Letter: Entropies of mixing and subsolidus phase relations of forsterite–fayalite (Mg₂SiO₄–Fe₂SiO₄) solid solution

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 T_N = 64.5 K. In forsterite-rich compositions a feature in the C_P 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, ΔC^xs_P, for the various Fe-Mg olivine solid-solution compositions were calculated applying the equation ΔC^xs_P= C^ss_P -[(1 - XFa) C_Po + X_Fa C_P^Fa] using fitted C_P polynomials for each composition. The calorimetric entropies at 298.15 K, Scal, were determined by solving the C_P integral . If a symmetric Margules mixing model ΔS^xs = Ws·X_Fa(1 -XFa) is taken to describe the entropy of mixing behavior for the Fo-Fa binary, it yields an interaction parameter of W_s = -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 W^Ol_S,Mg-Fe = -1.6 J/(mol·K) one can calculate a value for the excess Gibbs free energy of mixing of W^Ol_G,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 W^Ol_H,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.