Almandine: Lattice and non-lattice heat capacity behavior and standard thermodynamic properties

Abstract

The heat capacity of three synthetic polycrystalline almandine garnets (ideal formula Fe3Al2Si3O12) and one natural almandine-rich single crystal was measured. The samples were characterized by optical microscopy, electron microprobe analysis, X-ray powder diffraction, and Mossbauer spectroscopy. Measurements were performed in the temperature range 3 to 300 K using relaxation calorimetry and between 282 and 764 K using DSC methods. All garnets show a prominent λ-type heat-capacity anomaly at low temperatures resulting from a paramagnetic-antiferromagnetic phase transition. For two Fe3+-free or nearly Fe3+-free synthetic almandines, the phase transition is sharp and occurs at 9.2 K. Almandine samples that have ~3% Fe3+ show a λ-type peak that is less sharp and that occurs at 8.0 ± 0.2 K. The low- T C P data were adjusted slightly using the DSC results to improve the experimental accuracy. Integration of the low- T C P data yields calorimetric standard entropy, S∘ , values between 336.7 ± 0.8 and 337.8 ± 0.8 J/(mol·K). The smaller value is recommended as the best S∘ for end-member stoichiometric almandine, because it derives from the “best” Fe3+-free synthetic sample. The lattice (vibrational) heat capacity of almandine was calculated using the single-parameter phonon dispersion model of Komada and Westrum (1997), which allows the non-lattice heat capacity ( C ex) behavior to be modeled. An analysis shows the presence of an electronic heat-capacity contribution ( C el, Schottky anomaly) superimposed on a larger magnetic heat-capacity effect ( C mag) around 17 K. The calculated lattice entropy at 298.15 K is S vib = 303.3 J/(mol·K) and it contributes about 90% to the total standard entropy at 298 K. The non-lattice entropy is S ex = 33.4 J/(mol·K) and consists of S mag = 32.1 J/(mol·K) and S el = 1.3 J/(mol·K) contributions. The C P behavior for almandine above 298 K is given by the polynomial [in J/(mol·K)]: C P = 649.06 ( ± 4 ) - 3837.57 ( ± 122 ) · T - 0.5 - 1.44682 ( ± 0.06 ) · 10 7 · T - 2 + 1.94834 ( ± 0.09 ) · 10 9 · T - 3 which is calculated using the measured DSC data together with one published heat-content datum determined by transposed-drop calorimetry along with a new determination in this work that gives H 1181K − H 302K = 415.0 ± 3.2 kJ/mol. Using our S∘ value and the C P polynomial for almandine, we derived the enthalpy of formation, Δ H °f, from an analysis of experimental phase equilibrium results on the reactions almandine + 3rutile = 3ilmenite + sillimanite + 2quartz and 2ilmenite = 2Fe + 2rutile + O2. A Δ H °f = −5269.63 kJ/mol was obtained.