A low-temperature calorimetric study of synthetic (forsterite + fayalite) {(Mg 2SiO 4 + Fe 2SiO 4)} solid solutions: An analysis of vibrational, magnetic, and electronic contributions to the molar heat capacity and entropy of mixing

Abstract

The molar heat capacities ( C p,m ) of a series of synthetic forsterite (Fo)–fayalite (Fa), (Mg 2SiO 4 + Fe 2SiO 4), 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, Fo 10Fa 90, Fo 20Fa 80, Fo 30Fa 70, and Fo 40Fa 60. The corresponding Neel temperatures T N decrease linearly from 64.5 K in fayalite to 32.8 K in Fo 40Fa 60 following the relationship T N = 79.02 · x Fa − 14.07. Fo 50Fa 50 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, C el,m, C mag,m, and C vib,m from the experimental heat capacities ( C tot,m), we used a single-parametric phonon dispersion model to calculate C vib,m for the solid-solution members and fayalite. The C el,m + C mag,m(= C tot,m − C vib,m) contributions were fit to expressions describing a Schottky-type electronic anomaly and a paramagnetic–antiferromagnetic transition. For Fo 50Fa 50 and Mg-richer olivines, our analysis of C tot,m shows that also these compositions have a C mag,m contribution with a maximum around 25 K. Decomposition of the molar excess heat capacity C p ,m E into electronic, magnetic and vibrational contributions yields the largest absolute values for C mag,m E . Molar excess entropies of mixing S m E at T = 298.15 K were also calculated from the heat capacity data. Despite considerable C mag,m E , the molar magnetic excess entropy at T = 298.15 K S mag,m E ( 298.15 K ) 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 C mag,m E / T as a function of temperature largely cancel each other between 0 K and 298.15 K. The molar electronic excess heat capacity C el,m E is positive for all temperatures and compositions, S el,m E ( 298.15 K ) thus shows a positive contribution with a maximum of 0.8 J · K −1 · mol −1 for Fo 50Fa 50. The molar vibrational excess entropy S vib,m E ( 298.15 K ) is also slightly positive for most members (maximum of 1.0 J · K −1 · mol −1 for Fo 40Fa 60). The resulting overall molar excess entropy, S tot,m E ( 298.15 K ) = S vib,m E ( 298.15 K ) + S el,m E ( 298.15 K ) + S mag,m E ( 298.15 K ) along the (forsterite + fayalite) join is weakly negative within 2 σ-uncertainty. Smoothed values of the molar heat capacity C p,m , the molar entropies Δ 0 T S m , molar enthalpies Δ 0 T H m , and the molar Planck function Φ m have been tabulated at selected temperatures for all olivine compositions.