A low-temperature calorimetric study of synthetic (forsterite + fayalite) {(Mg2SiO4 + Fe2SiO4)} solid solutions: An analysis of vibrational, magnetic, and electronic contributions to the molar heat capacity and entropy of mixing

The molar heat capacities (Cp,m) of a series of synthetic forsterite (Fo)–fayalite (Fa), (Mg2SiO4 + Fe2SiO4), olivines have been measured between 5 K and 300 K on milligram-sized samples with the Physical Properties Measurement System (Quantum Design®). Sharp, λ-type heat capacity anomalies are observed in the Fe-rich compositions fayalite, Fo10Fa90, Fo20Fa80, Fo30Fa70, and Fo40Fa60. The corresponding Neel temperatures TN decrease linearly from 64.5 K in fayalite to 32.8 K in Fo40Fa60 following the relationship TN = 79.02 · xFa − 14.07. Fo50Fa50 and Mg-richer olivines show weak broad features in the heat capacity data around 15 K to 20 K that decrease in magnitude with increasing forsterite content. In order to derive and separate molar electronic, magnetic and vibrational heat capacity contributions, Cel,m, Cmag,m, and Cvib,m from the experimental heat capacities (Ctot,m), we used a single-parametric phonon dispersion model to calculate Cvib,m for the solid-solution members and fayalite. The Cel,m + Cmag,m(= Ctot,m − Cvib,m) contributions were fit to expressions describing a Schottky-type electronic anomaly and a paramagnetic–antiferromagnetic transition. For Fo50Fa50 and Mg-richer olivines, our analysis of Ctot,m shows that also these compositions have a Cmag,m contribution with a maximum around 25 K. Decomposition of the molar excess heat capacity Cp,mE into electronic, magnetic and vibrational contributions yields the largest absolute values for Cmag,mE. Molar excess entropies of mixing SmE at T = 298.15 K were also calculated from the heat capacity data. Despite considerable Cmag,mE, the molar magnetic excess entropy at T = 298.15 K Smag,mE(298.15K) is only weakly negative for the solid solution (1.7 J · K−1 · mol−1to 2.7 J · K−1 · mol−1), because positive and negative contributions of Cmag,mE/T as a function of temperature largely cancel each other between 0 K and 298.15 K. The molar electronic excess heat capacity Cel,mE is positive for all temperatures and compositions, Sel,mE(298.15K) thus shows a positive contribution with a maximum of 0.8 J · K−1 · mol−1 for Fo50Fa50. The molar vibrational excess entropy Svib,mE(298.15K) is also slightly positive for most members (maximum of 1.0 J · K−1 · mol−1 for Fo40Fa60). The resulting overall molar excess entropy, Stot,mE(298.15K)=Svib,mE(298.15K)+Sel,mE(298.15K)+Smag,mE(298.15K) along the (forsterite + fayalite) join is weakly negative within 2σ-uncertainty. Smoothed values of the molar heat capacity Cp,m, the molar entropies Δ0TSm, molar enthalpies Δ0THm, and the molar Planck function Φm have been tabulated at selected temperatures for all olivine compositions.