Solutions of the reference-hypernetted-chain equation with minimized free energy

Lado, F.; Foiles, Stephen M.; Ashcroft, N. W.

doi:10.1103/physreva.28.2374

Cited by 322 publications

(157 citation statements)

References 22 publications

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“…Here c(r) is the direct correlation function. Thermodynamic consistency (e.g., the virial pressure being equal to the thermodynamic pressure) is obtained by using the Lado-Foiles-Ashcroft (LFA) criterion (based on the Gibbs-Bogoliubov bound for the free energy) for determining B(r) using the hard-sphere model bridge function [56]. That is, the hard-sphere packing fraction η is selected according to an energy minimization that satisfies the LFA criterion.…”

Section: Calculation Of the Ion-ion Structure Factormentioning

confidence: 99%

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

et al. 2017

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We study the conductivities σ of (i) the equilibrium isochoric state (σis), (ii) the equilibrium isobaric state (σ ib ), and also the (iii) non-equilibrium ultrafast matter (UFM) state (σ uf ) with the ion temperature Ti less than the the electron temperature Te. Aluminum, lithium and carbon are considered, being increasingly complex warm dense matter (WDM) 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 σic, σ ib and σ uf . The NPA σ ib are closest to the available experimental data when compared to results from DFT+MD, 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 Te below 10 eV for carbon, compared to Al and Li, is clarified.

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Section: Calculation Of the Ion-ion Structure Factormentioning

confidence: 99%

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

et al. 2017

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“…We use the Reference Hyper-netted chain equation of Lado and Ashcroft. 51,52 Although this set of equations can only be solved numerically and convergence is not a trivial matter, an efficient algorithm due to Labik and Malijevsky 53 makes the calculations affordable with a modest amount of CPU time. Once g(r) is known, the pressure of the fluid may be calculated using the standard relation 54 :…”

Section: Application To a Polymer Modelmentioning

confidence: 99%

Equation of state and critical behavior of polymer models: A quantitative comparison between Wertheim’s thermodynamic perturbation theory and computer simulations

MacDowell

Mueller

Vega

et al. 2000

The Journal of Chemical Physics

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“…Thus the thermodynamic properties at the phase transition appear to be governed by the behavior of the bridge function in the high-density regions of the solid lattice and rather insensitive to its behavior elsewhere. This observation also has an analogy in liquid-state theory, where the behavior of the bridge function at particle-particle separations close to the location of the first peak in the radial distribution function has the greatest impact on the thermodynamic properties [15], and the behavior inside the core is largely irrelevant [21].…”

Section: A a Fcc Lattice Structurementioning

confidence: 88%

“…Remarkably, an analogous universality also appears to hold for B(r) at solid-fluid equilibrium for an fcc lattice, at least for the three repulsive potentials studied here. Rosenfeld [15,16] and Lado [21] were able to exploit the universality of b(r) in a quantitative way by using known bridge functions for hard spheres at different packing fractions b HS (r; η) as reference data. For any interaction potential, one could employ b(r) ≈ b HS (r; η * ) with the effective packing fraction η * chosen to satisfy thermodynamic consistency or minimize the free energy, under the conditions of interest.…”

Section: A a Fcc Lattice Structurementioning

confidence: 99%

Universal features of the free-energy functional at the freezing transition for repulsive potentials

Verma

Ford²

2011

Phys. Rev. E

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The free energy difference between coexisting solid and liquid phases is studied in the context of classical density functional theory (DFT). A bridge function is used to represent the higher-order (n > 2) terms in the perturbative expansion of the excess Helmholtz free energy, and the values of this bridge function within the solid lattice are determined by inversion using literature Monte Carlo simulation results. Four potential models, specifically hard-sphere and inverse 12th-, 6th-, and 4th-power repulsive, are studied. The face-centered cubic (fcc) solid is considered for the hard-sphere and inverse 12th-and 6th-power potentials, while the body-centered cubic (bcc) solid is considered for the inverse 6th-and 4th-power potentials. For a given solid structure there is a remarkable similarity among the bridge functions for different potentials that is analogous to the universality in the sum of elementary diagrams, or bridge functions, of liquid-state theory as originally observed by Rosenfeld and Ashcroft [Physical Review A 20, 1208-1235]. In further analogy with liquid-state theory, the bridge functions in the present problem are plotted as functionals of the second-order convolution term in the perturbative expansion. In each case, the plot indicates a unique functionality in the dense regions of the solid near the lattice sites but a scattered and nonunique behavior in the void regions. Interestingly, knowledge of the functional relationship in the unique region near the lattice sites seems to be sufficient to quantitatively model the solid-fluid phase transition. These qualitative observations are true for both fcc and bcc solid phases, although there are some quantitative differences between them. The findings suggest that pursuit of a closure-based DFT of solid-fluid transitions may be profitable.

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Solutions of the reference-hypernetted-chain equation with minimized free energy

Cited by 322 publications

References 22 publications

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

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

Equation of state and critical behavior of polymer models: A quantitative comparison between Wertheim’s thermodynamic perturbation theory and computer simulations

Universal features of the free-energy functional at the freezing transition for repulsive potentials

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