C between 1,050° and 850° C. The pressure at which the complete grossular-pyrope join is stable with quartz is estimated at 41 ± 1 kbar at 1,200 ° C. The pressure at which garnet appears according to reaction (2) is lowered by 5 kbar for a composition with anorthite and orthopyroxene (En_0.5Fs_0.5). Enstatite and plagioclase (An_0.5Ab_0.5) first produce garnet at 2 kbar higher pressure than enstatite and pure anorthite (reaction (2)). The calcium content of garnet in various divariant assemblages is relatively insensitive to temperature but very sensitive to pressure, it is therefore a useful geobarometer. At metamorphic temperatures of 700–850 °C pressures of 8–10 kbar are required for the formation of quartz-bearing garnet granulites containing calcic plagioclase and with (Mg/Mg+Fe) bulk = 0.5.     

Calorimetric study of olivine solid solutions in the system Mg2SiO4-Fe2SiO4

Solution enthalpies of synthetic olivine solid solutions in the system Mg₂SiO₄-Fe₂SiO₄ have been measured in molten 2PbO·B₂O₃ at 979 K. The enthalpy data show that olivine solid solutions have a positive enthalpy of mixing and the deviation from ideality is approximated as symmetric with respect to composition, in contrast to the previous study. Applying the symmetric regular solution model to the present enthalpy data, the interaction parameter of ethalpy (W_H) is estimated to be 5.3±1.7 kJ/mol (one cation site basis). Using this W_h and the published data on excess free energy of mixing, the nonideal parameter of entropy (W_s) of olivine solid solutions is estimated as 0.6±1.5 J/mol·K.