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.     

Low-temperature heat capacities,entropies and high-pressure phase relations of MgSiO<Subscript>3</Subscript> ilmenite and perovskite

Low-temperature isobaric heat capacities (C _p ) of MgSiO₃ ilmenite and perovskite were measured in the temperature range of 1.9–302.4 K with a thermal relaxation method using the Physical Properties Measurement System. The measured C _p of perovskite was higher than that of ilmenite in the whole temperature range studied. From the measured C _p , standard entropies at 298.15 K of MgSiO₃ ilmenite and perovskite were determined to be 53.7 ± 0.4 and 57.9 ± 0.3 J/mol K, respectively. The positive entropy change (4.2 ± 0.5 J/mol K) of the ilmenite–perovskite transition in MgSiO₃ is compatible with structural change across the transition in which coordination of Mg atoms is changed from sixfold to eightfold. Calculation of the ilmenite–perovskite transition boundary using the measured entropies and published enthalpy data gives an equilibrium transition boundary at about 20–23 GPa at 1,000–2,000 K with a Clapeyron slope of −2.4 ± 0.4 MPa/K at 1,600 K. The calculated boundary is almost consistent within the errors with those determined by high-pressure high-temperature in situ X-ray diffraction experiments.     

Thermodynamic properties of copper carbonates — malachite Cu2(OH)2CO3 and azurite Cu3(OH)2(CO3)2

The thermodynamic properties of the copper carbonates malachite and azurite have been studied by adiabatic calorimetry, by heat-flux Calvet Calorimetry, by differential thermal analysis (DTA) and by thermogravimetrie (TGA) analysis. The heat capacities, C _p ⁰ of natural malachite and azurite have been measured between 3.8 and 300 K by low-temperature adiabatic calorimetry. The heat capacity of azurite exhibits anomalous behavior at low temperatures. At 298.15 K the molar heat capacities C _p ⁰ and the third law entropies S _298.15 ⁰ are 228.5±1.4 and 254.4±3.8 J mol^?1 K^?1 for azurite and 154.3±0.93 and 166.3±2.5 J mol^?1 K^?1 for malachite. Enthalpies of solution at 973 K in lead borate 2PbO·B₂O₃ have been measured for heat treated malachite and azurite. The enthalpies of decomposition are 105.1±5.8 for azurite and 66.1±5.0 kJ mol^? for malachite. The enthalpies of formation from oxides of azurite and malachite determined by oxide melt solution calorimetry, are ?84.7±7.4 and ?52.5±5.9 kJ mol^?1, respectively. On the basis of the thermodynamic data obtained, phase relations of azurite and malachite in the system Cu²⁺-H₂O-CO₂ at 25 and 75 °C have been studied.     

Heat capacity and thermodynamic properties of GdPO<Subscript>4</Subscript> in the temperature range 0–1600 K

The heat capacity of gadolinium orthophosphate (GdPO₄) measured in the temperature range 11.15–344.11 K by adiabatic calorimetry and available literature data were used to calculate its thermodynamic functions at 0–1600 K. At 298.15 K, these functions are as follows: C _p ⁰(298.15 K) = 101.85 ± 0.05 J K⁻¹ mol⁻¹, S ⁰(298.15 K) = 123.82 ± 0.18 J K⁻¹ mol⁻¹, H ⁰(298.15 K)–H ⁰(0) = 17.250 ± 0.012 kJ mol⁻¹, and Φ ⁰(298.15 K) = 65.97 ± 0.18 J K⁻¹ mol⁻¹ The calculated Gibbs free energy of formation from the elements of GdPO₄ is Δ _f G ⁰ (298.15 K) = −1844.3 ± 4.7 kJ mol⁻¹.     

Heat capacity and thermodynamic functions of xenotime YPO<Subscript>4</Subscript>(c) at 0–1600 K

The heat capacity of xenotime YPO₄(c) was measured by adiabatic calorimetry at 4.78–348.07 K. Our experimental and literature data on H ⁰(T)-H ⁰(298.15 K) of Y orthophosphate were utilized to derive the C _p ⁰(T) function of xenotime at 0–1600 K, which was then used to calculate the values of thermodynamic functions: entropy, enthalpy change, and reduced Gibbs energy. These functions assume the following values at 298.15 K: C _p ⁰ (298.15 K) = 99.27 ± 0.02 J K⁻¹ mol⁻¹, S ⁰(298.15 K) = 93.86 ± 0.08 J K⁻¹ mol⁻¹, H ⁰(298.15 K) − H ⁰(0) = 15.944 ± 0.005 kJ mol⁻¹, Φ⁰(298.15 K) = 40.38 ± 0.08 J K⁻¹ mol⁻¹. The value of the free energy of formation Δ _f G ⁰(YPO₄, 298.15 K) is −1867.9 ± 1.7 kJ mol⁻¹.     

Heat capacity and thermodynamic functions of pretulite ScPO<Subscript>4</Subscript>(c) at 0–1600 K

The heat capacity of synthetic pretulite ScPO₄(c) was measured by adiabatic calorimetry within a temperature range of 12.13–345.31 K, and the temperature dependence of the pretulite heat capacity at 0–1600 K was derived from experimental and literature data on H ⁰(T)-H ⁰(298.15 K) for Sc orthophosphate. This dependence was used to calculate the values of the following thermodynamic functions: entropy, enthalpy change, and reduced Gibbs energy. They have the following values at 298.15 K: C _p ⁰ (298.15 K) = 97.45 ± 0.06 J K⁻¹ mol⁻¹, S ⁰(298.15 K) = 84.82 ± 0.18 J K⁻¹ mol⁻¹, H ⁰(298.15 K)-H ⁰(0) = 14.934 ± 0.016 kJ mol⁻¹, and Φ ⁰(298.15 K) = 34.73 ± 0.19 J K⁻¹mol⁻¹. The enthalpy of formation Δ _f H ⁰(ScPO₄, 298.15 K) = − 1893.6 ± 8.4 kJ mol⁻¹.     

Thermodynamic functions of eskolaite Cr<Subscript>2</Subscript>O<Subscript>3</Subscript>(c) at 0–1800 K

The heat capacity of eskolaite Cr₂O₃(c) was determined by adiabatic vacuum calorimetry at 11.99–355.83 K and by differential calorimetry at 320–480 K. Experimental data of the authors and data compiled from the literature were applied to calculate the heat capacity, entropy, and the enthalpy change of Cr₂O₃ within the temperature range of 0–1800 K. These functions have the following values at 298.15 K: C _p ⁰ (298.15) = 121.5 ± 0.2 J K⁻¹mol⁻¹, S ⁰(298.15) = 80.95 ± 0.14 J K⁻¹mol⁻¹, and H ⁰(298.15)-H ⁰(0) = 15.30±0.02 kJ mol⁻¹. Data were obtained on the transitions from the antiferromagnetic to paramagnetic states at 228–457 K; it was determined that this transition has the following parameters: Neel temperature T _N = 307 K, Δ _tr S = 6.11 ± 0.12 J K⁻¹mol⁻¹ and δ _tr H = 1.87 ± 0.04 kJ mol⁻¹.     

Physical properties of calcium aluminates from vibrational spectroscopy

Heat capacity (C_V) and entropy (S) as a function of temperature were calculated for phases in the CaO-Al₂O₃ system from vibrational spectra using a quasi-harmonic model. Calculated values of C_V at 298 K for the calcium aluminates may have uncertainties as small as ±1%, based on comparison with published calorimetric data for CaO, Al₂O₃, and CaAl₂O₄. For hibonite (CaAl₁₂O₁₉), we predict C_P as 519.3 J/mol-K and S as 391.7 J/mol-K, at 298 K. For grossite (CaAl₄O₇), calculated values of C_P as 195.9 J/mol-K and of S as 172.0 J/mol-K are slightly smaller than the available calorimetric data at 298 K, consistent with calorimetric data having been obtained from samples containing ∼10 wt% hibonite impurities. Thermal conductivity at 298 K (k₀) is predicted from peak widths of the vibrational modes using the damped harmonic oscillator model of a phonon gas. Calculations of k₀ for CaO and Al₂O₃ differ from the measurements by 17% and 5%, respectively. The discrepancy for lime is larger due to uncertainties in its peak widths. This comparison suggests that our results for the calcium aluminates should be more accurate than conventional measurements of k₀ which are commonly uncertain by ∼25%.     

Low-temperature thermodynamic properties of disordered zeolites of the natrolite group

 The heat capacity of paranatrolite and tetranatrolite with a disordered distribution of Al and Si atoms has been measured in the temperature range of 6–309 K using the adiabatic calorimetry technique. The composition of the samples is represented with the formula (Na_1.90K_0.22Ca_0.06)[Al_2.24Si_2.76O₁₀]·nH₂O, where n=3.10 for paranatrolite and n=2.31 for tetranatrolite. For both zeolites, thermodynamic functions (vibrational entropy, enthalpy, and free energy function) have been calculated. At T=298.15 K, the values of the heat capacity and entropy are 425.1 ± 0.8 and 419.1 ±0.8 J K⁻¹ mol⁻¹ for paranatrolite and 381.0 ± 0.7 and 383.2 ± 0.7 J K⁻¹ mol⁻¹ for tetranatrolite. Thermodynamic functions for tetranatrolite and paranatrolite with compositions corrected for the amount of extraframework cations and water molecules have also been calculated. The calculation for tetranatrolite with two water molecules and two extraframework cations per formula yields: C _p (298.15)=359.1 J K⁻¹ mol⁻¹, S(298.15) −S(0)=362.8 J K⁻¹ mol⁻¹. Comparing these values with the literature data for the (Al,Si)-ordered natrolite, we can conclude that the order in tetrahedral atoms does not affect the heat capacity. The analysis of derivatives dC/dT for natrolite, paranatrolite, and tetranatrolite has indicated that the water- cations subsystem within the highly hydrated zeolite may become unstable at temperatures above 200 K. Received: 30 July 2001 / Accepted: 15 November 2001     

Thermodynamic properties of glaucophane new data from calorimetric and spectroscopic measurements

New data concerning glaucophane are presented. New high temperature drop calorimetry data from 400 to 800 K are used to constrain the heat capacity at high temperature. Unpublished low temperature calorimetric data are used to estimate entropy up to 900 K. These data, corrected for composition, are fitted for C _p and S to the polynomial expressions (J · mol^?1 · K^?2) for T> 298.15 K: $$\begin{gathered} C_p = 11.4209 * 10^2 - 40.3212 * 10^2 /T^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} - 41.00068 * 10^6 /T^2 \hfill \\ + 52.1113 * 10^8 /T^3 \hfill \\ \end{gathered} $$ $$\begin{gathered} S = 539 + 11.4209 * 10^2 * \left( {\ln T - \ln 298.15} \right) - 80.6424 * 10^2 \hfill \\ * \left( {T^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} - 1/\left( {298.15} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } \right) + 20.50034 * 10^6 \hfill \\ * \left( {T^{ - 2} - 1/\left( {298.15} \right)^2 } \right) - 17.3704 * 10^8 * \left( {T^{ - 3} - \left( {1/298.15} \right)^3 } \right) \hfill \\ \end{gathered} $$ IR and Raman spectra from 50 to 3600 cm^?1 obtained on glaucophane crystals close to the end member composition are also presented. These spectroscopic data are used with other data (thermal expansion, acoustic velocities etc.) in vibrational modelling. This last method provides an independent way for the determination of the thermodynamic properties (C_p and entropy). The agreement between measured and calculated properties is excellent (less than 2% difference between 100 and 1000 K). It is therefore expected that vibrational modelling could be applied to other amphiboles for which spectroscopic data are available. Finally, the enthalpy of formation of glaucophane is calculated.     

Heat capacity and thermodynamic properties of andradite garnet,Ca3Fe2Si3O12, between 10 and 1000 K and revised values for ΔfGom (298.15 K) of hedenbergite and wollastonite

The heat capacity of synthetic andradite garnet (Ca₃Fe₂Si₃O₁₂) was measured between 9.6 and 365.5 K by cryogenic adiabatic calorimetry and from 340 to 990 K by differential scanning calorimetry. At 298.15 K C^o_p,m and S^o_m are 351.9 ± 0.7 and 316.4 ± 2.0 J/(mol·K), respectively.Andradite has a λ-peak in C^o_p,m with a maximum at 11.7 ± 0.2 K which is presumably associated with the antiferromagnetic ordering of the magnetic moments of the Fe³⁺ ions. The Gibbs free energy of formation, Δ_fG^o_m (298.15 K) of andradite is −5414.8 ± 5.5 kJ/mol and was obtained by combining our entropy and heat capacity data with the known breakdown of andradite to pseudowollastonite and hematite at ≈ 1410 to 1438 K. From a reexamination of the calcite + quartz = wollastonite equilibrium data we obtained Δ_fH^o_m (298.15 K) = − 1634.5 ± 1.8 kJ/mol for wollastonite.Between 300 and 1000 K the molar heat capacity of andradite can be represented by the equation C^o_p,m = 809.24 - 7.025 × 10−2T− 7.403 × 10³T−0.5 − 6.789 × 10⁵T−2. We have also used our thermochemical data for andradite to estimate the Gibbs free energy of formation of hedenbergite (CaFeSi₂O₆) for which we obtained Δ_fG^o_m (298.15 K) = −2674.3 ± 5.8 kJ/mol.     

The high-temperature heat capacity of natural calcite (CaCO3)

The heat capacity (C _P) of a natural sample of calcite (CaCO₃) has been measured from 350 to 775 K by differential scanning calorimetry (DSC). Heat capacities determined for a powdered sample and a single-crystal disc are in close agreement and have a total uncertainty of ±1 percent. The following equation for the heat capacity of calcite from 298 to 775 K was fit by least squares to the experimental data and constrained to join smoothly with the low-temperature heat capacity data of Staveley and Linford (1969) (C _P in J mol^?1 K^?1, T in K): $$\begin{gathered} C_p = - 184.79 + 0.32322T - 3,688,200T^{ - 2} \hfill \\ {\text{ }} - (1.2974{\text{ }} \times {\text{ 10}}^{ - {\text{4}}} )T^2 + 3,883.5T^{ - 1/2} \hfill \\ \end{gathered} $$ Combining this equation with the S ₂₉₈ ⁰ value from Staveley and Linford (1969), entropies for calcite are calculated and presented to 775 K. A simple method of extrapolating the heat capacity function of calcite above 775 K is presented. This method provides accurate entropies of calcite for high-temperature thermodynamic calculations, as evidenced by calculation of the equilibrium: CaCO_{3 (s)}=CaO_(s)+CO_{2 (s)}.     

Calorimetric Study of Natural Anapaite

The thermochemical study of natural hydrous calcium and iron phosphate, anapaite Ca₂Fe(PO₄)₂ · 4H₂O (Kerch iron ore deposit, Crimea, Russia), was carried out using high-temperature melt solution calorimetry with a Tian-Kalvet microcalorimeter. The enthalpy of formation of the mineral from elements was obtained to be Δ _f H_el°(298.15 K) =–4812 ± 16 kJ/mol. The values of the standard entropy and the Gibbs energy of anapaite formation are S°(298.15 K) = 404.2 J/K mol and Δ _f G_el°(298.15 K) =–4352 ± 16 kJ/mol, respectively.     

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.     

Thermophysical properties of ilvaite CaFe 2 2+ Fe3+Si2O7O (OH); heat capacity from 7 to 920 K and thermal expansion between 298 and 856 K

The heat capacity of ilvaite from Seriphos, Greece was measured by adiabatic shield calorimetry (6.4 to 380.7 K) and by differential scanning calorimetry (340 to 950 K). The thermal expansion of ilvaite was also investigated, by X-ray methods, between 308 and 853 K. At 298.15 K the standard molar heat capacity and entropy for ilvaite are 298.9±0.6 and 292.3±0.6 J/(mol. K) respectively. Between 333 and 343 K ilvaite changes from monoclinic to orthorhombic. The antiferromagnetic transition is shown by a hump in C _p ⁰ with a Néel temperature of 121.9±0.5 K. A rounded hump in C _p ⁰ between 330 and 400 K may possibily arise from the thermally activated electron delocalization (hopping) known to take place in this temperature region.     

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.     

Phase equilibrium and calorimetric study of the transition of MnTiO3 from the ilmenite to the lithium niobate structure and implications for the stability field of perovskite

The phase boundary between MnTiO₃ I (ilmenite structure) and MnTiO₃ II (lithium niobate structure) has been determined by analysis of quench products from reversal experiments in a cubic anvil apparatus at 1073–1673 K and 43–75 kbar using mixtures of MnTiO₃ I and II as starting materials. Tight brackets of the boundary give P(kbar)=121.2−0.045 T(K). Thermodynamic analysis of this boundary gives ΔH^o=5300±1000 J·mol⁻¹, ΔS^o = 1.98 ±1J·K⁻¹· mol⁻¹. The enthalpy of transformation obtained directly by transposed-temperature-drop calorimetry is 8359 ±2575 J·mol⁻¹. Possible topologies of the phase relations among the ilmenite, lithium niobate, and perovskite polymorphs are constrained using the above data and the observed (reversible with hysteresis) transformation of II to III at 298 K and 20–30 kbar (Ross et al. 1989). The observed II–III transition is likely to lie on a metastable extension of the II–III boundary into the ilmenite field. However the reversed I–II boundary, with its negative dP/ dT does represent stable equilibrium between ilmenite and lithium niobate, as opposed to the lithium niobate being a quench product of perovskite. We suggest a topology in which the perovskite occurs stably at low T and high P with a triple point (I, II, III) at or below 1073 K near 70 kbar. The I–II boundary would have a negative P-T slope while the II–III and I–III boundaries would be positive, implying that entropy decreases in the order lithium niobate, ilmenite, perovskite. The inferred positive slope of the ilmenite-perovskite transition in MnTiO₃ is different from the negative slopes in silicates and germanates. These thermochemical parameters are discussed in terms of crystal structure and lattice vibrations.     

Thermodynamic properties of Pd chloride complexes and the Pd2+(aq) ion in aqueous solutions

Based on the expert review of literature data on the thermodynamic properties of species in the Cl-Pd system, stepwise and overall stability constants are recommended for species of the composition [PdCl _n ]^{2 ? n} , and the standard electrode potential of the half-cell PdCl ₄ ^2? /Pd(c) is evaluated at E _298,15° = 0.646 ± 0.007 V, which corresponds to Δ _f G _298.15° = ?400.4 ± 1.4 kJ/mol for the ion PdCl ₄ ^2? (aq). Derived from calorimetric data, Δ _f H _298.15° PdCl ₄ ^2? (aq) = ?524.6 ± 1.6 kJ/mol and Δ _f H _298.15° Pd²⁺(aq) = 189.7 ± 2.6 kJ/mol. The assumed values of the overall stability constant of the PdCl ₄ ^2? ion and the standard electrode potential of the PdCl ₄ ^2? /Pd(c) half-cell correspond to Δ _f G _298.15° = 190.1 ± 1.4 kJ/mol and S _298.15° = ?94.2 ± 10 J/(mol K) for the Pd²⁺(aq) ion.     

Thermodynamic and magnetic properties of knorringite garnet (Mg3Cr2Si3O12) based on low-temperature calorimetry and magnetic susceptibility measurements

The low-temperature heat capacity of knorringite garnet (Mg₃Cr₂Si₃O₁₂) was measured between 2 and 300 K, and thermochemical functions were derived from the results. The measured heat capacity curves show a sharp lambda-shaped anomaly peaking at around 5.1 K. Magnetic susceptibility data show that the transition is caused by antiferromagnetic ordering. From the C _p data, we suggest a standard entropy (298.15 K) of 301 ± 2.5 J mol^?1 K^?1 for Mg₃Cr₂Si₃O₁₂. The new data are also used in conjunction with previous experimental results to constrain ?H _f ° for knorringite.     

Revised values for the Gibbs free energy of formation of [Al(OH)4 aq−], diaspore,boehmite and bayerite at 298.15 K and 1 bar,the thermodynamic properties of kaolinite to 800 K and 1 bar,and the heats of solution of several gibbsite samples

Solution calorimetric measurements compared with solubility determinations from the literature for the same samples of gibbsite have provided a direct thermochemical cycle through which the Gibbs free energy of formation of [Al(OH)_{4 aq}^?] can be determined. The Gibbs free energy of formation of [Al(OH)_{4 aq}^?] at 298.15 K is ?1305 ± 1 kJ/mol. These heat-of-solution results show no significant difference in the thermodynamic properties of gibbsite particles in the range from 50 to 0.05 μm.The Gibbs free energies of formation at 298.15 K and 1 bar pressure of diaspore, boehmite and bayerite are ?9210 ± 5.0, ?918.4 ± 2.1 and ?1153 ± 2 kJ/mol based upon the Gibbs free energy of [A1(OH)_{4 aq}^?] calculated in this paper and the acceptance of ?1582.2 ± 1.3 and ?1154.9 ± 1.2 kJ/mol for the Gibbs free energy of formation of corundum and gibbsite, respectively.Values for the Gibbs free energy formation of [Al(OH)_{2 aq}⁺] and [AlO_{2 aq}^?] were also calculated as ?914.2 ± 2.1 and ?830.9 ± 2.1 kJ/mol, respectively. The use of [AlC_{2 aq}^?] as a chemical species is discouraged.A revised Gibbs free energy of formation for [H₄SiO_4aq⁰] was recalculated from calorimetric data yielding a value of ?1307.5 ± 1.7 kJ/mol which is in good agreement with the results obtained from several solubility studies.Smoothed values for the thermodynamic functions C_P⁰, ($\text{H}{}_{\mathrm{T}}{}^0\text{- H}{}_{298}{}^0\text{)}\text{T}$, $\text{(}\text{G}{}_{\mathrm{T}}{}^0\text{- H}{}_{298}{}^0\text{)}\text{T}$, S_T⁰ - S₀⁰, $\text{ΔH}{}_{\mathrm{?,298}}{}^0$ kaolinite are listed at integral temperatures between 298.15 and 800 K. The heat capacity of kaolinite at temperatures between 250 and 800 K may be calculated from the following equation: C_P⁰ = 1430.26 ? 0.78850 T + 3.0340 × 10^?4T² ?1.85158 × 10^?4T²$\text{1}\text{2}\text{+ 8.3341 × 10}{}^6\text{T}{}^{\mathrm{?2}}$.The thermodynamic properties of most of the geologically important Al-bearing phases have been referenced to the same reference state for Al, namely gibbsite.