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.

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.

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, τ 1 (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.

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.

In this work, we study the crystalline nuclei growth in glassy systems focusing primarily on the early stages of the process, at which the size of a growing nucleus is still comparable with the critical size. On the basis of molecular dynamics simulation results for two crystallizing glassy systems, we evaluate the growth laws of the crystalline nuclei and the parameters of the growth kinetics at the temperatures corresponding to deep supercoolings; herein, the statistical treatment of the simulation results is done within the mean-first-passage-time method. It is found for the considered systems at different temperatures that the crystal growth laws rescaled onto the waiting times of the criticallysized nucleus follow the unified dependence, that can simplify significantly theoretical description of the post-nucleation growth of crystalline nuclei. The evaluated size-dependent growth rates are characterized by 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 a critical size. It is suggested to consider the temperature dependencies of the crystal growth rate characteristics by using the reduced temperature scale T . 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 for glassy systems follow the unified power-law dependencies. This finding is supported by available simulation results; the correspondence with the experimental data for the crystal growth rate in glassy systems at the temperatures near the glass transition is also discussed.

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.

Kinetic rate factors of crystallization have a direct effect on formation and growth of an ordered solid phase in supercooled liquids and glasses. Using 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 n c . We find that for the growing nuclei, whose sizes are larger than the critical size n c , 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 n c , 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 sizes n > 3n c particles.

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