Yukawa-Friedel-tail pair potentials for warm dense matter applications.

Accurate equations of state (EOS) and plasma transport properties are essential for numerical simulations of warm dense matter encountered in many high-energy-density situations. Molecular dynamics (MD) is a simulation method that generates EOS and transport data using an externally provided potential to dynamically evolve the particles without further reference to the electrons. To minimize computational cost, pair potentials needed in MD may be obtained from the neutral-pseudoatom (NPA) approach, a form of single-ion density functional theory (DFT), where many-ion effects are included via ion-ion correlation functionals. Standard N-ion DFT-MD provides pair potentials via the force matching technique but at much greater computational cost. Here we propose a simple analytic model for pair potentials with physically meaningful parameters based on a Yukawa form with a thermally damped Friedel tail (YFT) applicable to systems containing free electrons. The YFT model accurately fits NPA pair potentials or the nonparametric force-matched potentials from N-ion DFT-MD, showing excellent agreement for a wide range of conditions. The YFT form provides accurate extrapolations of the NPA or force-matched potentials for small and large particle separations within a physical model. Our method can be adopted to treat plasma mixtures, allowing for large-scale simulations of multispecies warm dense matter.

Ionization of carbon at 10-100 times the diamond density and in the 10

The behavior of partially ionized hot compressed matter is critical to the study of planetary interiors as well as nuclear fusion studies. A recent quantum study of carbon in the 10-70 Gbar range and at a temperature of 100 eV used N-atom density functional theory (DFT) with N∼32-64 and molecular dynamics (MD). This involves band-structure-type electronic calculations and averaging over many MD-generated ion configurations. The calculated average number of free electrons per ion, viz., Z[over ¯], was systematically higher than from a standard average-atom quantum calculation. To clarify this offset, we examine the effect of the self-interaction error in such estimates and the possibility of carbon being in a granular plasma state containing Coulomb crystals with a magic number. The electrical conductivity, pressure, and compressibility of the carbon system are examined. The very low conductivity and the high-Z[over ¯] results of DFT MD point to the existence of carbon in a complex, nonuniform, low-conducting dispersed phase, possibly containing magic-number Coulomb crystals. The neutral pseudoatom estimate of Z[over ¯], conductivity, compressibility, and pressure reported here pertain to the uniform liquid.

Liquid-Liquid Phase Transitions in Silicon.

We use computationally simple neutral pseudoatom ("average atom") density functional theory (DFT) and standard DFT to elucidate liquid-liquid phase transitions (LPTs) in liquid silicon. An ionization-driven transition and three LPTs including the known LPT near 2.5 g/cm^{3} are found. They are robust even to 1 eV. The pair distributions functions, pair potentials, electrical conductivities, and compressibilites are reported. The LPTs are elucidated within a Fermi liquid picture of electron scattering at the Fermi energy that complements the transient covalent bonding picture.

Fertilizer usage and cadmium in soils, crops and food.

Phosphate fertilizers were first implicated by Schroeder and Balassa (Science 140(3568):819-820, 1963) for increasing the Cd concentration in cultivated soils and crops. This suggestion has become a part of the accepted paradigm on soil toxicity. Consequently, stringent fertilizer control programs to monitor Cd have been launched. Attempts to link Cd toxicity and fertilizers to chronic diseases, sometimes with good evidence, but mostly on less certain data are frequent. A re-assessment of this "accepted" paradigm is timely, given the larger body of data available today. The data show that both the input and output of Cd per hectare from fertilizers are negligibly small compared to the total amount of Cd/hectare usually present in the soil itself. Calculations based on current agricultural practices are used to show that it will take centuries to double the ambient soil Cd level, even after neglecting leaching and other removal effects. The concern of long-term agriculture should be the depletion of available phosphate fertilizers, rather than the negligible contamination of the soil by trace metals from fertilizer inputs. This conclusion is confirmed by showing that the claimed correlations between fertilizer input and Cd accumulation in crops are not robust. Alternative scenarios that explain the data are presented. Thus, soil acidulation on fertilizer loading and the effect of Mg, Zn and F ions contained in fertilizers are considered using recent [Formula: see text], [Formula: see text] and [Formula: see text] ion-association theories. The protective role of ions like Zn, Se, Fe is emphasized, and the question of Cd toxicity in the presence of other ions is considered. These help to clarify difficulties in the standard point of view. This analysis does not modify the accepted views on Cd contamination by airborne delivery, smoking, and industrial activity, or algal blooms caused by phosphates.

Ion-ion dynamic structure factor, acoustic modes, and equation of state of two-temperature warm dense aluminum.

The ion-ion dynamical structure factor and the equation of state of warm dense aluminum in a two-temperature quasiequilibrium state, with the electron temperature higher than the ion temperature, are investigated using molecular-dynamics simulations based on ion-ion pair potentials constructed from a neutral pseudoatom model. Such pair potentials based on density functional theory are parameter-free and depend directly on the electron temperature and indirectly on the ion temperature, enabling efficient computation of two-temperature properties. Comparison with ab initio simulations and with other average-atom calculations for equilibrium aluminum shows good agreement, justifying a study of quasiequilibrium situations. Analyzing the van Hove function, we find that ion-ion correlations vanish in a time significantly smaller than the electron-ion relaxation time so that dynamical properties have a physical meaning for the quasiequilibrium state. A significant increase in the speed of sound is predicted from the modification of the dispersion relation of the ion acoustic mode as the electron temperature is increased. The two-temperature equation of state including the free energy, internal energy, and pressure is also presented.

Chronic kidney disease of unknown etiology and the effect of multiple-ion interactions.

High incidence of chronic kidney disease of unknown etiology (CKDU) prevalent in many countries (e.g., Sri Lanka, equatorial America) is reviewed in the context of recent experimental work and using our understanding of the hydration of ions and proteins. Qualitative considerations based on Hofmeister-type action of these ions, as well as quantitative electrochemical models for the Gibbs free energy change for ionpair formation, are used to explain why (1) fluoride and water hardness due to magnesium ions (but not due to calcium ions) and similarly (2) cadmium ions in the presence of suitable pairing ions can be expected to be more nephrotoxic, while arsenite in the presence of fluoride and hardness may be expected to be less nephrotoxic. No synergy of arsenic with calcium hardness is found. The analysis is applied to a variety of ionic species that may be found in typical water sources to predict their likely combined electrochemical action. These results clarify the origins of chronic kidney disease that has reached epidemic proportions in the North Central Province of Sri Lanka as being most likely due to the joint presence of fluoride and magnesium ions in drinking water. The conclusion is further strengthened by a study of the dietary load of Cd and other toxins in the affected regions and in the healthy regions where the dietary toxin loads and lifestyles are similar, and found to be safe especially when the mitigating effects of micronutrient ionic forms of Zn, Se, as well as corrections for bioavailability are taken into account. The resulting etiological picture is consistent with the views of most workers in the field who have suspected that fluoride and other ions found in the hard water stagnant in shallow household wells were the major causative factors of the disease. Similar incidence of CKDu found in other hot tropical climates is likely to have similar origins.

Equation of state, phonons, and lattice stability of ultrafast warm dense matter.

Using the two-temperature model for ultrafast matter (UFM), we compare the equation of state, pair-distribution functions g(r), and phonons using the neutral pseudoatom (NPA) model with results from density functional theory (DFT) codes and molecular dynamics (MD) simulations for Al, Li, and Na. The NPA approach uses state-dependent first-principles pseudopotentials from an "all-electron" DFT calculation with finite-T exchange-correlation functional (XCF). It provides pair potentials, structure factors, the "bound" and "free" states, as well as a mean ionization Z[over ¯] unambiguously. These are not easily accessible via DFT+MD calculations which become prohibitive for T/T_{F} exceeding ∼0.6, where T_{F} is the Fermi temperature. Hence, both DFT+MD and NPA methods can be compared up to ∼8eV, while higher T can be addressed via the NPA. The high-T_{e} phonon calculations raise the question of UFM lattice stability and surface ablation in thin UFM samples. The ablation forces in a UFM slab are used to define an "ablation time" competing with phonon formation times in thin UFM samples. Excellent agreement for all properties is found between NPA and standard DFT codes, even for Li where a strongly nonlocal pseudopotential is used in DFT codes. The need to use pseudopotentials appropriate to the ionization state Z[over ¯] is emphasized. The effect of finite-T XCF is illustrated via its effect on the pressure and the electron-density distribution at a nucleus.

Isochoric, isobaric, and ultrafast conductivities of aluminum, lithium, and carbon in the warm dense matter regime.

We study the conductivities σ of (i) the equilibrium isochoric state σ_{is}, (ii) the equilibrium isobaric state σ_{ib}, and also the (iii) nonequilibrium ultrafast matter state σ_{uf} with the ion temperature T_{i} less than the electron temperature T_{e}. Aluminum, lithium, and carbon are considered, being increasingly complex warm dense matter systems, with carbon having transient covalent bonds. First-principles calculations, i.e., neutral-pseudoatom (NPA) calculations and density-functional theory (DFT) with molecular-dynamics (MD) simulations, are compared where possible with experimental data to characterize σ_{ic}, σ_{ib}, and σ_{uf}. The NPA σ_{ib} is closest to the available experimental data when compared to results from DFT with MD simulations, where simulations of about 64-125 atoms are typically used. The published conductivities for Li are reviewed and the value at a temperature of 4.5 eV is examined using supporting x-ray Thomson-scattering calculations. A physical picture of the variations of σ with temperature and density applicable to these materials is given. The insensitivity of σ to T_{e} below 10 eV for carbon, compared to Al and Li, is clarified.

Pair potentials for warm dense matter and their application to x-ray Thomson scattering in aluminum and beryllium.

Ultrafast laser experiments yield increasingly reliable data on warm dense matter, but their interpretation requires theoretical models. We employ an efficient density functional neutral-pseudoatom hypernetted-chain (NPA-HNC) model with accuracy comparable to ab initio simulations and which provides first-principles pseudopotentials and pair potentials for warm-dense matter. It avoids the use of (i) ad hoc core-repulsion models and (ii) "Yukawa screening" and (iii) need not assume ion-electron thermal equilibrium. Computations of the x-ray Thomson scattering (XRTS) spectra of aluminum and beryllium are compared with recent experiments and with density-functional-theory molecular-dynamics (DFT-MD) simulations. The NPA-HNC structure factors, compressibilities, phonons, and conductivities agree closely with DFT-MD results, while Yukawa screening gives misleading results. The analysis of the XRTS data for two of the experiments, using two-temperature quasi-equilibrium models, is supported by calculations of their temperature relaxation times.

Dynamic conductivity and plasmon profile of aluminum in the ultra-fast-matter regime.

We use an explicitly isochoric two-temperature theory to analyze recent x-ray laser scattering data for aluminum in the ultra-fast-matter (UFM) regime up to 6 eV. The observed surprisingly low conductivities are explained by including strong electron-ion scattering effects using the phase shifts calculated via the neutral-pseudo-atom model. The difference between the static conductivity for UFM-Al and equilibrium aluminum in the warm-dense matter state is clearly brought out by comparisons with available density-fucntional+molecular-dynamics simulations. Thus the applicability of the Mermin model to UFM is questioned. The static and dynamic conductivity, collision frequency, and the plasmon line shape, evaluated within the simplest Born approximation for UFM aluminum, are in good agreement with experiment.

Chronic kidney disease of unknown aetiology and ground-water ionicity: study based on Sri Lanka.

High incidence of chronic kidney disease of unknown aetiology (CKDU) in Sri Lanka is shown to correlate with the presence of irrigation works and rivers that bring-in 'nonpoint source' fertilizer runoff from intensely agricultural regions. We review previous attempts to link CKDU with As, Cd and other standard toxins. Those studies (e.g. the WHO-sponsored study), while providing a wealth of data, are inconclusive in regard to aetiology. Here, we present new proposals based on increased ionicity of drinking water due to fertilizer runoff into the river system, redox processes in the soil and features of 'tank'-cascades and aquifers. The consequent chronic exposure to high ionicity in drinking water is proposed to debilitate the kidney via a Hofmeister-type (i.e. protein-denaturing) mechanism.

Partial ionization in dense plasmas: comparisons among average-atom density functional models.

Nuclei interacting with electrons in dense plasmas acquire electronic bound states, modify continuum states, generate resonances and hopping electron states, and generate short-range ionic order. The mean ionization state (MIS), i.e, the mean charge Z of an average ion in such plasmas, is a valuable concept: Pseudopotentials, pair-distribution functions, equations of state, transport properties, energy-relaxation rates, opacity, radiative processes, etc., can all be formulated using the MIS of the plasma more concisely than with an all-electron description. However, the MIS does not have a unique definition and is used and defined differently in different statistical models of plasmas. Here, using the MIS formulations of several average-atom models based on density functional theory, we compare numerical results for Be, Al, and Cu plasmas for conditions inclusive of incomplete atomic ionization and partial electron degeneracy. By contrasting modern orbital-based models with orbital-free Thomas-Fermi models, we quantify the effects of shell structure, continuum resonances, the role of exchange and correlation, and the effects of different choices of the fundamental cell and boundary conditions. Finally, the role of the MIS in plasma applications is illustrated in the context of x-ray Thomson scattering in warm dense matter.

Electron-ion and ion-ion potentials for modeling warm dense matter: Applications to laser-heated or shock-compressed Al and Si.

The pair interactions Uij(r) determine the thermodynamics and linear transport properties of matter via the pair-distribution functions (PDFs), i.e., gij(r). Great simplicity is achieved if Uij(r) could be directly used to predict material properties via classical simulations, avoiding many-body wave functions. Warm dense matter (WDM) is encountered in quasiequilibria where the electron temperature Te differs from the ion temperature Ti, as in laser-heated or in shock-compressed matter. The electron PDFs gee(r) as perturbed by the ions are used to evaluate fully nonlocal exchange-correlation corrections to the free energy, using hydrogen as an example. Electron-ion potentials for ions with a bound core are discussed with Al and Si as examples, for WDM with Te≠Ti, and valid for times shorter than the electron-ion relaxation time. In some cases the potentials develop attractive regions and then become repulsive and "Yukawa-like" for higher Te. These results clarify the origin of initial phonon hardening and rapid release. Pair potentials for shock-heated WDM show that phonon hardening would not occur in most such systems. Defining meaningful quasiequilibrium static transport coefficients consistent with the dynamic values is addressed. There seems to be no meaningful "static conductivity" obtainable by extrapolating experimental or theoretical σ(ω,Ti,Te) to ω→0, unless Ti→Te as well. Illustrative calculations of quasistatic resistivities R(Ti,Te) of laser-heated as well as shock-heated aluminum and silicon are presented using our pseudopotentials, pair potentials, and classical integral equations. The quasistatic resistivities display clear differences in their temperature evolutions, but are not the strict ω→0 limits of the dynamic values.

Quantum corrections and bound-state effects in the energy relaxation of hot dense hydrogen.

Simple analytic formulas for energy relaxation (ER) in electron-ion systems, with quantum corrections, ion dynamics, and RPA-type screening are presented. ER in the presence of bound electrons is examined in view of recent simulations for ER in hydrogen in the range 10{20}-10{24} electrons/cc.

Temperature relaxation in hot dense hydrogen.

Temperature equilibration of hydrogen is studied for conditions relevant to inertial confinement fusion. New molecular-dynamics simulations and results from quantum many-body theory are compared with Landau-Spitzer predictions for temperatures T with 50

Pair-distribution functions of two-temperature two-mass systems: comparison of molecular dynamics, classical-map hypernetted chain, quantum Monte Carlo, and Kohn-Sham calculations for dense hydrogen.

Two-temperature, two-mass quasiequilibrium plasmas may occur in electron-ion plasmas, nuclear-matter, as well as in electron-hole condensed-matter systems. Dense two-temperature hydrogen plasmas straddle the difficult partially degenerate regime of electron densities and temperatures which are important in astrophysics, in inertial-confinement fusion research, and other areas of warm dense-matter physics. Results from quantum Monte Carlo (QMC) are used to benchmark the procedures used in classical molecular-dynamics simulations and hypernetted chain (HNC) and classical-map HNC (CHNC) methods to derive electron-electron and electron-proton pair-distribution functions. Where QMC is not available, we used Kohn-Sham results as the reference calculation. Then, nonequilibrium molecular dynamics for two-temperature, two-mass plasmas are used to obtain pair distribution functions without specifying the interspecies cross temperature. Using these results, the correct HNC and CHNC procedures for the evaluation of pair-distribution functions in two-temperature two-mass two-component charged fluids are established and results for a mass ratio of 1:5, typical of electron-hole fluids, are presented.

The interaction of nitrogen molecules with (4, 0) single-walled carbon nanotube: electronic and structural effects.

The electronic structure and energetics of (4, 0) single-walled carbon nanotubes (CNTs) interacting with nitrogen have been studied using density-functional calculations. We show that the nanotubes become covered with a stable sheath of N(2) molecules. We have constructed potential energy curves which can be used for the thermodynamic analysis of N(2) adsorption and desorption processes. Our results show that any analysis of the observed properties (for example thermodynamics, stability, and photoluminescence) of air-exposed CNTs needs to consider the N(2) adsorbed on the CNTs.

Static and dynamic conductivity of warm dense matter within a density-functional approach: application to aluminum and gold.

The conductivity sigma(omega) of dense Al and Au plasmas is considered where all the needed inputs are obtained from density-functional theory (DFT). These calculations involve a self-consistent determination of (i) the equation of state and the ionization balance, (ii) evaluation of the ion-ion and ion-electron pair-distribution functions, (iii) determination of the scattering amplitudes, and finally the conductivity. We present results for Al and Au for compressions 0.1-2.0, and in the temperature range T=0.1-10 eV. Excellent agreement with recent first-principles calculations using multi-ion density-functional molecular dynamics is obtained where the data fields overlap. We review first-principles approaches to the optical conductivity, including many-body perturbation theory, molecular-dynamics evaluations, and simplified time-dependent DFT. The modification to the Drude conductivity in the presence of shallow bound states in typical Al plasmas is examined and numerical results are given at the level of the Fermi Golden Rule and an approximate time-dependent DFT.

Spin-polarized stable phases of the 2D electron fluid at finite temperatures.

The Helmholtz free energy F of the 2D electron fluid is calculated using a mapping to a classical Coulomb fluid [Phys. Rev. Lett. 87, 206404 (2001)]]. For density parameters r(s) such that approximately 25>r(s), the fluid is unpolarized at all temperatures t=T/E(F), where E(F) is the Fermi energy. For higher r(s), the system is fully spin polarized for t smaller than approximately 0.35, and partially polarized for approximately 0.35