Isothermal equation of state of crystalline and glassy materials from optical measurements in diamond anvil cells

Here, we present a method to study the equation of state of opaque amorphous and crystalline materials in diamond anvil cells. The approach is based on measurements of sample dimensions using high-resolution optical microscopy. Data on the volumetric strain as a function of pressure allow deriving the isothermal equation of state of the studied material. The analysis of optical images is fully automatized and allows measuring the sample dimensions with the precision of about 60 nm. The methodology was validated by studying isothermal compression of ω-Ti up to 30 GPa in a Ne pressure transmitting medium. Within the accuracy of the measurements, the bulk modulus of ω-Ti determined using optical microscopy was similar to that obtained from x-ray diffraction. For glassy carbon compressed to ∼30 GPa, the previously unknown bulk modulus was found to be equal to K₀ = 28 (2) GPa [K' = 5.5(5)].

Determination of elastic moduli from measured acoustic velocities

Methods are evaluated in solution of the inverse problem associated with determination of elastic moduli for crystals of arbitrary symmetry from elastic wave velocities measured in many crystallographic directions. A package of MATLAB functions provides a robust and flexible environment for analysis of ultrasonic, Brillouin, or Impulsive Stimulated Light Scattering datasets. Three inverse algorithms are considered: the gradient-based methods of Levenberg-Marquardt and Backus-Gilbert, and a non-gradient-based (Nelder-Mead) simplex approach. Several data types are considered: body wave velocities alone, surface wave velocities plus a side constraint on X-ray-diffraction-based axes compressibilities, or joint body and surface wave velocities. The numerical algorithms are validated through comparisons with prior published results and through analysis of synthetic datasets. Although all approaches succeed in finding low-misfit solutions, the Levenberg-Marquardt method consistently demonstrates effectiveness and computational efficiency. However, linearized gradient-based methods, when applied to a strongly non-linear problem, may not adequately converge to the global minimum. The simplex method, while slower, is less susceptible to being trapped in local misfit minima. A "multi-start" strategy (initiate searches from more than one initial guess) provides better assurance that global minima have been located. Numerical estimates of parameter uncertainties based on Monte Carlo simulations are compared to formal uncertainties based on covariance calculations.

APPLICATIONS OF IMPULSIVE STIMULATED SCATTERING IN THE EARTH AND PLANETARY SCIENCES

▪ Abstract  The elastic, thermodynamic, and transport properties of crystals and fluids at high temperature and pressure play a central role in the earth and planetary sciences as well as in a variety of technologies. These properties also constitute a principal experimental constraint on the description of intermolecular interactions at short distances. Aspects of “impulsive stimulated scattering,” when adapted to measurements in the diamond-anvil high-pressure cell, provide an approach to the determination of a subset of equilibrium and dynamic properties at high density.

Sound Velocities in Olivine at Earth Mantle Pressures

The independent elastic constants of an upper mantle mineral, San Carlos olivine [(Mg(1.8)Fe(0.2))SiO(4)], were measured from 0 to 12.5 gigapascals. Evidence is offered in support of the proposition that the explicit temperature dependence of the bulk modulus is small over the range of temperatures and pressures thought to prevail above the 400-kilometer discontinuity, and thus the data can be extrapolated to estimate the properties of olivine under mantle conditions at a depth of 400 kilometers. In the absence of high-temperature data at high pressures, estimates are made of the properties of olivine under mantle conditions to a depth of 400 kilometers. In contrast with low-pressure laboratory data, the predicted covariance of shear and compressional velocities as a function of temperature nearly matches the seismically estimated value for the lower mantle.