Scott Crockett

Test of a theoretical equation of state for elemental solids and liquids

We propose a means for constructing highly accurate equations of state (EOS) for elemental solids and liquids essentially from first principles, based upon a particular decomposition of the underlying condensed matter Hamiltonian for the nuclei and electrons. We also point out that at low pressures the neglect of anharmonic and electron-phonon terms, both contained in this formalism, results in errors of less than 5% in the thermal parts of the thermodynamic functions. Then we explicitly display the forms of the remaining terms in the EOS, commenting on the use of experiment and electronic structure theory to evaluate them. We also construct an EOS for aluminum and compare the resulting Hugoniot curve with data up to 5 Mbar, both to illustrate our method and to see whether the approximation of neglecting anharmonicity etc. remains viable to such high pressures. We find a level of agreement with experiment that is consistent with the low-pressure results.

Mechanical and optical response of [100] lithium fluoride to multi-megabar dynamic pressures

An understanding of the mechanical and optical properties of lithium fluoride (LiF) is essential to its use as a transparent tamper and window for dynamic materials experiments. In order to improve models for this material, we applied iterative Lagrangian analysis to ten independent sets of data from magnetically driven planar shockless compression experiments on single crystal [100] LiF to pressures as high as 350 GPa. We found that the compression response disagreed with a prevalent tabular equation of state for LiF that is commonly used to interpret shockless compression experiments. We also present complementary data from ab initio calculations performed using the diffusion quantum Monte Carlo method. The agreement between these two data sets lends confidence to our interpretation. In order to aid in future experimental analysis, we have modified the tabular equation of state to match the new data. We have also extended knowledge of the optical properties of LiF via shock-compression and shockless compression experiments, refining the transmissibility limit, measuring the refractive index to ∼300 GPa, and confirming the nonlinear dependence of the refractive index on density. We present a new model for the refractive index of LiF that includes temperature dependence and describe a procedure for correcting apparent velocity to true velocity for dynamic compression experiments.

A Comparison of Theory and Experiment of the Bulk Sound Velocity in Aluminum Using a Two‐Phase EOS

We compute the bulk sound speed along the Hugoniot using a new solid‐liquid two‐phase equation of state (EOS) for aluminum [Chisolm, Crockett, and Wallace, to appear in Phys. Rev. B] and compare with experimental sound speeds from various sources. The experiment extends from the crystal through the entire solid‐liquid two‐phase region. The EOS and data closely agree on where the Hugoniot passes through the two‐phase region, which corresponds to where aluminum melts. The bulk sound speed in the crystal region is consistent with the data, given the uncertainty in the experimental procedure. We also estimate shear moduli by using the experimental longitudinal sound speed data and the calculated bulk modulus. The shear modulus satisfies the approximation GS/BS=constant, within experimental error bars, throughout the crystal region on the Hugoniot.

Global equation of state for copper

A new, tabular (SESAME format) equation of state for Cu, suitable for use in hydrodynamic simulations, is described and compared to experimental data. Pressures, internal energies, and Helmholtz free energies are tabulated as functions of temperature and density. The new equation of state builds on the theoretical investigations of Greeff, et al., (J. Phys. Chem. Solids 67, 2033 (2006)), but extends the range of densities and temperatures covered to 10-5-105 g/cc and 0-108K. The staticlattice cold curve is modeled using the semi-empirical stabilized jellium equation near ambient densities, LDA and GGA density-functional predictions at moderate compressions, and Thomas- Fermi-Dirac theory at high compressions. The Johnson ionic model, which smoothly interpolates between Debye-like and ideal-gas behavior, is employed to model contributions from atomic motion, and Thomas-Fermi-Dirac theory is used for contributions from thermal electronic excitations. Predictions for the compressibility, principle and porous...

Tabular equation of state for gold

A new, SESAME-type equation of state (EOS) , suitable for use in hydrodynamic calculations, is described for gold. Pressures, internal energies, and Helmholtz free energies are tabulated on a rectangular temperature-and-density grid, spanning densities from 0 - 36 g/cc, temperatures from 0 - 800 eV, and extending up to pressures of 800 GPa. The EOS is constructed using the standard decomposition of the pressure into a static-lattice cold curve, a thermal nuclear contribution, and a thermal electronic contribution. The cold curve is derived from existing diamond-anvil-cell measurements, the thermal nuclear contribution from the Johnson model, and the thermal electronic contribution using Thomas-Fermi-Dirac theory. Predictions of the new EOS (SESAME 2705) for the cold curve, roomtemperature isotherm, principal Hugoniot, thermal expansion, heat capacity, melt line, and vapor pressure compare favorably with experimental data and are superior to the EOS currently available in the SESAME library (SESAME 2700).

Orbital-free extension to Kohn-Sham density functional theory equation of state calculations: Application to silicon dioxide

The liquid regime equation of state of silicon dioxide SiO2 is calculated via quantum molecular dynamics in the density range of 5 to 15 g/cc and with temperatures from 0.5 to 100 eV, including the α-quartz and stishovite phase Hugoniot curves. Below 8 eV calculations are based on Kohn-Sham density functional theory (DFT), and above 8 eV a new orbital-free DFT formulation, presented here, based on matching Kohn-Sham DFT calculations is employed. Recent experimental shock data are found to be in very good agreement with the current results. Finally both experimental and simulation data are used in constructing a new liquid regime equation of state table for SiO2.

THE COLD EQUATION OF STATE OF TANTALUM

In high‐pressure isentropic compression experiments (ICE), the pressure is dominated by the cold curve. In order to obtain an accurate semi‐empirical cold curve for Ta, we calculate the thermal pressure from ab initio phonon and electronic excitation spectra. The cold curve is then inferred from ultrasonic and shock data. Our empirical cold pressure is compared to density functional calculations and found to be closer to the generalized gradient approximation at low pressure and to approach the local density approximation at high pressure.

Germanium multiphase equation of state

A new SESAME multiphase germanium equation of state (EOS) has been developed utilizing the best available experimental data and density functional theory (DFT) calculations. The equilibrium EOS includes the Ge I (diamond), the Ge II (β-Sn) and the liquid phases. The foundation of the EOS is based on density functional theory calculations which are used to determine the cold curve and the Debye temperature. Results are compared to Hugoniot data through the solid-solid and solid-liquid transitions. We propose some experiments to better understand the dynamics of this element.

A Gallium multiphase equation of state

A new SESAME multiphase Gallium equation of state (EOS) has been developed. It includes three of the solid phases (Ga I, Ga II, Ga III) and a fluid phase (liquid/gas). The EOS includes consistent latent heat between the phases. We compare the results to the liquid Hugoniot data. We also explore the possibility of re‐freezing via dynamic means such as isentropic and shock compression. We predict an unusual spontaneous spreading of low pressure shocks from STP.

AM363 martensitic stainless steel: A multiphase equation of state

A multiphase equation of state for stainless steel AM363 has been developed within the Opensesame approach and has been entered as material 4295 in the LANL-SESAME Library. Three phases were constructed separately: the low pressure martensitic phase, the austenitic phase and the liquid. Room temperature data and the explicit introduction of a magnetic contribution to the free energy determined the martensitic phase, while shock Hugoniot data was used to determine the austenitic phase and the phase boundaries. More experimental data or First Principles calculations would be useful to better characterize the liquid.