Heat capacity and entropic mixing behaviour of the orthopyroxene solid solution (Mg,Fe) ₂ Si ₂ O ₆

Abstract. The heat capacity (Cp) of synthetic members of the orthopyroxene solid solution enstatite (Mg2Si2O6: En)-ferrosilite (Fe2Si2O6: Fs) was measured at between 2 to 300 K using relaxation calorimetry and between 340 to 823 K using differential scanning calorimetry. The samples (nine solid-solution members plus En and Fs) were characterised by optical microscopy and by X-ray powder diffraction methods. The actual compositions of the solid-solution members were checked by comparing the cell volumes determined in this work with corresponding data in the literature which provide a correlation between cell volume and composition. The Cp's of the endmembers above room temperature can be represented by the following polynomials (J K−1 mol−1): CpEn=311.82±6.39-1824.09±220⋅T-0.5-6.83178±1.18×106⋅T-2+8.81577±1.81×108⋅T-3 and CpFs=393.14±6.06-3941.24±203⋅T-0.5+2.10688±1.06×106⋅T-2-2.97417(±1.62)×108⋅T-3. Compared to literature and data set values, the polynomial for En yields 1.5 % to 3 % lower heat capacities at high temperatures and should be preferred for phase equilibrium calculations >1000 K. The standard entropy of En was determined to be So=132.3±1.0 J K−1 mol−1 and that of Fs to be So=190.7±1.3 J K−1 mol−1 based on the Physical Properties Measurement System (PPMS) measurements. All solid-solution members and Fs show heat capacity anomalies below ∼50 K. Discrete Cp peaks, related to magnetic ordering, occur at a Néel temperature of TN=38.4 K in pure Fs, and a double peak occurs at 38 K and at 29 K in the composition En10Fs90. With further dilution of the magnetic Fe2+ ion, heat capacity anomalies are present in the form of broad shoulders in the Cp data between approximately 10 and 25 K. At the lowest temperatures, around 2 K, Schottky-type Cp anomalies are visible. By adopting a Kieffer model for the lattice part of Cp, the excess heat capacities of each compound were derived and decomposed into magnetic and electronic contributions. The calorimetric entropies at 298.15 K (Scal), when plotted against composition, indicate a linear relationship along the join; i.e. all Scal values fall on the line defining thermodynamic ideality within error. There are thus no excess entropies of mixing in the En–Fs orthopyroxene solid solution. The same holds true for the volumes.