Evaluation of shear moduli and other properties of silicates with the spinel structure from IR spectroscopy

Vibrational spectra are used to determine key physical properties of phases thought to be important in Earth's transition zone. Single-crystal infrare d (IR) reflectance spectra were measured for synthetic Mg, Fe, Ni, or Go-be aring silicates with the spinel structure. Peak parameters (frequency, damp ing coefficient, and oscillator strength) were determined for the fundament als, and for overtones, up to 3(rd) order. On average, the frequencies and damping coefficients of the overtones are simple multiples of the correspon ding parameters of the fundamental modes. Absorption spectra of thin films were measured at pressures (P) up to 370 kbar for gamma -Mg2SiO4 and up to 200 kbar for gamma -Fe2SiO4. Widths are nearly constant, but frequencies (v i) increase either linearly or quadratically with P, For weak peaks. the ab sorption widths have values close to their corresponding damping coefficien ts. For gamma -Fe2SiO4, ambient IR data predict heat capacity (C-v = 126 +/ - 2.5 J/mol.K), shear modulus (G = 875 +/- 15 kbar), and sound velocities ( u(p) = 8.20 +/- 0.05, u(s) = 4.25 +/- 0.06 km/s) at 298 K: pressure data gi ve partial derivativeG/partial derivativeP = 0.06, 0.44, or 0.91 if for the bulk modulus, partial derivativeK/partial derivativeP = 5, 4.5, or 4, resp ectively, and an average mode Gruneisen parameter of < gamma > = 1.45 +/- 0 .4, which implies that thermal expansivity is (21 +/- 1) x 10(-6)/K. For ga mma -Mg1.2Fe0.8SiO4, ambient IR data predict G = 1120 +/- 50 kbar, U-p = 9. 12 +/- 0.20, and u(s) = 5.18 +/- 0.20 km/s at 298 K, assuming that the freq uency of the acoustic mode is 225 to 240 cm(-1). This calculation uses K-s = 1995 kbar, which was obtained from recent compression data by assuming pa rtial derivativeK/partial derivativeP = 4. The above values provide a smoot h quadratic dependence of K, and G on Fe/(Fe + Mg). The trends suggest that partial derivativeK/partial derivativeP remains at 4 whereas partial deriv ativeG/partial derivativeP drops from similar to1 to similar to0.5 as Fe co ntent increases in ringwoodite. Acoustic fundamentals or overtones were use d successfully here to provide u, G, and their P and T derivatives for sili cate spinels. This method should work for other simple structures, and may be generally applicable.