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The equation of state (EOS) of materials at warm dense conditions poses significant challenges to both theory and experiment. We report a combined computational, modeling, and experimental investigation leveraging new theoretical and experimental capabilities to investigate warm-dense boron nitride (BN). The simulation methodologies include path integral Monte Carlo (PIMC), several density functional theory (DFT) molecular dynamics methods [plane-wave pseudopotential, Fermi operator expansion (FOE), and spectral quadrature (SQ)], activity expansion (actex), and all-electron Green's function Korringa-Kohn-Rostoker (mecca), and compute the pressure and internal energy of BN over a broad range of densities and temperatures. Our experiments were conducted at the Omega laser facility and the Hugoniot response of BN to unprecedented pressures (1200--2650 GPa). The EOSs computed using different methods cross validate one another in the warm-dense matter regime, and the experimental Hugoniot data are in good agreement with our theoretical predictions. By comparing the EOS results from different methods, we assess that the largest discrepancies between theoretical predictions are $\ensuremath{\lesssim}4%$ in pressure and $\ensuremath{\lesssim}3%$ in energy and occur at ${10}^{6}\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, slightly below the peak compression that corresponds to the $K$-shell ionization regime. At these conditions, we find remarkable consistency between the EOS from DFT calculations performed on different platforms and using different exchange-correlation functionals and those from PIMC using free-particle nodes. This provides strong evidence for the accuracy of both PIMC and DFT in the high-pressure, high-temperature regime. Moreover, the recently developed SQ and FOE methods produce EOS data that have significantly smaller statistical error bars than PIMC, and so represent significant advances for efficient computation at high temperatures. The shock Hugoniot predicted by PIMC, actex, and mecca shows a maximum compression ratio of $4.55\ifmmode\pm\else\textpm\fi{}0.05$ for an initial density of $2.26\phantom{\rule{0.28em}{0ex}}\mathrm{g}/{\mathrm{cm}}^{3}$, higher than the Thomas-Fermi predictions by about 5%. In addition, we construct tabular EOS models that are consistent with the first-principles simulations and the experimental data. Our findings clarify the ionic and electronic structure of BN over a broad range of temperatures and densities and quantify their roles in the EOS and properties of this material. The tabular models may be utilized for future simulations of laser-driven experiments that include BN as a candidate ablator material.

Alloys expand or contract as concentrations change, and the resulting relationship between atomic volume and alloy content is an important property of the solid. While a well-known approximation posits that the atomic volume varies linearly with concentration (Zen’s law), the actual variation is more complicated. Here we use the apparent size of the solute (solvent) atom and the elasticity to derive explicit analytical expressions for the atomic volume of binary solid alloys. Two approximations, continuum and terminal, are proposed. Deviations from Zen’s law are studied for 22 binary alloy systems.

We examine the performance of pure boron, boron carbide, high density carbon, and boron nitride ablators in the polar direct drive exploding pusher (PDXP) platform. The platform uses the polar direct drive configuration at the National Ignition Facility to drive high ion temperatures in a room temperature capsule and has potential applications for plasma physics studies and as a neutron source. The higher tensile strength of these materials compared to plastic enables a thinner ablator to support higher gas pressures, which could help optimize its performance for plasma physics experiments, while ablators containing boron enable the possibility of collecting additional data to constrain models of the platform. Applying recently developed and experimentally validated equation of state models for the boron materials, we examine the performance of these materials as ablators in 2D simulations, with particular focus on changes to the ablator and gas areal density, as well as the predicted symmetry of the inherently 2D implosion.

We report a theoretical equation of state (EOS) table for boron across a wide range of temperatures (5.1$\times$10$^4$-5.2$\times$10$^8$ K) and densities (0.25-49 g/cm$^3$), and experimental shock Hugoniot data at unprecedented high pressures (5608$\pm$118 GPa). The calculations are performed with full, first-principles methods combining path integral Monte Carlo (PIMC) at high temperatures and density functional theory molecular dynamics (DFT-MD) methods at lower temperatures. PIMC and DFT-MD cross-validate each other by providing coherent EOS (difference $, Comment: 12 pages, 9 figures, 2 tables

Using laser-generated shock waves, we have measured pressure, density, and temperature of LiH on the principal Hugoniot between 260 and 1100 GPa (2.6--11 Mbar) and on a second-shock Hugoniot up to 1400 GPa to near fivefold compression, extending the maximum pressure reached in non-nuclear experiments by a factor of two. We observe the onset of metal-like reflectivity consistent with temperature-induced ionization of the Li 2s electron, and no sign of additional changes in ionization up to the maximum pressure. Our measurements are in good agreement with gas gun, Z-machine, and underground test data and are accurately described by quantum molecular dynamics simulations. The results confirm the validity of equation of state models built on an average-atom description of the electron-thermal contribution to the free energy and a density-dependent Gr\"uneisen parameter to describe shock response of LiH over this pressure range.

An accurate determination of the immiscibility of helium in hydrogen has a direct impact on the understanding of the interior structure and of the evolution of Jovian planets. We extend our previous work on hydrogen-helium mixtures [Morales, Schwegler, Ceperley, Pierleoni, Hamel, and Caspersen, Proc. Natl. Acad. Sci. (USA) 106, 1324 (2009)] to lower pressures and lower temperatures, across the molecular dissociation regime in hydrogen to the low-pressure molecular liquid. Using density-functional-theory-based molecular dynamics together with thermodynamic integration techniques, we calculate the Gibbs free energy of the dense liquid as a function of pressure, temperature, and composition. We address the importance of the nonideal entropy of mixing in the solubility of helium in hydrogen and find that it is critically important in the molecular regime. The resulting demixing temperatures smoothly connect measurements done in diamond anvil cells to the high-temperature and -pressure conditions found in giant planet interiors.

We use molecular dynamics (MD) to simulate diffusion in molten aluminum-copper (AlCu) alloys. The self-diffusivities and Maxwell-Stefan diffusivities are calculated for AlCu mixtures using the Green-Kubo formulas at temperatures from 1000 to 4000 K and pressures from 0 to 25 GPa, along with additional points at higher temperatures and pressures. The diffusivities are corrected for finite-size effects. The Maxwell-Stefan diffusivity is compared to the diffusivity calculated from the self-diffusivities using a generalization of the Darken equation. We find that the effects of cross-correlation are small. Using the calculated self-diffusivities, we have assessed whether dilute hard-sphere and dilute Lennard-Jones models apply to the molten mixture. Neither of the two dilute gas diffusivities describes the diffusivity in molten Al and Cu. We report generalized analytic models for the self-diffusivities and interdiffusivity (mutual diffusivity) that fit the MD results well. The MD-derived transport coefficients are in good agreement with the available experimental data. We also report MD calculations of the viscosity and an analytic fit to those results. The ionic thermal conductivity is discussed briefly.

The properties of hydrogen-helium mixtures at Mbar pressures and intermediate temperatures (4000 to 10000 K) are calculated with first-principles molecular dynamics simulations. We determine the equation of state as a function of density, temperature, and composition and, using thermodynamic integration, we estimate the Gibbs free energy of mixing, thereby determining the temperature, at a given pressure, when helium becomes insoluble in dense metallic hydrogen. These results are directly relevant to models of the interior structure and evolution of Jovian planets. We find that the temperatures for the demixing of helium and hydrogen are sufficiently high to cross the planetary adiabat of Saturn at pressures around 5 Mbar; helium is partially miscible throughout a significant portion of the interior of Saturn, and to a lesser extent in Jupiter., 6 pages, 7 figures. Published in "Proceedings of the National Academy of Sciences USA"

We report the computational advances that have enabled the first micron-scale simulation of a Kelvin-Helmholtz (KH) instability using molecular dynamics (MD). The advances are in three key areas for massively parallel computation such as on BlueGene/L (BG/L): fault tolerance, application kernel optimization, and highly efficient parallel I/O. In particular, we have developed novel capabilities for handling hardware parity errors and improving the speed of interatomic force calculations, while achieving near optimal I/O speeds on BG/L, allowing us to achieve excellent scalability and improve overall application performance. As a result we have successfully conducted a 2-billion atom KH simulation amounting to 2.8 CPU-millennia of run time, including a single, continuous simulation run in excess of 1.5 CPU-millennia. We have also conducted 9-billion and 62.5-billion atom KH simulations. The current optimized ddcMD code is benchmarked at 115.1 TFlop/s in our scaling study and 103.9 TFlop/s in a sustained science run, with additional improvements ongoing. These improvements enabled us to run the first MD simulations of micron-scale systems developing the KH instability.

For planets other than Earth, interpretation of the composition and structure depends largely on comparing the mass and radius with the composition expected given their distance from the parent star. The composition implies a mass-radius relation which relies heavily on equations of state calculated from electronic structure theory and measured experimentally on Earth. We lay out a method for deriving and testing equations of state, and deduce mass-radius and mass-pressure relations for key materials whose equation of state is reasonably well established, and for differentiated Fe/rock. We find that variations in the equation of state, such as may arise when extrapolating from low pressure data, can have significant effects on predicted mass- radius relations, and on planetary pressure profiles. The relations are compared with the observed masses and radii of planets and exoplanets. Kepler-10b is apparently 'Earth- like,' likely with a proportionately larger core than Earth's, nominally 2/3 of the mass of the planet. CoRoT-7b is consistent with a rocky mantle over an Fe-based core which is likely to be proportionately smaller than Earth's. GJ 1214b lies between the mass-radius curves for H2O and CH4, suggesting an 'icy' composition with a relatively large core or a relatively large proportion of H2O. CoRoT-2b is less dense than the hydrogen relation, which could be explained by an anomalously high degree of heating or by higher than assumed atmospheric opacity. HAT-P-2b is slightly denser than the mass-radius relation for hydrogen, suggesting the presence of a significant amount of matter of higher atomic number. CoRoT-3b lies close to the hydrogen relation. The pressure at the center of Kepler-10b is 1.5+1.2-1.0 TPa. The central pressure in CoRoT-7b is probably close to 0.8TPa, though may be up to 2TPa., Added more recent exoplanets. Tidied text and references. Added extra "rock" compositions. Responded to referee comments