Mean-field model of melting in superheated crystals based on a single experimentally measurable order parameter

Melting is one of the most studied phase transitions important for atomic, molecular, colloidal, and protein systems. However, there is currently no microscopic experimentally accessible criteria that can be used to reliably track a system evolution across the transition, while providing insights into melting nucleation and melting front evolution. To address this, we developed a theoretical mean-field framework with the normalised mean-square displacement between particles in neighbouring Voronoi cells serving as the local order parameter, measurable experimentally. We tested the framework in a number of colloidal and in silico particle-resolved experiments against systems with significantly different (Brownian and Newtonian) dynamic regimes and found that it provides excellent description of system evolution across melting point. This new approach suggests a broad scope for application in diverse areas of science from materials through to biology and beyond. Consequently, the results of this work provide a new guidance for nucleation theory of melting and are of broad interest in condensed matter, chemical physics, physical chemistry, materials science, and soft matter.

V-T theory for the self-intermediate scattering function in a monatomic liquid

In V-T theory the atomic motion is harmonic vibrations in a liquid-specific potential energy valley, plus transits, which move the system rapidly among the multitude of such valleys. In its first application to the self intermediate scattering function (SISF), V-T theory produced an accurate account of molecular dynamics (MD) data at all wave numbers q and time t. Recently, analysis of the mean square displacement (MSD) resolved a crossover behavior that was not observed in the SISF study. Our purpose here is to apply the more accurate MSD calibration to the SISF, and assess the results. We derive and discuss the theoretical equations for vibrational and transit contributions to the SISF. The time evolution is divided into three successive intervals: the vibrational interval when the vibrational contribution alone accurately accounts for the MD data; the crossover when the vibrational contribution saturates and the transit contribution becomes resolved; and the diffusive interval when the transit contribution alone accurately accounts for the MD data. The resulting theoretical error is extremely small at all q and t. V-T theory is compared to mode-coupling theories for the MSD and SISF, and to recent developments in Brownian motion experiments and theory.

A topotactic transition in a liquid crystal compound

The title compound has two crystal phases related by an enantiotropic single-crystal-to-single-crystal transition and a nematic liquid crystalline phase before transition to the isotropic liquid phase.

First-principles calculation of entropy for liquid metals

We demonstrate the accurate calculation of entropies and free energies for a variety of liquid metals using an extension of the two-phase thermodynamic (2PT) model based on a decomposition of the velocity autocorrelation function into gas-like (hard sphere) and solid-like (harmonic) subsystems. The hard sphere model for the gas-like component is shown to give systematically high entropies for liquid metals as a direct result of the unphysical Lorentzian high-frequency tail. Using a memory function framework we derive a generally applicable velocity autocorrelation and frequency spectrum for the diffusive component which recovers the low-frequency (long-time) behavior of the hard sphere model while providing for realistic short-time coherence and high-frequency tails to the spectrum. This approach provides a significant increase in the accuracy of the calculated entropies for liquid metals and is compared to ambient pressure data for liquid sodium, aluminum, gallium, tin, and iron. The use of this method for the determination of melt boundaries is demonstrated with a calculation of the high-pressure bcc melt boundary for sodium. With the significantly improved accuracy available with the memory function treatment for softer interatomic potentials, the 2PT model for entropy calculations should find broader application in high energy density science, warm dense matter, planetary science, geophysics, and material science.

Melting entropy of nanocrystals: an approach from statistical physics

Considering size effect on the equations obtained from statistical mechanical theories for the entropy of crystal and liquid phases, a new model has been developed for the melting entropy of nanocrystals, including the effects of the quasi-harmonic, anharmonic and electronic components of the overall melting entropy. Then with the use of our suggested new proportionality between the melting point and the entropy temperature (θ(0)), the melting entropy of nanocrystals has been obtained in terms of their melting point. Moreover, for the first time, the size-dependency of the electronic component of the overall melting entropy, arising from the change in the electronic ground-state of the nanocrystal upon melting, has been taken into account to calculate the melting entropy of nanocrystals. Through neglecting the effect of the electronic component, the present model can corroborate the previous model for size-dependent melting entropy of crystals represented by Jiang and Shi. The present model has been validated by the available computer simulation results for Ag and V nanoparticles. Moreover, a fairly constant function has been introduced which couples the melting temperature, the entropy temperature and the atomic density of elements to each other.

Single-random-valley approximation in vibration-transit theory of liquid dynamics

The first goal of vibration-transit theory is to be able to calculate from a tractable partition function and without adjustable parameters the thermodynamic properties of the elemental monatomic liquids. The key hypothesis is that the random class of potential energy valleys dominates the statistical mechanics of the liquid at temperatures above melting T approximately greater than Tm and that these valleys are macroscopically uniform in the thermodynamic limit. This allows us to use a single random valley to calculate the vibrational contribution to liquid properties, exactly in the thermodynamic limit, and as an approximation at finite number of particles N . This approximation is tested here for liquid Na with a physically realistic potential based on electronic structure theory. Steepest descent quenches were made from the molecular dynamics equilibrium liquid (N=500) at temperatures from 0.90Tm to 3.31Tm, and six potential parameters were calculated for each structure, namely, the potential energy and five principal moments of the vibrational frequency distribution. The results show temperature-independent means and small standard deviations for all potential parameters, consistent with random valley uniformity at N-->infinity, and with finite- N broadening at N=500. The expected error in the single random valley approximation for Na at N=500 and T approximately greater than Tm is 0.1% for the entropy and 0.5% for the internal energy, negligible in the current development of liquid dynamics theory. In related quench studies of recent years, the common finding of nearly temperature-independent means of structural potential energy properties at T approximately greater than Tm suggests that the single random valley approximation might also apply to systems more complicated than the elemental liquids.

Observation of single transits in supercooled monatomic liquids

A transit is the motion of a system from one many-particle potential energy valley to another. We report the observation of transits in molecular dynamics calculations of supercooled liquid argon and sodium. Each transit is a correlated simultaneous shift in the equilibrium positions of a small local group of particles, as revealed in the fluctuating graphs of the particle coordinates versus time. To the best of our knowledge, this is the first reported direct observation of transit motion in a monatomic liquid in thermal equilibrium. We found transits involving 2-11 particles, having mean shift in equilibrium position on the order of 0.4R(1) in argon and 0.25R(1) in sodium, where R1 is the nearest neighbor distance. The time it takes for a transit to occur is approximately one mean vibrational period, confirming that transits are fast.

Relation between transport and thermodynamic properties in liquid sp-electron metals near freezing

Classical statistical mechanics based on assumed pair potentials leads, for liquid metals, to an approximate relation between shear viscosity eta, surface tension sigma, and thermal velocity vT defined as (kBT/M)(1/2), with M the ionic mass. Theory predicts for the dimensionless grouping sigma/etav(T) evaluated at the melting temperature Tm a single value 15 / 16; liquid sp-electron metals exhibit, however, a scatter from around 0.7 to 2.3. Therefore, an alternative grouping sigma/etav(s), with v(s) the velocity of sound, is considered here in detail, first using experimental data and second using both theoretical and semiempirical arguments. The scatter of sigma/etav(s) at Tm is less than for the earlier grouping, and also insight can be gained as to various physical factors determining sigma/etav(s). In essence, this quantity is proportional to the product of two factors, both dimensionless, namely, the surface thickness L measured in units of the mean interionic separation, and the square root of the energy Mv(2)s, measured in units of the thermal energy kBTm. Theoretical estimates are made of both of these factors, in fair accord with the experimental data.

Compression dependence of the melting of elements

In normal melting there is no significant change in the electronic structure, while in anomalous melting the crystal and liquid have different electronic structures. For those elements that melt normally at zero pressure, the pressure derivative of the melting temperature is shown to follow the normal melting rule. For Ar, Na, K and Hg, the normal melting properties continue to hold to high compression, and in Hg it appears that the strong higher-order correlations in the liquid are gradually weakened by compression. The normal melting process is described by two sets of nearly independent parameters: universal statistical factors, and factors depending on the interatomic forces. Anomalous melting is related to a compression induced solid-solid-liquid triple point, and Cs is observed to change from normal to anomalous as its first triple point is approached.