A low-temperature calorimetric study of synthetic (forsterite plus 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 (C-p,C-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 ((R))). Sharp, k-type heat capacity anomalies are observed in the Fe-rich compositions fayalite, Fo(10)Fa(90), Fo(20)Fa(80), Fo(30)Fa(70), and Fo(40)Fa(60). The corresponding Neel temperatures T-N decrease linearly from 64.5 K in fayalite to 32.8 K in Fo(40)Fa(60) following the relationship T-N = 79.02 . x(Fa) - 14.07. Fo(50)Fa(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,C-m,C- C-mag,C-m,C- and C-vib,C-m from the experimental heat capacities (C-tot,C-m), we used a single-parametric phonon dispersion model to calculate C-vib,C-m for the solid-solution members and fayalite. The C-el,C-m + C-mag,C-m(= C-tot,C-m - C-vib,C-m) contributions were fit to expressions describing a Schottky-type electronic anomaly and a paramagnetic-antiferromagnetic transition. For Fo(50)Fa(50) and Mg-richer olivines, our analysis of C-tot,C-m shows that also these compositions have a C-mag,C-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 mixingp S-m(E) C-mag,m,(E). Molar magnetic excess entropies of mixing S-m(E) at T = 298.15 K were also calculated from the heat capacity data. Despite Considerable 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 rnag,m mag,m of CE (1.7 J . K-1 mol(-1) to 2.7 J . K-1 . mol(-1)), because positive and negative contributions of C-el,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-vib,m(E) (298.15 K) thus shows a positive contribution with a maximum of 0.8 J . K-1 mol(-1) for Fo(50)Fa(50). The molar vibrational SE 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(40)Fa(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) to Vi el magp TSttt, join is weakly negative within 2 sigma-uncertainty. Smoothed values of the molar heat capacity C-p,C-m,C- the molar entropies Delta(T)(0) S-m,S- molar enthalpies A T H., and the molar Planck function phi(m) have been tabulated at selected temperatures for all olivine compositions. (c) 2006 Elsevier Ltd. All rights reserved.