Thermodynamic properties of pyrope and grossular from vibrational spectroscopy

Heat capacity C_v 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. Preferred values of thermodynamic properties in J/mol K at 298.15 K are C_p(Py)=326.0±0.5, S(Py)=256±1, C_p(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. -from Authors