The Line of the Unit Compressibility Factor (Zeno-Line) for Crystal States.

We study the behavior of the line of the unit compressibility factor (Zeno-line) in crystalline states. We used the Lennard-Jones system, experimental P-V-T data for a number of substances, and the Debye model. We found that, contrary to the case of the liquid states, the Zeno-line in a crystal is not a straight line at the density-temperature plane. However, the corresponding pressure-temperature dependence appears to be quasi-linear. As a result, this line in the solid state can be defined by the only one point where the Zeno-line crosses the melting curve.

Similarity Laws for the Lines of Ideal Free Energy and Chemical Potential in Supercritical Fluids.

We have found the curves on the density-temperature plane, along which the values of free energy and chemical potential correspond to ideal gas quantities. At first, we have applied the van der Waals equation to construct them and to derive their equations. Then we have shown that the same lines for real substances (Ar, N2, CH4, SF6, H2, H2O) and for the model Lennard-Jones system constructed on the basis of the measurements data and calculations are well matched with the derived equations. The validity and deviations from the obtained similarity laws are discussed.

The Zeno Line for Al, Cu, and U.

We show that the property of linearity for a line of unit compressibility factor (Zeno line) can be confirmed for metals (Al, Cu, and U) in liquid phase. The embedded atom potentials (EAM) have been used to describe the interaction between the particles. The numerical simulations within Monte Carlo (MC) technique with the EAM potential have resulted in the straight Zeno-line for considered metals and have allowed us to define the Zeno line parameters. The similarity relations between the critical and the Zeno line parameters, which were observed previously for nonmetallic substances, have appeared to be valid for Al and Cu as well. For uranium there is a contradiction between the calculated and experimental data, indicating the limitation for these similarities.

The Wide-Range Method to Construct the Entire Coexistence Liquid-Gas Curve and to Determine the Critical Parameters of Metals.

A method to find the liquid-gas critical parameters of metallic elements is offered. It takes into account a nonanalytic behavior in the critical point vicinity and the Clapeyron-Clausius asymptotic behavior at low temperatures. The present approach provides good agreement with experimental data for a wide wealth of non-metallic substances and mercury and alkali metals, where the critical parameters and binodals are known from the measurements. We have also found the critical parameters and binodals for Al, Cu, Fe, and Zr, for which corresponding measurements are yet to be obtained.

The Similarity Relations Set on the Basis of Symmetrization of the Liquid-Vapor Phase Diagram.

An approach to symmetrize the liquid-vapor phase coexistence curve is proposed. It is based on the introduction of the lattice-like density x = ρ1/(ρ1 + ρ2), where ρ1 and ρ2 are the densities along the liquid-gas binodal. The global symmetrical phase diagram is created using experimental and simulation data for the real substances and models (noble gases, polyatomic molecules, organic substances and two metals, van der Waals system, Lennard-Jones system). The pressure and the temperature along the binodal are shown to satisfy some new similarity relations.

The similarity law for the Joule-Thomson inversion line.

We show that the expression for the Joule-Thomson inversion temperature following from the van der Waals equation and recorded in a form reduced to the Boyle values has a universal character and can be applied to many real substances and model systems.

Note: The universal relations for the critical point parameters.

The universal correlation between the reduced critical pressure, density, and temperature for different substances and model systems was found on the basis of analysis of experimental and numerical simulation data. We choose the Zeno line (ZL) parameters as the reducing units (ZL is the line along which the compressibility factor is unity). In these variables the critical and ZL parameters satisfy simple relations, which are valid for a great number of substances.

Regarding the universality of some consequences of the van der Waals equation in the supercritical domain.

We show that some of the thermodynamic regularities, following from the van der Waals (VDW) equation, are valid for the real substances and models described by completely different equations of state. These regularities relate to lines of ideal enthalpy, enthalpy minima, and isothermal compressibility maxima. The first one appears to be the straight line on the density-temperature plane, while for the two others there are universal relations, which are the same for various substances and models (argon and Lennard-Jones system as examples). The model systems were studied by Monte Carlo simulations (NVT MC), while experimental data were analyzed for the real substances. Our numerical calculations and the analysis of experimental data have shown that for the considered systems these curves are similar to the VDW ones.

Communication: Shock adiabat of atomic nitrogen at megabar pressures.

We use spherical cellular method combined with a self-consistent density functional approach (quasizone method) to calculate the band structure and bulk properties of atomic nitrogen at megabar pressures and densities 3.2÷3.6 g/cm(3). Thermodynamic functions and shock adiabat calculated by this method correspond to recent measurements, showing a sharp increase in pressure along the shock adiabat in this range of densities.

Application of the new scaling relations and global isomorphism to the study of liquid-vapor saturation pressure.

We apply the new scaling relations and global isomorphism between continuous and discrete systems to find of saturation pressure. On this basis, we obtain the expression for the saturation pressure containing the critical, Z line parameters and two fitting parameters. First we calculate the saturation pressure for a number of model systems and real substances the critical parameters for which are known and verify that the accuracy is acceptable in a wide liquid-gas temperature domain. Then we discuss situation with the saturation pressure for metals (aluminum and iron), the critical parameters for which are unknown in advance and lie in the domain of parameters still inaccessible for experiments.

Connection between the isobaric thermal expansion coefficient with the Zeno-line and critical-point parameters for liquids.

We have found the expression which connects the values of volumetric thermal expansion coefficients under low temperatures and pressures with the critical-point and Zeno-line parameters. The calculations based on this expression for different substances (NH(3), CO(2), hexane, Hg, and Cs) are in good agreement with experimental data at relatively low temperatures.

Cell model of hydrogen liquid at megabar pressures.

We present a new model for the quantum fluid resulting from the melting of crystal hydrogen at megabar pressures. This model is based on a cell approach that takes into account of localized electron states and the effect of proton degeneration. The predictions of our model are in good agreement with recent experimental results on the anomalies in the melting process.

Correspondence between thermodynamics of lattice models and real substances at the liquid-gas domain of the phase diagram.

We modify the projective transformation suggested earlier. (7) Within this modified transformation, the critical point and the Zeno-line of the lattice model are moved to the critical point and Zeno-line of simple liquids. Using analytical lattice calculations and numerical simulations, we show that the lattice binodals and critical isotherms transforms with sufficient accuracy into binodals and critical isotherms of real substances such as Cs, Hg, and NH(3), and other model systems with real system properties such as the van der Waals equation, Lennard-Jones systems.

The confirmation of the critical point-Zeno-line similarity set from the numerical modeling data for different interatomic potentials.

We use numerical simulation data for several model interatomic potentials to confirm the critical point-Zeno-line relations of similarity (CZS) for the liquid branch of the coexistence curve suggested earlier [E. M. Apfelbaum and V. S. Vorob'ev, J. Phys. Chem. B 112, 13064 (2008)]. These relations have been based on the analysis of experimental values for the critical point parameters and liquid-gas coexistence curves for a large number of real substances and two model systems. We show that the numerical modeling data as a whole confirm the CZS in the domain of the existence of liquid state. The deviations from CZS relations take place for two cases: (a) the numerically calculated coexistence curve gets into domain corresponding to solidification; (b) the liquid-vapor transition becomes metastable with respect to freezing.

Correspondence between the critical and the Zeno-line parameters for classical and quantum liquids.

We set new regularities between the effective compressibility factor at the critical point (Z*) and unit compressibility line (Zeno-line) parameters. For classical liquids, Z* is the ordinary compressibility factor Z(c), but for quantum liquids Z* depends on the de Boer parameters. As a result, we show that a wide group of real substances with the classical thermodynamical properties has Z(c) < 0.32. Classical mercury and quantum H(2), He(4), and He(3) have Z(c) or Z* > 0.37. Using the low temperature part of the liquid-gas coexistence curve obtained from experiment, we can find the critical parameters for metals (Al, Cu, W, U, and Zr) for which these parameters are unknown in advance and lie in the domain of parameters still inaccessible for experiment.

A new similarity found from the correspondence of the critical and Zeno-line parameters.

We find a new similarity based on the relation between the critical and unit compressibility line (Zeno-line) parameters. Our study relies on the fact that the Zeno-line must be tangential to the extension of the binodal liquid branch at the zero temperature domain. We show that this similarity faithfully describes both the numerical simulation data and experimental data for a wide class of real materials (17 gases, water, and 5 metals). Finally we make some predictions for metals which have critical parameters in the phase diagram domain still inaccessible for experiment.

Self-consistent electric field inside ordered dust structures.

We report finding a self-consistent electric field of electrons, ions, and dust grains inside an ordered dust cloud in glow discharge, and show that this field differs radically from that of an isolated grain. Besides, the screening radius coincides with the size of Wigner-Seitz cell. The value of potential necessary for containing dust particles in the direction perpendicular to the discharge axis is estimated. We show that the interaction potential energy of a system of ordered dust grains has a form characteristic of ionic crystals. Critical parameters for a liquidlike dust structure are estimated. The correlation function of dust grains obtained via this approach is compared with the measured function.

Regarding the theory of the Zeno line.

The line of thermodynamic states with a unit value of the compressibility factor was calculated for a Lennard-Jones system using four different approaches. We show that all four approaches give rise to a straight line on the density-temperature plane. Thus, we theoretically confirm that the Lennard-Jones system satisfies Zeno line regularity.

Regarding convergence curve of virial expansion for the Lennard-Jones system.

We calculate the convergence curve of the virial expansion for a Lennard-Jones system in the density-temperature plane using the approximate method based on the density expansion of the Ornstein-Zernike equation and the condition of thermodynamic consistency [J. Chem. Phys. 106, 6095 (1997)]. At subcritical temperatures, this curve is close to the binodal. At supercritical temperatures, the curve does not coincide with the freezing curve. In the latter case, the densities along the convergence line are distinctly smaller than the densities corresponding to the condensed state.

Corridor of existence of thermodynamically consistent solution of the Ornstein-Zernike equation.

We obtain the exact equation for a correction to the Ornstein-Zernike (OZ) equation based on the assumption of the uniqueness of thermodynamical functions. We show that this equation is reduced to a differential equation with one arbitrary parameter for the hard sphere model. The compressibility factor within narrow limits of this parameter variation can either coincide with one of the formulas obtained on the basis of analytical solutions of the OZ equation or assume all intermediate values lying in a corridor between these solutions. In particular, we find the value of this parameter when the thermodynamically consistent compressibility factor corresponds to the Carnahan-Stirling formula.