Thermodynamics of Fe-Mg olivines at mantle pressures; mid- and far-infrared spectroscopy at high pressure^*

The first far‐IR spectra of silicates at high pressure have been obtained by combining various state‐of‐the‐art technologies. Three olivines (Fo₁₀₀, Fo₈₇, and Fo₀) were studied at pressures of up to 425 kbar. In addition, mid‐IR data on Fo₁₀₀ were obtained up to 240 kbar. The same pressure responses (i.e., changes in peak position, area, etc.) were seen in the hydrostatic and nonhydrostatic experiments. By augmenting these data with mid‐IR studies at pressure by Xu et al. (1983), all IR modes in Mg‐Fe olivines are characterized as a function of pressure. The data corroborate the band assignments for olivine and the correlation of the forsterite and fayalite 1‐atm spectra by Hofmeister (1987), in that similar behavior with pressure is observed for analogous bands in these minerals, with each different type of vibrational motion having a distinct pressure response. The response to pressure of bands assigned to SiO₄ vibrations differs fundamentally from that of bands involving M ions in a manner that is consistent with the relative incompressibility of the SiO₄ tetrahedron. A gradual transformation from olivine to a more symmetric structure is supported by the generally continuous but individual responses of peak area and frequency to pressure, by the appearance of new bands at pressure, and by the occurrence of mode softening.

Initial values for the first mode Grüneisen parameter(γ_i ≡ –∂ln ν_i/∂ ln V) range from 0.10 to 2.0 such that far‐IR modes (translations or rotations) generally have values larger than unity, whereas mid‐IR modes (internal vibrations) all have values less than unity. At pressures significantly above the stability field of olivine, γ_i can become negative. Within the olivine stability field, γ_i; is nearly constant for the majority of the IR bands. The strong curvature of frequency with pressure, occurring for four to six modes for each mineral, allows accurate determination of not only the first but also the second Grüneisen parameter(q_i ≡ d ln γ_i/d ln V), such that q_i(0) ranges from zero to nine. It is not clear that integer values are required. Modes with q_i(0) greater than six have an appreciable pressure dependence q_i, suggesting that constant q_i, is not appropriate for the other bands. For the majority of bands, which do not exhibit curvature of frequency with either pressure or volume, γ_i(0) can be determined within ±20% and q_i(0) can be estimated as roughly -1.5 ± 3.0, by averaging values determined from polynomial fits of ν(V) and ν(P). The negative q_i values are mandated by the linear dependence of ν on P. These large uncertainties result from the interdependence of γ_i and q_i and are commonly and incorrectly ignored in computing Grüneisen parameters.