Bulletin of the American Physical Society
2005 14th APS Topical Conference on Shock Compression of Condensed Matter
Sunday–Friday, July 31–August 5 2005; Baltimore, MD
Session B6: Equation of State I |
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Chair: Eric Chisolm, Los Alamos National Laboratory Room: Hyatt Regency Chesapeake A/B |
Monday, August 1, 2005 9:00AM - 9:15AM |
B6.00001: Structural Phase Transitions {\&} Equation of State of Aluminum from First Principles Xia Lu, Sathya Hanagud EOS of Al and the associated structural phase transitions are of special interest in characterizing the mixture of Al with other metal oxides or metals to produce dual functional structural energetic materials. From first principles, we studied the phase transitions of Al at pressures up to 800 GPa and temperatures up to 1000 K. In the past, phase transitions fcc $\diamondsuit $ hcp $\diamondsuit $ bcc were studied at 0K. In this paper, by considering electronic and lattice thermal contributions, we present a phase diagram of Al by investigating the stability of the three phases at pressures and temperatures of interest. Phonon analysis is used for analyzing the phase structural stability. The free energy, due to the cold-curve, electronic and lattice thermal contributions, is used to calculate the EOS with phase transitions. The predicted EOSs are compared with experimental EOSs. Changes of the electronic structures and phonon characteristics with pressure and phase transitions are also discussed. Calculations at ground state are in the framework of DFT, using local density or generalized gradient approximation, and projector augmented wave method. The lattice thermal contributions are obtained by populating the quasiharmonic phonon modes, according to the Boltzmann statistics; the electronic thermal contributions by populating the electron band structures, according to the Fermi-Dirac statistics. [Preview Abstract] |
Monday, August 1, 2005 9:15AM - 9:30AM |
B6.00002: Thermodynamically based equation of state for shock wave studies. Application to the design of experiments on tin. Francois Buy, Christophe Voltz, Fabrice Llorca This work is devoted to the evaluation of the behavior of complex metals under shock wave loading. This first work presents a methodology proposed for the design of specific experiments performed for the validation of equation of state models. We focus on tin because, on the one hand, of the multiphase behavior this material exhibits and, on the other hand, of the numerous works realized in the past years. While C. Mabire in 2000 mainly drew her attention on the evaluation of tin melting curve, our present work is focused on the two solid phases that tin can reach under shock loading. A thermodynamically based equation of state has been implemented which gives the opportunity to point out singularities which can be activated under particular shock wave loading. In the pressure-temperature diagram, the superimposed Hugoniot and release paths put in evidence the onset of double shock and of release shock configurations. We compare original experimental configurations to VISAR measurements to investigate the validity and the efficiency of the model for predicting the thermodynamical state of tin. The results prove a good ability of the model for the interpretation of the experimental data. [Preview Abstract] |
Monday, August 1, 2005 9:30AM - 9:45AM |
B6.00003: Testing a Liquid EOS Model Against Cu Data S.D. Crockett, C.W. Greeff, J.D. Johnson We model the free energy of a liquid near melting by postulating that $\Delta S_V$, the entropy difference between solid and liquid at fixed volume, is independent of pressure, and that the melting curve follows the Lindemann law. We show that these two assumptions are consistent with the frequently used scaling assumption $c_v(V,T) = f(T/T_m(V))$, where $T_m(V)$ is the melting temperature. Using a solid free energy determined from {\em ab initio} phonon frequencies, we apply these assumptions to liquid Cu. We show that they are consistent with the Hugoniot sound speed data. We investigate the consequences of typical variations of $\Delta S_V$ for shock melting. We also investigate models for the shear modulus and the residual deviatoric stress in the shocked state. [Preview Abstract] |
Monday, August 1, 2005 9:45AM - 10:00AM |
B6.00004: Wide-Range Multiphase Equations of State for Matter in Tabular Form and Their Applications Pavel Levashov, Konstantin Khishchenko In this work to adapt wide-range multiphase equations of state for matter to simulations of shock-wave processes we developed two-dimensional tables of thermodynamic functions (such as pressure $P$ and internal energy $E$) and their derivatives depending on specific volume $V$ and temperature $T$ calculated by analytic formulas. For every region of stability of every phase state the rectangular mesh was constructed so that a phase boundary passed through the nodes of the mesh. For the regions of metastable states of superheated liquid and supercooled vapor at positive pressure as well as for the regions of solid state, melting region and liquid state at negative pressure the separate mesh was generated. The values of parameters in an auxiliary point of phase diagram are found as a result of bilinear or linear interpolation. One can use $(V, T)$, $(V, P)$ or $(V, E)$ as input parameters. The described way of interpolation guaranties high accuracy of calculations near phase boundaries. We present some applications of the developed equations of state for a number of problems of high energy density physics. We also plan to include the described tabular equations of state for several substances into the database on thermophysical properties at high pressures and temperatures (http://teos.ficp.ac.ru/rusbank/). The work is done under RFBR financial support, grant 04-07-90310, and the Russian Science Support Foundation, grant for talented young researchers. [Preview Abstract] |
Monday, August 1, 2005 10:00AM - 10:15AM |
B6.00005: Building of Equations of State with Numerous Phase Transitions --- Application to Bismuth Olivier Heuze Modelling of shock waves crossing material with several phase transitions requires the knowledge of the equation of state (E.o.S.) of the material and its thermodynamic properties. The phase transitions correspond to volume and entropy jumps and discontinuities of extensive properties of the different phases. Building a complete E.o.S. with numerous crystallographic phase transitions raises many issues. It is generally a function of volume and temperature although thermodynamic equilibrium is defined for given temperature and pressure. Experimental data are generally available only in the (P,T) plane. Only few experimental data exist about the volume jump and none for the entropy jump. We propose an algorithm to build complete E.o.S. including several solid/solid or solid/liquid phase transitions. Each phase has its own E.o.S. and independent parameters. The phase diagram is calculated from the Gibbs free energy minimum. The phase transition is calculated from the Gibbs free energy equality between two phases which provides the thermodynamic properties of their binary mixture, and volume and entropy jumps. We explain how to determine these jumps in accordance to thermodynamic rules and experimental data. Until now, such an approach was used in simple cases and limited to 2 or 3 phases. We have applied it in the general case to bismuth for which up to 11 phases have been identified. This study show the great influence of binary mixtures and triple points properties in released isentropes after shock waves. [Preview Abstract] |
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