Bruch S. Hemingway

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.

Heat capacity and phase equilibria of almandine, Fe3Al2Si3O12

Abstract The heat capacity of a synthetic almandine, Fe3Al2Si3O12, was measured from 6 to 350 K using equilibrium, intermittent-heating quasi-adiabatic calorimetry and from 420 to 1000 K using differential scanning calorimetry. These measurements yield Cp298 = 342.80 ± 1.4 J/mol · K and S298o = 342.60 J/mol · K. Mossbauer characterizations show the almandine to contain less than 2 ± 1% of the total iron as Fe3+. X-ray diffraction studies of this synthetic almandine yield a = 11.521 ± 0.001 A and V298o = 115.11 +- 0.01 cm3/mol, somewhat smaller than previously reported. The low-temperature Cp data indicate a lambda transition at 8.7 K related to an antiferromagnetic-paramagnetic transition with TN = 7.5 K. Modeling of the lattice contribution to the total entropy suggests the presence of entropy in excess of that attributable to the effects of lattice vibrations and the magnetic transition. This probably arises from a low-temperature electronic transition (Schottky contribution). Combination of the Cp data with existing thermodynamic and phase equilibrium data on almandine yields ΔGf,298o = −4938.3 kJ/mol and ΔHf,298o= —5261.3 kJ/mol for almandine when calculated from the elements. The equilibrium almandine = hercynite + fayalite + quartz limits the upper T P for almandine and is metastably located at ca. 570°C at P = 1 bar, with a dP dT of +17 bars/°C. This agrees well with reversed experiments on almandine stability when they are corrected for magnetite and hercynite solid-solutions. In ‖O2-T space, almandine oxidizes near QFM by the reactions almandine + O2 = magnetite + sillimanite + quartzandalmandine + 02 = hercynite + magnetite + quartz. With suitable correction for reduced activities of solid phases, these equilibria provide useful oxygen barometers for medium- to high-grade metamorphic rocks.

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.

The heat capacity of a natural monticellite and phase equilibria in the system CaO-MgO-SiO2-CO2

Abstract The heat capacity of a natural monticellite (Ca 1.00 Mg .09 Fe .91 Mn .01 Si 0.99 O 3.99 ) measured between 9.6 and 343 K using intermittent-heating, adiabatic calorimetry yields C p 0 (298) and S 298 0 of 123.64 ± 0.18 and 109.44 ± 0.16 J · mol −1 K −1 respectively. Extrapolation of this entropy value to end-member monticellite results in an S 0 298 = 108.1 ± 0.2 J · mol −1 K −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 T 0 ( J · mol −1 K −1 ) = S 298 0 + 164.79 In T + 15.337 · 10 −3 T + 22.791 · 10 5 T −2 − 968.94. Phase equilibria in the CaO-MgO-SiO 2 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 S 0 298 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-SiO 2 -CO 2 system was obtained with the ΔG 0 298 ( 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.

A room-temperature phase transition in maximum microcline - Heat capacity measurements

The thermal hysteresis in heat capacity measurements recently reported (Openshaw et al., 1976) for a maximum microcline prepared from Amelia albite by fused-salt ion-exchange is described in detail. The hysteresis is characterized by two limiting and reproducible curves which differ by 1% of the measured heat capacities. The lower curve, denoted curve B, represents the values obtained before the sample had been cooled below 300 K. Measurements made immediately after cooling the sample below 250 K followed a second parallel curve, curve A, to at least 370 K. Values intermediate to the two limiting curves were also obtained. The transitions from the B to the A curve were rapid and observed to occur three times. The time required to complete the transition from the A to the B curve increased from 39 h to 102 h in the two times it was observed to occur. The hysteresis is interpreted as evidence of a phase change in microcline at 300±10 K The heat effect associated with the phase change has not been evaluated.