Reinhard Boehler

Equation of state of sodium chloride up to 32 kbar and 500°C†

Abstract The length change of a 25mm long single crystal of NaCl has been determined as a function of hydrostatic pressure up to 32 kbar and temperatures up to 500°C using an electrical contact piezometer with tungsten carbide as a standard. The measurements were carried out in an end loaded piston cylinder apparatus. The length change of the tungsten carbide standard is small compared to that of NaCl and therefore reliable data are obtained. Compression data by Bridgman[1] and thermal expansion data by Kennametal Inc. were used for the equation of state of tungsten carbide. We estimated an absolute uncertainty in the length change measurement of NaCl of ±0.7%. The temperature was accurate within 0.3°C. The uncertainty in pressure is ±0.4%. The results are compared with Deckers [2] equation of state which is frequently used when NaCl is taken as a standard in high pressure work. At room temperature we find a smaller compression of NaCl than Decker and find excellent agreement with Bridgmans[3] data. At higher temperatures we find very good agreement between our data and Deckers equation of state.

Grüneisen parameter of NaCl at high compressions

A new method of determining the pressure dependence of the Gruneisen parameter is described. The measurements were carried out on NaCl to 33 kbar at room temperature using an end-loaded piston-cylinder apparatus. A fluid cell arrangement with Bridgman unsupported area seals was used. Changes of sample temperature associated with small adiabatic pressure changes were measured and the Gruneisen parameter could be calculated from the thermodynamic relationship γ = (KsT)(∂T∂P)s where Ks is the adiabatic bulk modulus. Our results are in excellent agreement with those reported by Roberts and Ruppin [1] who calculated the pressure dependence of γ from thermodynamic and ultrasonic data and in excellent agreement with those reported by Hardy and Karo [2] who carried out a lattice-dynamical calculation.

Pressure dependence of the thermodynamical Grüneisen parameter of fluids

Temperature changes associated with adiabatic pressure changes have been measured for water, mercury, pentane, isopentane, ethanol, methanol, and ether. For the first four fluids mentioned, the pressure dependence of the adiabatic bulk modulus, Ks, is known from ultrasonic measurements, and the Gruneisen parameter can be calculated using the thermodynamic relationship γth= (Ks/T)(lT/lP)s. For all fluids except water a large decrease of ΔT/ΔP with pressure is observed and the ΔT/ΔP curves converge at about 2.5 °C/kbar before freezing occurs. A considerable increase of γth with pressure is observed.

Thermal expansion of LiF at high pressures

Abstract Accurate data on the pressure-volume temperature relationship of LiF are presented and compared with recent X-ray measurements by Yagi[1]. Our measurement is a differential length change measurement between a 25 mm long single crystal of LiF and a tungsten carbide standard as previously described by Boehler and Kennedy [2]. A piston-cylinder apparatus with fluid cell arrangement was used up to 32 kbar and 400°C. In spite of the low compressibility of LiF our volume data are accurate within 0.07%. We find a much stronger decline of the thermal expansivity with pressure than Yagi. The values of α v · K T = ( ∂P ∂T ) v remain constant within the uncertainty over our pressure and temperature range.

Resistance heating of Fe and W in diamond-anvil cells

Abstract A new method for internally heating a diamond-anvil cell is described. Fine wires of iron or tungsten are resistively heated in a gasketed cell, thus providing a uniformly distributed pressure that can be measured in situ by employing the ruby scale. Temperatures of several thousand degrees have been measured by fitting a black body radiation function to the spectrum of the hot wire taken with an optical multi-channel analyzer. Temperatures as high as the melting temperature of tungsten have been achieved. The α−γ and α−ϵ phase transitions of iron have been studied, and the results show excellent agreement with previous data obtained with piston-cylinder or externally-heated diamond cells.

Measurement of the adiabats of quartz, forsterite, and magnesium oxide at high pressures and high temperatures and adiabatic gradient in the mantle

Abstract The geophysically-important adiabat (∂T/∂P)s has been measured at pressures up to 50 kbar and temperatures up to 1000°C. A simple power law describes the relationship between (∂T/∂P)s and the compression of the material. The power is independent of the material and of the temperature within the uncertainty. This consistency in the power allows the extrapolation of the adiabat to pressure and temperature conditions of the mantle of the earth. The adiabatic gradient is shown to be significantly smaller than the melting gradient.

Systematics in the melting behavior of the alkali metals from DAC measurements

Abstract The alkali metals K, Rb and Cs undergo a series of phase transitions that are related to a s-to-d electron transfer. These solid-solid transitions strongly affect the melting behavior in the vicinity of the transitions. An externally-heated diamond-anvil cell was used to measure melting temperatures of the alkali metals, Na, K, Rb and Cs at pressures to 150 kbar. Melting was determined visually by changes of the optical properties of the metals. Pressures were obtained from the known pressure and temperature shifts of the ruby line which can be used for accurate measurements to about 650 K. The melting temperature of sodium rises continuously with pressure. The slopes of the melting curves potassium and rubidium change appreciably at the bcc-fcc transitions at 110 and 90 kbar, respectively. An extremely steep melting curve of cesium is observed after the electronic transition at 42 kbar.

Grüneisen Parameter of Fluids and Metals under Compression

The Gruneisen parameter and adiabats of both solids and fluids play an important role in geophysical models. In the discussion of the convection of the outer core and the origin of the earths magnetic field, one needs to know the adiabatic gradient of the material in question. This gradient can only be calculated when the pressure dependence of the Gruneisen parameter and the adiabatic bulk modulus are known. Calculations of Gruneisen parameter at high compression from lattice theory or from thermodynamic data show considerable disagreement.