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 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.     

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.     

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     

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.     

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.     

Heat of formation of petalite, LiAlSi4O10

The enthalpy of formation of petalite, LiAlSi₄O₁₀, has been measured using high-temperature solution calorimetry. The measurements were carried out in a Calvet-type twin micro calorimeter at 728?°C. A 2PbO?·?B₂O₃ melt was used as a solvent. Tabulated heats of formation of the components and tabulated heat capacities of the reactants and the product (Robie and Hemingway 1995) were used to calculate the standard heat of formation of petalite from the measured heats of solution. The calculations yielded a mean value of Δ _f H ^pet _298.15=?4872±5.4 kJ mol^?1. This value may be compared to the heat of formation of Δ _f H ^pet _298.15= ?4886.5±6.3 kJ mol^?1 determined by the HF solution calorimetry by Bennington et?al. (1980). Faßhauer et?al. (1998) combined thermodynamic data with phase-equilibrium results to obtain best-fit thermodynamic results using the Bayes method, in order to derive an internally consistent dataset for phases in the NaAlSiO₄– LiAlSiO₄–Al₂O₃–SiO₂–H₂O system. They determined ?4865.6?±?0.8?kJ?mol^?1 as the enthalpy of formation of petalite, a value that is appreciably closer to the enthalpy found in this work.     

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.     

Thermodynamic properties of CoCr2O4: specific heat and magnetic entropy

We present the temperature dependence of the specific heat of CoCr₂O₄ between 2.08 K and 306 K in zero magnetic field. The lattice component can be described by the Komada–Westrum model with a characteristic temperature Θ_KW = 541 K. The entropy of the magnetic component amounts to 33.51 J mol^?1 K^?1 at T = 298.15 K, in good agreement with the magnetic entropy of Co²⁺ and Cr³⁺ ions with completely quenched orbital moments. We compare our results with data available in literature.     

Thermochemistry of monazite-(La) and dissakisite-(La): implications for monazite and allanite stability in metapelites

Thermochemical properties have been either measured or estimated for synthetic monazite, LaPO₄, and dissakisite, CaLaMgAl₂(SiO₄)₃OH, the Mg-equivalent of allanite. A dissakisite formation enthalpy of ?6,976.5 ± 10.0 kJ mol^?1 was derived from high-temperature drop-solution measurements in lead borate at 975 K. A third-law entropy value of 104.9 ± 1.6 J mol^?1 K^?1 was retrieved from low-temperature heat capacity (C _p) measured on synthetic LaPO₄ with an adiabatic calorimeter in the 30–300 K range. The C _p values of lanthanum phases were measured in the 143–723 K range by differential scanning calorimetry. In this study, La(OH)₃ appeared as suitable for drop solution in lead borate and represents an attractive alternative to La₂O₃. Pseudo-sections were calculated with the THERIAK-DOMINO software using the thermochemical data retrieved here for a simplified metapelitic composition (La = ∑REE + Y) and considering monazite and Fe-free epidotes along the dissakisite-clinozoïsite join, as the only REE-bearing minerals. Calculation shows a stability window for dissakisite-clinozoïsite epidotes (T between 250 and 550°C and P between 1 and 16 kbar), included in a wide monazite field. The P–T extension of this stability window depends on the bulk-rock Ca-content. Assuming that synthetic LaPO₄ and dissakisite-(La) are good analogues of natural monazite and allanite, these results are consistent with the REE-mineralogy sequence observed in metapelites, where (1) monazite is found to be stable below 250°C, (2) around 250–450°C, depending on the pressure, allanite forms at the expense of monazite and (3) towards amphibolite conditions, monazite reappears at the expense of allanite.     

Comparative study of the absorptive potential of raw and activated carbon <Emphasis Type="Italic">Acacia nilotica</Emphasis> for Reactive Black 5 dye

Acacia nilotica was used for the adsorption of Reactive Black 5 (RB5) dye from an aqueous solution. Both the raw and activated (with H₃PO₄) carbon forms of Acacia nilotica (RAN and ANAC, respectively) were used for comparison. Various parameters (including dye concentration, contact time, temperature, and pH) were optimized to obtain the maximum adsorption capacity. RAN and ANAC were characterized using Fourier transform infrared spectroscopy, scanning electron microscopy, and energy-dispersive X-ray spectroscopy. The maximum experimental adsorption capacities for RAN and ANAC were 34.79 and 41.01 mg g^?1, respectively, which agreed with the maximum adsorption capacities predicted by the Langmuir, Freundlich, and Dubinin–Radushkevich equilibrium isotherm models. The adsorption data of ANAC showed a good fit to the isotherm models based on the coefficient of determination (R ²): Langmuir type II (R ² = 0.99) > Freundlich (R ² = 0.9853) > Dubinin–Radushkevich (R ² = 0.9659). This result suggested monolayer adsorption of RB5 dye. The adsorption of RB5 dye followed pseudo-second-order kinetics. The RAN adsorbent reflected an exothermic reaction (enthalpy change, ΔH = ?0.006 kJ mol^?1) and increased randomness (standard entropy change, ΔS = 0.038 kJ mol^?1) at the solid–solution interface. In contrast, ANAC reflected both exothermic [?0.011 kJ mol^?1 (303–313 K)] and endothermic [0.003 kJ mol^?1 (313–323 K)] reactions. However, the ΔS value of ANAC was lower when the RB5 adsorption increased from 313 to 323 K. The negative values for the Gibbs free energy change at all temperatures indicated that the adsorption of RB5 dye onto RAN and ANAC was spontaneous in the forward direction.     

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.     

Premelting at fusion of titanite CaTiSiO5: a calorimetric study

An extensive anomalously rapid increase of relative enthalpy H(T) ? H(298 K) of crystalline CaTiSiO₅ was observed by means of high-temperature drop calorimetry when melting point is approached. X-ray diffraction analysis of the quenched products after drop in calorimeter shows that this effect is related to premelting. The determined excess enthalpy of crystals near the melting point reaches up to 115 kJ mol^?1, that is about 82 % of the total enthalpy of melting, indicating that the premelting effect reflects configurational changes in the bulk of the crystals rather than a surface melting or any other type of partial melting. The obtained results support the presumption that calorimetrically measured premelting effect in titanite reflects the energy-consuming temperature-induced disordering of the framework elements, Si and Ti, which are strongly bonded to oxygen.     

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.     

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.     

Application of the cBΩ model to the calculation of diffusion parameters of He in olivine

The validity of the thermodynamic cBΩ model is tested in terms of the experimentally determined diffusion coefficients of He in a natural Fe-bearing olivine (Fo₉₀) and a synthetic end-member forsterite (Mg₂SiO₄) over a broad temperature range (250–950 °C), as reported recently by Cherniak and Watson (Geochem Cosmochim Acta 84:269–279, 2012). The calculated activation enthalpies for each of the three crystallographic axes were found to be (134 ± 5), (137 ± 13) and (158 ± 4) kJ mol^?1 for the [100], [010] and [001] directions in forsterite, and (141 ± 9) kJ mol^?1 for the [010] direction in olivine, exhibiting a deviation of <1 % with the corresponding reported experimental values. Additional point defect parameters such as activation volume, activation entropy and activation Gibbs free energy were calculated as a function of temperature. The estimated activation volumes (3.2–3.9 ± 0.3 cm³ mol^?1) of He diffusion in olivine are comparable with other reported results for hydrogen and tracer diffusion of Mg cations in olivine. The pressure dependence of He diffusion coefficients was also determined, based on single experimental diffusion measurements at 2.6 and 2.7 GPa along the [001] direction in forsterite at 400 and 650 °C.     

Calorimetric determination of the enthalpy of Mg-Fe ordering in orthopyroxene

The enthalpy of Mg-Fe ordering in En₅₀Fs₅₀ orthopyroxene was measured using the transposed temperature drop calorimetric method. Heat effects associated with two consecutive drops were recorded. In the first drop, synthetic orthopyroxene samples equilibrated at 823?K, 0.1?MPa and a f?O₂ of the WI buffer were dropped from 823?K into the calorimeter, which was held at 1173?K. The measured heat effect corresponds to the enthalpy change due to the heat capacity of the sample from 823 to 1173?K and to the enthalpy associated with the (dis)ordering of Mg and Fe²⁺. In the second drop, the samples, with an Fe-Mg order corresponding to 1173?K, were dropped again from 823 to 1173?K. From the difference of the heat effects measured in the two experiments, the enthalpy of disordering associated with the temperature change from 823 to 1173?K was calculated to be ?1.73±0.04 J mol^?1. The observed enthalpy corresponds to a change in the mole fraction of iron on the M2 site, ΔX _Fe,M2=?0.096 ± 0.001, which leads to of ΔH ⁰ _exch of 18.0 ± 0.4 kJ mol^?1 for the exchange reaction: The degree of Fe-Mg order was characterized by ⁵⁷Fe Mössbauer resonance spectroscopy. In order to minimize the error due to the thickness of the absorber, the iron concentration of the absorber was reduced step by step from 5 to 1 mg?Fe?cm^?2. The iron distribution extrapolated to zero thickness was used for the calculations of the enthalpy of exchange reaction.     

Heat capacity and entropy of rutile (TiO<Subscript>2</Subscript>) and nepheline (NaAlSiO<Subscript>4</Subscript>)

 From heat capacities measured adiabatically at low temperatures, the standard entropies at 298.15 K of synthetic rutile (TiO₂) and nepheline (NaAlSiO₄) have been determined to be 50.0 ± 0.1 and 122.8 ± 0.3 J mol⁻¹ K, respectively. These values agree with previous measurements and in particular confirm the higher entropy of nepheline with respect to that of the less dense NaAlSiO₄ polymorph carnegieite. Received: 23 July 2001 / Accepted: 12 October 2001     

Thermodynamic mixing behavior of synthetic Ca-Tschermak–diopside pyroxene solid solutions: II. Heat of mixing and activity–composition relationships

The heat of mixing for the binary solid solution diopside–Ca-Tschermak was investigated at T = 980 K by lead borate solution calorimetry. A new statistical technique was applied to overcome the problem of using experimental data of various precisions. A two-parameter Margules model was fitted to the calorimetric data leading to W _CaTs–Di^H = 31.3 ± 3.4 kJ mol⁻¹ and W ^H _Di–CaTs = 2.4 ± 4.3 kJ mol⁻¹. The results are in good agreement with calorimetric data given in the literature. They agree also with enthalpy data that were extracted from phase equilibrium experiments. With configurational entropy values taken from the literature, the volume and the vibrational entropy, presented in Part I of this work, and the enthalpy data of this study, the activity–composition relationships of the diopside–Ca-Tschermak binary were calculated.     

Thermodynamic properties of chlorite and berthierine derived from calorimetric measurements

In the context of the deep waste disposal, we have investigated the respective stabilities of two iron-bearing clay minerals: berthierine ISGS from Illinois [USA; (Al_0.975FeIII_0.182FeII_1.422Mg_0.157Li_0.035Mn_0.002)(Si_1.332Al_0.668)O₅(OH)₄] and chlorite CCa-2 from Flagstaff Hill, California [USA; (Si_2.633Al_1.367)(Al_1.116FeIII_0.215Mg_2.952FeII_1.712Mn_0.012Ca_0.011)O₁₀(OH)₈]. For berthierine, the complete thermodynamic dataset was determined at 1 bar and from 2 to 310 K, using calorimetric methods. The standard enthalpies of formation were obtained by solution-reaction calorimetry at 298.15 K, and the heat capacities were measured by heat-pulse calorimetry. For chlorite, the standard enthalpy of formation is measured by solution-reaction calorimetry at 298.15 K. This is completing the entropy and heat capacity obtained previously by Gailhanou et al. (Geochim Cosmochim Acta 73:4738–4749, 2009) between 2 and 520 K, by using low-temperature adiabatic calorimetry and differential scanning calorimetry. For both minerals, the standard entropies and the Gibbs free energies of formation at 298.15 K were then calculated. An assessment of the measured properties could be carried out with respect to literature data. Eventually, the thermodynamic dataset allowed realizing theoretical calculations concerning the berthierine to chlorite transition. The latter showed that, from a thermodynamic viewpoint, the main factor controlling this transition is probably the composition of the berthierine and chlorite minerals and the nature of the secondary minerals rather than temperature.