Crystal nucleation and cluster-growth kinetics in a model glass under shear

Crystal nucleation and growth processes induced by an externally applied shear strain in a model metallic glass are studied by means of nonequilibrium molecular dynamics simulations, in a range of temperatures. We observe that the nucleation-growth process takes place after a transient, induction regime. The critical cluster size and the lag-time associated with this induction period are determined from a mean first-passage time analysis. The laws that describe the cluster growth process are studied as a function of temperature and strain rate. A theoretical model for crystallization kinetics that includes the time dependence for nucleation and cluster growth is developed within the framework of the Kolmogorov-Johnson-Mehl-Avrami scenario and is compared with the molecular dynamics data. Scalings for the cluster growth laws and for the crystallization kinetics are also proposed and tested. The observed nucleation rates are found to display a nonmonotonic strain rate dependency

Homogeneous nucleation: Comparison between two theories

The classical nucleation theory of Becker, D\"{o}ring and Zeldovich is compared with the Langer coarse-grained field approach to the nucleation phenomenon. Both formalisms have been applied to the condensation from a supersaturated vapor. It is shown that the nucleation rate derived in the classical theory can be expressed in a form equivalent to that of the field nucleation theory. This equivalence serves as an explanation of the puzzling fact that the numerical predictions of both theories for condensation of Xe and CO$_2$ are almost identical though the standard analytical expressions for the nucleation rates are different. The results obtained can help to link the theories of nucleation and their approximations.Comment: 12 pages, LaTeX, no figure

Igniting homogeneous nucleation

Transient homogeneous nucleation is studied in the limit of large critical sizes. Starting from pure monomers, three eras of transient nucleation are characterized in the classic Becker-D\"oring kinetic equations with two different models of discrete diffusivity: the classic Turnbull-Fisher formula and an expression describing thermally driven growth of the nucleus. The latter diffusivity yields time lags for nucleation which are much closer to values measured in experiments with disilicate glasses. After an initial stage in which the number of monomers decreases, many clusters of small size are produced and a continuous size distribution is created. During the second era, nucleii are increasing steadily in size in such a way that their distribution appears as a wave front advancing towards the critical size for steady nucleation. The nucleation rate at critical size is negligible during this era. After the wave front reaches critical size, it ignites the creation of supercritical clusters at a rate that increases monotonically until its steady value is reached. Analytical formulas for the transient nucleation rate and the time lag are obtained that improve classical ones and compare very well with direct numerical solutions.Comment: 32 pages, 6 figures, to appear in Phys. Rev.

Structure of the icosahedral Ti-Zr-Ni quasicrystal

The atomic structure of the icosahedral Ti-Zr-Ni quasicrystal is determined by invoking similarities to periodic crystalline phases, diffraction data and the results from ab initio calculations. The structure is modeled by decorations of the canonical cell tiling geometry. The initial decoration model is based on the structure of the Frank-Kasper phase W-TiZrNi, the 1/1 approximant structure of the quasicrystal. The decoration model is optimized using a new method of structural analysis combining a least-squares refinement of diffraction data with results from ab initio calculations. The resulting structural model of icosahedral Ti-Zr-Ni is interpreted as a simple decoration rule and structural details are discussed.Comment: 12 pages, 8 figure

Event-driven simulation of the state institution activity for the service provision based on business processes

The paper presents an approach, based on business processes, assessment and control of the state of the state institution, the social insurance Fund. The paper describes the application of business processes, such as items with clear measurable parameters that need to be determined, controlled and changed for management. The example of one of the business processes of the state institutions, which shows the ability to solve management tasks, is given. The authors of the paper demonstrate the possibility of applying the mathematical apparatus of imitative simulation for solving management tasks

Role of Hf on Phase Formation in Ti45Zr(38-x)Hf(x)Ni17 Liquids and Solids

Hafnium and zirconium are very similar, with almost identical sizes and chemical bonding characteristics. However, they behave differently when alloyed with Ti and Ni. A sharp phase formation boundary near 18-21 at.% Hf is observed in rapidly-quenched and as-cast Ti45Zr38-xHfxNi17 alloys. Rapidly-quenched samples that contain less than 18 at.% Hf form the icosahedral quasicrystal phase, whiles samples containing more than 21 at.% form the 3/2 rational approximant phase. In cast alloys, a C14 structure is observed for alloys with Hf lower than the boundary concentration, while a large-cell (11.93 ) FCC Ti2Ni-type structure is found in alloys with Hf concentrations above the boundary. To better understand the role of Hf on phase formation, the structural evolution with supercooling and the solidification behavior of liquid Ti45Zr38-xHfxNi17 alloys (x=0, 12, 18, 21, 38) were studied using the Beamline Electrostatic Levitation (BESL) technique using 125keV x-rays on the 6ID-D beamline at the Advanced Photon Source, Argonne National Laboratory. For all liquids primary crystallization was to a BCC solid solution phase; interestly, an increase in Hf concentration leads to a decrease in the BCC lattice parameter in spite of the chemical similarity between Zr and Hf. A Reitveld analysis confirmed that as in the cast alloys, the secondary phase that formed was the C14 below the phase formation boundary and a Ti2Ni-type structure at higher Hf concentrations. Both the liquidus temperature and the reduced undercooling change sharply on traversing the phase formation boundary concentration, suggesting a change in the liquid structure. Structural information from a Honeycutt-Anderson index analysis of reverse Monte Carlo fits to the S(q) liquid data will be presented to address this issue

Mechanism of Formation of Monodispersed Colloids by Aggregation of Nanosize Precursors

It has been experimentally established in numerous cases that precipitation of monodispersed colloids from homogeneous solutions is a complex process. Specifically, it was found that in many systems nuclei, produced rapidly in a supersaturated solution, grow to nanosize primary particles (singlets), which then coagulate to form much larger final colloids in a process dominated by irreversible capture of these singlets. This paper describes a kinetic model that explains the formation of dispersions of narrow size distribution in such systems. Numerical simulations of the kinetic equations, with experimental model parameter values, are reported. The model was tested for a system involving formation of uniform spherical gold particles by reduction of auric chloride in aqueous solutions. The calculated average size, the width of the particle size distribution, and the time scale of the process, agreed reasonably well with the experimental values.Comment: 38 pages in plain TeX and 7 JPG figure

Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview

Here, we review the basic concepts and applications of the phase-field-crystal (PFC) method, which is one of the latest simulation methodologies in materials science for problems, where atomic- and microscales are tightly coupled. The PFC method operates on atomic length and diffusive time scales, and thus constitutes a computationally efficient alternative to molecular simulation methods. Its intense development in materials science started fairly recently following the work by Elder et al. [Phys. Rev. Lett. 88 (2002), p. 245701]. Since these initial studies, dynamical density functional theory and thermodynamic concepts have been linked to the PFC approach to serve as further theoretical fundaments for the latter. In this review, we summarize these methodological development steps as well as the most important applications of the PFC method with a special focus on the interaction of development steps taken in hard and soft matter physics, respectively. Doing so, we hope to present today's state of the art in PFC modelling as well as the potential, which might still arise from this method in physics and materials science in the nearby future.Comment: 95 pages, 48 figure

Structure and Stability of an Amorphous Metal

Using molecular dynamics simulations, with a realistic many-body embedded-atom potential, and a novel method to characterize local order, we study the structure of pure nickel during the rapid quench of the liquid and in the resulting glass. In contrast with previous simulations with pair potentials, we find more crystalline order and fewer icosahedra for slower quenching rates, resulting in a glass less stable against crystallization. It is shown that there is not a specific amorphous structure, only the arrest of the transition from liquid to crystal, resulting in small crystalline clusters immersed in an amorphous matrix with the same structure of the liquid.Comment: 4 pages, 4 ps figs., to appear in Phys. Rev. Let

Homogeneous nucleation of quark-gluon plasma, finite size effects and long-lived metastable objects

The general formalism of homogeneous nucleation theory is applied to study the hadronization pattern of the ultra-relativistic quark-gluon plasma (QGP) undergoing a first order phase transition. A coalescence model is proposed to describe the evolution dynamics of hadronic clusters produced in the nucleation process. The size distribution of the nucleated clusters is important for the description of the plasma conversion. The model is most sensitive to the initial conditions of the QGP thermalization, time evolution of the energy density, and the interfacial energy of the plasma-hadronic matter interface. The rapidly expanding QGP is first supercooled by about $\Delta T = T - T_c = 4-6$. Then it reheats again up to the critical temperature T_c. Finally it breaks up into hadronic clusters and small droplets of plasma. This fast dynamics occurs within the first $5-10 fm/c$. The finite size effects and fluctuations near the critical temperature are studied. It is shown that a drop of longitudinally expanding QGP of the transverse radius below 4.5 fm can display a long-lived metastability. However, both in the rapid and in the delayed hadronization scenario, the bulk pion yield is emitted by sources as large as 3-4.5 fm. This may be detected experimentally both by a HBT interferometry signal and by the analysis of the rapidity distributions of particles in narrow p_T-intervals at small p_T on an event-by-event basis.Comment: 29 pages, incl. 12 figures and 1 table; to be published in Phys. Rev.