ABSTRACT
In applying vibration-transit (V-T) theory of liquid dynamics to the thermodynamic properties of monatomic liquids, the point has been reached where an improved model is needed for the small (approximately 10%) transit contribution. Toward this goal, an analysis of the available high-temperature experimental entropy data for elemental liquids was recently completed [D. C. Wallace, E. D. Chisolm, and N. Bock, Phys. Rev. E 79, 051201 (2009)]. This analysis yields a common curve of transit entropy vs T/thetatr, where T is temperature and thetatr is a scaling temperature for each element. In the present paper, a statistical mechanics model is constructed for the transit partition function, and is calibrated to the experimental transit entropy curve. The model has two scalar parameters, and captures the temperature scaling of experiment. The calibrated model fits the experimental liquid entropy to high accuracy at all temperatures. With no additional parameters, the model also agrees with both experiment and molecular dynamics for the internal energy vs. T for Na. With the calibrated transit model, V-T theory provides equations subject to ab initio evaluation for thermodynamic properties of monatomic liquids. This will allow the range of applicability of the theory, and its overall accuracy, to be determined. More generally, the hypothesis of V-T theory, which divides the many-atom potential energy valleys into random and symmetric classes, can also be tested for its application beyond monatomic systems.
ABSTRACT
It is possible in principle to probe the many-atom potential surface using density functional theory (DFT). This will allow us to apply DFT to the Hamiltonian formulation of atomic motion in monatomic liquids by Wallace [Phys. Rev. E 56, 4179 (1997)]. For a monatomic system, analysis of the potential surface is facilitated by the random and symmetric classification of potential-energy valleys. Since the random valleys are numerically dominant and uniform in their macroscopic potential properties, only a few quenches are necessary to establish these properties. Here we describe an efficient technique for doing this. Quenches are done from easily generated "stochastic" configurations, in which the nuclei are distributed uniformly within a constraint limiting the closeness of approach. For metallic Na with atomic pair potential interactions, it is shown that quenches from stochastic configurations and quenches from equilibrium liquid molecular dynamics configurations produce statistically identical distributions of the structural potential energy. Again for metallic Na, it is shown that DFT quenches from stochastic configurations provide the parameters which calibrate the Hamiltonian. A statistical mechanical analysis shows how the underlying potential properties can be extracted from the distributions found in quenches from stochastic configurations.
