Richard A. Robie

Low-temperature heat capacity of diopside glass (CaMgSi2O6): A calorimetric test of the configurational-entropy theory applied to the viscosity of liquid silicates

Heat-capacity measurements have been made between 8 and 370 K on an annealed and a rapidly quenched diopside glass. Between 15 and 200 K, Cp does not depend significantly on the thermal history of the glass. Below 15 K Cp is larger for the quenched than for the annealed specimen. The opposite is true above 200 K as a result of what is interpreted as a secondary relaxation around room temperature. The magnitude of these effects, however, is small enough that the relative entropies S(298)−S(0) of the glasses differ by only 0.5 J/mol K, i.e., a figure within the combined experimental uncertainties. The insensitivity of relative entropies to thermal history supports the assumption that the configurational heat capacity of the liquid may be taken as the heat capacity difference between the liquid and the glass (ΔCp). Furthermore, this insensitivity allows calculation of the residual entropies at 0 K of diopside glasses as a function of the fictive temperature from the entropy of fusion of diopside and the heat capacities of the crystalline, glassy and liquid phases. For a glass with a fictive temperature of 1005 K, for example, this calorimetric residual entropy is 24.3 ± 3 J/mol K, in agreement with the prediction made by RICHET (1984) from an analysis of the viscosity data with the configurational-entropy theory of relaxation processes of Adam and Gibbs (1965). In turn, all the viscosity measurements for liquid diopside, which span the range 0.5-4· 1013 poise, can be quantitatively reproduced through this theory with the calorimetrically determined entropies and ΔCp data. Finally, the unclear significance of “activation energies” for structural interpretations of viscosity data is emphasized, and the importance of ΔCp and glass-transition temperature systematics for determining the composition and temperature dependences of the viscosity is pointed out.

Elastic Constants of Calcite

The recent measurements of the elastic constants of calcite by Reddy and Subrahmanyam (1960) disagree with the values obtained independently by Voigt (1910) and Bhimasenachar (1945). The present authors, using an ultrasonic pulse technique at 3 Mc and 25°C, determined the elastic constants of calcite using the exact equations governing the wave velocities in the single crystal. The results are C11=13.7, C33=8.11, C44=3.50, C12=4.82, C13=5.68, and C14=−2.00, in units of 1011 dyn/cm2. Independent checks of several of the elastic constants were made employing other directions and polarizations of the wave velocities. With the exception of C13, these values substantially agree with the data of Voigt and Bhimasenachar.

Some Debye temperatures from single-crystal elastic constant data

The mean velocity of sound has been calculated for 14 crystalline solids by using the best recent values of their single‐crystal elastic stiffness constants. These mean sound velocities have been used to obtain the elastic Debye temperatures θDe for these materials. Models of the three wave velocity surfaces for calcite are illustrated.

Entropy and structure of silicate glasses and melts

Abstract Low-temperature adiabatic C p measurements have been made on NaAlSi 2 O 6 , MgSiO 3 , Ca 3 Al 2 Si 3 O 12 and Ca 1.5 Mg 1.5 Al 2 Si 3 O 12 glasses. Above about 50 K, these and previous data show that the heat capacity is an additive function of composition to within ±1% throughout the investigated glassforming part of the system CaO-MgO-Al 2 O 3 -SiO 2 . In view of the determining role of oxygen coordination polyhedra on the low-temperature entropy, this is interpreted as indicating that Si and Al are tetrahedrally coordinated in all these glasses, in agreement with structural data; whereas Ca and Mg remain octahedrally coordinated. In contrast, heat capacities and entropies are not additive functions of composition for alkali aluminosilicates, indicating increases in the coordination numbers of alkali elements from about six to nine when alumina is introduced. A thermochemical consequence of additivity of vibrational entropies of glasses is that entropies of mixing are essentially configurational for calcium and magnesium aluminosilicate melts. For alkali-bearing liquids, it is probable that vibrational entropies contribute significantly to entropies of mixing. At very low temperatures, the additive nature of the heat capacity with composition is less well followed, likely as a result of specific differences in medium-range order.

Low-temperature molar heat capacities and entropies of MnO2 (pyrolusite), Mn3O4 (hausmanite), and Mn2O3 (bixbyite)

Abstract Pyrolusite (MnO2), hausmanite (Mn3O4), and bixbyite (Mn2O3), are important ore minerals of manganese and accurate values for their thermodynamic properties are desirable to understand better the {p(O2), T} conditions of their formation. To provide accurate values for the entropies of these important manganese minerals, we have measured their heat capacities between approximately 5 and 380 K using a fully automatic adiabatically-shielded calorimeter. All three minerals are paramagnetic above 100 K and become antiferromagnetic or ferrimagnetic at lower temperatures. This transition is expressed by a sharp λ-type anomaly in Cpmo for each compound with Neel temperatures TN of (92.2±0.2), (43.1±0.2), and (79.45±0.05) K for MnO2, Mn3O4, and Mn2O3, respectively. In addition, at T ≈ 308 K, Mn2O3 undergoes a crystallographic transition, from orthorhombic (at low temperatures) to cubic. A significant thermal effect is associated with this change. Hausmanite is ferrimagnetic below TN and in addition to the normal λ-shape of the heat-capacity maxima in MnO2 and Mn2O3, it has a second rounded maximum at 40.5 K. The origin of this subsidiary bump in the heat capacity is unknown but may be related to a similar “anomalous bump” in the curve of magnetization against temperature at about 39 K observed by Dwight and Menyuk.(1) At 298.15 K the standard molar entropies of MnO2, Mn3O4, and Mn2O3, are (52.75±0.07), (164.1±0.2), and (113.7±0.2) J·K−1·mol−1, respectively. Our value for Mn3O4 is greater than that adopted in the National Bureau of Standards tables(2) by 14 per cent.

Specific Heats of Lunar Surface Materials from 90 to 350 Degrees Kelvin

The specific heats of lunar samples 10057 and 10084 returned by the Apollo 11 mission have been measured between 90 and 350 degrees Kelvin by use of an adiabatic calorimeter. The samples are representative of type A vesicular basalt-like rocks and of finely divided lunar soil. The specific heat of these materials changes smoothly from about 0.06 calorie per gram per degree at 90 degrees Kelvin to about 0.2 calorie per gram per degree at 350 degrees Kelvin. The thermal parameter γ=(kpC-� for the lunar surface will accordingly vary by a factor of about 2 between lunar noon and midnight.

Heat capacities of kaolinite from 7 to 380 K and of DMSO-intercalated kaolinite from 20 to 310 K; the entropy of kaolinite Al 2 Si 2 O 5 (OH) 4

The heat capacities of kaolinite (7 to 380 K) and of dimethyl sulfoxide (DMSO) intercalated kaolinite (20 to 310 K) were measured by adiabatically shielded calorimetry. The third law entropy of kaolinite, S298, is 200.9 ± 0.5 J½mol−1K−1.The “melting point” of the DMSO in the intercalate, 288.0 ± 0.2 K, is 3.7 K lower than that of pure DMSO, 291.67 K. The heat capacity of DMSO in the intercalate above 290 K is approximately 5.2 J·mol−1·K−1 smaller than that of pure liquid DMSO at the same temperature.

The entropy and Gibbs free energy of formation of the aluminum ion

A reevaluation of the entropy and Gibbs free energy of formation of Al3+(aq) yields −308 ± 15 J/K·mol and 489.4 ± 1.4kj/mol for S0298 and ΔG0ƒ,298 respectively. The standard electrode potential for aluminum is 1.691 ± 0.005 volts.

Melting and thermodynamic properties of pyrope (Mg3Al2Si3O12)

Abstract The heat capacity of Mg3Al2Si3O12 glass has been measured from 10 to 1000 K by adiabatic and differential scanning calorimetry. The heat capacity of crystalline pyrope has been determined from drop-calorimetry measurements between 820 and 1300 K. From these and previously published results a consistent set of thermodynamic data is presented for pyrope and Mg3Al2Si3O12 glass and liquid for the interval 0–2000 K. The enthalpy of fusion at 1570 ± 30 K, the metastable congruent 1-bar melting point, is 241 ± 12 kJ/mol .

Heat capacities of synthetic hedenbergite, ferrobustamite and CaFeSi2O6 glass

Heat capacities have been measured for synthetic hedenbergite (9–647 K), ferrobustamite (5–746 K) and CaFeSi2O6 glass (6–380 K) by low-temperature adiabatic and differential scanning calorimetry. The heat capacity of each of these structural forms of CaFeSiO6 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 Fe2+ 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, So298.15 − So0, is 174.2 ± 0.3, 180.5 ± 0.3 and 185.7 ± 0.4 J/mol·K for hedenbergite, ferrobustamite and CaFeSi2O6 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 Cop(J/mol·K) = 3l0.46 + 0.01257T-2039.93T−12 − 1.84604× l06T−2 and the heat capacity of ferrobustamite may be represented by Cop(J/mol·K) = 403.83−0.04444T+ 1.597× 10−5T2−3757.3T−12.