Evaluation of the grand-canonical partition function using expanded Wang-Landau simulations. IV. Performance of many-body force fields and tight-binding schemes for the fluid phases of silicon

Entropy scaling close to criticality: From simple to metallic systems

Entropy has recently drawn considerable interest both as a marker to detect the onset of phase transitions and as a reaction coordinate, or collective variable, to span phase transition pathways. We focus here on the behavior of entropy along the vapor-liquid phase coexistence and identify how the difference in entropy between the two coexisting phases vary in ideal and metallic systems along the coexistence curve. Using flat-histogram simulations, we determine the thermodynamic conditions of coexistence, critical parameters, including the critical entropy, and entropies along the binodal. We then apply our analysis to a series of systems that increasingly depart from ideality and adopt a metal-like character, through the gradual onset of the Friedel oscillation in an effective pair potential, and for a series of transition metals modeled with a many-body embedded-atoms force field. Projections of the phase boundary on the entropy-pressure and entropy-temperature planes exhibit two qualitatively different behaviors. While all systems modeled with an effective pair potential lead to an ideal-like behavior, the onset of many-body effects results in a departure from ideality and a markedly greater exponent for the variation of the entropy of vaporization with temperature away from the critical temperature.

How accurate for phonon models to predict the thermodynamics properties of crystals

Previous work has shown that thermodynamics properties calculated by phonon model with quasi-harmonic approximation (QHA) may differ badly from experiment in some cases. The inaccuracy was examined in the present work by comparing the results of QHA for argon and copper crystal with the ones of molecular dynamics simulations, partition functions obtained by a new method or experiment. It is shown that QHA works well for the systems of atomic volume smaller than 22 ų/atom and the accuracy gets lower and lower gradually with increasing of the atomic volume. Based on this fact, the disagreement (or agreement) between the thermodynamics properties of MgO, Si, CaO, ZrO₂ calculated in previous work by QHA and the experiments can be well understood.

Entropy in Molecular Fluids: Interplay between Interaction Complexity and Criticality

Using flat-histogram simulations, we calculate the entropy of molecular fluids along the vapor-liquid phase boundary. Our simulation approach is based on the evaluation of the canonical and grand-canonical partition functions, which, in turn, provide access to entropy through the statistical mechanics formalism. The results allow us to determine the critical entropy of molecular fluids and to uncover that the transition occurs symmetrically from an entropic standpoint. This can best be seen through the patterns exhibited by the thermodynamic variables temperature and pressure when plotted against the entropy of the coexisting phases. This behavior is found to hold for apolar, quadrupolar, and dipolar fluids. Finally, we identify functional forms that characterize the relation between thermodynamic variables and entropy along the coexistence curve up to the critical point.

Classical and quantum many-body effects on the critical properties and thermodynamic regularities of silicon

Using molecular simulation, we determine the critical properties of Si as well as the loci for several remarkable thermodynamic contours spanning the supercritical region of the phase diagram. We consider a classical three-body potential as well as a quantum (tight-binding) many-body model, and determine the loci for the ideality contours, including the Zeno line and the H line of ideal enthalpy. The two strategies (classical or quantum) lead to strongly asymmetric binodals and to critical properties in good agreement with each other. The Zeno and H lines are found to remain linear over a wide temperature interval, despite the changes in electronic structure undergone by the fluid along these contours. We also show that the classical and quantum model yield markedly different results for the parameters defining the H line, the exponents for the power-laws underlying the line of minima for the isothermal enthalpy and for the density required to achieve ideal behavior, most notably for the enthalpy.

Impact of Friedel oscillations on vapor-liquid equilibria and supercritical properties in two and three dimensions

We determine the impact of the Friedel oscillations on the phase behavior, critical properties, and thermodynamic contours in films [two dimensions (2D)] and bulk phases [three dimensions (3D)]. Using expanded Wang-Landau simulations, we calculate the grand-canonical partition function and, in turn, the thermodynamic properties of systems modeled with a linear combination of the Lennard-Jones and Dzugutov potentials, weighted by a parameter X (0<X<1). Varying X allows us to control the height of the first Friedel oscillation and to provide a complete characterization of the effect of the metal-like character in the potential on the thermodynamic properties over a wide range of conditions. For 3D systems, we are able to show that the critical parameters exhibit a linear dependence on X and that the loci for the thermodynamic state points, for which the system shows the same compressibility factor or enthalpy as an ideal gas, are two straight lines spanning the subcritical and supercritical regions of the phase diagram for all X values. Reducing the dimensionality to 2D results in a loss of impact of the Friedel oscillation on the critical properties, as evidenced by the virtually constant critical density across the range of X values. Furthermore, our results establish that the straightness of the two ideality lines is retained in 2D and is independent from the height of the first Friedel oscillation in the potential.

Scaling Laws and Critical Properties for fcc and hcp Metals

The determination of the critical parameters of metals has remained particularly challenging both experimentally, because of the very large temperatures involved, and theoretically, because of the many-body interactions that take place in metals. Moreover, experiments have shown that these systems exhibit an unusually strong asymmetry of their binodal. Recent theoretical work has led to new similarity laws, based on the calculation of the Zeno line and of the underlying Boyle parameters, which provided results for the critical properties of atomic and molecular systems in excellent agreement with experiments. Using the recently developed expanded Wang-Landau (EWL) simulation method, we evaluate the grand-canonical partition function, over a wide range of conditions, for 11 fcc and hcp metals (Ag, Al, Au, Be, Cu, Ir, Ni, Pb, Pd, Pt, and Rh), modeled with a many-body interaction potential. This allows us to calculate the binodal, Zeno line, and Boyle parameters and, in turn, obtain the critical properties for these systems. We also propose two scaling laws for the enthalpy and entropy of vaporization, and identify critical exponents of 0.4 and 1.22 for these two laws, respectively.