State dependent particle dynamics in liquid alkali metals

Theory of melting lines

Our understanding of the three basic states of matter (solids, liquids, and gases) is based on temperature and pressure phase diagrams with three phase transition lines: solid-gas, liquid-gas, and solid-liquid lines. There are analytical expressions P(T) for the first two lines derived on a purely general-theoretical thermodynamic basis. In contrast, there exists no similar function for the third, melting, line (ML). Here, we develop a general two-phase theory of MLs and their analytical form. This theory predicts the parabolic form of the MLs for normal melting, relates the MLs to thermal and elastic properties of liquid and solid phases, and quantitatively agrees with experimental MLs in different system types. We show that the parameters of the ML parabola are governed by fundamental physical constants. In this sense, parabolic MLs possess universality across different systems.

Viscosity and diffusion in life processes and tuning of fundamental constants

Viewed as one of the grandest questions in modern science, understanding fundamental physical constants has been discussed in high-energy particle physics, astronomy and cosmology. Here, I review how condensed matter and liquid physics gives new insights into fundamental constants and their tuning. This is based on two observations: first, cellular life and the existence of observers depend on viscosity and diffusion. Second, the lower bound on viscosity and upper bound on diffusion are set by fundamental constants, and I briefly review this result and related recent developments in liquid physics. I will subsequently show that bounds on viscosity, diffusion and the newly introduced fundamental velocity gradient in a biochemical machine can all be varied while keeping the fine-structure constant and the proton-to-electron mass ratio intact. This implies that it is possible to produce heavy elements in stars but have a viscous planet where all liquids have very high viscosity (for example that of tar or higher) and where life may not exist. Knowing the range of bio-friendly viscosity and diffusion, we will be able to calculate the range of fundamental constants which favour cellular life and observers and compare this tuning with that discussed in high-energy physics previously. This invites an inter-disciplinary research between condensed matter physics and life sciences, and I formulate several questions that life science can address. I finish with a conjecture of multiple tuning and an evolutionary mechanism.

Fast dynamics and high effective dimensionality of liquid fluidity

Fluidity, the ability of liquids to flow, is the key property distinguishing liquids from solids. This fluidity is set by the mobile transit atoms moving from one quasi-equilibrium point to the next. The nature of this transit motion is unknown. Here, we show that flow-enabling transits form a dynamically distinct sub-ensemble where atoms move on average faster than the overall system, with a manifestly non-Maxwellian velocity distribution. This is in contrast to solids and gases where no distinction of different ensembles can be made and where the distribution is always Maxwellian. The non-Maxwellian distribution is described by an exponent [Formula: see text] corresponding to high dimensionality of space. This is generally similar to extra synthetic dimensions in topological quantum matter, albeit higher dimensionality in liquids is not integer but is fractional. The dimensionality is close to 4 at melting and exceeds 4 at high temperature. [Formula: see text] has a maximum as a function of temperature and pressure in liquid and supercritical states, returning to its Maxwell value in the solid and gas states.

Glass transition as a topological phase transition

The glass transition is described as a phase transition in the system of topologically protected excitations in matter structure. The critical behavior of the system is considered in both static and dynamic cases. It is shown that the proposed model reproduces most of the characteristic thermodynamic and kinetic properties of glass transition: the Vogel-Fulcher-Tammann law, the behavior of susceptibility and nonlinear susceptibilities, and heat capacity behavior as well as the appearance of a boson peak in the frequency dependence of the dynamic structure factor near the glass transition temperature.

Universal Effect of Excitation Dispersion on the Heat Capacity and Gapped States in Fluids

The change in dispersion of high-frequency excitations in fluids, from an oscillating solidlike to a monotonic gaslike one, is shown for the first time to affect thermal behavior of heat capacity and the q-gap width in reciprocal space. With in silico study of liquified noble gases, liquid iron, liquid mercury, and model fluids, we established universal bilinear dependence of heat capacity on q-gap width, whereas the crossover precisely corresponds to the change in the excitation spectra. The results open novel prospects for studies of various fluids, from simple to molecular liquids and melts.

Sodium ion self-diffusion in molten NaBr probed over different length scales

The single-particle dynamics of sodium ions in molten sodium bromide has been investigated with quasielastic neutron scattering. A detailed and rather extensive data analysis procedure allowed determination of the pure sodium ion dynamics with increasing wave vector. Two different evaluation procedures agree perfectly on the resulting diffusion coefficient of sodium ions on long distances. A simple kinetic theory based on binary collisions of hard spheres is not able to reproduce the sodium diffusion coefficient. The derived reduced linewidth from modeling with a Lorentzian spectral function decreases with increasing wave vector towards the first structure factor maximum. That deviation from the hydrodynamic behavior signals the hindrance of the microscopic diffusion process due to the so-called cage effect when microscopic length scales are probed in a dense fluid. The observed quadratic wave-number-dependent decrease might be evidence for a coupling to density fluctuations as the source of the changes in the diffusion process. The results indicate that in the molten salt NaBr near the melting point the self-diffusion process might be governed by similar processes as already observed in dense metallic liquids.

The nature of collective excitations and their crossover at extreme supercritical conditions

Physical properties of an interacting system are governed by collective excitations, but their nature at extreme supercritical conditions is unknown. Here, we present direct evidence for propagating solid-like longitudinal phonon-like excitations with wavelengths extending to interatomic separations deep in the supercritical state at temperatures up to 3,300 times the critical temperature. We observe that the crossover of dispersion curves develops at k points reducing with temperature. We interpret this effect as the crossover from the collective phonon to the collisional mean-free path regime of particle dynamics and find that the crossover points are close to both the inverse of the shortest available wavelength in the system and to the particle mean free path inferred from experiments and theory. Notably, both the shortest wavelength and mean free path scale with temperature with the same power law, lending further support to our findings.

Stokes-Einstein relation of the liquid metal rubidium and its relationship to changes in the microscopic dynamics with increasing temperature

For liquid rubidium the Stokes-Einstein (SE) relation is well fulfilled near the melting point with an effective hydrodynamic diameter, which agrees well with a value from structural investigations. A wealth of thermodynamic and microscopic data exists for a wide range of temperatures for liquid rubidium and hence it represents a good test bed to challenge the SE relation with rising temperature from an experimental point of view. We performed classical molecular dynamics simulations to complement the existing experimental data using a pseudopotential, which describes perfectly the structure and dynamics of liquid rubidium. The derived SE relation from combining experimental shear viscosity data with simulated diffusion coefficients reveals a weak violation at about 1.3T_{melting}≈400 K. The microscopic relaxation dynamics on nearest neighbor distances from neutron spectroscopy demonstrate distinct changes in the amplitude with rising temperature. The derived average relaxation time for density fluctuations on this length scale shows a non-Arrhenius behavior, with a slope change around 1.5T_{melting}≈450 K. Combining the simulated macroscopic self-diffusion coefficient with that microscopic average relaxation time, a distinct violation of the SE relation in the same temperature range can be demonstrated. One can conclude that the changes in the collective dynamics, a mirror of the correlated movements of the particles, are at the origin for the violation of the SE relation. The changes in the dynamics can be understood as a transition from a more viscous liquid metal to a more fluid-like liquid above the crossover temperature range of 1.3-1.5 T_{melting}. The decay of the amplitude of density fluctuations in liquid aluminium, lead, and rubidium demonstrates a remarkable agreement and points to a universal thermal crossover in the dynamics of liquid metals.

Thermodynamics at Solid-Liquid Interfaces

The variation of the liquid properties in the vicinity of a solid surface complicates the description of heat transfer along solid-liquid interfaces. Using Molecular Dynamics simulations, this investigation aims to understand how the material properties, particularly the strength of the solid-liquid interaction, affect the thermal conductivity of the liquid at the interface. The molecular model consists of liquid argon confined by two parallel, smooth, solid walls, separated by a distance of 6.58 σ. We find that the component of the thermal conductivity parallel to the surface increases with the affinity of the solid and liquid.

Self-consistent description of local density dynamics in simple liquids. The case of molten lithium

The dynamic structure factor is the quantity, which can be measured by means of Brillouin light-scattering as well as by means of inelastic scattering of neutrons and x-rays. The spectral (or frequency) moments of the dynamic structure factor define directly the sum rules of the scattering law. The theoretical scheme formulated in this study allows one to describe the dynamics of local density fluctuations in simple liquids and to obtain the expression of the dynamic structure factor in terms of the spectral moments. The theory satisfies all the sum rules, and the obtained expression for the dynamic structure factor yields correct extrapolations into the hydrodynamic limit as well as into the free-particle dynamics limit. We discuss correspondence of this theory with the generalized hydrodynamics and with the viscoelastic models, which are commonly used to analyze the data of inelastic neutron and x-ray scattering in liquids. In particular, we reveal that the postulated condition of the viscoelastic model for the memory function can be directly obtained within the presented theory. The dynamic structure factor of liquid lithium is computed on the basis of the presented theory, and various features of the scattering spectra are evaluated. It is found that the theoretical results are in agreement with inelastic x-ray scattering data.

Lagrangian formulation and symmetrical description of liquid dynamics

Theoretical description of liquids has been primarily based on the hydrodynamic approach and its generalization to the solid-like regime. We show that the same liquid properties can be derived starting from solid-like equations and generalizing them to account for the hydrodynamic flow. Both approaches predict propagating shear waves with the notable gap in k-space. This gives an important symmetry of liquids regarding their description. We subsequently construct a two-field Lagrangian of liquid dynamics where the dissipative hydrodynamic and solid-like terms are treated on equal footing. The Lagrangian predicts two gapped waves propagating in opposite space-time directions. The dissipative and mass terms compete by promoting gaps in k-space and energy, respectively. When bare mass is close to the field hopping frequency, both gaps close and the dissipative term annihilates the bare mass.

Crossover between liquidlike and gaslike behavior in CH_{4} at 400 K

We report experimental evidence for a crossover between a liquidlike state and a gaslike state in fluid methane (CH_{4}). This crossover is observed in all of our experiments, up to a temperature of 397 K, 2.1 times the critical temperature of methane. The crossover has been characterized with both Raman spectroscopy and x-ray diffraction in a number of separate experiments, and confirmed to be reversible. We associate this crossover with the Frenkel line-a recently hypothesized crossover in dynamic properties of fluids extending to arbitrarily high pressure and temperature, dividing the phase diagram into separate regions where the fluid possesses liquidlike and gaslike properties. On the liquidlike side the Raman-active vibration increases in frequency linearly as pressure is increased, as expected due to the repulsive interaction between adjacent molecules. On the gaslike side this competes with the attractive van der Waals potential leading the vibration frequency to decrease as pressure is increased.

Emergence and Evolution of the k Gap in Spectra of Liquid and Supercritical States

Fundamental understanding of strongly interacting systems necessarily involves collective modes, but their nature and evolution is not generally understood in dynamically disordered and strongly interacting systems such as liquids and supercritical fluids. We report the results of extensive molecular dynamics simulations and provide direct evidence that liquids develop a gap in a solidlike transverse spectrum in the reciprocal space, with no propagating modes between zero and a threshold value. In addition to the liquid state, this result importantly applies to the supercritical state of matter. We show that the emerging gap increases with the inverse of liquid relaxation time and discuss how the gap affects properties of liquid and supercritical states.

Direct links between dynamical, thermodynamic, and structural properties of liquids: Modeling results

We develop an approach to liquid thermodynamics based on collective modes. We perform extensive molecular-dynamics simulations of noble, molecular, and metallic liquids, and we provide direct evidence that liquid energy and specific heat are well-described by the temperature dependence of the Frenkel (hopping) frequency. The agreement between predicted and calculated thermodynamic properties is seen in the notably wide range of temperature spanning tens of thousands of Kelvin. The range includes both subcritical liquids and supercritical fluids. We discuss the structural crossover and interrelationships between the structure, dynamics, and thermodynamics of liquids and supercritical fluids.

Crossover of collective modes and positive sound dispersion in supercritical state

Supercritical state has been viewed as an intermediate state between gases and liquids with largely unknown physical properties. Here, we address the important ability of supercritical fluids to sustain collective excitations. We directly study propagating modes on the basis of correlation functions calculated in molecular dynamics simulations and find that the supercritical system sustains propagating solid-like transverse modes below the Frenkel line but not above where there is one longitudinal mode only. Important thermodynamic implications of this finding are discussed. We directly detect positive sound dispersion (PSD) below the Frenkel line where transverse modes are operative and quantitatively explain its magnitude on the basis of transverse and longitudinal velocities. PSD disappears above the Frenkel line which therefore demarcates the supercritical phase diagram into two areas where PSD does and does not operate.

De Gennes Narrowing and Hard-Sphere Approach

The energy width Δω of the quasielastic coherent dynamic structure factor S(Q, ω) for a simple liquid exhibits the oscillating dependence on wavenumber Q with the sharp minimum at Qmax corresponding to the maximum of the structure factor S(Q). The only known expression for Δω(Q) was derived for a dense hard-sphere (HS) fluid (Cohen et al., Phys. Rev. Lett. 1987, 59, 2872). Though this expression has been frequently used for the analysis of the experimental data obtained for liquid metals, until now, it has never been tested against a true HS fluid. A test performed by means of HS molecular dynamic simulations reveals a considerable discrepancy between the simulations results and the examined model. The main output of the analysis is the finding that the ΔωHS(Q) behavior is defined in terms of the average cage size, ⟨Lc⟩, rather than of the HS diameter, σHS. The simulated ΔωHS(Q) has been compared with the results for the soft-spherical potential. The microscopic dynamics of the soft-sphere fluid shows significant difference in comparison to the HS system. Nevertheless, the diffusive mobility of soft spheres can be characterized within the HS approximation using an effective diameter, σeff, and this parameter can be found from Δω(Q) at Q ≈ Qmax. A similar result has been obtained for the neutron scattering data measured for liquid Rb.

Br diffusion in molten NaBr explored by coherent quasielastic neutron scattering

Molten sodium bromide has been investigated by quasielastic neutron scattering focusing on the wave vector range around the first structure factor peak. The linewidth of the scattering function shows a narrowing around the wave number of the structure factor peak, known as deGennes narrowing. In a monatomic system, this narrowing or in the time domain slowing down, has been related to a self-diffusion process of the caged particle. Here we show that this methodology can be applied to the molten alkali halide NaBr. The incoherent scattering from the sodium ions at small wave vectors provides the self-diffusion coefficient of sodium and the dynamics of bromine ions can be studied at wave numbers around the structure factor peak. With input from molecular dynamics simulations on the partial structure factors, diffusion coefficients of the bromine ions can be obtained. These experimentally derived diffusion coefficients are in good agreement with molecular dynamics simulation results. This methodology to extract self-diffusion coefficients from coherent quasielastic neutron scattering is applicable to binary fluids in general when one particle dominates the scattering response at the structure factor maximum.

Anomalous vacuum energy and stability of a quantum liquid

We show that the vacuum (zero-point) energy of a low-temperature quantum liquid is a variable property which changes with the state of the system, in notable contrast to the static vacuum energy in solids commonly considered. We further show that this energy is inherently anomalous: it decreases with temperature and gives a negative contribution to a system's heat capacity. This effect operates in an equilibrium and macroscopic system, in marked contrast to small or out-of-equilibrium configurations discussed previously. We find that the negative contribution is over-compensated by the positive term from the excitation of longitudinal fluctuations and demonstrate how the overall positive heat capacity is related to the stability of a condensed phase at the microscopic level.

Collective modes and thermodynamics of the liquid state

Strongly interacting, dynamically disordered and with no small parameter, liquids took a theoretical status between gases and solids with the historical tradition of hydrodynamic description as the starting point. We review different approaches to liquids as well as recent experimental and theoretical work, and propose that liquids do not need classifying in terms of their proximity to gases and solids or any categorizing for that matter. Instead, they are a unique system in their own class with a notably mixed dynamical state in contrast to pure dynamical states of solids and gases. We start with explaining how the first-principles approach to liquids is an intractable, exponentially complex problem of coupled non-linear oscillators with bifurcations. This is followed by a reduction of the problem based on liquid relaxation time τ representing non-perturbative treatment of strong interactions. On the basis of τ, solid-like high-frequency modes are predicted and we review related recent experiments. We demonstrate how the propagation of these modes can be derived by generalizing either hydrodynamic or elasticity equations. We comment on the historical trend to approach liquids using hydrodynamics and compare it to an alternative solid-like approach. We subsequently discuss how collective modes evolve with temperature and how this evolution affects liquid energy and heat capacity as well as other properties such as fast sound. Here, our emphasis is on understanding experimental data in real, rather than model, liquids. Highlighting the dominant role of solid-like high-frequency modes for liquid energy and heat capacity, we review a wide range of liquids: subcritical low-viscous liquids, supercritical state with two different dynamical and thermodynamic regimes separated by the Frenkel line, highly-viscous liquids in the glass transformation range and liquid-glass transition. We subsequently discuss the fairly recent area of liquid-liquid phase transitions, the area where the solid-like properties of liquids have become further apparent. We then discuss gas-like and solid-like approaches to quantum liquids and theoretical issues that are similar to the classical case. Finally, we summarize the emergent view of liquids as a unique system with a mixed dynamical state, and list several areas where interesting insights may appear and continue the extraordinary liquid story.

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

We have recently proposed the dynamic transition of molecular hydrogen in gas giants around 10 GPa based on the recent understanding of a supercritical state related to the Frenkel line. In the preceding Comment, Bryk makes several remarks with regard to the Frenkel line and its relationship to the speed of sound. We disagree with this discussion and respond to it in this Reply.

Duality of liquids

Liquids flow, and in this sense are close to gases. At the same time, interactions in liquids are strong as in solids. The combination of these two properties is believed to be the ultimate obstacle to constructing a general theory of liquids. Here, we adopt a new approach: instead of focusing on the problem of strong interactions, we zero in on the relative contributions of vibrational and diffusional motion. We show that liquid energy and specific heat are given, to a very good approximation, by their vibrational contributions as in solids over almost entire range of relaxation time in which liquids exist as such, and demonstrate that this result is consistent with liquid entropy exceeding solid entropy. Our analysis therefore reveals an interesting duality of liquids not hitherto known: they are close to solids from the thermodynamic perspective and to flowing gases. We discuss several implications of this result.

The phonon theory of liquid thermodynamics

Heat capacity of matter is considered to be its most important property because it holds information about system's degrees of freedom as well as the regime in which the system operates, classical or quantum. Heat capacity is well understood in gases and solids but not in the third main state of matter, liquids, and is not discussed in physics textbooks as a result. The perceived difficulty is that interactions in a liquid are both strong and system-specific, implying that the energy strongly depends on the liquid type and that, therefore, liquid energy can not be calculated in general form. Here, we develop a phonon theory of liquids where this problem is avoided. The theory covers both classical and quantum regimes. We demonstrate good agreement of calculated and experimental heat capacity of 21 liquids, including noble, metallic, molecular and hydrogen-bonded network liquids in a wide range of temperature and pressure.

Copper ion liquid-like thermoelectrics

Advanced thermoelectric technology offers a potential for converting waste industrial heat into useful electricity, and an emission-free method for solid state cooling. Worldwide efforts to find materials with thermoelectric figure of merit, zT values significantly above unity, are frequently focused on crystalline semiconductors with low thermal conductivity. Here we report on Cu(2-x)Se, which reaches a zT of 1.5 at 1,000 K, among the highest values for any bulk materials. Whereas the Se atoms in Cu(2-x)Se form a rigid face-centred cubic lattice, providing a crystalline pathway for semiconducting electrons (or more precisely holes), the copper ions are highly disordered around the Se sublattice and are superionic with liquid-like mobility. This extraordinary 'liquid-like' behaviour of copper ions around a crystalline sublattice of Se in Cu(2-x)Se results in an intrinsically very low lattice thermal conductivity which enables high zT in this otherwise simple semiconductor. This unusual combination of properties leads to an ideal thermoelectric material. The results indicate a new strategy and direction for high-efficiency thermoelectric materials by exploring systems where there exists a crystalline sublattice for electronic conduction surrounded by liquid-like ions.

Two liquid states of matter: a dynamic line on a phase diagram

It is generally agreed that the supercritical region of a liquid consists of one single state (supercritical fluid). On the other hand, we show here that liquids in this region exist in two qualitatively different states: "rigid" and "nonrigid" liquids. Rigid to nonrigid transition corresponds to the condition τ≈τ(0), where τ is the liquid relaxation time and τ(0) is the minimal period of transverse quasiharmonic waves. This condition defines a new dynamic crossover line on the phase diagram and corresponds to the loss of shear stiffness of a liquid at all available frequencies and, consequently, to the qualitative change in many important liquid properties. We analyze this line theoretically as well as in real and model fluids and show that the transition corresponds to the disappearance of high-frequency sound, to the disappearance of roton minima, qualitative changes in the temperature dependencies of sound velocity, diffusion, viscous flow, and thermal conductivity, an increase in particle thermal speed to half the speed of sound, and a reduction in the constant volume specific heat to 2k(B) per particle. In contrast to the Widom line that exists near the critical point only, the new dynamic line is universal: It separates two liquid states at arbitrarily high pressure and temperature and exists in systems where liquid-gas transition and the critical point are absent altogether. We propose to call the new dynamic line on the phase diagram "Frenkel line".

Generalized thermodynamic and transport properties. I. Simple liquids

We propose a method by which the generalized transport properties and coefficients at all wavelengths and frequencies can be obtained by inversion of an exact kinetic equation. The necessary data are the density-density, energy-energy, and density-energy time correlation functions, which can be obtained by molecular-dynamics simulation. In addition, also the coupling between viscous stress tensor and energy flux vector can be obtained without approximation. This allows one to check the validity of the Markov assumption in a straightforward way. As a first test case, the theory is applied to liquid argon in two thermodynamic states. For this system, we calculate and discuss generalized thermodynamic (enthalpy, specific heats, and thermal expansion) and transport properties (longitudinal viscosity, thermal conductivity).

Slow Dynamics in Liquid Metals as Seen by QENS

The quasielastic dynamics in liquid metals has been investigated by neutron scattering extensively during the past years. Precise measurements of the self-particle dynamics and the coherent quasielastic response provided conclusive evidence that the relaxation dynamics is governed by at least two processes. These two time scales in the correlation functions appear as two dynamical processes in their associated memory functions. One process shows a fast decay and is related to stochastic binary collisions. The second slow process stems from a non-linear coupling of slow collective modes. These slow density fluctuations arise mainly from the dynamics around the structure factor maximum. A rigorous treatment of these effects can be accomplished by mode coupling theory. A few selective experiments from monatomic metals are presented to demonstrate the influence of slow effects on the dynamics. Experiments and MD-simulations show a surprising good agreement with predictions of mode coupling theory on a quantitative level. The slow decay process appears to be related to structural arrest in the supercooled state and might indicate a link to the solidification process, starting deep in the liquid state. Accurate quasielastic neutron scattering experiments are still and will remain a fundamental pillar for elucidating the complex dynamics in the liquid state of metals.

Introduction to Quasielastic Neutron Scattering

This tutorial introduction has been written for people who are not specialized in neutron scattering or in other scattering methods but who are interested and would like to get an impression and learn about the method of Quasielastic Neutron Scattering (QENS). The theoretical (scattering process) as well as the experimental basics (neutron sources, neutron scattering instruments, experimental periphery) are explained in a generally understandable way, with only the most essential formulas. QENS addresses the stochastic dynamics in condensed matter, and it is pointed out for which problems and for which systems in condensed matter research QENS is a powerful method. Thus sufficient information is provided to enable non-experts to think about their own QENS experiment and to understand related literature in this area of research.

Understanding the problem of glass transition on the basis of elastic waves in a liquid

We propose that the properties of a glass transition can be understood on the basis of elastic waves. Elastic waves originating from atomic jumps in a liquid propagate local expansion due to the anharmonicity of the interatomic potential. This creates dynamic compressive stress, which increases the activation barrier for other events in a liquid. The non-trivial point is that the range of propagation of high-frequency elastic waves, d(el), increases with liquid relaxation time τ. A self-consistent calculation shows that this increase gives the Vogel-Fulcher-Tammann (VFT) law. In the proposed theory, we discuss the origin of two dynamic crossovers in a liquid: (1) the crossover from exponential to non-exponential and from Arrhenius to VFT relaxation at high temperature and (2) the crossover from the VFT to a more Arrhenius-like relaxation at low temperature. The corresponding values of τ at the two crossovers are in quantitative parameter-free agreement with experiments. The origin of the second crossover allows us to reconcile the ongoing controversy surrounding the possible divergence of τ. The crossover to Arrhenius relaxation universally takes place when d(el) reaches system size, thus avoiding divergence and associated theoretical complications such as identifying the nature of the phase transition and the second phase itself. Finally, we discuss the effect of volume on τ and the origin of liquid fragility.