A new quotidian equation of state (QEOS) for hot dense matter

Abstract

The quotidian equation of state (QEOS) is a general-purpose equation of state model for use in hydrodynamic simulation of high-pressure phenomena. Electronic properties are obtained from a modified Thomas–Fermi statistical model, while ion thermal motion is described by a multiphase equation of state combining Debye, Grüneisen, Lindemann, and fluid-scaling laws. The theory gives smooth and usable predictions for ionization state, pressure, energy, entropy, and Helmholtz free energy. When necessary, the results may be modified by a temperature-dependent pressure multiplier which greatly extends the class of materials that can be treated with reasonable accuracy. In this paper a comprehensive evaluation of the resulting thermodynamic data is given including comparison with other theories and shock-wave data.

Equation of state, occupation probabilities and conductivities in the average atom Purgatorio code

“…This is illustrated in Fig. 3, in which Hugoniot curves are compared for the Thomas-Fermi-based QEOS model [10], Purgatorio using Hedin-Lundqvist (HL) LDA form for exchange and correlation, and Purgatorio with a Gupta-Rajagopal temperature-dependent exchange potential [12]. A simple ideal-gas ion-thermal contribution has been added to the Purgatorio results; this accounts for the differences between the HL results and QEOS at low pressures where ion-thermal contributions dominate the EOS.…”

“…[3][4][5][6]]. These models represent a significant advance in complexity beyond the commonly used Thomas-Fermi and related approaches [7][8][9][10].…”

Multiphase equation of state for carbon addressing high pressures and temperatures

“…The natural choice for F elec throughout this wide range is an atom-in-jellium approach in which a C ion is placed in a neutral cell embedded in a uniform electron gas of the appropriate density (specified by the choice of V ). Such average-atom models have a long history in the construction of equations of state for materials over wide ranges of compression and temperature [12,17,70]. The variant we used for our work of Ref.…”

“…The individual phase free energy models were fitted to the results of DFT-MD calculations. Since the final multiphase EOS model was designed to be used in continuum dynamics (hydrocode) simulations spanning a wider range of conditions, these researchers embedded their detailed three-phase EOS model into a more coarse-grained model [17] that respected the ideal gas limits at high T and low ρ and the Thomas-Fermi limit [12] at high ρ. While satisfactory in a broad sense, this older EOS model suffers from three main drawbacks: (1) The embedding of the DFT-based 3-phase model into the coarsegrained model created kinks in the thermodynamic functions, even though an attempt was made to smooth out such features by interpolation.…”

“…No embedding into a simpler model [17] is performed. The two extra phases included are the sc and sh phases.…”