Atom-in-jellium equations of state in the high-energy-density regime

Plasma ionization balance in chemical-picture and average-atom models

We propose an approximate method to calculate ion partition functions in the context of the chemical-picture representation of plasmas as an interacting mixture of various ions and free electrons under the local-thermodynamic-equilibrium conditions. The method uses the superconfiguration approach and implies that the first-order corrections to the energies of excited electron configurations due to the electron-electron interaction may be replaced by a similar first-order correction to the energy of the basic configuration of an ion with the same number of bound electrons. The method enables one to significantly speed up the calculations and generally provides quite accurate results. Using the method proposed, plasma ionization balance and average ion charges calculated on the base of the chemical-picture representation show a good agreement with the relevant average-atom data. For the case of weak electron-ion nonideality, we provide approximate relations between the chemical-picture and average-atom values of the average ion charge, chemical potential, and plasma-density depression of ionization potential.

Equation of state modeling with pseudoatom molecular dynamics

Using a modified version of the pseudoatom molecular-dynamics approach, the silicon and oxygen equations of state were generated and then employed to construct the equation of state of silicon dioxide. The results are supported by the close agreement with ab initio simulations of the silicon pressure and experimental shock Hugoniot of silicon dioxide. Ion thermal contributions to thermodynamic functions provided by the PAMD simulations are compared to their counterparts obtained with the one-component plasma and charged-hard-sphere approximations.

High-temperature ion-thermal behavior from average-atom calculations

Atom-in-jellium calculations of the Einstein frequency were used to calculate the mean displacement of an ion over a wide range of compression and temperature. Expressed as a fraction of the Wigner-Seitz radius, the displacement is a measure of the asymptotic freedom of the ion at high temperature, and thus of the change in heat capacity from six to three quadratic degrees of freedom per atom. A functional form for free energy was proposed based on the Maxwell-Boltzmann distribution as a correction to the Debye free energy, with a single free parameter representing the effective density of potential modes to be saturated. This parameter was investigated using molecular dynamics simulations, and found to be ∼0.2 per atom. In this way, the ion-thermal contribution can be calculated for a wide-range equation of state (EOS) without requiring a large number of molecular dynamics simulations. Example calculations were performed for carbon, including the sensitivity of key EOS loci to ionic freedom.

Probing the Solid Phase of Noble Metal Copper at Terapascal Conditions

Ramp compression along a low-temperature adiabat offers a unique avenue to explore the physical properties of materials at the highest densities of their solid form, a region inaccessible by single shock compression. Using the National Ignition Facility and OMEGA laser facilities, copper samples were ramp compressed to peak pressures of 2.30 TPa and densities of nearly 30  g/cc, providing fundamental information regarding the compressibility and phase of copper at pressures more than 5 times greater than previously explored. Through x-ray diffraction measurements, we find that the ambient face-centered-cubic structure is preserved up to 1.15 TPa. The ramp compression equation-of-state measurements shows that there are no discontinuities in sound velocities up to 2.30 TPa, suggesting this phase is likely stable up to the peak pressures measured, as predicted by first-principal calculations. The high precision of these quasiabsolute measurements enables us to provide essential benchmarks for advanced computational studies on the behavior of dense monoatomic materials under extreme conditions that constitute a stringent test for solid-state quantum theory. We find that both density-functional theory and the stabilized jellium model, which assumes that the ionic structure can be replaced by an ionic charge distribution by constant positive-charge background, reproduces our data well. Further, our data could serve to establish new international secondary scales of pressure in the terapascal range that is becoming experimentally accessible with advanced static and dynamic compression techniques.