Entropies of mixing and subsolidus phase relations of forsterite-fayalite(Mg2SiO4-Fe2SiO4) solid solution

The heat capacities of a series of synthetic forsterite (Fo)-fayalite (Fa), Mg2SO4-Fe2SO4, 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, 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, Delta C-P(XS), for the various Fe-Mg olivine solid-solution compositions were calculated applying the equation Delta C-P(XS) = C-P(SS) - [(1 - X-Fa) G(P)(Fo) + X-Fa C-P(Fa)] using fitted C-P polynomials for each composition. The calorimetric entropies at 298.15 K, S-cal, were determined by solving the C-P integral S-cal.298.15 = f(0)(298.15) C-p/T dT. If a symmetric Margules mixing model Delta S-xs, = W-s.X-Fa (1 - X-Fa) 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-S.Mg-Fe(Ol), = -1.6 J/(mol.K) one can calculate a value for the excess Gibbs free energy of mixing of W-G.Mg-Fe(Ol) = 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-H,Mg-Fe(Ol) = 5.3 kJ/mol. This W-G,Mg-Fe(Ol), 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.