Heterogeneous-elasticity theory of instantaneous normal modes in liquids.

Since decades, the concept of vibrational density of states in glasses has been mirrored in liquids by the instantaneous-normal-mode spectrum. In glasses instantaneous configurations are believed to be situated close to minima of the potential-energy hypersurface and all eigenvalues of the associated Hessian matrix are positive. In liquids this is no longer true, and modes corresponding to both positive and negative eigenvalues exist. The instantaneous-normal-mode spectrum has been numerically investigated in the past, and it has been demonstrated to bring important information on the liquid dynamics and transport properties. A systematic deeper theoretical understanding is now needed. Heterogeneous-elasticity theory has proven to be particularly successful in explaining many details of the low-frequency excitations in glasses, ranging from the thoroughly studied boson peak, to other anomalies related to the crossover between wave-like and random-matrix-like excitations. Here we present an extension of heterogeneous-elasticity theory to the liquid state, and show that the outcome of the theory agrees well to the results of extensive molecular-dynamics simulations of a model liquid at different temperatures. We find that the spectrum of eigenvalues [Formula: see text] has a sharp maximum close to (but not at) [Formula: see text], and decreases monotonically with [Formula: see text] on both its stable and unstable side. We show that the spectral shape strongly depends on temperature, being symmetric at high temperatures and becoming rather asymmetric at low temperatures, close to the dynamical critical temperature. Most importantly, we demonstrate that the theory naturally reproduces a surprising phenomenon, a zero-energy spectral singularity with a cusp-like character developing in the vibrational spectra upon cooling. This feature, known from a few previous numerical studies, has been generally overlooked in the past due to a misleading representation of the data. We provide a thorough analysis of this issue, based on both very accurate predictions of our theory, and computational studies of model liquid systems with extended size.

Stress fluctuations and adiabatic speed of sound in liquids: a simple way to estimate it from ab initio simulations.

One of the fundamental quantities in dynamics of the liquid state, the adiabatic speed of sound [Formula: see text], is extremely difficult to predict from computer simulations, especially in ab initio simulations. Here we derive an expression for the instantaneous correlator of fluctuations of longitudinal component of stress tensor, which contains [Formula: see text] along with others quantities easy accessible via classical and ab initio computer simulations. We show that the proposed methodology works well in the case of Lennard-Jones and soft-sphere simple fluids, Kr-Ar liquid mixture in connection with simulations with effective pair interactions as well as for liquid Sb, fluid Hg and molten NaCl from ab initio simulations.

Comment on "Deformations, relaxation, and broken symmetries in liquids, solids, and glasses: A unified topological field theory".

We discuss a field-theoretical approach to liquids, solids, and glasses, published recently [Phys. Rev. E 105, 034108 (2022)10.1103/PhysRevE.105.034108], which aims to describe these materials in a common formalism. We argue that such a formalism contradicts the known hydrodynamic theory of classical liquids. In particular, the authors miss the important particle-number conservation law and the density fluctuations as a hydrodynamic slow variable. This results in an exotic mechanism of hydrodynamic sound instead of the standard hydrodynamic one due to combined particle-number and momentum conservation, a fact well documented in fluid-mechanics textbooks.

Modeling the instantaneous normal mode spectra of liquids as that of unstable elastic media.

We study the instantaneous normal mode (INM) spectrum of a simulated soft-sphere liquid at different equilibrium temperatures T We find that the spectrum of eigenvalues [Formula: see text] has a sharp maximum near (but not at) [Formula: see text] and decreases monotonically with [Formula: see text] on both the stable and unstable sides of the spectrum. The spectral shape strongly depends on temperature. It is rather asymmetric at low temperatures (close to the dynamical critical temperature) and becomes symmetric at high temperatures. To explain these findings we present a mean-field theory for [Formula: see text], which is based on a heterogeneous elasticity model, in which the local shear moduli exhibit spatial fluctuations, including negative values. We find good agreement between the simulation data and the model calculations, done with the help of the self-consistent Born approximation (SCBA), when we take the variance of the fluctuations to be proportional to the temperature T More importantly, we find an empirical correlation of the positions of the maxima of [Formula: see text] with the low-frequency exponent of the density of the vibrational modes of the glasses obtained by quenching to [Formula: see text] from the temperature T We discuss the present findings in connection to the liquid to glass transformation and its precursor phenomena.

Comment on "Explaining the specific heat of liquids based on instantaneous normal modes".

In a recent paper [Phys. Rev. E 104, 014103 (2021)10.1103/PhysRevE.104.014103] Baggioli and Zaccone formulate a theoretical description of the specific heat of liquids by using Debye's expression for the specific heat of solids and inserting a density of states which they claim to represent the instantaneous-normal-mode (INM) spectrum of a liquid. However, the quantum-mechanical procedure of Debye cannot be used for the relaxational excitations of a classical liquid. Furthermore, the authors' formula for the INM spectrum does not represent the known INM spectra of simple liquids, and the derivation of this formula from their model equation of motion is mathematically in error. These and a number of other inconsistencies render their work not very helpful for studying the specific heat of liquids.

Pressure-induced effects in the spectra of collective excitations in pure liquid metals.

Collective dynamics of metallic melts at high pressures is one of the open issues of condensed matter physics. By means of ab initio molecular dynamics simulations, we examine features of dispersions of collective excitations through transverse current spectral functions, as a function of pressure. Typical metallic melts, such as Li and Na monovalent metals as well as Al, Pb and In polyvalent metals are considered. We firmly establish the emergence of a second branch of high-frequency transverse modes with pressure in these metals, that we associate with the pronounced high-frequency shoulder in the vibrational density of states. Similar correlation also exist with the low frequency modes. The origin of the pressure-induced evolution of transverse excitations in liquid metals is discussed.

Pressure evolution of transverse collective excitations in liquid Al along the melting line.

Evolution of structure and dynamics of liquid Al with pressure along the melting line up to 300 GPa has been studied by means of ab initio molecular dynamics simulations. An analysis of structural properties shows that liquid Al undergoes uniform compression with pressure associated with a competition of the existing icosahedral local order with bcc ordering above 200 GPa. Dispersion of collective excitations indicates the presence of two branches of transverse nonpropagative modes in the second pseudo-Brillouin zone. Under pressure, the second high-frequency branch manifests as the second peak position in transverse current correlation functions, while, for ambient pressure, it corresponds to a smeared-out high-frequency shoulder. We report a correspondence of the peak locations in vibrational density of states with these two transverse collective excitations as well as their linear evolution with density.

Low viscosity of the Earth's inner core.

The Earth's solid inner core is a highly attenuating medium. It consists mainly of iron. The high attenuation of sound wave propagation in the inner core is at odds with the widely accepted paradigm of hexagonal close-packed phase stability under inner core conditions, because sound waves propagate through the hexagonal iron without energy dissipation. Here we show by first-principles molecular dynamics that the body-centered cubic phase of iron, recently demonstrated to be thermodynamically stable under the inner core conditions, is considerably less elastic than the hexagonal phase. Being a crystalline phase, the body-centered cubic phase of iron possesses the viscosity close to that of a liquid iron. The high attenuation of sound in the inner core is due to the unique diffusion characteristic of the body-centered cubic phase. The low viscosity of iron in the inner core enables the convection and resolves a number of controversies.

Simple-to-Complex Transformation in Liquid Rubidium.

We investigated the atomic structure of liquid Rb along an isothermal path at 573 K, up to 23 GPa, by X-ray diffraction measurements. By raising the pressure, we observed a liquid-liquid transformation from a simple metallic liquid to a complex one. The transition occurs at 7.5 ± 1 GPa which is slightly above the first maximum of the T-P melting line. This transformation is traced back to the density-induced hybridization of highest electronic orbitals leading to the accumulation of valence electrons between Rb atoms and to the formation of interstitial atomic shells, a behavior that Rb shares with Cs and is likely to be common to all alkali metals.

Non-hydrodynamic transverse collective excitations in hard-sphere fluids.

Collective excitations in hard-sphere fluids were studied in a wide range of wave numbers and packing fractions η by means of molecular dynamics simulations. We report the observation of non-hydrodynamic transverse excitations for packing fractions η≥0.395 in the shape of transverse current spectral functions. Dispersion of longitudinal excitations in the whole range of packing fractions shows a negative deviation from the linear hydrodynamic law with increasing wave numbers even for dense hard-sphere fluids where the transverse excitations were observed. These results do not support a recent proposal within the "Frenkel line" approach that the positive sound dispersion in liquids is defined by transverse excitations. We report calculations of the cutoff "Frenkel frequencies" for transverse excitations in hard-sphere fluids and discuss their consistency with the estimated dispersions of shear waves.

A search for manifestation of two types of collective excitations in dynamic structure of a liquid metal: Ab initio study of collective excitations in liquid Na.

Using a combination of ab initio molecular dynamics and several fit models for dynamic structure of liquid metals, we explore an issue of possible manifestation of non-acoustic collective excitations in longitudinal dynamics having liquid Na as a case study. A model with two damped harmonic oscillators (DHOs) in time domain is used for analysis of the density-density time correlation functions. Another similar model with two propagating contributions and three lowest exact sum rules is considered, as well as an extended hydrodynamic model known as thermo-viscoelastic one which permits two types of propagating modes outside the hydrodynamic region to be used for comparison with ab initio obtained time correlation functions and calculations of dispersions of collective excitations. Our results do not support recent suggestions that, even in simple liquid metals, non-hydrodynamics transverse excitations contribute to the longitudinal collective dynamics and can be detected as a DHO-like spectral shape at their transverse frequency. We found that the thermo-viscoelastic dynamic model permits perfect description of the density-density and current-current time correlation functions of the liquid Na in a wide range of wave numbers, which implies that the origin of the non-hydrodynamic collective excitations contributing to longitudinal dynamics can be short-wavelength heat waves.

Efficient analytical expressions for dynamic structure of liquid binary alloys: K-Cs as a case study.

A fitting scheme for analysis of collective dynamics in liquid binary alloys is proposed. It is based on explicit treatment of contributions from three relaxing modes and two types of propagating modes to the partial density-density time correlation functions and corresponding partial dynamic structure factors. Exact sum rules for each partial dynamic structure factor were taken into account. The proposed fitting scheme was applied to the liquid equimolar K-Cs alloy. Analysis of simulation-derived partial time correlation functions as well as of their corresponding Bhatia-Thornton 'number-concentration' combinations allowed dispersion and damping of the two branches of collective excitations and the behaviour of relaxing modes in a wide range of wave numbers to be obtained. A comparison with the inelastic neutron-scattering intensities for the liquid K-Cs alloy was performed.

Synthesis of heavy hydrocarbons at the core-mantle boundary.

The synthesis of complex organic molecules with C-C bonds is possible under conditions of reduced activity of oxygen. We have found performing ab initio molecular dynamics simulations of the C-O-H-Fe system that such conditions exist at the core-mantle boundary (CMB). H2O and CO2 delivered to the CMB by subducting slabs provide a source for hydrogen and carbon. The mixture of H2O and CO2 subjected to high pressure (130 GPa) and temperature (4000 to 4500 K) does not lead to synthesis of complex hydrocarbons. However, when Fe is added to the system, C-C bonds emerge. It means that oil might be a more abundant mineral than previously thought.

Pressure-induced emergence of unusually high-frequency transverse excitations in a liquid alkali metal: Evidence of two types of collective excitations contributing to the transverse dynamics at high pressures.

Unlike phonons in crystals, the collective excitations in liquids cannot be treated as propagation of harmonic displacements of atoms around stable local energy minima. The viscoelasticity of liquids, reflected in transition from the adiabatic to elastic high-frequency speed of sound and in absence of the long-wavelength transverse excitations, results in dispersions of longitudinal (L) and transverse (T) collective excitations essentially different from the typical phonon ones. Practically, nothing is known about the effect of high pressure on the dispersion of collective excitations in liquids, which causes strong changes in liquid structure. Here dispersions of L and T collective excitations in liquid Li in the range of pressures up to 186 GPa were studied by ab initio simulations. Two methodologies for dispersion calculations were used: direct estimation from the peak positions of the L/T current spectral functions and simulation-based calculations of wavenumber-dependent collective eigenmodes. It is found that at ambient pressure, the longitudinal and transverse dynamics are well separated, while at high pressures, the transverse current spectral functions, density of vibrational states, and dispersions of collective excitations yield evidence of two types of propagating modes that contribute strongly to transverse dynamics. Emergence of the unusually high-frequency transverse modes gives evidence of the breakdown of a regular viscoelastic theory of transverse dynamics, which is based on coupling of a single transverse propagating mode with shear relaxation. The explanation of the observed high-frequency shift above the viscoelastic value is given by the presence of another branch of collective excitations. With the pressure increasing, coupling between the two types of collective excitations is rationalized within a proposed extended viscoelastic model of transverse dynamics.

Comment on "Dynamic transition of supercritical hydrogen: Defining the boundary between interior and atmosphere in gas giants".

Trachenko et al. [Phys. Rev. E 89, 032126 (2014)] have argued for the existence of a "Frenkel line" in fluid hydrogen that separates "rigid" and "nonrigid" regimes in a supercritical region. On that basis, they proposed a criterion for locating the boundary between the interior and the atmosphere for gas giants. This Comment shows that the two methods they use to locate the transition between the rigid and nonrigid states are both questionable, which casts doubt on the claims in the paper.

Collective excitations in 2D hard-disc fluid.

Collective dynamics of a two-dimensional (2D) hard-disc fluid was studied by molecular dynamics simulations in the range of packing fractions that covers states up to the freezing. Some striking features concerning collective excitations in this system were observed. In particular, the short-wavelength shear waves while being absent at low packing fractions were observed in the range of high packing fractions, just before the freezing transition in a 2D hard-disc fluid. In contrast, the so-called "positive sound dispersion" typically observed in dense Lennard-Jones-like fluids, was not detected for the 2D hard-disc fluid. The ratio of specific heats in the 2D hard-disc fluid shows a monotonic increase with density approaching the freezing, resembling in this way the similar behavior in the vicinity of the Widom line in the case of supercritical fluids.