Liquid state thermodynamics and the dynamic compression of solids

Abstract

The thermodynamic properties of simple solids at high pressures may be calculated from liquid state thermodynamics by treating the solid for certain structural purposes as a supercooled liquid. In particular, the energy and pressure at arbitrary temperatures and densities can be obtained from expressions that are reasonably simple functionals of the pair potential. This permits the direct use of dynamic compression data as a test of a given pair potential without resorting to the usual methods that reduce the Hugoniot. Alternatively, the method can be used to perform a reduction of a shock Hugoniot by selecting from a general space of pair potentials the one that reproduces best both the known thermodynamic quantities and the Hugoniot curve. The resulting pair potential is then invoked to generate the zero temperature data, thereby also performing the required ‘‘reduction.’’ These methods are applied to a model of the inert gas solids.

Derivation of Coarse Grained Models for Multiscale Simulation of Liquid Crystalline Phase Transitions

“…To derive our CG nonbonded potentials, we have followed a philosophy, which is slightly different from the ones that have been followed traditionally in structure based coarse graining. Our method shares some resemblance with classical density functional theories of liquids, which have been quite successful in understanding several problems of soft condensed matter, like freezing of simple and colloidal liquids, glass transition of simple liquids, and phase transitions in liquid crystals. − The key point behind this class of theories is the observation that the short ranged order in the ordered phase is not very different from that in the disordered phase at a suitable density and temperature. The basic physics lies in the observation that as one approaches the actual phase transition from the high temperature side, the solid state forms due to an instability which occurs in the liquid state.…”

“…In the present context, the chosen reference state is that of a supercooled isotropic liquid with residual short-range LC order. In spirit this procedure is similar to attempts at understanding the freezing transition of several soft matter systems by classical density functional theories. − Recently, there have been a few attempts at describing lower symmetry phases of complex fluids (molecular crystals, LC nematics) by using potentials derived in the higher symmetry phase (isotropic liquid). , …”

Thermodynamically stable one-component quasicrystals: A density-functional survey of relative stabilities

“…For practical purposes, various approximations for F p have been proposed. Jones and Ashcroft [25] and Curtin [41] have calculated the free energy of the LJ solid by approximating the spherical average of the two-particle density in the solid by that in the isotropic liquid, thereby ignoring any dependence upon solid structure. Clearly this is insufficient for comparing relative stabilites of different solid structures.…”

“…(24) and (27) For fixed ρ s , T , and pseudopotential parameters Z and r c , the free energy functional is computed from Eqs. (14), (19), (24), (25), and (27) for a given solid structure and then minimized with respect to α to obtain the free energy. For the hcp crystal, additional minimization with respect to the c/a ratio is performed.…”

“…1, the basic form of φ(r) for the simple metals lends itself naturally to a perturbation approach, wherein the full pair potential is sensibly split into a short-range reference potential φ o (r) and a perturbation potential φ p (r) = φ(r) − φ o (r). Such an approach has already been applied successfully to the structure and thermodynamics of Lennard-Jones liquids [13,32] and solids [22,24,25,33,34] and of metallic liquids [35,36] and solids [37]. The Helmholtz free energy may be correspondingly separated and formally expressed in the exact form [21] F…”