Low-temperature Adiabatic Calorimetry Research Articles

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, Cp0of 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 Cp0and the third law entropies S298.150are 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.

Magnetocaloric effect and main parameters of Bi 2Sr 2Ca 2Cu 3Oy textured ceramic superconductor

Low-temperature adiabatic calorimetry in fields up to 4 T is used to study the change in entropy, ΔS, at the transition to the mixed state in Bi 2Sr 2Ca 2Cu 3 O y textured ceramics. The slope of the upper critical field was evaluated using magnetoresistance measurements and taking into account a fluctuation contribution to the conductivity at T > T c . Near T c ΔS/ ΔH≈0.5 Oe K −1 in the direction normal to the ab-plane, d H c2 ⊥ ab / d ≈ −0.4 T K −1, d H c2 ‖ ab / dT≈ − 13 T K −1. These values give the Ginzburg-Landau parameters k ⊥ ≈ 16 and k ‖ ≈ 450. It is shown that the region T>60 K is a validity interval of the Ginzburg-Landau theory. The value of the lower critical field H cl(0) ≈ 1300 Oe is estimated.

An internally consistent model for the thermodynamic properties of Fe-Mg-titanomagnetite-aluminate spinels

A model is developed for the thermodynamic properties of Fe2+−Mg2+-aluminate-titanate-ferrite spinels of space group Fd3m. The model incorporates an expression for the configurational entropy of mixing which accounts for long-range order over tetrahedral and octahedral sites. Short-range order or departures from cubic symmetry are not considered. The non-configurational Gibbs energy is formulated as a second degree Taylor expansion in six linearly independent composition and ordering variables. The model parameters are calibrated to reproduce miscibility gap constraints, order-disorder phenomena in MgAl2O4 and MgFe2O4, and Fe2+−Mg2+ partitioning data between olivine and: (1) aluminate spinels; (2) ferrite spinels; (3) titanate spinels; (4) mixed aluminate-ferrite spinels. This calibration is achieved without invoking non-configurational excess entropies of mixing. The model predicts that the ordering state of FeAl2O4 is more normal than that of MgAl2O4. It also successfully accounts for heat of solution measurements and activity-composition relations in the constituent binaries. Phase equilibrium constraints require that the structure of Fe3O4 is more inverse than random at all temperatures and that Mg2+ has a strong tetrahedral site preference with respect to that of Fe2+. The analysis suggests that in the titanates short range order on octahedral sites may be significant at temperatures as high as 1300° C. Constraints developed from calibrating the thermodynamic properties of Fe2+−Mg2+-aluminatetitanate-ferrite spinel solid solutions permit extension of the database of Berman (1988) to include estimates of the end-member properties of hercynite (FeAl2O4), ulvospinel (Fe2TiO4), MgFe2O4 and cubic Mg2TiO4. In constructing these estimates, provision is made for low-temperature magnetic entropy contributions and the energetic consequences of disordering the aluminates and the ferrites. These estimates are consistent with all of the available low-temperature adiabatic calorimetry, high-temperature heat content, and heat of solution measurements on the end-members. The analysis implies that there is a substantial heat capacity anomaly in the range 300°–900° C associated with disordering of the MgAl2O4 structure while that in FeAl2O4 becomes significant at temperatures above 700° C. The same heat capacity response in the ferrites indicates that the order/disorder transformation is coupled to the antiferromagnetic-paramagnetic transition in MgFe2O4 but takes place well above the ferrimagnetic-paramagnetic transition in magnetite. The proposed model is internally consistent with solution theory reported elsewhere for Fe2+−Mg2+ olivines and orthopyroxenes (Sack and Ghiorso 1989), rhombohedral oxides (Ghiorso 1990a) and the remaining end-member properties of Berman (1988).

Some new aspects of adiabatic calorimetry at low temperatures

Aspects of low temperature adiabatic calorimetry which we have developed in the past several years are reviewed with emphasis laid on the role which the matured experimental method can play in physical chemistry of condensed phases. Two types of adiabatic calorimeters are described, both of which work between 13 and 373 K on small amounts of samples and are fully computer-controlled. Some recent results of measurement on ammonium hydrogen oxalate hemihydrate, the thiourea carbon tetrabromide inclusion compound, schizophyllan solutions and swelling of vermiculite are presented to illustrate the versatility of the adiabatic calorimetry. Measurement of time dependent properties is also discussed.

Heat capacity measurements for cryolite (Na 3AlF 6) and reactions in the system NaFeAlSiOF

The heat capacity of cryolite (Na 3AlF 6) has been measured from 7 to 1000 K by low-temperature adiabatic and high-temperature differential scanning calorimetry. Low-temperature data were obtained on material from the same hand specimen in the calorimetric laboratories of the University of Michigan and U.S. Geological Survey. The results obtained are in good agreement, and yield average values for the entropy of cryolite of: S 0 298 = 238.5 J/ mol K S 0 T− S 0 298 = 145.114 ln T+ 193.009∗10 −3T− 10.366∗ 10 5 T 2 − 872.89 J/ mol K (273−836.5 K) Δ S Trans = 9.9 J/ mol K S 0 T− S 0 298 =198.414 ln T+73.203∗ 10 −3T−63.814∗ 10 5 T 2 −1113.11 J/ mol K (836.5−1153 K) with the transition temperature between α- and β-cryolite taken at 836.5 K. These data have been combined with data in the literature to calculate phase equilibria for the system NaFeAlSiOF. The resultant phase diagrams allow constraints to be placed on the fO 2, fF 2, aSiO 2 and T conditions of formation for assemblages in alkalic rocks. A sample application suggests that log fO 2 is approximately −19.2, log fF 2 is −31.9 to −33.2, and aSiO 2 is −1.06 at assumed P T conditions of 1000 K, 1 bar for the villiaumite-bearing Ilimaussaq intrusion in southwestern Greenland.

Heat capacities of synthetic hedenbergite, ferrobustamite and CaFeSi 2O 6 glass

Heat capacities have been measured for synthetic hedenbergite (9–647 K), ferrobustamite (5–746 K) and CaFeSi 2O 6 glass (6–380 K) by low-temperature adiabatic and differential scanning calorimetry. The heat capacity of each of these structural forms of CaFeSiO 6 exhibits anomalous behavior at low temperatures. The X-peak in the hedenbergite heat-capacity curve at 34.5 K is due to antiferromagnetic ordering of the Fe 2+ ions. Ferrobustamite has a bump in its heat-capacity curve at temperatures less than 20 K, which could be due to weak cooperative magnetic ordering or to a Schottky anomaly. Surprisingly, a broad peak with a maximum at 68 K is present in the heat-capacity curve of the glass. If this maximum, which occurs at a higher temperature than in hedenbergite is caused by magnetic ordering, it could indicate that the range of distortions of the iron sites in the glass is quite small and that coupling between iron atoms is stronger in the glass than in the edge-shared octahedral chains of hedenbergite. The standard entropy change, S o 298.15 − S o 0, is 174.2 ± 0.3, 180.5 ± 0.3 and 185.7 ± 0.4 J/mol·K for hedenbergite, ferrobustamite and CaFeSi 2O 6 glass, respectively. Ferrobustamite is partially disordered in Ca-Fe distribution at high temperatures, but the dependence of the configuratonal entropy on temperature cannot be evaluated due to a lack of information. At high temperatures (298–1600 K), the heat capacity of hedenbergite may be represented by the equation C o p (J/mol·K) = 3 l0.46 + 0.01257 T-2039.93 T −1 2 − 1.84604× l0 6T −2 and the heat capacity of ferrobustamite may be represented by C o p (J/mol·K) = 403.83−0.04444T+ 1.597× 10 −5T 2−3757.3T −1 2 .

Thermochemistry of inorganic sulfur compounds IX. Molar heat capacity of KHSO 5(cr) from 5 to 300 K, and the partial molar entropy of HSO 5−(aq)

Low-temperature adiabatic calorimetry was used to determine the molar heat capacity and, by derivation, other thermodynamic properties of KHSO 5(cr). At T = 298.15 K, C p,m o( T) = (140.44±0.70) J·K −1·mol −1 and S m o( T) = (171.73±0.86) J·K −1·mol −1. The aqueous solubility of KHSO 5 is (3.167±0.007) mol·kg −1 at 273.15 K and the equilibrium water-vapor pressure above KHSO 5·H 2O is (1.41±0.03) kPa at 298.15 K. From the experimental quantities are deduced ( T = 298.15 K): S m o(HSO 5 −, aq) = (212.3±3.9) J·K −1·mol −1, and a standard potential of (1.842±0.010) V for the aqueous half-reaction: HSO 5 − + 2H + + 2e − = HSO 4 − + H 2O.

Thermodynamic properties of α-rhombohedral boron from 16.05 to 714.5 K

The enthalpy H T − H 298.15 and the heat capacity C p of α-rhombohedral boron have been determined experimentally by mixing isothermal calorimetry in the temperature range 298.15–714.5 K. The equations H T − H 298.15 = f 1( T) and C p = f 2( T) are obtained. The smoothed values of the basic thermodynamic properties of α-rhombohedral boron were found by processing the experimental data on low temperature heat capacities measured by low temperature adiabatic calorimetry in the temperature range 16.05–317.9 K. A curve for the Debye temperature versus T is constructed.

The heat-capacity of ilmenite and phase equilibria in the system Fe-T-O

Low temperature adiabatic calorimetry and high temperature differential scanning calorimetry have been used to measure the heat-capacity of ilmenite (FeTiO 3) from 5 to 1000 K. These measurements yield S 298 0 = 108.9 J/( mol · K). Calculations from published experimental data on the reduction of ilmenite yield Δ 298 0( I1) = −1153.9 kJ/( mol · K). These new data, combined with available experimental and thermodynamic data for other phases, have been used to calculate phase equilibria in the system Fe-Ti-O. Calculations for the subsystem Ti-O show that extremely low values of ƒO 2 are necessary to stabilize TiO, the mineral hongquiite reported from the Tao district in China. This mineral may not be TiO, and it should be re-examined for substitution of other elements such as N or C. Consideration of solid-solution models for phases in the system Fe-Ti-O allows derivation of a new thermometer/oxybarometer for assemblages of ferropseudobrookite-pseudobrookite ss and hematite-ilmenite ss. Preliminary application of this new thermometer/oxybarometer to lunar and terrestrial lavas gives reasonable estimates of oxygen fugacities, but generally yields subsolidus temperatures, suggesting re-equilibration of one or more phases during cooling.

The densities of liquid argon, krypton xenon, oxygen, nitrogen, carbon monoxide methane, and carbon tetrafluoride along the orthobaric liquid curve

The densities along the orthobaric liquid curve of the following liquefied gases have been measured with a precision of a few parts in 10 4: argon (86 to 118 K); krypton (118 to 164 K); xenon (164 to 219 K); oxygen (80 to 121 K); nitrogen (78 to 105 K); carbon monoxide (78 to 111 K); methane (92 to 151 K); carbon tetrafluoride (91 to 185 K). The measurements were made on a sample of about 9 cm 3 in a glass pyknometer, which was incorporated in a cryostat assembly similar to that used in conventional lowtemperature adiabatic calorimetry. The results have been considered from the point of view of the law of corresponding states. When the volume is plotted as a fraction of the critical volume V c against temperature expressed as a fraction of the critical temperature T c, the results for liquid krypton, xenon, and nitrogen conform to a common curve. By changing the “best” values of V c for argon and oxygen by about 0.5 per cent (which is probably within the uncertainty limits of these values of V c), the points for these two liquids could also be made to fall on the same curve. But there are indications of small divergences from this curve for methane and carbon monoxide, even if the values of V c adopted for these two substances are altered. Over the temperature ranges studied, the so-called rectilinear diameter for all eight substances examined is in fact a very slight curve, but extrapolation to the critical temperature of a least-squares straight line gives values of the critical volume within about one per cent of the literature values.

Conduction electron scattering by ionized donors in InSb at 80°K

The heat capacity of natural chalcanthite (copper sulfate pentahydrate, CuSO4·5H2O) from the deposit Kosmurun has been measured by the method of low-temperature adiabatic calorimetry over the temperature range of (4.3–320) K. The identity of the mineral was proved by methods of XRD, EMPA, IR and Raman spectroscopy. The thermodynamic functions have been calculated based on the experimental data on the heat capacity. The lattice component of heat capacity below 20 K was extracted. The standard values of the heat capacity and entropy for natural chalcanthite are as follows: C°p,m = 288.0 ± 0.4 J·mol−1 K−1, S°m = 295.2 ± 0.8 J mol−1 K−1.

Heat Capacities and Thermodynamic Properties of Two Tetramethylammonium Halides

Heat capacities of tetramethylammonium chloride and bromide were determined by low-temperature adiabatic calorimetry from 5° to 350°K. Derived thermodynamic properties were then calculated. Two transitions were found in the chloride: a sharp, apparently first-order transition occurs at 75.76°K with an entropy of transition of 0.37 cal mole—1 °K—1 and a lambda-shaped transition at 184.85°K with an entropy increment of 0.14 cal mole—1 °K—1. No anomaly has been observed in the bromide. Molal values of heat capacity, entropy, and free energy function at 298.15°K for the chloride and the bromide are: 37.51, 38.64, 45.58, 47.99, and —23.36, —25.36 cal mole—1 °K—1, respectively.

Heat capacities of three paramagnetic alums at low temperatures

The heat capacities of potassium chromic alum, ferric ammonium alum and chrome methylamine alum have been measured in the liquid helium and hydrogen temperature ranges by the method of low temperature adiabatic calorimetry. The specific heats between 1 and 4.2°K have been represented by the relations c p = 0.135 T 2 + 4.11 x 1 0 − 3 T 3 J/mole - deg ⁡ , c p = 0.112 T 2 + 3.52 x 1 0 − 3 T 3 J/mole - deg ⁡ , and c p = 0.162 T 2 + 3.91 x 1 0 − 3 T 3 J/mole - deg ⁡ . for the respective alums. The Debye characteristic temperature and the crystalline splitting parameter have been computed for each alum. The values of the former are 77.9°K, 82.3°K and 79.2°K and of the latter 0.247°K, 0.192°K and 0.273°K respectively for CrK-, FeNH 4 and CrCH 3 NH 3 alum. These results have been compared with those of other investigators. Finally the observed deviations in the hydrogen temperature region have been reported.