Arrhenius Crossover Temperature of Glass-Forming Liquids Predicted by an Artificial Neural Network.

The Arrhenius crossover temperature, TA, corresponds to a thermodynamic state wherein the atomistic dynamics of a liquid becomes heterogeneous and cooperative; and the activation barrier of diffusion dynamics becomes temperature-dependent at temperatures below TA. The theoretical estimation of this temperature is difficult for some types of materials, especially silicates and borates. In these materials, self-diffusion as a function of the temperature T is reproduced by the Arrhenius law, where the activation barrier practically independent on the temperature T. The purpose of the present work was to establish the relationship between the Arrhenius crossover temperature TA and the physical properties of liquids directly related to their glass-forming ability. Using a machine learning model, the crossover temperature TA was calculated for silicates, borates, organic compounds and metal melts of various compositions. The empirical values of the glass transition temperature Tg, the melting temperature Tm, the ratio of these temperatures Tg/Tm and the fragility index m were applied as input parameters. It has been established that the temperatures Tg and Tm are significant parameters, whereas their ratio Tg/Tm and the fragility index m do not correlate much with the temperature TA. An important result of the present work is the analytical equation relating the temperatures Tg, Tm and TA, and that, from the algebraic point of view, is the equation for a second-order curved surface. It was shown that this equation allows one to correctly estimate the temperature TA for a large class of materials, regardless of their compositions and glass-forming abilities.

Direct evaluation of attachment and detachment rate factors of atoms in crystallizing supercooled liquids.

Kinetic rate factors of crystallization have a direct effect on formation and growth of an ordered solid phase in supercooled liquids and glasses. Using the crystallizing Lennard-Jones liquid as an example, in the present work, we perform a direct quantitative estimation of values of the key crystallization kinetic rate factors-the rate g+ of particle attachments to a crystalline nucleus and the rate g- of particle detachments from a nucleus. We propose a numerical approach, according to which a statistical treatment of the results of molecular dynamics simulations was performed without using any model functions and/or fitting parameters. This approach allows one to accurately estimate the critical nucleus size nc. We find that for the growing nuclei, whose sizes are larger than the critical size nc, the dependence of these kinetic rate factors on the nucleus size n follows a power law. In the case of the subnucleation regime, when the nuclei are smaller than nc, the n-dependence of the quantity g+ is strongly determined by the inherent microscopic properties of a system, and this dependence cannot be described in the framework of any universal law (for example, a power law). It has been established that the dependence of the growth rate of a crystalline nucleus on its size goes into the stationary regime at the size n > 3nc particles.

Extended short-range order determines the overall structure of liquid gallium.

Polyvalent metal melts (gallium, tin, bismuth, etc.) have microscopic structural features, which are detected by neutron and X-ray diffraction and which are absent in simple liquids. Based on neutron and X-ray diffraction data and the results of ab initio molecular dynamics simulations for liquid gallium, we examine the structure of this liquid metal at the atomistic level. Time-resolved cluster analysis allows one to reveal that the short-range structural order in liquid gallium is determined by a range of the correlation lengths. This analysis, performed on a set of independent samples corresponding to equilibrium liquid phase, discloses that there are no stable crystalline domains and molecule-like Ga2 dimers typical for crystal phases of gallium. The structure of liquid gallium can be reproduced by the simplified model of the close-packed system of soft quasi-spheres. The results can be applied to analyze the fine structure of other polyvalent liquid metals.

Corrigendum: Self-consistent description of local density dynamics in simple liquids. The Case of Molten Lithium (2018 J. Phys.: Condens. Matter} 30 085102).

We inform about typos in our article [Mokshin A V and Galimzyanov B N 2018 J. Phys.: Condens. Matter 30 085102].

Kinetics of crystalline nuclei growth in glassy systems.

In this work, we study crystalline nuclei growth in glassy systems, focusing primarily on the early stages of the process, during which the size of a growing nucleus is still comparable with the critical size. On the basis of molecular dynamics simulation results obtained for two crystallizing glassy systems, we evaluate the growth laws of the crystalline nuclei and the parameters of the growth kinetics at temperatures corresponding to deep supercooling; herein, a statistical treatment of the simulation results is carried out using the mean-first-passage-time method. It is found that for the considered systems at different temperatures, the crystal growth laws that were rescaled onto the waiting times of the critically-sized nuclei follow a unified dependence, and can significantly simplify the theoretical description of the post-nucleation growth of crystalline nuclei. The evaluated size-dependent growth rates are characterized by a transition to the steady-state growth regime, which depends on the temperature and occurs in the glassy systems when the size of a growing nucleus becomes two-three times larger than the critical size. It is suggested that the temperature dependencies of the crystal growth rate characteristics should be considered by using the reduced temperature scale T[combining tilde]. Thus, it is revealed that the scaled values of the crystal growth rate characteristics (namely, the steady-state growth rate and the attachment rate for the critically-sized nucleus) as functions of the reduced temperature T[combining tilde] for glassy systems follow unified power-law dependencies. This finding is supported by the available simulation results; the correspondence with the experimental data for the crystal growth rates in glassy systems at temperatures near the glass transition is also discussed.

Scaling law for crystal nucleation time in glasses.

Due to high viscosity, glassy systems evolve slowly to the ordered state. Results of molecular dynamics simulation reveal that the structural ordering in glasses becomes observable over "experimental" (finite) time-scale for the range of phase diagram with high values of pressure. We show that the structural ordering in glasses at such conditions is initiated through the nucleation mechanism, and the mechanism spreads to the states at extremely deep levels of supercooling. We find that the scaled values of the nucleation time, τ1 (average waiting time of the first nucleus with the critical size), in glassy systems as a function of the reduced temperature, T˜, are collapsed onto a single line reproducible by the power-law dependence. This scaling is supported by the simulation results for the model glassy systems for a wide range of temperatures as well as by the experimental data for the stoichiometric glasses at the temperatures near the glass transition.

A method for analyzing the non-stationary nucleation and overall transition kinetics: a case of water.

We present the statistical method as a direct extension of the mean first-passage time concept to the analysis of molecular dynamics simulation data of a phase transformation. According to the method, the mean first-passage time trajectories for the first (i = 1) as well as for the subsequent (i = 2, 3, 4,[ellipsis (horizontal)]) nucleation events should be extracted that allows one to calculate the time-dependent nucleation rate, the critical value of the order parameter (the critical size), the waiting times for the nucleation events, and the growth law of the nuclei - i.e., all the terms, which are usually necessary to characterize the overall transition kinetics. There are no restrictions in the application of the method by the specific thermodynamic regions; and the nucleation rate parameters are extracted according to their basic definitions. The method differs from the Wedekind-Bartell scheme and its modification [A. V. Mokshin and B. N. Galimzyanov, J. Phys. Chem. B 116, 11959 (2012)], where the passage-times for the first (largest) nucleus are evaluated only and where the average waiting time for the first nucleation event is accessible instead of the true steady-state nucleation time scale. We demonstrate an efficiency of the method by its application to the analysis of the vapor-to-liquid transition kinetics in water at the different temperatures. The nucleation rate/time characteristics and the droplet growth parameters are computed on the basis of the coarse-grained molecular dynamics simulation data.

Extension of classical nucleation theory for uniformly sheared systems.

Nucleation is an out-of-equilibrium process that can be strongly affected by the presence of external fields. In this paper, we report a simple extension of classical nucleation theory to systems submitted to an homogeneous shear flow. The theory involves accounting for the anisotropy of the critical nucleus formation and introduces a shear-rate-dependent effective temperature. This extended theory is used to analyze the results of extensive molecular dynamics simulations that explore a broad range of shear rates and undercoolings. At fixed temperature, a maximum in the nucleation rate is observed, when the relaxation time of the system is comparable to the inverse shear rate. In contrast to previous studies, our approach does not require a modification of the thermodynamic description, as the effect of shear is mainly embodied into a modification of the kinetic prefactor and of the temperature.

Steady-state homogeneous nucleation and growth of water droplets: extended numerical treatment.

The steady-state homogeneous vapor-to-liquid nucleation and the succeeding liquid droplet growth process are studied for water systems by means of the coarse-grained molecular dynamics simulations with the mW model suggested originally by Molinero et al. [Molinero, V.; Moore, E. B. J. Phys. Chem. B 2009, 113, 4008-4016]. The investigation covers the temperature range 273 ≤ T/K ≤ 363 and the system's pressure p ~/= 1 atm. The thermodynamic integration scheme and the extended mean first passage time method as tools to find the nucleation and cluster growth characteristics are applied. The surface tension is numerically estimated and is compared with the experimental data for the considered temperature range. We extract the nucleation characteristics such as the steady-state nucleation rate, the critical cluster size, the nucleation barrier, and the Zeldovich factor and perform the comparison with the other simulation results and test the treatment of the simulation results within the classical nucleation theory. We found that the liquid droplet growth is unsteady and follows the power law. Also, the growth laws exhibit the features unified for all of the considered temperatures. The geometry of the nucleated droplets is also studied.