A calorimetric study of garnet solid solutions

Natural aluminosilicate garnets, E3 Al2 Si 3 O12, with E = Fe2+, Mn 2+, Mg, and Ca, are substitutional solid solutions and knowledge of their chemical and physical properties is important for many different mineralogical, petrological and geophysical studies. In addition to the need for obtaining a thermodynamic description of garnet, one needs to investigate their micro/nanoscopic properties that affect macroscopic thermodynamic mixing behavior. Lattice strain is thought to produce elastic energies. However, experimental measurements that directly determined micro/nanoscopic strain are few in number. In order to address these questions, it is proposed to investigate the macroscopic thermodynamic mixing and crystal-chemical properties of three binary garnet solid solutions, namely almandine-pyrope - (Fe,Mg)3 Al2 Si 3 O12, almandine-spessartine - (Fe,Mn)3 Al2 Si 3 O12 and spessartine-grossular - (Mn,Ca)3 Al2 Si 3 O12. In order to do this, it is proposed to undertake: 1) low temperature heat-pulse heat capacity measurements between 2 K and 300 K, 2) DSC Cp measurements between 280 K and 900 K and 3) powder synchrotron X-ray measurements at 5 K. The results obtained will be important in two respects. First, they will permit a better understanding of the nature of strain with respect to solid-solution behavior in garnet, as well as in silicates in general. Second, they will permit the construction of more quantitative thermodynamic mixing models that can be used in petrological and geophysical studies of various geological processes.

The main goal of this project was to determine quantitatively the thermodynamic properties of important rock-forming silicate garnet end members and binary substitutional solid solutions. The investigation focused on determinations of the standard entropy, So, and the calorimetric excess entropy of mixing, ?Sex,cal. We think, this goal was accomplished successfully. Calorimetric measurements were made to determine the heat capacity, Cp, i.e. using low-temperature relaxation calorimetry of the Physical Properties Measurement System (PPMS), and differential scanning calorimetry (DSC). From the Cp data obtained, the standard entropy, So, for three garnet end members and the calorimetric excess entropy, ?Sex,cal, for two garnet binary solid-solutions were derived. The excess enthalpy, ?Hex, of both garnet binaries was also determined using published phase equilibrium data and by applying the autocorrelation analysis to published IR spectra. Finally, from ?Sex,cal and ?Hex, ?Gex, which is the function that governs thermodynamic stability, could be calculated.Garnet end-members: For end-member grossular (Ca3Al2Si3O12) So = 260 J/mol?K was obtained from the calorimetric measurements as the standard entropy value. Its enthalpy of formation, ?Hof, was determined to be -6627 kJ/mol.From the low-temperature Cp data of katoite (hydrogrossular - Ca3Al2H12O12), So = 421.7 1.6 J/mol?K was determined.For end-member almandine (Fe3Al2Si3O12) So = 336.7 0.8 J/mol?K was obtained from the calorimetric measurements and ?Hof = -5269.63 kJ/mol was calculated.Garnet solid-solutions:For the almandine-spessartine binary (Fe3Al2Si3O12 - Mn3Al2Si3O12) the calorimetric entropy at 298 K shows ideal mixing behaviour within error. Thus, the Margules entropy interaction parameter, WS,FeMngrt, is zero. Thermodynamic analysis of published phase equilibrium data shows that the excess Gibbs free energy of mixing, ?Gex, for Fe-Mn in garnet is positive with the largest deviations from ideality at spessartine-rich compositions. Margules enthalpy parameters of WH,FeMngrt = 4170 518 J/cation?mol and WH,MnFe = 1221 588 J/cation?mol were derived.The calorimetric entropy at 298 K for the grossular-spessartine binary (Ca3Al2Si3O12 - Mn3Al2Si3O12), shows a slight positive deviation from ideality giving an excess calorimetric entropy with a maximum value of ~2 J/mol?K. ?Sex,cal vs. composition behavior is consistent with symmetric Ca-Mn mixing, as described by the Margules entropy parameter WS,CaMngrt = 3.8 2.0 J/cation?mol?K. Thermodynamic analysis of published experimental phase equilibrium data yielded a symmetric Margules enthalpy parameter of WH,CaMngrt = 3.2 0.3 kJ/cation?mol. This describes the excess enthalpy, ?Hex, behavior with a maximum of 0.8 kJ/mol. Calculated values of ?Gex are small, so that Ca-Mn mixing in garnet is close to ideal at most geological P-T conditions.