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Mineralogical Society of America, American Mineralogist, 10(97), p. 1771-1782, 2012

DOI: 10.2138/am.2012.4163

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

Journal article published in 2012 by Edgar Dachs, Charles A. Geiger, Artur Benisek
This paper is available in a repository.
This paper is available in a repository.

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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 Mössbauer 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 Cp data were adjusted slightly using the DSC results to improve the experimental accuracy. Integration of the low-T Cp 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" Fe 3+-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 (Cex) behavior to be modeled. An analysis shows the presence of an electronic heat-capacity contribu-tion (Cel , Schottky anomaly) superimposed on a larger magnetic heat-capacity effect (Cmag) around 17 K. The calculated lattice entropy at 298.15 K is Svib = 303.3 J/(mol⋅K) and it contributes about 90% to the total standard entropy at 298 K. The non-lattice entropy is Sex = 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 Cp behavior for almandine above 298 K is given by the polynomial [in J/(mol⋅K)]: Cp = 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 H1181K – H302K = 415.0 ± 3.2 kJ/mol. Using our S° value and the Cp polynomial for almandine, we derived the enthalpy of formation, ∆H°f , from an analysis of experimental phase equilibrium results on the reactions almandine + 3rutile = 3ilmenite + sillimanite + 2quartz and 2ilmenite = 2Fe + 2rutile + O 2 . A ∆H°f = –5269.63 kJ/mol was obtained.