Marvin Ross

Soft‐Sphere Equation of State

The pressure and entropy for soft‐sphere particles interacting with an inverse twelfth‐power potential are determined using the Monte Carlo method. The solid‐phase entropy is calculated in two ways: by integrating the single‐occupancy equation of state from the low density limit to solid densities, and by using solid‐phase Monte Carlo pressures to evaluate the anharmonic corrections to the lattice‐dynamics high‐density limit. The two methods agree, and the entropy is used to locate the melting transition. The computed results are compared with the predictions of the virial series, lattice dynamics, perturbation theories, and cell models. For the fluid phase, perturbation theory is very accurate up to two‐thirds of the freezing density. For the solid phase, a correlated cell model predicts pressures very close to the Monte Carlo results.

A high‐density fluid‐perturbation theory based on an inverse 12th‐power hard‐sphere reference system

A variational theory is developed that is accurate at normal liquid densities and densities up to 4 times that of the argon triple point. This theory uses the inverse 12th‐power potential as a reference system. The properties of this reference system are expressed in terms of hard‐sphere packing fractions by using a modified form of hard‐space variational theory. As a result of this ’’bootstrapping,’’ a variational procedure may be followed that employs the inverse 12th‐power system as a reference but uses the hard‐sphere packing fraction as the scaling parameter with which to minimize the Helmholtz free energy.

Repulsive forces of simple molecules and mixtures at high density and temperature

Shock wave data for liquid Ar, Xe, N2, O2, CO2, CH4, and CO have been used to test the possibility that the repulsive pair potential of these fluids scale in accordance with the ’’Law of Corresponding States.’’ This is found to be approximately valid to a compression of about 2.5 times liquid density. The law has been applied to compressed mixtures of N2 and O2 and a theoretical prediction of the detonation velocity and pressure of liquid NO is found to be in excellent agreement with experiment.

The equation of state of molecular hydrogen at very high densitya)

In the preceding paper new shock‐wave results were reported on liquid hydrogen and deuterium up to a pressure of 76 GPa (760 kbar). In the present paper an effective pair potential is determined from these results and used in calculations of fluid and solid isotherms, melting curves, and the metallic transition pressure. The agreement with available data is good and the metallic transition is predicted to be near 300 GPa (3 Mbar).

Melting curve of aluminum in a diamond cell to 0.8 Mbar: implications for iron

Abstract The melting curve of aluminum was measured in a laser-heated diamond cell up to a pressure of 0.8 Mbar in order to test the agreement between this technique and shock wave measurements, which has been lacking in the case for iron. At this pressure, which is over an order of magnitude higher than in previous experiments [1, 2], the melting temperature is 3800 K, comparable to that measured for iron at 2 Mbar [3]. The present results for aluminum extrapolate smoothly to the previous melting measurements in a multi-anvil apparatus to 60 kbar and to the calculated shock melting point of 4750 K at 1.25 Mbar. They are also in excellent agreement with theoretical calculations. A review of the shock data reported for Al, Ta and Mo, close-packed metals, in which a break in the sound velocity-pressure curve is used to determine the melting pressure, shows that the change in velocity at melting is about 10% for all three metals. In the case of iron, the sound velocity data have been used to infer two transitions: a solid-solid transition at 2.0 Mbar and melting at 2.4 Mbar, each of these transitions having about a 5% change in sound velocity. It is unlikely that a phase transition between close-packed cubic structures will have a 5% velocity change, the same as is found in the melting transition. We therefore suggest that for iron there exists only a single transition, starting at 2.0 Mbar, a region of incomplete shock melting between 2 and 2.4 Mbar, and a total change in sound velocity of about 10%, which is closer to the value of the other metals studied. This interpretation introduces a very good agreement between the shock melting results of Brown and McQueen [4] and diamond cell measurements for iron [3] which has up to now been lacking.

Temperature measurements of shock-compressed liquid hydrogen: implications for the interior of Jupiter

Shock temperatures of hydrogen up to 5200 kelvin were measured optically at pressures up to 83 gigapascals (830 kilobars). At highest pressures, the measured temperatures are substantially lower than predicted. These lower temperatures are caused by a continuous dissociative phase transition above 20 gigapascals. Because hydrogen is in thermal equilibrium in shock-compression experiments, the theory derived from the shock data can be applied to Jupiter. The planets molecular envelope is cooler and has much less temperature variation than previously believed. The continuous dissociative phase transition suggests that there is no sharp boundary between Jupiters molecular mantle and its metallic core. A possible convectively quiescent boundary layer might induce an additional layer in the molecular region, as has been predicted.

A theoretical analysis of the shock compression experiments of the liquid hydrogen isotopes and a prediction of their metallic transition

Shock compression experiments in which the liquid hydrogen isotopes were compressed as much as sevenfold in density to pressures of the order of 900 kbar are analyzed to obtain an effective intermolecular potential. Because temperatures as high as 7000°K are generated during the shock process, this potential is most accurate in the highly repulsive, small separation region, and is thereby well suited to calculate the properties of dense molecular hydrogen in the region of the metallic transition. By equating the Gibbs free energies of the metal and molecular phases, we calculate the pressure and density of the metallic transition. Unfortunately, the large experimental error and the sensitivity of the transition to the free energy allows us only to estimate a lower bound of 2 to 3 Mbar for the transition pressures.

The argon melting curve to very high pressures

The melting curve of Ar has been measured to 717 K and 60 kbar using a new interferometric technique in a diamond anvil cell. Theoretical calculations are in excellent agreement with the measurements

The repulsive forces in dense argon

Shock wave compression curves for liquid argon were computed using a number of recently proposed pair potentials. The results are compared to experiment and used to evaluate the accuracy of the repulsive potential. Recent molecular beam results are found to be in excellent agreement with the shock data.

HIGH PRESSURE EQUATIONS OF STATE: THEORY AND APPLICATIONS

This article reviews theoretical equations of state of solids and dense liquids and their applications to studies of melting, shock compression, matter at extreme conditions and planetary interiors.