Letter: Entropies of mixing and subsolidus phase relations of forsteritefayalite (Mg2SiO4Fe2SiO4) solid solution
-
Edgar Dachs
and
Charles A. Geiger
Abstract
The heat capacities of a series of synthetic forsterite (Fo).fayalite (Fa), Mg2SiO4.Fe2SiO4, olivines have been measured between 5 and 300 K on milligram-sized samples with the Physical Properties Measurement System (Quantum Design). The heat capacities for fayalite and fayalite-rich olivine are marked by a sharp lambda-type anomaly defining a transition from the paramagnetic to an antiferromagentic state, which in the case of fayalite occurs at TN = 64.5 K. In forsterite-rich compositions a feature in the CP data around 25 K is observable and it could possibly be linked to a magnetic transition. Additionally, all Fe-bearing olivines show a Schottky-type anomaly. Excess heat capacities of mixing, ΔCxsP, for the various Fe-Mg olivine solid-solution compositions were calculated applying the equation ΔCxsP= CssP -[(1 - XFa) CPo + XFa CPFa] using fitted CP polynomials for each composition. The calorimetric entropies at 298.15 K, Scal, were determined by solving the CP integral
. If a symmetric Margules mixing model ΔSxs = Ws·XFa(1 -XFa) is taken to describe the entropy of mixing behavior for the Fo-Fa binary, it yields an interaction parameter of Ws = -1.6 ± 1.7 J/(mol·K) on a onecation basis. The calorimetric data thus indicate ideal entropy of mixing behavior. Adopting, however, a value of WOlS,Mg-Fe = -1.6 J/(mol·K) one can calculate a value for the excess Gibbs free energy of mixing of WOlG,Mg-Fe = 6.9 kJ/mol at 1000 K using the most recent solution calorimetric study of Kojitani and Akaogi (1994) on Fo-Fa olivine with WOlH,Mg-Fe = 5.3 kJ/mol. This WOl G,Mg-Fe value should be considered a maximum upper limit for thermodynamic nonideality. Using solely calorimetric data, the T-X phase diagram for the Fo-Fa binary is calculated at 1 bar and 50 kbar and compared to that obtained from a model-dependent thermodynamic analysis. The results suggest that exsolution in Fe-Mg olivine should only be possible in low-temperature environments depending on kinetic behavior.
© 2015 by Walter de Gruyter Berlin/Boston
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