Thermodynamic properties and stability of AlF-bearing titanite CaTiOSiO4–CaAlFSiO4

Abstract

Calorimetric and experimental data on AlF-bearing titanite are presented that yield thermodynamic properties of CaAlFSiO4, as well as activity-composition relations of binary titanite CaTiOSiO4–CaAlFSiO4. The heat capacity of synthetic CaAlFSiO4 was measured with differential scanning calorimetry between 170 and 850 K: C P =689.96–0.38647T+2911300T –2–8356.1T –0.5+0.00016179T 2 Based on low-temperature heat capacity calculations with lattice vibrational theory (Debye model), the calorimetric entropy of CaAlFSiO4 can be expected to lie between 104.7 and 118.1 J mol–1 K–1. The temperature of the P21/a to A2/a phase change was determined calorimetrically for a titanite with X Al=0.09 (Ttransition =390 K). The decrease of the transition temperature at a rate of about 11 K per mol% CaAlFSiO4 is in good agreement with previous TEM investigations. The displacement of the reaction anorthite + fluorite = CaAlFSiO4 in the presence of CaTiOSiO4 was studied with high P–T experiments. Titanite behaves as a non-ideal, symmetrical solid-solution. The thermodynamic properties of CaAlFSiO4 consistent with a multi-site mixing model are: % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavTnhis1MBaeXatLxBI9gBam % XvP5wqSXMqHnxAJn0BKvguHDwzZbqegm0B1jxALjhiov2Daebbnrfi % fHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaqFr0xc9pk % 0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qqQ8frFve9 % Fve9Ff0dmeaabaqaciaacaGaaeqabaWaaeaaeaaakeaafaqaaiWaca % aabaGaeeyrauKaeeOBa4MaeeiDaqNaeeiAaGMaeeyyaeMaeeiBaWMa % eeiCaaNaeeyEaKNaeeiiaaIaee4Ba8MaeeOzayMaeeiiaaIaeeOzay % Maee4Ba8MaeeOCaiNaeeyBa0MaeeyyaeMaeeiDaqNaeeyAaKMaee4B % a8MaeeOBa4MaeeiiaaIaeeikaGIaeeyzauMaeeiBaWMaeeyzauMaee % yBa0MaeeyzauMaeeOBa4MaeeiDaqNaee4CamNaeeykaKIaeeiiaaIa % emizaq2aaSbaaSqaaiabdAgaMbqabaGccqWGibasdaahaaWcbeqaai % abicdaWaaaaOqaaiabg2da9iabgkHiTiabikdaYiabiEda3iabisda % 0iabicdaWiabc6caUiabiIda4iabgglaXkabiodaZiabc6caUiabic % daWiabbccaGiabbUgaRjabbQeakjabb2gaTjabb+gaVjabbYgaSnaa % CaaaleqabaGaeyOeI0IaeGymaedaaaGcbaGaee4uamLaeeiDaqNaee % yyaeMaeeOBa4MaeeizaqMaeeyyaeMaeeOCaiNaeeizaqMaeeiiaaIa % ee4CamNaeeiDaqNaeeyyaeMaeeiDaqNaeeyzauMaeeiiaaIaeeyzau % MaeeOBa4MaeeiDaqNaeeOCaiNaee4Ba8MaeeiCaaNaeeyEaKNaeeii % aaIaee4uam1aaWbaaSqabeaacqqGWaamaaaakeaacqqG9aqpcqqGXa % qmcqqGWaamcqqG0aancqqGUaGlcqqG5aqocqGHXcqScqqGXaqmcqqG % UaGlcqqGXaqmcqqGGaaicqqGkbGscqqGTbqBcqqGVbWBcqqGSbaBda % ahaaWcbeqaaiabgkHiTiabigdaXaaakiabbUealnaaCaaaleqabaGa % eyOeI0IaeGymaedaaaGcbaGaeeyta0KaeeyyaeMaeeOCaiNaee4zaC % MaeeyDauNaeeiBaWMaeeyzauMaee4CamNaeeiiaaIaeeiCaaNaeeyy % aeMaeeOCaiNaeeyyaeMaeeyBa0MaeeyzauMaeeiDaqNaeeyzauMaee % OCaiNaeeiiaaYaamWaaeaacqWGxbWvdaWgaaWcbaGaemisaG0aaWba % aWqabeaacqGHsislaaaaleqaaOGaeeivaqLaem4vaC1aaSbaaSqaai % abdohaZbqabaaakiaawUfacaGLDbaaaeaacqGH9aqpcqaIXaqmcqaI % ZaWmcqGGUaGlcqaI2aGncqGHXcqScqaIWaamcqGGUaGlcqaI0aanca % aMe8UaeeOsaOKaeeyBa0Maee4Ba8MaeeiBaW2aaWbaaSqabeaacqGH % sislcqaIXaqmaaaaaaaa!E403! $$\matrix{ {{\rm Enthalpy of formation (elements) }d_f H^0 } \hfill & { = - 2740.8 \pm 3.0{\rm kJmol}^{ - 1} } \hfill \cr {{\rm Standard state entropy S}^{\rm 0} } \hfill & {{\rm = 104}{\rm .9} \pm {\rm 1}{\rm .1 Jmol}^{ - 1} {\rm K}^{ - 1} } \hfill \cr {{\rm Margules parameter }\left[ {W_{H^ - } {\rm T}W_s } \right]} \hfill & { = 13.6 \pm 0.4\;{\rm Jmol}^{ - 1} } \hfill \cr } $$ The pressure dependence of the Margules parameter (W V ) was determined from the excess volume of mixing based on XRD measurements (214±18 J mol–1 kbar–1), as well as refined from the piston-cylinder experimental results (198±114 J mol–1 kbar–1), demonstrating consistency between crystal structure data and thermodynamic properties. The stability of AlF-bearing titanite Ca(Ti,Al)(O,F)SiO4 was investigated by thermodynamic modelling in the system Ca–Al–Si–Ti–O–F–H–C and subsystems. The petrogenetic grids are in good agreement with natural mineral assemblages, in that very Al-rich titanite (X Al>0.65±0.15) is generally absent because it is either unstable with respect to other phases, or its stability field lies outside the P–T conditions realised on Earth. The grids explain both the predominant occurrence of natural Al-rich titanite at high metamorphic grade such as eclogite facies conditions, as well as its scarcity in blueschist facies rocks. Wide spacing of the Al-isopleths for titanite of many high-grade assemblages prevents their use as geobarometers or thermometers. The instability of end-member CaAlFSiO4 with respect to other phases in most assemblages modelled here is consistent with the hypothesis that the presence of structural stresses in the crystal lattice of CaAlFSiO4 influences its thermodynamic stability. The titanite structure is not well suited to accommodate Al and F instead of Ti and O, causing the relatively high Gibbs free energy of CaAlFSiO4, manifested in its standard state properties. Thus, the increasing amount of CaAlFSiO4 along the binary join is the reason why titanite with X Al>0.65±0.15 becomes unstable in most petrogenetic grids presented here. The compositional limit of natural titanite (X Al≈0.54) probably reflects the point beyond which the less stable end member begins to dominate the solid-solution, affecting both crystal structure and thermodynamic stability.