Pressure Derivatives Of Moduli Research Articles

Single-crystal elasticity of pyrope and MgO to 20 GPa by Brillouin scattering in the diamond cell

The single-crystal elastic properties of synthetic pyrope (Mg 3Al 2Si 3O 12) and periclase (MgO) have been measured by Brillouin scattering in a diamond anvil cell (DAC) up to 20 GPa. A 16:3:1 mixture of methanol–ethanol–water was used as a pressure-transmitting medium. Above the freezing pressure of this medium (∼14 GPa), heat treatment and accompanying stress relaxation produces quasi-hydrostatic conditions. An analysis of geometric errors associated with the DAC indicates that the DAC introduces an additional uncertainty in velocity of ≤0.5% (as compared to measurements in air), if there is no vignetting of the incident and scattered beams. The nonhydrostaticity caused by freezing of the pressure-transmitting medium results in lower velocities and elastic moduli than are obtained under hydrostatic conditions, and this leads to an overestimation of the second pressure derivatives of the elastic moduli. Fitting our hydrostatic data to finite-strain equations of state yields the following adiabatic bulk ( K S) and shear ( μ) moduli and their pressure derivatives: K S=163.2(10), K′=3.96(10), Kʺ=−0.044(20), μ=130.2(10), μ′=2.35(10), μʺ=−0.040(20) for MgO and K S=171.2(20), K′=4.1(3), μ=93.7 (20), μ′=1.3(2) for pyrope, where primes indicate pressure derivatives of moduli. Our results for MgO are in excellent agreement with previous ultrasonic measurements performed at lower pressures, and in particular the values of K′ agree to within a few percent. Our data are in good agreement with recent compression measurements on pyrope to pressures exceeding 20 GPa, suggesting that Brillouin scattering is an accurate method for high-pressure density and elastic moduli measurements. Pyrope is nearly elastically isotropic at ambient conditions and remains isotropic over the pressure range studied here. In contrast, the elastic anisotropy of MgO is observed to decrease dramatically with increasing pressure, becoming elastically isotropic at ∼21.5 GPa.

A seismic equation of state II. Shear properties and thermodynamics of the lower mantle

For most solids at normal conditions the effect of temperature on the elastic properties is controlled mainly by the variation of volume. Volume dependent extrinsic effects dominate at low pressure and high temperature. Under these conditions one expects that the relative changes in shear velocity, due to lateral temperature gradients in the mantle, should be similar to changes in compressional velocity. However, at high pressure, the extrinsic contribution is suppressed, particularly for the bulk modulus, and variations of seismic velocities are due primarily to changes in the rigidity. Seismic data for the lower mantle are used to estimate the two Grüneisen parameters and related parameters such as the temperature and pressure derivatives of the elastic moduli and thermal expansion. Standard assumptions about the volume dependence of the elastic moduli based on high temperature behavior of solids are shown to be inaccurate for the lower mantle. The Grüneisen-type parameters for the lower mantle are (∂ ln K S ∂ ln ρ) P = δ S = 1.8 − 1.0, (∂ ln K S ∂ ln ρ) S = 3 − 3.8, (∂ ln G ∂ ln ρ) P = 5.8 − 7.0, (∂ ln G ∂ ln ρ) S = 2.4 − 2.6 and γ = 1.3 − 1.1 . These are based on the radial and lateral variations of seismic velocity and density. The zero-pressure high-temperature values for the coefficient of thermal expansion and the Grüneisen ratio are estimated as α 0 = 3.8 × 10 −5 K −1 and γ 0 = 1.4. The seismic data imply (∂ ln γ ∂ ln ρ) = −1 + ϵ and −(∂ ln α ∂ ln ρ) ∼ 2 − 3 . The effect of temperature on the pressure derivatives of the moduli is also estimated. The lattice conductivity, K L, increases rapidly with depth, contributing to a lowering of the Rayleigh number in the lower mantle and a large thickness for deep thermal boundary layers. Temperature is less effective in altering density and seismic velocity at depth than assumed in geophysical modeling. Temperature induced phase changes are more important than temperature per se. These considerations cast doubt on the thermal interpretation of deep slab anomalies and, therefore, on the deep slab penetration hypothesis.