Theoretical estimates of the logarithmic phonon spectral moment for monatomic liquids

We calculate the logarithmic moment of the phonon frequency spectrum at a single density for 29 monatomic liquids using two methods, both suggested by Wallace's theory of liquid dynamics: The first method relies on liquid entropy data, the second on neutron scattering data in the crystal phase. This theory predicts that for a class of elements called ``normal melters,'' including all 29 of these materials, the two estimates should closely match, and we find that they agree to within a few percent. We also perform the same calculations for four ``anomalous melters,'' for which we expect the two estimates to differ markedly; we find that they disagree by factors almost up to three. From our results we conclude that the liquid entropy estimates of the logarithmic moment, applicable both to normal and anomalous melters, are trustworthy to a few percent, which makes them reliable for use in estimates of various liquid transport coefficients.Comment: 13 pages, 1 figure. Published versio

A Mean Atom Trajectory Model for Monatomic Liquids

A recent description of the motion of atoms in a classical monatomic system in liquid and supercooled liquid states divides the motion into two parts: oscillations within a given many-particle potential valley, and transit motion which carries the system from one many-particle valley to another. Building on this picture, we construct a model for the trajectory of an average atom in the system. The trajectory consists of oscillations at the normal-mode distribution of frequencies, representing motion within a fluctuating single-particle well, interspersed with position- and velocity-conserving transits to similar adjacent wells. For the supercooled liquid in nondiffusing states, the model gives velocity and displacement autocorrelation functions which exactly match those found in the many-particle harmonic approximation, and which are known to agree almost precisely with molecular dynamics (MD) simulations of liquid Na. At higher temperatures, by allowing transits to proceed at a temperature-dependent rate, the model gives velocity autocorrelation functions which are also in remarkably good agreement with MD simulations of Na at up to three times its melting temperature. Two independent processes in the model relax velocity autocorrelations: (a) dephasing due to the presence of many frequency components, which operates at all temperatures but which produces zero diffusion, and (b) the transit process, which increases with increasing temperature and which produces diffusion.Comment: 22 pages, 7 figure

Temperature dependence of dynamic slowing down in monatomic liquids from V-T theory

For an MD system representing a monatomic liquid, the distribution of $3N$-dimensional potential energy structures consists of two classes, random and symmetric. This distribution is shown and discussed for liquid Na. The random class constitutes the liquid phase domain. In V-T theory, the liquid atomic motion consists of prescribed vibrations in a random valley, plus parameterized transit motions between valleys. The theory has been strongly verified at 395.1K, a bit above melting. Our goal here is to test this theory for its ability to explain the temperature ($T$) dependence of the mean square displacement (MSD) at $T\leq395.1$K. The test results are positive at 204.6K, where the time evolution equations, controlled by a transit rate decreasing with $T$, accurately account for MD data for the MSD. To test at significantly lower $T$, where the MD system does not remain in the liquid phase, the theoretical liquid MSD is calibrated for $T\leq$ 204.6K. The Kob-Andersen (K-A) dynamic slowing down graph is shown for liquid Na at $T\leq395.1$K. The following observations are discussed in terms of the atomic motion. (a) The agreement between pure vibrational motion and MD data for time correlation functions in the vibrational interval is so far highly accurate. (b) The "bump" ahead of the plateau in the MSD at low $T$ is attributed to the vibrational excess. (c) The K-A graph from theory for liquid Na, and the same graphs from MD data for a liquid Lennard-Jones binary mixture (BMLJ) and liquid silica, are identical in the ballistic period and in the purely diffusive time interval. (d) The glass transition proceeds in the symmetric manifold. These and other discussions confirm that V-T theory can explain the $T$ dependence observed in K-A graphs.Comment: 7 figure

An improved model for the transit entropy of monatomic liquids

In the original formulation of vibration-transit (V-T) theory for monatomic liquid dynamics, the transit contribution to entropy was taken to be a universal constant, calibrated to the constant-volume entropy of melting. This model suffers two deficiencies: (a) it does not account for experimental entropy differences of 2% among elemental liquids, and (b) it implies a value of zero for the transit contribution to internal energy. The purpose of this paper is to correct these deficiencies. To this end, the V-T equation for entropy is fitted to an overall accuracy of 0.1% to the available experimental high temperature entropy data for elemental liquids. The theory contains two nuclear motion contributions: (a) the dominant vibrational contribution S_{vib}(T/\theta_0), where T is temperature and \theta_0 is the vibrational characteristic temperature, and (b) the transit contribution S_{tr}(T/\theta_{tr}), where \theta_{tr} is a scaling temperature for each liquid. The appearance of a common functional form of S_{tr} for all the liquids studied is a property of the experimental data, when analyzed via the V-T formula. The resulting S_{tr} implies the correct transit contribution to internal energy. The theoretical entropy of melting is derived, in a single formula applying to normal and anomalous melting alike. An ab initio calculation of \theta_0, based on density functional theory, is reported for liquid Na and Cu. Comparison of these calculations with the above analysis of experimental entropy data provides verification of V-T theory. In view of the present results, techniques currently being applied in ab initio simulations of liquid properties can be employed to advantage in the further testing and development of V-T theory.Comment: 7 pages, 1 figure, REVTeX, added 1 reference, corrected typos to match published versio

Velocity Autocorrelation and Harmonic Motion in Supercooled Nondiffusing Monatomic Liquids

Studies of the many-body potential surface of liquid sodium have shown that it consists of a great many intersecting nearly harmonic valleys, a large fraction of which have the same frequency spectra. This suggests that a sufficiently supercooled state of this system, remaining in a single valley, would execute nearly harmonic motion. To test this hypothesis, we have compared $\hat{Z}(t)$, the normalized velocity autocorrelation function, calculated from MD simulations to that predicted under the assumption of purely harmonic motion. We find nearly perfect agreement between the two, suggesting that the harmonic approximation captures all essential features of the motion.Comment: 12 pages, 2 figure

Application of Vibration-Transit Theory of Liquid Dynamics to the Brillouin Peak Dispersion Curve

The Brillouin peak appears in the dynamic structure factor S(q,w), and the dispersion curve is the Brillouin peak frequency as function of q. The theoretical function underlying S(q,w) is the density autocorrelation function F(q,t). A broadly successful description of time correlation functions is provided by mode coupling theory, which expresses F(q,t) in terms of processes through which the density fluctuations decay. In contrast, vibration-transit (V-T) theory is a Hamiltonian formulation of monatomic liquid dynamics in which the motion consists of vibrations within a many-particle random valley, interspersed with nearly instantaneous transits between such valleys. Here, V-T theory is applied to S(q,w). The theoretical vibrational contribution to S(q,w) is the sum of independent scattering cross sections from the normal vibrational modes, and contains no explicit reference to decay processes. For a theoretical model of liquid Na, we show that the vibrational contribution with no adjustable parameters gives an excellent account of the Brillouin peak dispersion curve, as compared to MD calculations and to experimental data

Atomic Motion from the Mean Square Displacement in a Monatomic Liquid

V-T theory is constructed in the many-body Hamiltonian formulation, and differs at the foundation from current liquid dynamics theories. In V-T theory the liquid atomic motion consists of two contributions, normal mode vibrations in a single representative potential energy valley, and transits, which carry the system across boundaries between valleys. The mean square displacement time correlation function (the MSD) is a direct measure of the atomic motion , and our goal is to determine if the V-T formalism can produce a physically sensible account of this motion. We employ molecular dynamics (MD) data for a system representing liquid Na, and find the motion evolves in three successive time intervals: On the first "vibrational" interval, the vibrational motion alone gives a highly accurate account of the MD data; on the second "crossover" interval, the vibrational MSD saturates to a constant while the transit motion builds up from zero; on the third "random walk" interval, the transit motion produces a purely diffusive random walk of the vibrational equilibrium positions. This motional evolution agrees with, and adds refinement to, the MSD atomic motion as described by current liquid dynamics theories.Comment: 5 pages, 5 figure

Application of vibration-transit theory to distinct dynamic response for a monatomic liquid

We examine the distinct part of the density autocorrelation function Fd(q,t), also called the intermediate scattering function, from the point of view of the vibration-transit (V-T) theory of monatomic liquid dynamics. A similar study has been reported for the self part, and we study the self and distinct parts separately because their damping processes are not simply related. We begin with the perfect vibrational system, which provides precise definitions of the liquid correlations, and provides the vibrational approximation Fdvib(q,t) at all q and t. Two independent liquid correlations are defined, motional and structural, and these are decorrelated sequentially, with a crossover time tc(q). This is done by two independent decorrelation processes: the first, vibrational dephasing, is naturally present in Fdvib(q,t) and operates to damp the motional correlation; the second, transit-induced decorrelation, is invoked to enhance the damping of motional correlation, and then to damp the structural correlation. A microscopic model is made for the "transit drift", the averaged transit motion that damps motional correlation on 0 < t < tc(q). Following the previously developed self-decorrelation theory, a microscopic model is also made for the "transit random walk," which damps the structural correlation on t > tc(q). The complete model incorporates a property common to both self and distinct decorrelation: simple exponential decay following a delay period, where the delay is tc(q, the time required for the random walk to emerge from the drift. Our final result is an accurate expression for Fd(q,t) for all q through the first peak in Sd(q). The theory is calibrated and tested using molecular dynamics (MD) calculations for liquid Na at 395K; however, the theory itself does not depend on MD, and we consider other means for calibrating it.Comment: 12 pages, 10 figure

Time correlation functions in Vibration-Transit theory of liquid dynamics

Within the framework of V-T theory of monatomic liquid dynamics, an exact equation is derived for a general equilibrium time correlation function. The purely vibrational contribution to such a function expresses the system's motion in one extended harmonic random valley. This contribution is analytically tractable and has no adjustable parameters. While this contribution alone dominates the thermodynamic properties, both vibrations and transits will make important contributions to time correlation functions. By way of example, the V-T formulation of time correlation functions is applied to the dynamic structure factor S(q,w). The vibrational contribution alone is shown to be in near perfect agreement with low-temperature molecular dynamics simulations, and a model simulating the transit contribution with three adjustable parameters achieves equally good agreement with molecular dynamics results in the liquid regime. The theory indicates that transits will broaden without shifting the Rayleigh and Brillouin peaks in S(q,w), and this behavior is confirmed by the MD calculations. We find the vibrational contribution alone gives the location and much of the width of the liquid-state Brillouin peak. We also discuss this approach to liquid dynamics compared with potential energy landscape formalisms and mode coupling theory, drawing attention to the distinctive features of our approach and to some potential energy landscape results which support our picture of the liquid state

Thermal electronic excitations in liquid metals

Thermal electronic excitations in metal crystals are calculated by starting with a reference structure for the nuclei: the crystal structure of the appropriate phase. Here we explain the corresponding theory for metal liquids, starting with an appropriate reference structure for a liquid. We explain the significance of these structures, and we briefly review how to find them and calculate their properties. Then we examine the electronic densities of states for liquid structures of Na, Al, and Cu, comparing them to their crystal forms. Next we explain how to calculate the dominant electronic thermal excitation term, considering issues of accuracy that do not arise in the crystal theory. Finally we briefly discuss the contribution from the interaction between excited electrons and moving nuclei.Comment: Minor corrections to references and PACS number