Redefinition of the mode Grüneisen parameter for polyatomic substances and thermodynamic implications

Although the value of the thermal Grüneisen parameter (γth) should be obtained by averaging spectroscopic measurements of mode Grüneisen parameters [γ_i ≡ (K_T/ν_i)∂ν_i/∂P, where K_T is isothermal bulk modulus, ν is frequency, and P is pressure], in practice, the average (γ_i) is up to 25% lower than γth. This discrepancy limits the accuracy of inferring physical properties from spectroscopic data and their application to geophysics. The problem arises because the above formula is physically meaningful only for monatomic or diatomic solids. We redefine γ_i to allow for the presence of functional groups in polyatomic crystal structures, and test the formula against spinel- and olivine-group minerals that have well-constrained spectra at pressure, band assignments, thermodynamic properties, and elastic moduli, and represent two types of functional groups. Our revised formula [γ_i ≡ (K_x/ν_i)∂ν_i/∂P] uses polyhedral bulk moduli (K_x) appropriate to the particular atomic motion associated with each vibrational mode, which results in equal values for (γ_i), γth, and γ_LA (the Grüneisen parameter of the longitudinal acoustic mode). Similar revisions lead to the pressure derivatives of these parameters being equal. Accounting for differential compression intrinsic to structures with functional groups improves the accuracy with which spectroscopic models predict thermodynamic properties and link to elastic properties.