Material Properties at High Energy Density from Quantum Molecular Dynamics

1. Material Properties at High Energy Density from Quantum Molecular Dynamics 

2. Sandia�s Z Machine is used for several HEDP experimental campaigns

3. HEDP computer simulations rely on �physics packages�: Conductivities, Equations of State, and Opacities

4. Modifications of the Lee-More conductivity algorithms were made to obtain an improved wide-range model*

5. A demanding application: Ultra-high velocity magnetically launched flyer plates (30 km/sec, Multi-Mbar pressures)

6. We simulated these magnetically launched flyer plates using the modified Lee-More (LMD) conductivities

8. Density Functional Theory (DFT) is a formally exact representation of the N electron Schr�dinger Equation

9. We are using Density Functional Theory (DFT) to perform Quantum Molecular Dynamics (QMD) simulations of Warm Dense Matter

10. The Kubo-Greenwood formula is used to calculate the frequency dependent electrical conductivity

11. At liquid aluminum densities just below solid, the optical conductivity is well fit by the Drude model

12. At lower density, where phase separation ispronounced, a gap begins to form at low energy

13. At low densities and higher temperatures, a Drudecomponent reemerges in the optical conductivity

14. The QMD-KG results are in good agreement with Alan DeSilva�s exploding wire data

15. The calculated liquid aluminum conductivities are higher than the improved Lee-More (LMD) model predictions

16. Flyer plate simulations with the QMD based conductivities give very good agreement with experiment

17. The absorption has the proper Hagen-Rubens low frequency behavior, consistent with the dc conductivity

18. We are using quantum molecular dynamics simulations with density functional theory to build manifestly consistent conductivity, EOS, and opacity models This is an animation. We start with a QMD simulation (using density functional theory) at a given density and temperature. The figure shows the Fe, Cr, and Ni atoms (in atomic rations of 38:11:5) along with an iso-surface of the electron density. From this molecular dynamics simulation we extract the Energy and Pressure from time averages (typically over 1 to 2 picoseconds). These quantities (over a suitable grid) can be used to generate and equation of state. In this case we used fits to a soft sphere model in the warm dense matter regime and blended with SESAME at high temperatures and densities. (Thermodynamic consistency was enforced through thermodynamic integration of the pressure.) For selected snapshots (10 or 20), we extract the eigenvalues and wavefunctions and use the Kubo-Greenwood formula to compute the optical conductivity for each snapshot. These are averaged to produce an average optical conductivity. The optical conductivity gives us the dc conductivity in the zero frequency limit, and, through the application of the Kramers-Kronig relations, the low energy (< approx 50 eV) opacities and other optical properties (reflectivities). In this manner we have generated the electrical conductivity model, the equation of state, and the low energy opacities on a manifestly consistent basis. The final figure shows a color coded conductivity phase space (Log scale ! ) with some special lines or features from the equation of state. Also shown is a snapshot of an exploding stainless steel wire projected into this phase space (black triangles). The snapshot is just at the instant when the voltage on the wire is beginning to collapse as a consequence of the large conducting corona that has formed around the wire (note the low density, high temperature, and high conductivity component). This figure illustrates the complexity of phase space we need to accurately model in order to perform truly representative simulations. With these advances we have had unprecedented success in modeling magnetically launched flyer plates for our Z EOS work, as well as modeling single exploding wires (Cornell aluminum and Sandia stainless steel).This is an animation. We start with a QMD simulation (using density functional theory) at a given density and temperature. The figure shows the Fe, Cr, and Ni atoms (in atomic rations of 38:11:5) along with an iso-surface of the electron density. From this molecular dynamics simulation we extract the Energy and Pressure from time averages (typically over 1 to 2 picoseconds). These quantities (over a suitable grid) can be used to generate and equation of state. In this case we used fits to a soft sphere model in the warm dense matter regime and blended with SESAME at high temperatures and densities. (Thermodynamic consistency was enforced through thermodynamic integration of the pressure.) For selected snapshots (10 or 20), we extract the eigenvalues and wavefunctions and use the Kubo-Greenwood formula to compute the optical conductivity for each snapshot. These are averaged to produce an average optical conductivity. The optical conductivity gives us the dc conductivity in the zero frequency limit, and, through the application of the Kramers-Kronig relations, the low energy (< approx 50 eV) opacities and other optical properties (reflectivities). In this manner we have generated the electrical conductivity model, the equation of state, and the low energy opacities on a manifestly consistent basis. The final figure shows a color coded conductivity phase space (Log scale ! ) with some special lines or features from the equation of state. Also shown is a snapshot of an exploding stainless steel wire projected into this phase space (black triangles). The snapshot is just at the instant when the voltage on the wire is beginning to collapse as a consequence of the large conducting corona that has formed around the wire (note the low density, high temperature, and high conductivity component). This figure illustrates the complexity of phase space we need to accurately model in order to perform truly representative simulations. With these advances we have had unprecedented success in modeling magnetically launched flyer plates for our Z EOS work, as well as modeling single exploding wires (Cornell aluminum and Sandia stainless steel).

19. Recent and active research areas Principal Hugoniot and reshock properties of deuterium Principal Hugoniot and Isentrope of aluminum, release isentropes QMD based conductivity models for Al, W, Be, and stainless steel Shock melting of Be and diamond (National Ignition Campaign) Electrical and thermodynamic properties of water at high energy densities Liquid-vapor critical points for Al, W, and stainless steel Research on advanced electronic structure methods for HEDP (finite temperature Exact Exchange, finite temperature GW)