Low-temperature heat capacity and thermodynamic properties of PrPO<Subscript>4</Subscript>

The heat capacity of praseodymium orthophosphate PrPO₄ was measured by adiabatic and relaxation calorimetric techniques at 5.12–345.54 K, and these data were utilized to calculate thermodynamic functions of PrPO₄ at 6–350 K. The Gibbs free energy of PrPO₄ formation Δ_fG⁰(298.15 K) is evaluated at 1851.8 ± 4.7 kJ mol^–1.     

High-temperature heat capacity and thermodynamic properties for end-member titanite (CaTiSiO5)

 The heat capacity of end-member titanite and (CaTiSiO₅) glass has been measured in the range 328–938 K using differential scanning calorimetry. The data show a weak λ-shaped anomaly at 483 ± 5 K, presumably associated with the well-known low-pressure P2₁/a ⇆ A2/a transition, in good agreement with previous studies. A value of 0.196 ± 0.007 kJ mol⁻¹ for the enthalpy of the P2₁/a ⇆ A2/a transition was determined by integration of the area under the curve for a temperature interval of 438–528 K, bracketing the anomaly. The heat capacity data for end-member titanite and (CaTiSiO₅) glass can be reproduced within <1% using the derived empirical equations (temperature in K, pressure in bars):

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     

Low-temperature heat capacity of magnesioferrite (MgFe2O4)

The low-temperature heat capacity of magnesioferrite (MgFe₂O₄) was measured between 1.5 K and 300 K, and thermochemical functions were derived from the results. No heat capacity anomaly was observed. From our data, we suggest a standard entropy (298.15 K) for magnesioferrite of 120.8±0.6 J mol⁻¹ K⁻¹, which is about 2.4 J mol⁻¹ K⁻¹ higher than previously reported calorimetric studies; but is in rough agreement with predictions from sets of internally consistent thermodynamic data.     

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)}.     

A new method to calculate end-member thermodynamic properties of minerals from their constituent polyhedra II: heat capacity, compressibility and thermal expansion

Thermodynamic calculations in petrology are generally performed at pressures and temperatures beyond the standard state conditions. Accurate prediction of mineral equilibria therefore requires knowledge of the heat capacity, thermal expansion and compressibility for the minerals involved. Unfortunately, such data are not always available. In this contribution we present a data set to estimate the heat capacity, thermal expansion and compressibility of mineral end‐members from their constituent polyhedra, based on the premise that the thermodynamic properties of minerals can be described by a linear combination of the fractional properties of their constituents. As such, only the crystallography of the phase of interest needs to be known. This approach is especially powerful for hypothetical mineral end‐members and for minerals, for which the experimental determination of their thermodynamic properties is difficult. The data set consists of the properties for 35 polyhedra in the system K–Na–Ca–Li–Be–Mg–Mn–Fe–Co–Ni–Zn–Al–Ti–Si–H, determined by multiple linear regression analysis on a data set of 111 published end‐member thermodynamic properties. The large number of polyhedra determined allows calculation of a much larger variety of phases than was previously possible, and the choice of constituents together with the large number of thermodynamic input data results in estimates with associated uncertainty of generally <5%. The quality of the data appears to be sufficiently accurate for thermodynamic modelling as demonstrated by modelling the stability of margarite in the CASH system and the position of the talc–staurolite–chloritoid–pyrope absent invariant point in the KMASH system. In both cases, our results overlap within error with published equivalents.     

Changes of specific heat capacity and heat capacity during weathering

An approach is presented which must be followed in the study of a deep-weathering profile. The present research pursues the evaluation of changes in specific heat capacity and heat capacity during weathering. For the first step to obtain the values of specific heat capacity and heat capacity in practical use, the mutual relationships among vertical changes in various kinds of rock properties are investigated in a weathering profile of granite. Two derivable formulas for estimating the values of specific heat capacity and volumetric heat capacity in weathered rock have been theoretically derived from the values of some properties. The changes of specific heat capacity and volumetric heat capacity in rock during natural weathering are also evaluated on the basis of the available data of physical properties.     

Preliminary phase relations involving glaucophane and applications to high pressure petrology: new heat capacity and thermodynamic data

New heat capacity measurements and cell volume data are presented for a very magnesian glaucophane from a Tauern Window eclogite. These data are combined with estimated entropy, thermal expansion, and compressibility data to generate an enthalpy of formation for glaucophane from experimentally determined phase equilibria. The data are supported by preliminary experiments of the author and provide consistent calculations on the pressure of formation of the Tauern eclogites and on the position of the blueschist-greenschist transformation reaction as studied experimentally by Maruyama et al. (1986). The resulting thermodynamic data for glaucophane may be combined with the dataset of Holland and Powell (1985) to calculate phase relations for blueschists and eclogites. The stability of magnesian glaucophane lies in the pressure range between 8 and 32 kbars at 400° C and between 13 and 33 kbars at 600° C, and the unusual eclogite assemblage of glaucophane+kyanite from the Tauern Window is restricted to pressures above 20 kbars at high water activity.     

The heat capacity of two natural chlorite group minerals derived from differential scanning calorimetry

The heat capacity of natural chamosite (X_Fe=0.889) and clinochlore (X_Fe=0.116) were measured by differential scanning calorimetry (DSC). The samples were characterised by X-ray diffraction, microprobe analysis and Mössbauer spectroscopy. DSC measurements between 143 and 623?K were made following the procedure of Bosenick et?al. (1996). The fitted data for natural chamosite (CA) in J?mol^?1?K^?1 give: C _p,CA = 1224.3–10.685?×?10³?×?T ^??0.5???6.4389?× 10⁶?×T ^??2?+?8.0279?×?10⁸?×?T ^??3 and for the natural clinochlore (CE): C _p,CE = 1200.5–10.908?×?10³?×T ^??0.5?? 5.6941?×?10⁶?×?T ^??2?+?7.1166?×?10⁸?×?T ^??3. The corrected C _p-polynomial for pure end-member chamosite (Fe₅Al)[Si₃AlO₁₀](OH)₈ is C _p,CAcor = 1248.3–11.116?× 10³?×?T ^??0.5???5.1623?×?10⁶?×?T ^??2?+?7.1867?×?10⁸×T ^??3 and the corrected C _p-polynomial for pure end-member clinochlore (Mg₅Al)[Si₃AlO₁₀](OH)₈ is C _p,CEcor = 1191.3–10.665?×?10³?×?T ^??0.5???6.5136?×?10⁶?×?T ^??2?+ 7.7206?×?10⁸?×?T ^??3. The corrected C _p-polynomial for clinochlore is in excellent agreement with that in the internally consistent data sets of Berman (1988) and Holland and Powell (1998). The derived C _p-polynomial for chamosite (C _p,CAcor) leads to a 4.4% higher heat capacity, at 300?K, compared to that estimated by Holland and Powell (1998) based on a summation method. The corrected C _p-polynomial (C _p,CAcor) is, however, in excellent agreement with the computed C _p-polynomial given by Saccocia and Seyfried (1993), thus supporting the reliability of Berman and Brown's (1985) estimation method of heat capacities.     

Heat capacity of γ-Fe2SiO4 between 5 and 303 K and derived thermodynamic properties

A multi-anvil device was used to synthesize 24 mg of pure γ-Fe₂SiO₄ crystals at 8.5 GPa and 1,273 K. The low-temperature heat capacity (C _p) of γ-Fe₂SiO₄ was measured between 5 and 303 K using the heat capacity option of a physical properties measurement system. The measured heat capacity data show a broad λ-transition at 11.8 K. The difference in the C _p between fayalite and γ-Fe₂SiO₄ is reduced as the temperature increases in the range of 50–300 K. The gap in C _p data between 300 and 350 K of γ-Fe₂SiO₄ is an impediment to calculation of a precise C _p equation above 298 K that can be used for phase equilibrium calculations at high temperatures and high pressures. The C _p and entropy of γ-Fe₂SiO₄ at standard temperature and pressure (S°₂₉₈) are 131.1 ± 0.6 and 140.2 ± 0.4 J mol⁻¹ K⁻¹, respectively. The Gibbs free energy at standard pressure and temperature (ΔG° _f,298) is calculated to be −1,369.3 ± 2.7 J mol⁻¹ based on the new entropy data. The phase boundary for the fayalite–γ-Fe₂SiO₄ transition at 298 K based on current thermodynamic data is located at 2.4 ± 0.6 GPa with a slope of 25.4 bars/K, consistent with extrapolated results of previous experimental studies.     

The thermodynamic properties of radium

The enthalpy, Gibbs free energy, and entropies of aqueous radium species and radium solids have been evaluated from empirical data, or estimated when necessary for 25°C and 1 bar. Estimates were based on such approaches as extrapolation of the thermodynamic properties of Ca, Sr, and Ba complexes and solids plotted against cationic radii and charge to radius functions, and the use of the Fuoss or electrostatic mathematical models of ion pair formation (Langmuir, 1979). Resultant log K (assoc) and ΔH⁰ (assoc) (kcal/mol) values are: for RaOH⁺ 0.5 and 1.1; RaCl⁺ ?0.10 and 0.50; RaCO⁰₃ 2.5 and 1.07; and RaSO⁰₄ 2.75 and 1.3. Log Ksp and ΔH⁰ (dissoc) (kcal/mol) values for RaCO₃(c) and RaSO₄(c) are ?8.3 and ?2.8, and ?10.26 and ?9.4, respectively.Trace Ra solid solution in salts of Pb and of the lighter alkaline earths, has been appraised based on published distribution coefficient (D) data, where D ～- (mM²⁺)(N_RaX)/(mRa²⁺)(N_MX) (m and N are the aqueous molality and mole fraction of Ra and cation M in salt X, respectively. The empirical solid solution data have been used to derive both enthalpies and Gibbs free energies of solid solution of trace Ra in sulfate and carbonate minerals up to 100°C. Results show that in every case D values decrease with increasing temperature. Among the sulfate and carbonate minerals, D values decrease for the following minerals in the order: anhydrite > celestite > anglesite > barite > aragonite > strontianite > witherite > cerussite.     

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.     

Low-temperature compatibility relations of the assemblage quartz-paragonite and the thermodynamic status of the phase rectorite

The reaction 3 Na-montmorillonite + 2 albite 3 paragonite + 8 quartz has been studied experimentally using starting materials composed of natural low albite, kaolinite and quartz. Rate studies at 2, 4 and 7 kb demonstrate that the reaction takes place at 335–315° C from lower to higher pressures. Attempts to reverse this reaction with runs lasting several months were without success. Comparison with pertinent data from natural mineral assemblages indicate that despite non-reversal, the data presented here may be very near to the true lower thermal compatibility limit of the assemblage quartz-paragonite.The above reaction becomes metastable beyond the upper pressure stability limit of the phase Na-montmorillonite; it is replaced here by another reaction 1 albite + 1 kaolinite 1 paragonite + 2 quartz + 1 H₂O, as suggested originally by Zen (1960). A P-T-grid showing possible compatibility relations of the assemblage quartz-paragonite is provided (Fig. 4). Perusal of natural assemblages belonging to the subsystem Na₂O-Al₂O₃-SiO₂-H₂O lends credence to this grid.In course of the rate studies reported here, various regular paragonite-sodium montmorillonite mixed-layer phases were encountered (Fig. 2); the 11 regular mixed-layer phase represents the synthetic analogue of the mineral rectorite (sometimes called allevardite), widely recorded from deep diagenetic and anchimetamorphic environments. Results of rate-studies (Fig. 3) suggest that the mixed-layer phases are all transient, metastable products obtained during the transformation of the albite-Na-montmorillonite assemblage to paragonite-quartz. As such, rectorite and related mixed-layer phases on the join montmorillonite-paragonite, are always less stable relative to the assemblage Na-montmorillonite-paragonite.     

High-temperature thermodynamic properties of alkali feldspars

Recent hydrofluoric acid solution calorimetric data are used to derive standard enthalpies and Gibbs free energies of formation of low-albite, high-albite, NaAlSi₃O₈ glass, microcline, sanidine, and KAlSi₃O₈ glass. The data are presented as high-temperature functions from 298.15 to 1400° K.     

Halocarbons in the environment: estimates of thermodynamic properties for aqueous chloroethylene species and their stabilities in natural settings

Standard partial molal thermodynamic parameters for the aqueous chlorinated-ethylene species, perchloroethylene (PCE), trichloroethylene (TCE), 1,1-dichloroethylene (1,1-DCE), cis-1,2-dichloroethylene (cis-1,2-DCE), trans-1,2-dichloroethylene (trans-1,2,-DCE), and vinyl chloride (VC) have been estimated by using experimental gas-solubility data and correlation algorithms. The provided thermodynamic values may be used to calculate properties of reactions involving the aqueous chloroethylene species at a wide range of temperatures and pressures. Estimated values for the chloroethylenes were used, along with published values for minerals, gases, aqueous ions, and aqueous neutral organic species, to calculate the stability of chloroethylene species in equilibrium with the minerals magnetite, hematite, pyrite, and pyrrhotite in the subsurface. Estimated values for the aqueous chloroethylenes were also used to calculate reduction potentials for microbially-mediated reductive dechlorination half-reactions at elevated temperatures. Calculations indicate that all aqueous chloroethylene species are energetically favored to decompose to ethylene(aq) under a wide range of conditions in the subsurface, by both abiotic and biotic pathways. Anaerobic microbially mediated degradation is especially favored under conditions at least sufficiently reducing to promote sulfate-reduction, but not under conditions sufficient for microbial denitrification, pyrolusite reduction, or ferric-iron reduction.     

Calculated thermodynamic properties of silica polymorphs

Accurate interatomic potentials have been employed to compute the phonon density of states of αquartz, stishovite and coesite polymorphs of silica. The temperature variation of several thermodynamic properties is calculated by using the phonon density of states to describe the vibrational entropy contribution to the free energy. Results for these polymorphs are in surprisingly good agreement with available experimental data. Moreover, the microscopic origin of quantitative differences in the heat capacity behavior of low and high density polymorphs is established.