High-temperature heat capacity and thermodynamic properties for end-member titanite (CaTiSiO_5)

摘要

The heat capacity of end-member titanite and (CaTiSiO_5) 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 P2_1/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 P2_1/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 (CaTiSiO_5) glass can be reproduced within <1% using the derived empirical equations (temperature in K, pressure in bars): C_p~(glass) = (114.7155 * 10~6)/(T~3) + (-908.3 * 10~(-3))/(T~2) + (0.3170 * 10~5)/T + (-0.8484 * 10~4)/(T~(1/2)) +0.5796 * 10~3 + (-21.75) * 10~(-2) T + 7.8731 * 10~(-5) T~2 (1) C_p~(solid) = (-2.3952 * 10~6)/(T~3) + (-5.8601 * 10~(-3))/(T~2) + (0.2239 * 10~5)/T + (-0.5913 * 10~4)/(T~(1/2)) + 0.4277 * 10~3 + (-7.772) * 10~(-2) T + 1.3751 * 10~(-5) T~2 + 3.0877 ∑ from 1 to k = 2 of (τ~(3·(2k-1)))/(2k - 1) for τ = T/(T_(transition)) ≤ 1 or 2.3034 ∑ from 1 to k = 2 of (τ~(-5·(2k-1)))/(2k - 1) for τ = T/(T_(transition)) ≥ 1 (2) The available enthalpy of vitrification (80.78 ± 3.59 kJ mol~(-1)), and the new heat capacity equations for solid and glass can be used to estimate (1) the enthalpy of fusion of end-member titanite (122.24 ± 0.2 kJ mol~(-1)), (2) the entropy of fusion of end-member titanite (73.85 ± 0.1 J/mol K~(-1), and (3) a theoretical glass transition temperature of 1130 ± 55 K. The latter is in considerable disagreement with the experimentally determined glass transition temperature of 1013 ± 3 K. This discrepancy vanishes when either the adopted enthalpy of vitrification or the liquid heat content, or both, are adjusted. Calculations using Eq. (2), new P-V-T data for titanite, different but also internally consistent thermodynamic data for anorthite, rutile, and kyanite, and experimental data for the reaction: anorthite + rutile = titanite + kyanite strongly suggest: (1) the practice to adjust the enthalpy of formation of titanite to fit phase equilibrium data may be erroneous, and (2) it is probably the currently accepted entropy of 129.2 ± 0.8 J/mol K~(-1) that may need revision to a smaller value.