A measurement of the equation of state of carbon envelopes of white dwarfs.

White dwarfs represent the final state of evolution for most stars1-3. Certain classes of white dwarfs pulsate4,5, leading to observable brightness variations, and analysis of these variations with theoretical stellar models probes their internal structure. Modelling of these pulsating stars provides stringent tests of white dwarf models and a detailed picture of the outcome of the late stages of stellar evolution6. However, the high-energy-density states that exist in white dwarfs are extremely difficult to reach and to measure in the laboratory, so theoretical predictions are largely untested at these conditions. Here we report measurements of the relationship between pressure and density along the principal shock Hugoniot (equations describing the state of the sample material before and after the passage of the shock derived from conservation laws) of hydrocarbon to within five per cent. The observed maximum compressibility is consistent with theoretical models that include detailed electronic structure. This is relevant for the equation of state of matter at pressures ranging from 100 million to 450 million atmospheres, where the understanding of white dwarf physics is sensitive to the equation of state and where models differ considerably. The measurements test these equation-of-state relations that are used in the modelling of white dwarfs and inertial confinement fusion experiments7,8, and we predict an increase in compressibility due to ionization of the inner-core orbitals of carbon. We also find that a detailed treatment of the electronic structure and the electron degeneracy pressure is required to capture the measured shape of the pressure-density evolution for hydrocarbon before peak compression. Our results illuminate the equation of state of the white dwarf envelope (the region surrounding the stellar core that contains partially ionized and partially degenerate non-ideal plasmas), which is a weak link in the constitutive physics informing the structure and evolution of white dwarf stars9.

Nonideal mixing effects in warm dense matter studied with first-principles computer simulations.

We study nonideal mixing effects in the regime of warm dense matter (WDM) by computing the shock Hugoniot curves of BN, MgO, and MgSiO3. First, we derive these curves from the equations of state (EOS) of the fully interacting systems, which were obtained using a combination of path integral Monte Carlo calculations at high temperature and density functional molecular dynamics simulations at lower temperatures. We then use the ideal mixing approximation at constant pressure and temperature to rederive these Hugoniot curves from the EOS tables of the individual elements. We find that the linear mixing approximation works remarkably well at temperatures above ∼2 × 105 K, where the shock compression ratio exceeds ∼3.2. The shape of the Hugoniot curve of each compound is well reproduced. Regions of increased shock compression, which emerge because of the ionization of L and K shell electrons, are well represented, and the maximum compression ratio of the Hugoniot curves is reproduced with high precision. Some deviations are seen near the onset of the L shell ionization regime, where ionization equilibrium in the fully interacting system cannot be well reproduced by the ideal mixing approximation. This approximation also breaks down at lower temperatures, where chemical bonds play an increasingly important role. However, the results imply that the equilibrium properties of binary and ternary mixtures in the regime of WDM can be derived from the EOS tables of the individual elements. This significantly simplifies the characterization of binary and ternary mixtures in the WDM and plasma phases, which otherwise requires large numbers of more computationally expensive first-principles computer simulations.

Time-Resolved X-ray Emission Spectroscopy and Resonant Inelastic X-ray Scattering Spectroscopy of Laser Irradiated Carbon.

The existence of liquid carbon as an intermediate phase preceding the formation of novel carbon materials has been a point of contention for several decades. Experimental observation of such a liquid state requires nonthermal melting of solid carbon materials at various laser fluences and pulse properties. Reflectivity experiments performed in the mid-1980s reached opposing conclusions regarding the metallic or insulating properties of the purported liquid state. Time-resolved X-ray absorption studies showed shortening of C-C bonds and increasing diffraction densities, thought to evidence a liquid or glassy carbon state, respectively. Nevertheless, none of these experiments provided information on the electronic structure of the proposed liquid state. Herein, we report the results of time-resolved resonant inelastic X-ray scattering (RIXS) and time-resolved X-ray emission spectroscopy (XES) studies on amorphous carbon (a-C) and ultrananocrystalline diamond (UNCD) as a function of delay time between the irradiating pulse and X-ray probe. For both a-C and UNCD, we attribute decreases in RIXS or XES signals to transition blocking, relaxation, and finally, ablation. Increased signal at 20 ps following the irradiation of the UNCD is attributed to the probable formation of nanoscale structures in the ablation plume. Differences in the amount of signal observed between a-C and UNCD are explained by the difference in sample thickness and, specifically, incomplete melting of the UNCD film. Comparisons to spectral simulations based on MD trajectories at extreme conditions indicate that the carbon state in our experiments is crystalline. Normal mode analysis confirmed that symmetrical bending or stretching of the C-C bonds in the diamond lattice results in XES spectra with small intensity differences. Overall, we observed no evidence of melting to a liquid state, as determined by the lack of changes in the spectral properties for up to 100 ps delays following the melting pulses.

Ligand-mediated modification of the electronic structure of CdSe quantum dots.

X-ray absorption spectroscopy and ab initio modeling of the experimental spectra have been used to investigate the effects of surface passivation on the unoccupied electronic states of CdSe quantum dots (QDs). Significant differences are observed in the unoccupied electronic structure of the CdSe QDs, which are shown to arise from variations in specific ligand-surface bonding interactions.

Theoretical analysis of the anomalous spectral splitting of tetracene in 4He droplets.

We present a theoretical analysis of the electronic absorption spectra of tetracene in (4)He droplets based on many-body quantum simulations. Using the path integral ground state approach, we calculate one- and two-body reduced density matrices of the most strongly localized He atoms near the molecule surface and use these to investigate the helium ground-state quantum coherence and correlations when tetracene is in its electronic ground and excited states. We identify a trio of quasi-one-dimensional, strongly localized atoms adsorbed along the long axis of the molecule that show some quantum coherence among themselves but far less with the remaining solvating helium. We evaluate the single-particle natural orbitals of the localized He atoms by diagonalization of the one-body density matrix and use these to construct single- and many-particle solvating helium basis states with which the zero-phonon spectral features of the tetracene-(4)He(N) absorption spectrum are then calculated. The absorption spectrum resulting from the three-body density matrix for the strongly bound trio of helium atoms is in very good agreement with the experimental data, accounting quantitatively for the anomalous splitting of the zero-phonon line [Hartmann, M.; Lindinger, A.; Toennies, J. P.; Vilesov, A. F. Chem. Phys. 1998, 239, 139; Krasnokutski, S.; Rouillé, G.; Huisken, F. Chem. Phys. Lett. 2005, 406, 386]. Our results indicate that the combination of strong localization and the quasi-one-dimensional nature of trios of helium atoms adsorbed along the long axis of tetracene leads to a quantum coherent, yet highly correlated ground state for the helium density closest to the molecule. The spectroscopic analysis shows that this feature accounts quantitatively for the anomalous splittings and hitherto unexplained fine structure observed in the absorption spectra of tetracene and suggests that it may be responsible for the corresponding zero-phonon splittings in other quasi-one-dimensional planar aromatic molecules.

Simultaneous compression and opacity data from time-series radiography with a Lagrangian marker.

Time-resolved radiography can be used to obtain absolute shock Hugoniot states by simultaneously measuring at least two mechanical parameters of the shock, and this technique is particularly suitable for one-dimensional converging shocks where a single experiment probes a range of pressures as the converging shock strengthens. However, at sufficiently high pressures, the shocked material becomes hot enough that the x-ray opacity falls significantly. If the system includes a Lagrangian marker such that the mass within the marker is known, this additional information can be used to constrain the opacity as well as the Hugoniot state. In the limit that the opacity changes only on shock heating, and not significantly on subsequent isentropic compression, the opacity of the shocked material can be determined uniquely. More generally, it is necessary to assume the form of the variation of opacity with isentropic compression or to introduce multiple marker layers. Alternatively, assuming either the equation of state or the opacity, the presence of a marker layer in such experiments enables the non-assumed property to be deduced more accurately than from the radiographic density reconstruction alone. An example analysis is shown for measurements of a converging shock wave in polystyrene at the National Ignition Facility.

Benchmarking boron carbide equation of state using computation and experiment.

Boron carbide (B_{4}C) is of both fundamental scientific and practical interest due to its structural complexity and how it changes upon compression, as well as its many industrial uses and potential for use in inertial confinement fusion (ICF) and high-energy density physics experiments. We report the results of a comprehensive computational study of the equation of state (EOS) of B_{4}C in the liquid, warm dense matter, and plasma phases. Our calculations are cross-validated by comparisons with Hugoniot measurements up to 61 megabar from planar shock experiments performed at the National Ignition Facility (NIF). Our computational methods include path integral Monte Carlo, activity expansion, as well as all-electron Green's function Korringa-Kohn-Rostoker and molecular dynamics that are both based on density functional theory. We calculate the pressure-internal energy EOS of B_{4}C over a broad range of temperatures (∼6×10^{3}-5×10^{8} K) and densities (0.025-50 g/cm^{3}). We assess that the largest discrepancies between theoretical predictions are ≲5% near the compression maximum at 1-2×10^{6} K. This is the warm-dense state in which the K shell significantly ionizes and has posed grand challenges to theory and experiment. By comparing with different EOS models, we find a Purgatorio model (LEOS 2122) that agrees with our calculations. The maximum discrepancies in pressure between our first-principles predictions and LEOS 2122 are ∼18% and occur at temperatures between 6×10^{3}-2×10^{5} K, which we believe originate from differences in the ion thermal term and the cold curve that are modeled in LEOS 2122 in comparison with our first-principles calculations. To account for potential differences in the ion thermal term, we have developed three new equation-of-state models that are consistent with theoretical calculations and experiment. We apply these new models to 1D hydrodynamic simulations of a polar direct-drive NIF implosion, demonstrating that these new models are now available for future ICF design studies.

Spectral shifts and helium configurations in 4He(N)-tetracene clusters.

Spectral shifts of electronic transitions of tetracene in helium droplets are investigated in a theoretical study of (4)He(N)-tetracene clusters with 1 < or = N < or = 150. Utilizing a pairwise interaction for the S(0) state of tetracene with helium that is extended by semiempirical terms to construct a potential for the S(1) state of tetracene with helium, the spectral shift is calculated from path integral Monte Carlo calculations of the helium equilibrium properties with tetracene in the S(0) and S(1) states at T = 0 and at T = 0.625 K. The calculated spectral shifts are in quantitative agreement with available experimental measurements for small values of N (< or = 8) at T approximately 0.4 K and show qualitative agreement for larger N (10-20). The extrapolated value of the spectral shift in large droplets (N approximately 10(4)) is approximately 90% of the experimentally measured value. We find no evidence of multiple configurations of helium for any cluster size for either the S(0) or S(1) state of tetracene. These results suggest that the observed spectral splitting of electronic transitions of tetracene in large helium droplets is not due to the coexistence of static metastable helium densities, unlike the situation previously analyzed for the phthalocyanine molecule.

Heat-release equation of state and thermal conductivity of warm dense carbon by proton differential heating.

Warm dense carbon is generated at 0.3-2.0 g/cc and 1-7 eV by proton heating. The release equation of state (EOS) after heating and thermal conductivity of warm dense carbon are studied experimentally in this regime using a Au/C dual-layer target to initiate a temperature gradient and two picosecond time-resolved diagnostics to probe the surface expansion and heat flow. Comparison between the data and simulations using various EOSs and thermal conductivity models is quantified with a statistical χ^{2} analysis. Out of seven EOS tables and five thermal conductivity models, only L9061 with the Lee-More model provides a probability above 50% to match all data.

Theoretical and experimental investigation of the equation of state of boron plasmas.

We report a theoretical equation of state (EOS) table for boron across a wide range of temperatures (5.1×10^{4}-5.2×10^{8} K) and densities (0.25-49 g/cm^{3}) and experimental shock Hugoniot data at unprecedented high pressures (5608±118 GPa). The calculations are performed with 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 <1.5 Hartree/boron in energy and <5% in pressure) at 5.1×10^{5} K. The Hugoniot measurement is conducted at the National Ignition Facility using a planar shock platform. The pressure-density relation found in our shock experiment is on top of the shock Hugoniot profile predicted with our first-principles EOS and a semiempirical EOS table (LEOS 50). We investigate the self-diffusivity and the effect of thermal and pressure-driven ionization on the EOS and shock compression behavior in high-pressure and -temperature conditions. We also study the sensitivity of a polar direct-drive exploding pusher platform to pressure variations based on applying pressure multipliers to LEOS 50 and by utilizing a new EOS model based on our ab initio simulations via one-dimensional radiation-hydrodynamic calculations. The results are valuable for future theoretical and experimental studies and engineering design in high-energy density research.

Density-functional calculations of transport properties in the nondegenerate limit and the role of electron-electron scattering.

We compute electrical and thermal conductivities of hydrogen plasmas in the nondegenerate regime using Kohn-Sham density functional theory (DFT) and an application of the Kubo-Greenwood response formula, and demonstrate that for thermal conductivity, the mean-field treatment of the electron-electron (e-e) interaction therein is insufficient to reproduce the weak-coupling limit obtained by plasma kinetic theories. An explicit e-e scattering correction to the DFT is posited by appealing to Matthiessen's Rule and the results of our computations of conductivities with the quantum Lenard-Balescu (QLB) equation. Further motivation of our correction is provided by an argument arising from the Zubarev quantum kinetic theory approach. Significant emphasis is placed on our efforts to produce properly converged results for plasma transport using Kohn-Sham DFT, so that an accurate assessment of the importance and efficacy of our e-e scattering corrections to the thermal conductivity can be made.

Molecular simulations of the pressure, temperature, and chemical potential dependencies of clay swelling.

A new method for the determination of clay swelling thermodynamics from computer simulation is discussed and evaluated. This method allows for the determination of temperature, pressure, and water chemical potential dependence of clay swelling from simulations at a single thermodynamic state point. The temperature dependence and pressure dependence of clay swelling are shown to be directly related to the composite system entropy and volume change, respectively, that accompany swelling. Expressions for the chemical potential dependence of clay swelling are used to determine constant pressure layer spacing and adsorption isotherms, quantities that are well suited for comparison with experimental measurements. This method is evaluated through grand isoshear ensemble simulations of Na-montmorillonite, a prototypical swelling clay. Approximations associated with all expressions are discussed with explicit calculations used to demonstrate their regimes of validity.

Molecular dynamics simulations and generalized Lenard-Balescu calculations of electron-ion temperature equilibration in plasmas.

We study the problem of electron-ion temperature equilibration in plasmas. We consider pure H at various densities and temperatures and Ar-doped H at temperatures high enough so that the Ar is fully ionized. Two theoretical approaches are used: classical molecular dynamics (MD) with statistical two-body potentials and a generalized Lenard-Balescu (GLB) theory capable of treating multicomponent weakly coupled plasmas. The GLB is used in two modes: (1) with the quantum dielectric response in the random-phase approximation (RPA) together with the pure Coulomb interaction and (2) with the classical (ℏ→0) dielectric response (both with and without local-field corrections) together with the statistical potentials. We find that the MD results are described very well by classical GLB including the statistical potentials and without local-field corrections (RPA only); worse agreement is found when static local-field effects are included, in contradiction to the classical pure-Coulomb case with like charges. The results of the various approaches are all in excellent agreement with pure-Coulomb quantum GLB when the temperature is high enough. In addition, we show that classical calculations with statistical potentials derived from the exact quantum two-body density matrix produce results in far better agreement with pure-Coulomb quantum GLB than classical calculations performed with older existing statistical potentials.

Multiple solvation configurations around phthalocyanine in helium droplets.

Recent measurements of the emission spectrum of phthalocyanine solvated in superfluid helium nanodroplets exhibit a constant 10.3 cm(-1) splitting of each emission line relative to the absorption spectrum. This splitting has been attributed to two distinct helium environments near the surface of the phthalocyanine molecule. Rigid-body path-integral Monte Carlo provides a means of investigating the origin of the splitting on a detailed microscopic level. Path-integral Monte Carlo simulations of 4He(N)-phthalocyanine at 0.625 K with N ranging from 24 to 150 show two distinct helium configurations. One configuration is commensurate with the molecular substrate and the other is a triangular lattice. We investigate the energetics of these two configurations and use a method for calculating electronic spectral shifts for aromatic molecule-rare-gas clusters due to dispersive interactions to estimate the spectral splitting that would arise from the two helium configurations seen for N=150. The results are in reasonable agreement with the experimentally measured splitting, supporting the existence of two distinct local helium environments near the surface of the molecule in the nanodroplets.

Free energy, energy, and entropy of swelling in Cs-, Na-, and Sr-montmorillonite clays.

A Monte Carlo method for grand canonical and grand isoshear ensemble simulations has been used to characterize the free energy, energy, and entropy of clay mineral swelling. The Monte Carlo approach was found to be more efficient at simulating water content fluctuations in the highly constrained clay environment than a previously developed molecular dynamics method. Swelling thermodynamics calculated for Cs-, Na-, and Sr-montmorillonite clays indicate a strong dependence of swelling on the interlayer ion identity, in agreement with various experimental measurements. The Sr clay swells most readily, and both the Na and Sr clays prefer expanded states (two-layer hydrate or greater) when in contact with bulk water. In contrast, swelling is inhibited in the Cs clay. Differences in swelling behavior are traced directly to the tendency of the different ions to hydrate. The swelling free energies are decomposed into their energetic and entropic components, revealing an overall energetic driving force for the swelling phenomena. Entropic effects provide a smaller, mediating role in the swelling processes. The results provide a unique molecular perspective on experimentally well-characterized swelling phenomena.