Heat capacities and entropies of mixing of pyrope-grossular (Mg3Al2Si3O12-Ca3Al2Si3O12) garnet solid solutions: A low-temperature calorimetric and a thermodynamic investigation

Dachs, E. and Geiger, C. A. (2006) Heat capacities and entropies of mixing of pyrope-grossular (Mg3Al2Si3O12-Ca3Al2Si3O12) garnet solid solutions: A low-temperature calorimetric and a thermodynamic investigation American Mineralogist, 91 (5-6). pp. 894-906. DOI 10.2138/am.2006.2005.

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Abstract

The low-temperature heat capacities for a series of synthetic garnets along the pyrope-grossular (Py-Gr) join were measured with the heat capacity option of the Physical Properties Measurement System (PPMS) produced by Quantum Design. The measurements were performed between 5 and 300 K on milligram-sized polycrystalline garnets that have been well characterized in previous studies. The C-p measurements indicate positive excess heat capacities (Delta C-P(xs)) for all solid-solution compositions at temperatures < 50 K with a maximum value of 2.31 +/- 0.18 J/(mol(.)K) for the composition Py(50)Gr(50) at about 35 K. Pyrope-rich garnets (i.e., Py(90)Gr(10) and Py(75)Gr(25)) have no or slightly positive Delta C-P(xs) at higher temperatures, whereas grossular-rich garnets (i.e., Py(10)Gr(90) and Py(25)Gr(75)) show negative Delta C-P(xs) values in the temperature range between 50 and 150 K. At T > 150 K, Delta C-P(xs) values scatter around zero for all compositions and the experimental error is too large to permit a clear determination of whether Delta C-P(xs) is different from zero within 2 sigma uncertainty. Excess entropies (Delta S-ex) at 298.15 K, calculated from the Cp data of the various solid-solution members, are asymmetric in nature with the largest positive deviations in pyrope-rich compositions. An asymmetric Margules mixing model was found to be inappropriate for modeling the Delta S-xs-X data and, thus, a two-parameter Redlich-Kister model was used to describe the excess entropy-composition relationships. Using this macroscopic mixing model for the excess entropy, a T-X diagram for Py-Gr garnets was calculated using different published values for the excess enthalpies of mixing. The effect of short range Ca-Mg order in the solid solution also was considered in the calculations. The calculations give a solvus for the pyrope-grossular join with a higher critical temperature in the range 850-1330 degrees C at X-Gr = 0.35 compared to previous thermodynamic models (T-crit < 600 degrees C) that use symmetric mixing models to describe the excess entropy. Unmixing of garnets in nature, as documented from occurrences in ultramatic diatremes may, therefore, have occurred at higher temperatures than previously thought. The atomistic and lattice-dynamic properties of Py-Gr garnets are reviewed and compared to the macroscopic Cp data. Published IR and Raman spectra are consistent with the occurrence of positive Delta C-P(xs) values at low temperatures.

Document Type: Article
Keywords: calorimetry pyrope-grossular garnet solid solutions thermodynamics excess heat capacities excess entropies local structural heterogeneity synthetic pyrope lattice-vibrations minerals powder model diffraction silicates behavior
Research affiliation: Kiel University
Refereed: No
DOI etc.: 10.2138/am.2006.2005
ISSN: 0003-004X
Date Deposited: 12 Jan 2012 05:55
Last Modified: 08 Oct 2012 10:23
URI: http://eprints.uni-kiel.de/id/eprint/15981

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