Session R7: CM.1 Equation of State: Modeling, Sponsored Invited Talk

Recent developments in ab initio equations of state for ICF applications

I present a brief review of recent work that we at Lawrence Livermore National Laboratory have conducted on the development of accurate EOS models for DT fuel, as well as for two candidate ablator materials: Glow Discharge Polymer, and diamond. Emphasis will be placed on the use of ab initio electronic structure methods in producing data with which the EOS models are fit, as well as details of the EOS models themselves. Also discussed is the use of a variety of experimental data in the validation of these models.   

Useful microscopic concepts for high pressure phenomena

A better understanding of the macroscopic behavior of crystalline solids under pressure can be achieved introducing microscopic concepts as the local compressibility ($\kappa_i$=-$\frac{1}{V} \frac{\partial V}{\partial p}$) and the local pressure ($p_i$=-$\frac{\partial E}{\partial V_i}$). Both are derived from topological analysis of crystalline electron densities. This formalism allows for a partition of the unit cell volume ($V$) into disjoint atomic-like regions such that $V$=$\sum_i V_i$, $i$ runs over all different atomic constituents. Using this topological partition, the compressibility of the crystal is recovered: $\kappa$= $\sum_i \frac{V_i}{V} \kappa_i$. Although local pressures are not additive, their reciprocals are: $\frac{1}{p}$=$\sum_i \frac{1}{p_i}$, where $p$ is the thermodynamic pressure. This fact leads to the interpretation of the atomic constituents of crystals as parallel mechanical resistors when pressure is applied. Consequently, atomic-like mechanical resistances and mechanical conductances can be defined. After extensive first principles calculations, computed results of these local properties reveal systematic trends for crystal families under pressure, as we illustrate for II-VI binary semiconductors and oxide spinels.   

Multiphase Equations of State for Structural Materials at High Pressures

Equations of state for materials over a wide range of pressures and temperatures are needed for numerical simulations of processes in shock-compressed media. Accuracy of calculation results is determined mainly by adequacy of equation of state of a medium. In this work, a new multiphase equation-of-state model is proposed with taking into account the polymorphic phase transformations, melting, evaporation and ionization. Thermodynamic calculations are carried out for metals, alkali halides, and polymer materials in a broad region of the phase diagram. Obtained results are presented in comparison with available data of experiments at high dynamic pressures in shock and release waves.   

Shock Invariants and Conservation Laws in (1$+$1) Dimensions

The origin of scaling laws in shocked condensed matter provides clues concerning energy and momentum transport connecting the unshocked state to the stationary shocked state. One notable scaling law relating the shock rise time to the peak shock pressure (``Fourth Power Law'' (D. Grady) is observed in a wide range of homogeneous materials and for a wide range of pressures. This scaling law may be more fundamentally related to a shock invariant quantity defined by the product of the energy dissipated per unit mass and the duration over which the energy is dissipated. We show that using the energy-momentum tensor, commonly used in physics to describe symmetries and conservation laws, can be used to constrain the transport and corresponding shock structure in 2 dimensions (1 space$+$1 time). The empirical scaling laws mentioned above follow as a natural consequence of the known conservation laws. The implications are far reaching and this may be the first non-perturbative calculation of shock entropy in a strong shock. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 Lawrence Livermore National Security, LLC.   

Role of anharmonicity in the phonon contribution to the Gr\"uneisen parameter

The Gr\"uneisen parameter $\gamma$ is directly related to the thermal expansion of a solid and to its equation of state (EOS). Several formulations of $\gamma$ based on the isothermal EOS and pressure derivatives of elastic moduli have been developed over the years and predict different values for $\gamma$ at zero pressure and its pressure dependence. The uncertainty in these ``mechanical'' models can be addressed by density functional theory (DFT) calculations using the Mie-Gr\"uneisen formulation in which the vibrational contribution to the pressure is treated within the quasi-harmonic approximation while the static contribution is accounted by the cold curve. However, the vibrational Gr\"uneisen need not agree with either the thermodynamic value or any of the mechanical models, and is in fact overestimated in transition metals. We examine the difference between the vibrational and thermodynamic Gr\"uneisen parameter employing both classical molecular dynamics and lattice dynamics and utilizing classical interatomic potentials for bcc and fcc crystals constructed to have similar elastic moduli and cold curves but with different degrees of anharmonicity and transverse and longitudinal Brillouin edge zone phonon frequencies.