L. J. Slutsky

The elastic constants of San Carlos olivine to 17 GPa

All elastic constants, the average bulk and shear moduli, and the lattice parameters of San Carlos olivine (Fo90) (initial density 3.355 gm/cm3) have been determined to a pressure of 12 GPa at room temperature. Measurements of c11, c33, c13, and c55 have been extended to 17 GPa. The pressure dependence of the adiabatic, isotropic (Hashin-Shtrikman bounds) bulk modulus, and shear modulus may be expressed as KHS = 129.4 + 4.29 P and by GHS = 78 + 1.71P - 0.027 P2, where both the pressure and the moduli are in gigapascals. The isothermal compression of olivine is described by a bulk modulus given as KT = 126.3 + 4.28 P. Elastic constants other than c55 can be adequately represented by a linear relationship in pressure. In the order (c11, c12, c13, c22, c23, c33, c44, c55, c66) the 1 bar intercepts (gigapascal units) are (320.5, 68.1, 71.6, 196.5, 76.8, 233.5, 64.0, 77.0, 78.7). The first derivatives are (6.54, 3.86, 3.57, 5.38, 3.37, 5.51, 1.67, 1.81, 1.93). The second derivative for c55 is −0.070 GPa−1. Incompressibilities for the three axes may also be expressed as linear relationships with pressure. In the order of a, b, and c axes the intercepts in gigapascals are (547.8, 285.8, 381.8) and the first derivatives are (20.1, 12.3, 14.0).

The elastic constants of an aluminous orthopyroxene to 12.5 GPa

The elastic constants, average bulk and shear moduli, and lattice parameters of Kilbourne Hole orthopyroxene [(Mg1.63Fe0.17Ca0.04Mn0.01)(Al0.12Cr0.01)(Si1.89Al0.11)O6] have been determined to a pressure of 12.5 GPa. The molar ratio Mg/(Mg+Fe) in the sample is 0.91 and 5 wt % of Al2O3 and 1 wt % of CaO are present. The bulk modulus, in gigpascals, expressed as a function of the pressure (with an rms misfit of 0.5%) is K = 115.4 + 7.82P - 0.18P2. The unusually large pressure derivative of bulk modulus at 1 bar decreases to a more typical value (∼4) at high pressure. The isotropic shear modulus is linear within experimental uncertainty (the rms misfit is 0.5%) with G = 77.9 + 1.44P. At 1 bar the isotropic longitudinal and shear velocities 8.15 and 4.86 km/s, respectively are approximately 3% faster than those found in nonaluminous orthopyroxenes. Above 4 GPa the average compressional wave velocities in the orthopyroxene exceed those in olivine. These results call into question the assumption, common in models created to interpret mantle seismic data, that high velocities in garnet are balanced by low velocities in orthopyroxene.

Direct simulation of continuous wave electron paramagnetic resonance spectra from Brownian dynamics trajectories

A method is developed for the direct simulation of continuous wave electron paramagentic resonance (CW‐EPR) line shapes from molecular trajectories. The method is applied to the cases of an axially symmetric nitroxide spin label undergoing two different types of motion (i) two‐site jumping motion and (ii) isotropic rotational Brownian motion. Probabilistic models are developed that generate trajectories stable for large numbers of evolution time steps. Spectra at both 10 (X band) and 35 (Q band) GHz of satisfactory quality are generated from 40 trajectories of 214 steps sampled at 0.05 ns intervals. The resulting calculations illustrate that this method can be used as a basis of CW‐EPR spectral simulation for systems undergoing arbitrarily complex dynamics using trajectories generated by classical Brownian dynamics.

The thermal diffusivity of water at high pressures and temperatures

Thermal diffusivities of fluid water have been measured to a pressure of 3.5 GPa, a density of 1.4 g cm−3 and a temperature of 400 °C. Above 100 °C, both the diffusivities and the related conductivities are found, unexpectedly, to scale as the square-root of absolute temperature; in contrast, the excess conductivities are highly dependent on temperature. Measurements at 25 °C, extending into a metastable regime with respect to ice VI, do not scale in this manner and this anomalous behavior is not suppressed by pressures up to 1.3 GPa.

SPEED OF SOUND AND EQUATION OF STATE FOR FLUID OXYGEN TO 10 GPA

The speed of sound in supercritical, fluid oxygen has been measured up to the freezing points of 6.0 GPa at 30 °C and 10.5 GPa at 200 °C. The oxygen was contained in a diamond–anvil cell and pressure was measured on the ruby scale. The measurements were used to establish an equation of state. Additionally, the fluid-β phase boundary was determined between 15 and 180 °C to a precision of 0.02 GPa.

Ultrasonic and Infrared Studies of the Lambda Transition in NaNo3

The velocity and attenuation of longitudinal and transverse acoustic waves propagating along the three‐fold axis of NaNO3 have been measured from room temperature to 300°C. Strong frequency‐dependent ultrasonic attenuation is observed at temperatures immediately above and below the λ point. From the attenuation a relaxation time for the equilibration of the long‐range order at constant entropy of 4.3 × 10−10 sec is estimated. The totally symmetric stretching mode of the nitrate ion, inactive in the ordered NaNO3 structure, is possibly active in the high‐temperature disordered phase. A weak infrared absorption is found at an elevated temperature at the anticipated frequency of ν1 in NaNO3. The temperature variation of the absorption through the transition is consistent with the notion that there is no abrupt change in short‐range order at the λ point.

Surface van der Waals Forces

Adsorption isotherms at very high coverage of (CH3)4C and (CH3)4Si on flat gold surfaces are found to imply a potential energy of interaction between the molecule and metal which varies at the inverse square of the distance between the molecule and the metal surface.

Elastic constants, interatomic forces, and equation of state of β‐oxygen at high pressure

The six independent elastic constants of β‐oxygen have been measured over a pressure range extending from 6.0 to 9.5 GPa. Neither central forces between individual atoms, nor central forces augmented by the interactions between axial distributions of charge can give a reasonable account of the data. Force constant matrices were found which can account for the elastic data and the previously observed librational frequency. These matrices are based on general, short range forces with many‐body interactions only among atoms contained in the same pair of molecules. Vibrational densities of states, distributions of individual‐mode Gruneisen parameters, heat capacities, and the equation of state derived from the pressure dependence of the elastic moduli are presented.

Thermal diffusivity of fluid oxygen to 12 GPa and 300 °C

The thermal diffusivity of fluid oxygen in the diamond-anvil cell has been measured from 1 to 12.6 GPa and 25 to 300 °C. These constitute the first experimental measurements of thermal transport properties of simple fluids above 1 GPa. Diffusivities are found to rise sharply from a minimum at intermediate pressures and then to level off at ∼6 GPa. Thermal conductivities derived from these measurements do not vary as √T, rather the excess conductivities are approximately independent of temperature. The diffusivities of nitrogen, previously measured to 1 GPa, closely match those of oxygen when scaled as suggested by a simple, corresponding states theory.

Measuring Speed of Sound and Thermal Diffusivity in the Diamond-Anvil Cell

Transient grating spectroscopy in the diamond-anvil high-pressure cell permits, in favorable cases, determination of the equation of state and thermal transport properties of fluids at high temperatures and pressures. Measurements of the speed of sound and thermodynamic properties of aqueous Na2SO4to 3.4 GPa at 300°C and the thermal diffusivity of oxygen are reported as examples of the application of this technique.