A calorimetric investigation of spessartine: Vibrational and magnetic heat capacity

Abstract

The heat capacity ( C p ) of two synthetic spessartine samples (Sps) was measured on 20–30 mg-size samples in the temperature range 2–864 K by relaxation calorimetry (RC) and differential scanning calorimetry (DSC). The polycrystalline spessartine samples were synthesized in two different laboratories at high pressures and temperatures from glass and oxide-mixture starting materials and characterized by X-ray powder diffraction and electron-microprobe analysis. The low-temperature heat capacity data show a prominent lambda transition with a peak at 6.2 K, which is interpreted to be the result of a paramagnetic–antiferromagnetic phase transition. The DSC data around ambient T agree excellently with the RC data and can be represented by the C p polynomial for T > 250 K: C p Sps = 610 - 3060 · T - 0.5 - 1.45 · 10 7 · T - 2 + 1.82 · 10 9 · T - 3 . Integration of the low temperature C p data yields a calorimetric standard entropy for the two different samples of S o = 334.6 ± 2.7 J/mol · K and 336.0 ± 2.7 J/mol · K. The preferred standard third-law entropy for spessartine is S o = 335.3 ± 3.8 J/mol · K, which is the mean value from the two separate determinations. The lattice (vibrational) heat capacity of spessartine was calculated using the single-parameter phonon dispersion model of Komada and Westrum. The lattice entropy at 298.15 K is S vib 298.15 = 297.7 J / mol · K , which represents 89% of the calorimetric entropy. The magnetic heat capacity and entropy of spessartine, S mag , at 298.15 K were also calculated. The S mag of the two samples is 38.7 and 37.4 J/mol · K, which is 87% and 83% of the maximum possible magnetic entropy given by 3Rln6 = 44.7 J/mol · K. Published model-dependent lattice-dynamic calculations of S vib 298.15 are analyzed and compared to the experimental data. Using the calorimetrically determined S o and the C p polynomial for spessartine, together with high P– T experimental phase-equilibrium data on Mn 2+–Mg partitioning between garnet and olivine, allows calculation of the standard enthalpy of formation of spessartine. This gives Δ H f , Sps o = - 5693.6 ± 1.4 kJ / mol , a value nearly 50 kJ more negative than some published values. The Gibbs free energy of spessartine was also calculated and gives Δ G f , Sps o = - 5364.3 kJ / mol at 298.15 K. The new standard entropy and enthalpy of formation values for spessartine lead to revised estimates for the enthalpies of formation of other Mn 2+-silicates. Resulting Δ H f o values for Mn-biotite, Mn-chlorite, Mn-cordierite, Mn-staurolite and Mn-chloritoid are 7–34 kJ more negative than their values listed in the thermodynamic database “THERMOCALC”. As an example, the new standard entropy and enthalpy of formation for spessartine have been applied to Mn–Fe partitioning between garnet and orthopyroxene from manganiferous iron formations. Excellent agreement between the predicted and observed distribution coefficient was obtained.