Thermodynamic Self-consistency Research Articles

Sampling-free computation of finite temperature material properties in isochoric and isobaric ensembles using the mean-field anharmonic bond model

The recently introduced mean-field anharmonic bond model has shown remarkable accuracy in predicting finite temperature free energies for certain potential models of fcc crystals without thermodynamic sampling. In this work, we extend the model to treat modern machine learning potentials in both isochoric and isobaric ensembles while preserving existing vibrational correlations and ensuring thermodynamic self-consistency. Testing against molecular dynamics simulations of bulk fcc Al and Cu, we find free energies with an accuracy of a few meV/atom up to the melting temperature under typical operating pressures, with similar accuracy for thermal expansion. Our sampling-free estimation is universally superior to the quasiharmonic approximation for less than ten percent of the computational cost and many orders of magnitude more efficient than thermodynamic integration. We discuss applications of the method in modern computational materials science workflows. Published by the American Physical Society 2024

Experimental Measurements and Thermodynamic Optimization of the NaCl+RbCl Phase Diagram.

In this study, the phase diagram of the NaCl+RbCl binary system was measured using differential scanning calorimetry, and the measured molar percentages of the binary mixture RbCl ranged from 12 to 97 mol%, updating and extending the experimental data for this binary system. The liquid phase of this system was thermodynamically modeled using a modified quasichemical model, and a computer optimization program for evaluation of the experimental data on phase equilibria and other thermodynamic data was developed based on this model. All thermodynamic models of the NaCl+RbCl binary system were constructed; calculations of the phase diagram, enthalpy of mixing, and activity coefficient of NaCl of the NaCl+RbCl binary system were completed using the obtained model parameters; and the calculated eutectic point positions were xRbCl = 0.567 and 550.2 °C. The calculated results were able to reproduce the various types of experimental data well, and the thermodynamic self-consistency between different types of experimental data was demonstrated.

Strange quark matter and proto-strange stars in a baryon density-dependent quark mass model * *Supported by the National Natural Science Foundation of China (11875052, 11575190, 11135011)

The properties of strange quark matter and the structures of (proto-)strange stars are studied within the framework of a baryon density-dependent quark mass model, where a novel quark mass scaling and self-consistent thermodynamic treatment are adopted. Our results indicate that the perturbative interaction has a significant impact on the properties of strange quark matter. It is determined that the energy per baryon increases with temperature, while the free energy decreases and eventually becomes negative. At fixed temperatures, the pressure at the minimum free energy per baryon is zero, suggesting that the thermodynamic self-consistency is preserved. Furthermore, the sound velocity v in quark matter approaches the extreme relativistic limit ( ) as the density increases. By increasing the strengths of the confinement parameter D and perturbation parameter C, the tendency for v to approach the extreme relativistic limit at high density is slightly weakened. For (proto-)strange stars, the novel quark mass scaling can accommodate massive proto-strange stars with their maximum mass surpassing twice the solar mass by considering the isentropic stages along the star evolution line, where the entropy per baryon of the star matter is set to be 0.5 and 1 with the lepton fraction = 0.4.

Anharmonic free energy of lattice vibrations in fcc crystals from a mean-field bond

It has recently been shown that the ab initio anharmonic free energy of fcc crystals can be approximated to meV/atom accuracy by a lattice of anharmonic nearest-neighbor bonds, where the bonding potential can be efficiently parametrized from the target system. We develop a mean-field approach for the free energy of a general bond lattice, analytically accounting for strong bond-bond correlations while enforcing material compatibility and thermodynamic self-consistency. Applying our fundamentally anharmonic model to fcc crystals yields free energies within meV/atom of brute force thermodynamic integration for core seconds of computational effort. Potential applications of this approach in computational materials science are discussed.

Integral-equation theories of fluid phase equilibria in simple fluids

We briefly review the application of integral equation theories (IETs) of the fluid state in order to predict fluid phase equilibria of simple fluids. In spite of the relatively simple picture emerging from an isotropic pair potential, IETs have been instrumental in the last few decades to show a quite complex phase behaviour, where multiple critical points are observed in the phase diagram. The application of thermodynamic self-consistency within the theory is shown to dramatically improve the reliability of IETs, allowing them to become a valid and computationally cheap tool, in comparison to computer simulation, to investigate the limits of stability of the fluid phase.

GUP deformed phase-space and axiomatic thermodynamic self-consistency

Based on the generalized uncertainty principle (GUP) with a deformation of the phase-space, the partition function has recently been modified. In the present work, we analyze the self-consistency of the axiomatic thermodynamics derived from the deformed partition function. First, we set up the thermodynamic quantities such as pressure, energy density, entropy and number density, then we extend the study for testing the approval of consistency. We found that the deformed phase-space satisfies the axiomatic self-consistency of thermodynamics. We would expect the effects of GUP to be more pronounced at high frequencies, but the used deformed phase-space factor would still diverge as [Formula: see text] approaches [Formula: see text].

On the statistical thermodynamics of quantum gases

On the basis of the grand canonical Gibbs ensemble, using the virial theorem and the equations of motion for Green’s functions, it was shown that the thermodynamic functions of a one-component quantum gas are uniquely determined by the two-particle Green’s function outside the framework of perturbation theory. A thermodynamic self-consistency condition is formulated, which makes it possible to select approximate expressions for the two-particle Green’s function.

Mixing-rules calculations and AAMD simulations for EOSs of deuterium–xenon mixtures

We present the calculated equations of state (EOSs) for deuterium–xenon mixtures using mixing rules. Three mixing rules, which are the ideal rule, volume rule, and pressure rule, were used for the calculations, and the thermodynamic self-consistency was evaluated. The volume rule predicts the pressures of mixtures rather accurately, but it fails in the predictions of energies. The pressure ionization has an impact on energy and pressure. Furthermore, the calculated results of the mixing rules were compared with average-atom molecular dynamics (AAMD) simulations, and the pressure rule performs better than the ideal and volume rules over the investigated range.

The uniform quantized electron gas revisited

In this article we continue and extend our recent work on the correlation energy of the quantized electron gas of uniform density at temperature . As before, we utilize the methods, properties, and results obtained by means of classical statistical mechanics. These were extended to quantized systems via the Feynman path integral formalism. The latter translates the quantum problem into a classical polymer problem in four dimensions. Again, the well known RPA (random phase approximation) is recovered as a basic result which we then modify and improve upon. Here we analyze the condition of thermodynamic self-consistency. Our numerical calculations exhibit a remarkable agreement with well known results of a standard parameterization of Monte Carlo correlation energies.

On thermodynamic self-consistency of generic axiomatic-nonextensive statistics

Generic axiomatic-nonextensive statistics introduces two asymptotic properties, to each of which a scaling function is assigned. The first and second scaling properties are characterized by the exponents c and d, respectively. In the thermodynamic limit, a grand-canonical ensemble can be formulated. The thermodynamic properties of a relativistic ideal gas of hadron resonances are studied, analytically. It is found that this generic statistics satisfies the requirements of the equilibrium thermodynamics. Essential aspects of the thermodynamic self-consistency are clarified. Analytical expressions are proposed for the statistical fits of various transverse momentum distributions measured in most-central collisions at different collision energies and colliding systems. Estimations for the freezeout temperature (Tch) and the baryon chemical potential (μb) and the exponents c and d are determined. The earlier are found compatible with the parameters deduced from Boltzmann-Gibbs (BG) statistics (extensive), while the latter refer to generic nonextensivities. The resulting equivalence class (c,d) is associated with stretched exponentials, where Lambert function reaches its asymptotic stability. In some measurements, the resulting nonextensive entropy is linearly composed on extensive entropies. Apart from power-scaling, the particle ratios and yields are excellent quantities to highlighting whether the particle production takes place (non)extensively. Various particle ratios and yields measured by the STAR experiment in central collisions at 200, 62.4 and 7.7 GeV are fitted with this novel approach. We found that both c and d < 1, i.e. referring to neither BG- nor Tsallis-type statistics, but to (c,d)-entropy, where Lambert functions exponentially rise. The freezeout temperature and baryon chemical potential are found comparable with the ones deduced from BG statistics (extensive). We conclude that the particle production at STAR energies is likely a nonextensive process but not necessarily BG or Tsallis type.

Polyakov loop and gluon quasiparticles: A self-consistent approach to Yang–Mills thermodynamics

We present a quasiparticle model for the pure gauge sector of QCD, in which transverse quasigluons propagate in a Polyakov loop background field. By incorporating thermodynamic self-consistency in the approach, we show that our Polyakov loop extended quasiparticle model allows an accurate description of recent lattice results for all the thermodynamic quantities, including the Polyakov loop expectation value, in the deconfined phase. The related quasigluon mass exhibits a distinct temperature dependence, which is connected with the non-perturbative behavior seen in the scaled interaction measure of the pure gauge theory.

A three-dimensional phase field model for nanowire growth by the vapor–liquid–solid mechanism

We present a three-dimensional multi-phase field model for catalyzed nanowire (NW) growth by the vapor–liquid–solid (VLS) mechanism. The equation of motion contains both a Ginzburg–Landau term for deposition and a diffusion (Cahn–Hilliard) term for interface relaxation without deposition. Direct deposition from vapor to solid, which competes with NW crystal growth through the molten catalyst droplet, is suppressed by assigning a very small kinetic coefficient at the solid–vapor interface. The thermodynamic self-consistency of the model is demonstrated by its ability to reproduce the equilibrium contact angles at the VLS junction. The incorporation of orientation dependent gradient energy leads to faceting of the solid–liquid and solid–vapor interfaces. The model successfully captures the curved shape of the NW base and the Gibbs–Thomson effect on growth velocity.

Weighted correlation approach: An extended version with applications to the hard-sphere fluid

The purpose of this study is to extend the weighted correlation approach (WCA) for inhomogeneous fluids. It now introduces a generic expression to evaluate the single-particle direct correlation function in terms of a series of pair direct correlation functions weighted by different correlation-weight functions and adjustable weight factors. When applied for practical use, however, approximations of the pair direct correlation functions have to be made, together with appropriate definitions of the weighted densities and the choices of the correlation-weight functions. The WCA approach would, then, not only help us to connect and compare different strategies and their underlying assumptions in the density functional approaches, but also enable us to propose and apply density functional theory methods to predict the density profile of, e.g., the hard-sphere fluid confined between a pair of parallel planar hard walls. Numerical results of the extended WCA approach, against the Monte Carlo (MC) simulations in a range of surface separations and bulk densities, suggest that it is capable of representing the fine features of the hard-sphere density distributions. The WCA results also agree well with the calculations from the fundamental measure theory. In addition, the thermodynamic self-consistency of the WCA approach is confirmed by its fairly good agreement with the MC fitted data for the surface tension of a hard-sphere fluid at a planar hard wall. All these tests show that a pure WCA approach can be constructed to investigate the states of ionic hard-sphere fluids.

Thermodynamically consistent closure approximation for hard spheres systems

We present a new closure relation that is an extension of the Percus-Yevick approximation. In the proposed closure, we introduce an additional term and a mixing coefficient that can be determined by imposing a condition of thermodynamic self-consistency. Moreover, the mixing coefficient is calculated analytically within a linear approximation. In the case of a monodisperse system of hard spheres, we compare the results of our model to well-established thermodynamic expressions and also to the structural properties of fairly known closure approximations. In the second case, and using an equivalent scheme, the new closure relation is extended to the depletion potential between two large hard spheres immersed in a liquid of small hard spheres. In both cases, the results of our model are in good agreement with numerical simulations performed at intermediate concentrations.

On the importance of thermodynamic self-consistency for calculating clusterlike pair correlations in hard-core double Yukawa fluids

Understanding the mechanisms of clustering in colloids, nanoparticles, and proteins is of significant interest in material science and both chemical and pharmaceutical industries. Recently, using an integral equation theory formalism, Bomont et al. [J. Chem. Phys. 132, 184508 (2010)] studied theoretically the temperature dependence, at a fixed density, of the cluster formation in systems where particles interact with a hard-core double Yukawa potential composed of a short-range attraction and a long-range repulsion. In this paper, we provide evidence that the low-q peak in the static structure factor, frequently associated with the formation of clusters, is a common behavior in systems with competing interactions. In particular, we demonstrate that, based on a thermodynamic self-consistency criterion, accurate structural functions are obtained for different choices of closure relations. Moreover, we explore the dependence of the low-q peak on the particle number density, temperature, and potential parameters. Our findings indicate that enforcing thermodynamic self-consistency is the key factor to calculate both thermodynamic properties and static structure factors, including the low-q behavior, for colloidal dispersions with both attractive and repulsive interactions. Additionally, a simple analysis of the mean number of neighboring particles provides a qualitative description of some of the cluster features.

Thermodynamic self-consistency issues related to the Cluster Variation Method: The case of the BCC Cr–Fe (Chromium–Iron) system

The Cluster Variation Method (CVM), introduced over 50 years ago by Prof. Dr. Ryoichi Kikuchi, is applied to the thermodynamic modeling of the BCC Cr–Fe system in the irregular tetrahedron approximation, using experimental thermochemical data as initial input for accessing the model parameters. The results are checked against independent data on the low-temperature miscibility gap, using increasingly accurate thermodynamic models, first by the inclusion of the magnetic degrees of freedom of iron and then also by the inclusion of the magnetic degrees of freedom of chromium. It is shown that a reasonably accurate description of the phase diagram at the iron-rich side ( i.e. the miscibility gap borders and the Curie line) is obtained, but only at expense of the agreement with the above mentioned thermochemical data. Reasons for these inconsistencies are discussed, especially with regard to the need of introducing vibrational degrees of freedom in the CVM model.

Self-consistent Ornstein-Zernike approximation for molecules with soft cores

The self-consistent Ornstein-Zernike approximation (SCOZA) is an accurate liquid state theory. So far it has been tied to interactions composed of hard core repulsion and long-range attraction, whereas real molecules have soft core repulsion at short distances. In the present work, this is taken into account through the introduction of an effective hard core with a diameter that depends upon temperature only. It is found that the contribution to the configurational internal energy due to the repulsive reference fluid is of prime importance and must be included in the thermodynamic self-consistency requirement on which SCOZA is based. An approximate but accurate evaluation of this contribution relies on the virial theorem to gauge the amplitude of the pair distribution function close to the molecular surface. Finally, the SCOZA equation is transformed by which the problem is reformulated in terms of the usual SCOZA with fixed hard core reference system and temperature-dependent interaction.

Nonequivalent operator representations for Bose-condensed systems

The necessity of accurately taking into account the existence of nonequivalent operator representations associated with canonical transformations is discussed. It is demonstrated that Bose systems in the presence of the Bose-Einstein condensate and without it correspond to different Fock spaces, orthogonal to each other. A composite representation for the field operators is constructed allowing for a self-consistent description of Bose-condensed systems. Equations of motion are derived from the given Hamiltonian, which guarantees the validity of conservation laws and thermodynamic self-consistency. At the same time, the particle spectrum obtained either from diagonalizing this Hamiltonian or from linearizing the field-operator equations of motion has no gap. The condition of the condensate existence assures the absence of the gap in the spectrum, irrespectively to the approximation involved. The suggested self-consistent theory is both conserving and gapless.

A simple SCOZA for simple fluids

A simple version of the self-consistent Ornstein–Zernike approach (SCOZA) is investigated quantitatively. The simplification consists of retaining thermodynamic self-consistency between the compressibility and energy routes to thermodynamics from the pair distribution function g( r). However, we do not require that g( r) be identically zero within the hard repulsive core of the models we consider here. The resulting theory lends itself to analysis of Hamiltonian models to which the earlier SCOZA formulation cannot be readily applied as well as providing a convenient means of analyzing simpler models. We choose the hard-core Yukawa fluid as an illustrative example to calibrate the accuracy of the new version. The results are compared with our earlier SCOZA and simulation results, and a suggestion is given to systematically improve the accuracy of the theory in the applications that warrant so doing.

Configurational Temperature of Charge-Stabilized Colloidal Monolayers

Recent theoretical advances show that the temperature of a system in equilibrium can be measured from static snapshots of its constituents' instantaneous configurations, without regard to their dynamics. We report the first measurements of the configurational temperature in an experimental system. In particular, we introduce a hierarchy of hyperconfigurational temperature definitions, which we use to analyze monolayers of charge-stabilized colloidal spheres. Equality of the hyperconfigurational and bulk thermodynamic temperatures provides previously lacking thermodynamic self-consistency checks for the measured colloidal pair potentials, and thereby casts new light on anomalous like-charge colloidal attractions induced by geometric confinement.