Bulletin of the American Physical Society
15th APS Topical Conference on Shock Compression of Condensed Matter
Volume 52, Number 8
Sunday–Friday, June 24–29, 2007; Kohala Coast, Hawaii
Session M5: Equation of State III |
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Chair: Carl Greeff, Los Alamos National Laboratory Room: Fairmont Orchid Hotel Plaza III |
Wednesday, June 27, 2007 10:30AM - 10:45AM |
M5.00001: Computational study of the equation of state of hydrogen using the Coupled Electron-Ion Monte Carlo Method Miguel Morales, Kris Delaney, David Ceperley, Carlo Pierleoni We study the equation of state of liquid hydrogen at Mbar pressures, in the regime of pressure dissociation/ionization, using the Coupled Electron-Ion Monte Carlo (CEIMC) method. Our aim is to accurately describe the crossover from the molecular to the atomic regime. The CEIMC method is based on the Born-Oppenheimer approximation and consists of a Monte Carlo simulation of the ionic degrees of freedom (either with path integals or classical Metropolis) using a potential energy surface obtained from a zero temperature QMC method. The electronic calculation is done using either Variational Monte Carlo or the more accurate Reptation Quantum Monte Carlo. A Slater-Jastrow wavefunction is used, with an analytical RPA Jastrow term and one-body orbitals, obtained from a fast band structure calculation, with backflow corrections. In addition to the thermodynamic and structural properties of the dense fluid, we will discuss the influence of quantum effects on the protons. We also compare our results with recent calculations obtained using Born-Oppenheimer Molecular Dynamics. [Preview Abstract] |
Wednesday, June 27, 2007 10:45AM - 11:00AM |
M5.00002: The effect of functionals on the Equation of State using Density Functional Theory cold curves Ann E. Mattsson, John H. Carpenter With increasing computer power more complicated systems can be investigated by modeling and simulation efforts. These demanding simulations put unprecedented strain on the Equation of State (EOS). EOS models that have been perfectly adequate for smaller simulations can fail in unexpected ways for these more challenging applications. With the aim of improving the EOS, models are often fitted to calculated data in parts of the parameter space where little or no experimental data is available. For example, data calculated with the Quantum Molecular Dynamics (QMD) technique may be used in the warm dense matter regime. In this paper we focus on another type of calculated data, cold curves calculated with Density Functional Theory (DFT). The ultimate accuracy of a DFT or QMD calculation, although QMD is not addressed here, is governed by the choice of approximation for the exchange-correlation energy functional that embodies all many-body effects. We will discuss how the accuracy of the approximate functionals, manifested in the calculated cold curves, translate into accuracy for the EOS in different parts of the parameter space. [Preview Abstract] |
Wednesday, June 27, 2007 11:00AM - 11:15AM |
M5.00003: Analysis of Cold Curve Forms for High--Pressure Physics John Carpenter, Igor Lomonosov An extensive collection of cold curve forms is analyzed using aluminum as a representative material. The cold pressure curves are compared with theoretical calculations up to 100 fold compressions. Furthermore, the effect of the curves on the Al Hugoniot at pressures of up to 100 Mbar is compared with a sampling of the available experimental data. An optimal cold curve form for equation of state applications is developed which describes the correct behavior near normal density and also in the asymptotic compression limit. [Preview Abstract] |
Wednesday, June 27, 2007 11:15AM - 11:30AM |
M5.00004: Estimate of shock Hugoniot adiabat of liquids from hydrodynamics Eric Bouton, Pierre Vidal Predicting the Hugoniot shock states in liquids is of fundamental interest for numerical simulations and experimental investigations. Shock states are generally obtained from shock velocity (D) and material speed (u) measurements. In this paper, we propose two hydrodynamical methods for estimating the (D-u) Hugoniot curve of liquids from easily measured properties of the initial state. The first method is based upon the well-known experimental fact that for many liquids the shock adiabat is unique in a normalized plot. We then propose a quadratic form for this universal Hugoniot with only two parameters derived from physical considerations without fitting the experimental data. This relation is valid for liquids that do not undergo shock-induced phase under shock-pressure. The second method is based upon the differentiation of the Rankine-Hugoniot relations with the initial temperature considered as a variable and under the constraint of a unique nondimensional shock adiabat. We then obtain an ordinary differential equation (ODE) for the shock velocity D in the variable u. Upon integration, both methods predict the shock Hugoniot of liquid Nitromethane with a 10 {\%} accuracy for any initial temperature varying in the range from 250 K to 360K. [Preview Abstract] |
Wednesday, June 27, 2007 11:30AM - 11:45AM |
M5.00005: A Finite Srain, Non-Reactive EOS for PBX9502 Brian Lambourn, Nicholas Whitworth, Caroline Handley, Hugh James Like some liquids, the shock velocity - particle velocity relation for PBX9502 is initially curved, but tends to a linear relation for stronger shocks. Because of this, the method developed by Jeanloz of finding a Taylor expansion form for the principal isentrope cannot be used to develop an equation of state (EOS). Instead, the principal isentrope has been found from the Hugoniot by integration, using an analytic form for the variation of Gruneisen Gamma with specific volume. The isentrope has been extended by plausible extrapolations, both beyond the maximum Hugoniot compression and into the expansion regime. Finally an analytic fit has been made to the resulting principal isentrope to develop a Mie-Gruneisen form of EOS. [Preview Abstract] |
Wednesday, June 27, 2007 11:45AM - 12:00PM |
M5.00006: Equations of State of Dual Functional Mixtures Of Structural Energetic Materials Sathya Hanagud, Rusislava Zaharieva, Xia Lu Currently, the electronic structure and the equation of state of metals can be determined by the use of the density functional theory. However, the subject is still an active research field for disordered materials like alloys. This paper, however, is concerned with mixtures like aluminum, nickel and nickel oxide and not alloys. In general the mixture can be disordered and the ratio of the constituents can vary to accommodate the needed application and the associated structural design. In this paper, thermodynamically complete equations of state of mixtures are obtained from first principles calculations. Specifically mixtures of aluminum and nickel or nickel oxide, titanium and silicon, with binders and porosity, are considered. First, EOS of individual components is determined. Then, a super cell is constructed by the use of other disordered theories but noting the fact that we are considering mixtures and not alloys. Methods similar to the direct sampling method, quasi-random structures method and virtual crystal approximation are used to represent proper mixture architecture, with porosity. The results are then bridged to continuum though statistical mechanics techniques and compared with the results obtained from continuum mixture theories. To determine thermal effects, lattice thermal contributions and electron thermal contributions are included. The transition states are also discussed. [Preview Abstract] |
Wednesday, June 27, 2007 12:00PM - 12:15PM |
M5.00007: Analytical Equations of State for use in Hydro-Codes John Maw Hydro-code users often need to decide whether to use a tabular or analytical equation of state (EOS) in simulations. Many good, wide range,tabular forms have been generated, particularly for metals, often based on ab-initio electronic structure calculations. For other materials, including alloys and organics, tables either do not exist or are of limited accuracy. Analytical EOS forms can be generated quickly for novel materials where tabular forms are not available but are only as good as the experimental data used to generate them. However, they do have the advantage that they can be easily modified to assess the sensitivity of simulations to EOS uncertainties. A tabular form can only be modified by re-generating the EOS from scratch. This paper considers a number of analytical EOS forms with particular emphasis on those that give realistic descriptions of low density and off-Hugoniot states far from the regimes where they have been validated. The issues of robustness, an essential requirement of EOS for hydro-code simulations are addressed. Temperatures are not explicitly calculated in EOS of the form P(V,E) but may be required for use in material strength models. Simple methods are discussed for calculating temperatures that are thermodynamically consistent with an analytical EOS. [Preview Abstract] |
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