Linear mixing rule in screened binary ionic mixtures

Addendum to "Equation of state of classical Coulomb plasma mixtures"

Recently developed analytic approximation for the equation of state of fully ionized nonideal electron-ion plasma mixtures [A. Y. Potekhin, G. Chabrier, and F. J. Rogers, Phys. Rev. E 79, 016411 (2009)], which covers the transition between the weak and strong Coulomb coupling regimes and reproduces numerical results obtained in the hypernetted-chain (HNC) approximation, is modified in order to fit the small deviations from the linear mixing in the strong-coupling regime, revealed by recent Monte Carlo simulations. In addition, a mixing rule is proposed for the regime of weak coupling, which generalizes post-Debye density corrections to the case of mixtures and numerically agrees with the HNC approximation in that regime.

Orbital-free molecular dynamics simulations of a warm dense mixture: examination of the excess-pressure matching rule

A form of the linear mixing rule involving the equality of excess pressures is tested with various mole fractions and various types of orbital-free molecular dynamics simulations. For all the cases considered, this mixing rule yields, within statistical error, the pressure of a mixture of helium and iron obtained by a direct simulation. In an attempt to interpret the robustness of the mixing rule, we show that it can be derived from thermodynamic stability if the system is regarded as a mixture of independent effective average atoms. The success of the mixing rule applied with equations of state including various degrees of approximation leads us to suggest its use in the thermodynamic domain where quantum molecular dynamics can be implemented.

Equation of state of classical Coulomb plasma mixtures

We develop analytic approximations of thermodynamic functions of fully ionized nonideal electron-ion plasma mixtures. In the regime of strong Coulomb coupling, we use our previously developed analytic approximations for the free energy of one-component plasmas with rigid and polarizable electron background and apply the linear mixing rule (LMR). Other thermodynamic functions are obtained through analytic derivation of this free energy. In order to obtain an analytic approximation for the intermediate coupling and transition to the Debye-Hückel limit, we perform hypernetted-chain calculations of the free energy, internal energy, and pressure for mixtures of different ion species and introduce a correction to the LMR, which allows a smooth transition from strong to weak Coulomb coupling, in agreement with the numerical results.

Direct verification of mixing rules in the hot and dense regime

We perform orbital-free molecular dynamics simulations in the hot and dense regime for two mixtures: equimolar helium-iron and asymmetric deuterium-copper plasmas. For thermodynamic properties, we test two isobaric-isothermal mixing rules whose definitions involve either the equality of total pressures or the equality of the so-defined excess pressures of the components; the pressure and internal energy obtained by direct simulations are in very good agreement with those given by the mixing rule involving the equality of excess pressures. The viscosity of the deuterium-copper mixture is also extracted from a direct simulation and compared to the result given by a mixing rule applied to the viscosities of the pure elements. Finally, for structural properties, the effective charges given by the isobaric-isothermal mixing rule for the average atom model, used in the binary ionic mixture model, yield partial pair distribution functions in good agreement with those obtained by a direct simulation.

Equation of state for partially ionized carbon at high temperatures

Equation of state for partially ionized carbon at temperatures T approximately > or = 10(5) K is calculated in a wide range of densities, using the method of free energy minimization in the framework of the chemical picture of plasmas. The free energy model includes the internal partition functions of bound species. The latter are calculated by a self-consistent treatment of each ionization stage in the plasma environment taking into account pressure ionization. The long-range Coulomb interactions between ions and screening of the ions by free electrons are included using our previously published analytical model.