A calorimetric investigation of spessartine: Vibrational and magnetic heat capacity

The heat capacity (C,,) of two synthetic spessartine samples (Sps) was measured oil 20-30 mg-size samples in the temperature range 2-864 K by relaxation calorimetry (RC) and differential scanning calorinictry (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,, 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-ulb(298.15) = 297.7 J/mol.K, which represents 89% of the calorimetric entropy. The magnetic heat capacity and entropy of spessartme, 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 S-ulb(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 oil Mn2+-Mg partitioning between garnet and olivine, allows calculation of the standard enthalpy of formation of spessartine. This gives Delta 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 Delta 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 Mn2+-silicates. Resulting Delta H-f(o) values for Mn-biotite, Mn-chlotire, 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. (C) 2009 Elsevier Ltd. All rights reserved.