Abstract
Heat capacity Cv and entropy S for pyrope and grossular are calculated using a statistical thermodynamic approach and a density of states derived from previous single-crystal infrared and Raman spectra obtained for natural, nearly end-member garnets. Calculations of CP agree with calorimetric data from ~150 to ~1000 K, within 0.6% for pyrope and within 1% for grossular. Results for S parallel the calorimetric values but are of fset by propagation of the heat capacity mismatch at low temperatures, through the integration of CP/T over temperature. Calculated S for pyrope is offset by about – 10 J/mol K, and S of grossular is offset by +8 J/mol K. Calorimetic data at low temperatures (50–150 K) are outside the limit of uncertainty in spectroscopic derivation, possibly because of positional disorder of Mg in pyrope or replacement of SiO4 by 4OH in grossular, or both. This conclusion is supported by comparison of relative entropies, in that the theory predicts that the entropy of pyrope is less than that of grossular, whereas calorimetric measurements yielded the opposite result. Preferred values of thermodynamic properties in J/mol K at 298.15 K are CP(Py) : 326.0 ± 0.5, S(Py) = 256 ± l, CP(Gr) = 333.5 ± 0.5, and S(Gr) = 265 ± 2. Excess entropy of grossular compared to pyrope results from the larger mass of the Ca ion; however, its magnitude is limited by the large size of the Ca ion, which dilates the Si-O bond through edge sharing of the larger dodecahedra with the tetrahedra, leading to changes in the force constants that raise the frequency of the lowest lying translations of the SiO4 tetrahedron. This type of compositional dependence of bonding is inferred to regulate mixing properties of garnets.
