Abstract
We report on a theoretical study of equation of state (EOS) properties of fluid and dense plasma mixtures of xenon and deuterium to explore and illustrate the basic physics of the mixing of a light element with a heavy element. Accurate EOS models are crucial to achieve highfidelity hydrodynamics simulations of many highenergydensity phenomena, for example inertial confinement fusion and strong shock waves. While the EOS is often tabulated for separate species, the equation of state for arbitrary mixtures is generally not available, requiring properties of the mixture to be approximated by combining physical properties of the pure systems. Density functional theory (DFT) at elevatedtemperature is used to assess the thermodynamics of the xenondeuterium mixture at different mass ratios. The DFT simulations are unbiased as to elemental species and therefore provide comparable accuracy when describing total energies, pressures, and other physical properties of mixtures as they do for pure systems. The study focuses on addressing the accuracy of different mixing rules in the temperature range 1000–40 000 K for pressures between 100 and 600 GPa (1–6 Mbar), thus, including the challenging warm dense matter regime of the phase diagram. We find that a mix rule taking into account pressure equilibration between the two species performs very well over the investigated range.
This work was supported by the NNSA Science Campaigns. We thank Dr. Joel Kress at Los Alamos National Laboratory for valuable discussions on mix rules and QMD simulations. Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under Contract DEAC0494AL85000.
I. INTRODUCTION
II. METHOD
III. RESULTS
IV. SUMMARY AND DISCUSSION
Key Topics
 Density functional theory
 40.0
 Equations of state
 32.0
 High pressure
 22.0
 Materials properties
 7.0
 Plasma properties
 5.0
G21B1/00
Figures
Flowchart depicting the algorithm used to find the fixed average pressure within the NVT ensemble. This scheme is repeated until a 4 ps simulation is within the desired pressure window. Reprinted with permission from T. R. Mattsson and R. J. Magyar, “Shock compression of condensed matter2009,” AIP Conf. Proc. 1426, 1196 (2009). Copyright 2009 American Institute of Physics.
Flowchart depicting the algorithm used to find the fixed average pressure within the NVT ensemble. This scheme is repeated until a 4 ps simulation is within the desired pressure window. Reprinted with permission from T. R. Mattsson and R. J. Magyar, “Shock compression of condensed matter2009,” AIP Conf. Proc. 1426, 1196 (2009). Copyright 2009 American Institute of Physics.
Snapshot of the electron charge density contour of a XeD mixture with mass ratio x = 0.3 and density from a DFT/QMD AM05 calculation. The yellow surface is the isodensity surface value 0.8 at 1 Mbar and 5kK. Deuterium atoms are blue and xenon atoms are light purple.
Snapshot of the electron charge density contour of a XeD mixture with mass ratio x = 0.3 and density from a DFT/QMD AM05 calculation. The yellow surface is the isodensity surface value 0.8 at 1 Mbar and 5kK. Deuterium atoms are blue and xenon atoms are light purple.
Snapshot of the electron charge density contour of a XeD mixture with mass ratio x = 0.3 and density from a DFT/QMD AM05 calculation. The yellow surface is the isodensity surface value 0.8 at 3 Mbar and 10 kK. Deuterium atoms are blue and xenon atoms are light purple. Note that much of the valence change of Xe has been removed and is shared in a delocalized fashion amongst deuterium atoms.
Snapshot of the electron charge density contour of a XeD mixture with mass ratio x = 0.3 and density from a DFT/QMD AM05 calculation. The yellow surface is the isodensity surface value 0.8 at 3 Mbar and 10 kK. Deuterium atoms are blue and xenon atoms are light purple. Note that much of the valence change of Xe has been removed and is shared in a delocalized fashion amongst deuterium atoms.
The curves show the exact (DFT/QMD with AM05—flat black) results for the explicit mixture at 10 kK and 3 Mbar and the results of mixing rules constructed using pure material EOS: ideal—longdashed red, volume—dashed black, and pressure—shortdashed blue. The maximum errors occurs around the mixing ratio of x = 0.3 and is expected to peak at a 1:1 molar mixture corresponding to x = 0.015. The total density ρ varies from 15.71 g/cc on the left to 1.932 g/cc on the right. The EOS models used are D5365 and Xe5191. The DFT/QMD and EOS values for the pure materials differ by 5.6% for Xe and 16.3% for D.
The curves show the exact (DFT/QMD with AM05—flat black) results for the explicit mixture at 10 kK and 3 Mbar and the results of mixing rules constructed using pure material EOS: ideal—longdashed red, volume—dashed black, and pressure—shortdashed blue. The maximum errors occurs around the mixing ratio of x = 0.3 and is expected to peak at a 1:1 molar mixture corresponding to x = 0.015. The total density ρ varies from 15.71 g/cc on the left to 1.932 g/cc on the right. The EOS models used are D5365 and Xe5191. The DFT/QMD and EOS values for the pure materials differ by 5.6% for Xe and 16.3% for D.
Ratio of the density found using the calculated partial densities from Amagat's rule, Eq. (4) , and the individual species densities at target pressure to the actual total density. This is an exclusively DFT way of testing Amagat's rule without evoking approximate EOS values.
Ratio of the density found using the calculated partial densities from Amagat's rule, Eq. (4) , and the individual species densities at target pressure to the actual total density. This is an exclusively DFT way of testing Amagat's rule without evoking approximate EOS values.
The curves show the exact (DFT/QMD with AM05—flat black) results for the explicit mixture at 10 kK and 1, 3, and 6 Mbar and the results of mixing rules constructed using pure material EOS: ideal—longdashed red, volume—dashed black, and pressure—shortdashed blue.
The curves show the exact (DFT/QMD with AM05—flat black) results for the explicit mixture at 10 kK and 1, 3, and 6 Mbar and the results of mixing rules constructed using pure material EOS: ideal—longdashed red, volume—dashed black, and pressure—shortdashed blue.
Mixing scans at 3 Mbar and T = 5 kK, 10 kK, and 20 kK. The curves show the pressures predicted by various mixing rules using pure materials EOS or DFT data: Exact(DFT/QMD with AM05)—flat black, Ideal—longdashed red, volume—dashed black, and pressure—shortdashed blue.
Mixing scans at 3 Mbar and T = 5 kK, 10 kK, and 20 kK. The curves show the pressures predicted by various mixing rules using pure materials EOS or DFT data: Exact(DFT/QMD with AM05)—flat black, Ideal—longdashed red, volume—dashed black, and pressure—shortdashed blue.
Tables
Root mean square errors over sampled mass mixture compositions (x) for various mixing rules versus results of DFT/QMD using AM05 for XeD mixtures.
Root mean square errors over sampled mass mixture compositions (x) for various mixing rules versus results of DFT/QMD using AM05 for XeD mixtures.
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