Crystallization Of Supercooled Liquid Research Articles

Kinetics of inherent processes counteracting crystallization in supercooled monatomic liquid

Crystallization of supercooled liquids is mainly determined by two competing processes associated with the transition of particles (atoms) from liquid phase to crystalline one and, vice versa, with the return of particles from crystalline phase to liquid one. The quantitative characteristics of these processes are the so-called attachment rate and the detachment rate , which determine how particles change their belonging from one phase to another. In the present study, a correspondence rule between the rates and as functions of the size N of growing crystalline nuclei is defined for the first time. In contrast to the well-known detailed balance condition, which relates and at (where n c is the critical nucleus size) and is satisfied only at the beginning of the nucleation regime, the found correspondence rule is fulfilled at all the main stages of crystallization kinetics (crystal nucleation, growth and coalescence). On the example of crystallizing supercooled Lennard–Jones liquid, the rate was calculated for the first time at different supercooling levels and for the wide range of nucleus sizes . It was found that for the whole range of nucleus sizes, the detachment rate is only % less than the attachment rate . This is direct evidence that the role of the processes that counteract crystallization remains significant at all the stages of crystallization. Based on the obtained results, a kinetic equation was formulated for the time-dependent distribution function of the nucleus sizes, that is an alternative to the well-known kinetic Becker–Döring–Zeldovich–Frenkel equation.

Unveiling nucleation dynamics by seeded and spontaneous crystallization in supercooled liquids

Crystallization of supercooled liquids and glasses is of gargantuan scientific and industrial importance. However, investigating its early stages is experimentally very challenging because of the nanometric size and very short lifetime of the critical nuclei; therefore, computer simulations can substantially assist in unveiling the nucleation mechanism and dynamics. In this work, we determined the critical nucleus sizes, the transport coefficient at the nucleus/liquid interface, and the interfacial free energy employing the seeding approach at shallow supercoolings combined with spontaneous homogeneous nucleation rates (Jss) at deep supercoolings in barium sulfide liquid. The nucleation rates were calculated using the MD results for the relevant physical properties and theoretical values of the driving force without any adjustable parameter, and agree quite well with the Jss obtained directly by MD simulations. The results confirm the ability of the seeding method to estimate nucleation parameters. They not only corroborate recent findings for mW water, hard spheres, Lennard-Jones, and zinc selenide models, but also show the best simulations-CNT calculations agreement ever. As this set of relevant outcomes is dispersed for other substances; here we combined and discussed them together to reinforce and generalize the soundness of the Classical Nucleation Theory in describing and predicting crystal nucleation rates for various supercooled liquids.

Preface

The 9th International Conference on Materials Science (ICMS2020) was held at the National University of Mongolia from September 10 to 13, 2020 in Ulaanbaatar. Unfortunately, the global pandemic had a bad effect on the event. Therefore, some of the participants could not attend the conference in person. A significant part of the participants (more than 50 people) were accommodated in the hall and more than 25 people participated in absentia. Since at this time it is difficult to predict the end of the pandemic, and the termination of the exchange and discussion of scientific results may negatively affect the research of many scientific groups, it was decided to hold this traditional conference using video presentations. Participants from Russia presented their reports and presentations in electronic form (video reports and posters) and were demonstrated at section meetings. In total - about 80 participants.Organisers were some known scientific organizations:National University of Mongolia, Ulaanbaatar, Mongolia, National University of Mongolia, Mongolia, Inner Mongolian Normal University, China, Institute of Physical Materials Science, Siberian Branch of the Russian Academy of Sciences, Russia, Mongolian Academy of Sciences, Mongolia, German-Mongolian Institute for Resources and Technology and Erdenet Mining Corporation SOE, Mongolia.Scientific committee was consisted of famous scientists:Prof. J.Davaasambuu (National University of Mongolia)Prof. U.Pietsch (University of Siegen, Germany)Prof. G.Eckold (University of Goettingen, Germany)Prof. O.Tegus (Inner Mongolian Normal University, China)Dr. A.Nomoev (IPMS SB RUS, Russia)Prof. S.Gorfman (Tel Aviv University, Israel)Prof. S.Bardakhanov (Buryat State University, Russia)Prof. P.Daniel (Le-Mans University, France)Prof. B.Battsengel (GMIT, Mongolia)Dr. B.B.Damdinov (SFU, Krasnoyarsk, Russia)Acad. O.Penyazkov (A.V.Lykov Institute, Belarus)Acad. D.Sangaa (Mongolian Academy of Sciences)Acad. J.Temuujin (Mongolian Academy of Sciences)Dr. V.Koledov (IRE, RAS, Russia)Dr. P.Altantsog (Mongolian Academy of SciencesAll materials were reviewed by the editors: Dr. N. Tuvjargal and Prof. J.Davaasambuu from Department of Physics, Faculty of Arts and Sciences, National University of Mongolia.The conference consisted of plenary presentations for 30 minutes and session reports for 15 minutes. There were 35 oral reports and 29 posters in total. The organizers have provided 5 minutes for questions that can be asked in person or via the Internet.The objectives of the conference were to bring together scientists working in the field of materials science from around the world, to exchange ideas, recent research results in this area and to offer a platform for the initiation of scientific cooperation between Mongolian and foreign scientists. The conference was focused on the structures, properties and applications of new materials as well as their characterization techniques.Topics were: Materials science, Condensed matter physics, Computational methods, Experimental methods and instrumentation, Laser spectroscopy.At the conference, nanotechnology-related studies related to quantum effects, such as carrier tunneling, controlled changes in the structure of energy bands, quantization of energy spectra of charge carriers and spin phenomena, and the study of new physical features of semiconductor nanostructures, were discussed. The topic were a description of the transport properties of various ion-exchange membranes, crystallization of supercooled liquids and amorphous solids, increase the corrosion resistance of aluminum alloys, obtaining nanoscale metal and alloy powders. Numerical simulation of phonon crystals with time-dependent properties of a periodic structure, computer simulation by the molecular dynamics method, the processes of structure formation of nanoclusters of an alloy of silver and copper were presented.The organizers and participants of ICMS 2020 noted the high scientific level of the presented reports.

Comment on "Crystallization of Supercooled Liquids: Self-Consistency Correction of the Steady-State Nucleation Rate" by Abyzov et al., Entropy 2020, 22, 558.

It is shown that in the growth region (above the critical nucleation size) the transient distributions obtained numerically from the Becker-Döring equation (BDE) by Abyzov et al., Entropy 2020, 22, 558, are in accurate correspondence with the matched asymptotic (singular perturbation) solution by Shneidman, Sov. Phys. Tech. Phys. 1988, 33, 1338. The solution is unmodified by “self-consistency” corrections which affect only the steady state rate. Sensitivity of the results to selection of a specific form of the BDE (the “nucleation model”) also is briefly discussed.

Crystallization of Supercooled Liquids: Self-Consistency Correction of the Steady-State Nucleation Rate.

Crystal nucleation can be described by a set of kinetic equations that appropriately account for both the thermodynamic and kinetic factors governing this process. The mathematical analysis of this set of equations allows one to formulate analytical expressions for the basic characteristics of nucleation, i.e., the steady-state nucleation rate and the steady-state cluster-size distribution. These two quantities depend on the work of formation, , of crystal clusters of size n and, in particular, on the work of critical cluster formation, . The first term in the expression for describes changes in the bulk contributions (expressed by the chemical potential difference, ) to the Gibbs free energy caused by cluster formation, whereas the second one reflects surface contributions (expressed by the surface tension, : , , where is a parameter describing the size of the particles in the liquid undergoing crystallization), n is the number of particles (atoms or molecules) in a crystallite, and defines the size of the critical crystallite, corresponding to the maximum (in general, a saddle point) of the Gibbs free energy, G. The work of cluster formation is commonly identified with the difference between the Gibbs free energy of a system containing a cluster with n particles and the homogeneous initial state. For the formation of a “cluster” of size , no work is required. However, the commonly used relation for given above leads to a finite value for . By this reason, for a correct determination of the work of cluster formation, a self-consistency correction should be introduced employing instead of an expression of the form . Such self-consistency correction is usually omitted assuming that the inequality holds. In the present paper, we show that: (i) This inequality is frequently not fulfilled in crystal nucleation processes. (ii) The form and the results of the numerical solution of the set of kinetic equations are not affected by self-consistency corrections. However, (iii) the predictions of the analytical relations for the steady-state nucleation rate and the steady-state cluster-size distribution differ considerably in dependence of whether such correction is introduced or not. In particular, neglecting the self-consistency correction overestimates the work of critical cluster formation and leads, consequently, to far too low theoretical values for the steady-state nucleation rates. For the system studied here as a typical example (lithium disilicate, ), the resulting deviations from the correct values may reach 20 orders of magnitude. Consequently, neglecting self-consistency corrections may result in severe errors in the interpretation of experimental data if, as it is usually done, the analytical relations for the steady-state nucleation rate or the steady-state cluster-size distribution are employed for their determination.

Thermal Effects on the Crystallization Kinetics, and Interfacial Adhesion of Single-Crystal Phase-Change Gallium.

Although substrates play an important role upon crystallization of supercooled liquids, the influences of surface temperature and thermal property have remained elusive. Here, the crystallization of supercooled phase-change gallium (Ga) on substrates with different thermal conductivity is studied. The effect of interfacial temperature on the crystallization kinetics, which dictates thermo-mechanical stresses between the substrate and the crystallized Ga, is investigated. At an elevated surface temperature, close to the melting point of Ga, an extended single-crystal growth of Ga on dielectric substrates due to layering effect and annealing is realized without the application of external fields. Adhesive strength at the interfaces depends on the thermal conductivity and initial surface temperature of the substrates. This insight can be applicable to other liquid metals for industrial applications, and sheds more light on phase-change memory crystallization.

A promising "metastable" liquid crystal stationary phase for gas chromatography

The liquid crystal state is an ordered physical state between a solid and a liquid. Previous research, in gas chromatography, proved that it provides a geometric selectivity, which allows the separation of geometric position isomers and cis-trans isomers that are difficult to separate on conventional gas chromatography stationary phases (polydimethyl siloxane derived and polyethylene glycol stationary phases). However, their use was generally very limited by the rather high temperature at which they must be operated, normally above the solid-liquid crystal transition temperature. In the present study we are interested in a new synthesized material, 1,4- bis (4-bromohexyloxy benzoate) phenyl (BHOBP). The first characterizations of BHOBP were carried out by thermogravimetric analysis, hot-stage optical microscopy and differential scanning calorimetry to control the thermal stability of the BHOBP as well as the nematic texture of the mesophase highlighted in a well-defined temperature range (120 °C-200 °C). When heated, the solid compound led to a stable liquid crystal state. Its cooling has revealed "a new metastable physical state, which is the supercooled liquid crystal phase". After these first characterizations, the new material was used as a stationary phase for gas chromatography. The BHOBP was deposited in a capillary column by the dynamic method. The inverse gas chromatography study of the column revealed a solid-stable nematic phase transition temperature, in agreement with the first characterization methods. The stable liquid crystal phase showed good resolutions in the analysis of some geometric isomers of low volatility as PAHs. The presence of the supercooled liquid crystal state in the chromatographic column has also been confirmed. This new metastable state is particularly interesting because it enlarged the scope of this material by improving the resolution of several mixtures. Thus, the separation of highly volatile mixtures of geometric isomers (e.g. cis and trans-decalin) was achieved only through this metastable mesophase confirming its unique selectivity. The metastable liquid crystal, used at 80 °C, has also exhibited an original behavior by its stability after several weeks of use at the same temperature, maintaining constant retention factors and selectivity.

Interaction of supercooled droplets and nonspherical ice crystals with a solid body in a mixed cloud

Mathematical models of nonspherical particles’ motion in nonuniform flow were proposed for continuous flow approach as well as for single particles’ motion simulation. Lagrangian approach was used to simulate aerosol flow with nonspherical particles around transversal cylinder. Peculiarities of supercooled water crystallization were investigated via cryostat, infrared spectroscopy, and original devices for supercooled droplets’ impact simulation. The results of the experimental study of the supercooled water crystallization are presented. The relationship between the parameters of intermolecular interaction with the parameters of macroscopic phenomena accompanying the crystallization of supercooled water was determined. Mathematical models of the supercooled liquid crystallization and the expression for the minimum rate for the beginning of the supercooled droplets crystallization on impact with the surface of the aircraft were developed. The numerical and experimental evaluations of physical parameters characterizing the supercooled liquid crystallization in the icing problem are performed. Two-phase boundary layer formation near nanostructutred surface was investigated via molecular dynamics method.

Crystallization of supercooled liquid and amorphous silicene

Crystallization under isothermal condition of supercooled liquid and amorphous silicene (a-silicene) models has been studied via molecular dynamics (MD) simulation with Stillinger-Weber (SW) interaction potential. Supercooled liquid and a-silicene models containing 104 atoms are obtained via the rapid solidification process from the melt. At each given temperature below and above Tg, models are annealed from 5 ns up to 8 ns in order to investigate aging effect on two-dimensional structural arrangement of disordered Si-atoms. Time dependence of thermodynamic and structural quantities is analyzed including potential energy, radial distribution function (RDF), coordination number, buckling degree, ring and bond-angle distribution. We find that 2D-crystallization of supercooled liquid and a-silicene exhibits a first-order behavior. Time-temperature-transformation (TTT) diagram exhibits a commonly nose-shape by analyzing a wide temperature range from supercooled liquid to amorphous state. High critical cooling rates of a-silicene are found indicating low glass-formation ability of the system. Thermodynamic properties of crystallization of silicenes attained after-aging are studied in details and we clarify a novel scenario of crystallization. A homogenous tendency of natural quenched-in nucleation atoms aggregate into larger clusters in 2D Si supercooled liquid sheet. Consequently, a polycrystalline layer of silicene is developed with decent low-numbered chain defects as grain boundary. In contrast, crystallization of a-silicene shows a partial crystallization behavior: Crystal clusters are found to exhibit a heterogeneous growth in models obtained below Tg. Crystal formed from a-silicene is a quasi-equilibrium state with a large number of defects still existed in models after a long relaxing time.

Control of crystallization behaviour of supercooled liquid composed of lithium disilicate on platinum substrate

Crystalline lithium disilicate (Li2Si2O5, LS2) materials, which have excellent mechanical properties with high transparency, should be obtained efficiently through the crystallization of supercooled liquid composed of LS2. However, in addition to LS2, a lithium monosilicate (Li2SiO3, LS) phase is also precipitated during the crystallization of the liquid. The precipitation of the LS phase renders it difficult to obtain a single-phase LS2 material. Here, we show that by altering the oxygen partial pressure, it is possible to change the selectivity of the precipitated phase by controlling the interfacial phenomena that occur between the liquid and platinum contact material. During cooling of the supercooled liquid, the type of precipitated phase can be controlled by optimizing the atmosphere and type of contact material. This methodology can be applied for the fabrication of other functional materials and does not require the use of other additives.

Critical nucleus size for crystallization of supercooled liquids in two dimensions.

Using molecular dynamics simulations, we study the crystallization of supercooled liquids in two dimensions in which particles interact with other particles via the Lennard-Jones-Gauss potential. We first prepare supercooled liquids at various temperatures by rapid quenching from the melt. The simulations are performed with a crystalline seed inserted at the center of the initial system. We investigate the time evolution of the inserted nucleus and its surroundings and determine the critical nucleus size n_{c} defined as the smallest nucleus which survives. The results show that n_{c} scales as ∼(T_{m}-T)^{-2} with the melting temperature T_{m}, as expected in the classical nucleation theory. We also obtain the crystallization time at various temperatures as a function of nucleus size and show that the presence of a crystalline seed significantly affects the crystallization time when the temperature is higher than the characteristic temperature T^{*} at which the crystallization time becomes the shortest. This indicates that the crystallization is controlled by thermodynamics in this temperature range. When the temperature is lower than T^{*}, the effect of the inserted nucleus on crystallization is less significant, which indicates that crystallization is controlled by emergence and merging of small crystalline nuclei.

Conversion of isothermal and isochronal crystallization in a supercooled liquid through additivity rule

In the present work, the compatibility of additivity rule with the crystallization behavior of an Au50Cu25.5Ag7.5Si17 glass forming alloy on the conditions of both isothermal and isochronal transformations is investigated. Taking advantages of the ultrafast heating and cooling rates of the Flash DSC technique, we verified the additivity rule in a solidification process for the first time. It is proved to be effective in predicting the beginning and the end of isochronal crystallizations during continuous heating and cooling from the kinetic analysis of corresponding experimental isothermal transformation. The predicted isochronal curves are fairly in accordance with the experimental results, especially for the incubation and crystallization processes during rapid solidification of the glass forming liquid. The compatibility of additivity rule enables a conversion between isothermal and isochronal transformations for the crystallization of supercooled liquid even during solidification from the melt.

Thermalization calorimetry: A simple method for investigating glass transition and crystallization of supercooled liquids

We present a simple method for fast and cheap thermal analysis on supercooled glass-forming liquids. This “Thermalization Calorimetry” technique is based on monitoring the temperature and its rate of change during heating or cooling of a sample for which the thermal power input comes from heat conduction through an insulating material, i.e., is proportional to the temperature difference between sample and surroundings. The monitored signal reflects the sample’s specific heat and is sensitive to exo- and endothermic processes. The technique is useful for studying supercooled liquids and their crystallization, e.g., for locating the glass transition and melting point(s), as well as for investigating the stability against crystallization and estimating the relative change in specific heat between the solid and liquid phases at the glass transition.

A simple diatomic potential that prevents crystallization in supercooled liquids simulations

We study a simple and versatile diatomic potential function coined to prevent crystallization in supercooled liquids. We show that the corresponding liquid does not crystallize even with very long simulation runs at the lowest temperature that we can access with ergodic simulations. The medium displays the usual features of supercooled materials and a non-Arrhenius dependence of the diffusion coefficient and α relaxation time with temperature. We also observe the breakdown of the Stokes–Einstein relation at low temperatures.

Crystallization of supercooled liquid and glassy Fe thin films

Isothermal crystallization of supercooled liquid and glassy Fe thin films has been studied via molecular dynamics (MD) simulations with a many-body potential of the embedded atom method (EAM). Supercooled liquid and glassy Fe thin films are obtained by cooling from the melts. Models at a given temperature are annealed for a long time in order to study crystallization process. Time dependence of various thermodynamic and structural quantities upon annealing is analyzed including potential energy, radial distribution function (RDF), coordination number distribution, fraction of atoms of various crystalline orders etc. We find that crystallization of supercooled liquid and glassy states exhibits a first-order behavior. Time–temperature-transformation (TTT) diagram is found for a wide temperature range from a supercooled liquid to a deeply glassy state and it exhibits a nose shape like that commonly found. Atomic mechanism of crystallization is studied in details via analysis of the spatio-temporal arrangements of crystalline atoms occurred during annealing and we find a quite new scenario of crystallization unlike that thought in the past. Crystalline atoms have a tendency to form clusters including a single extra-large percolation one. Crystalline phase is formed via enhancement of atomic population of the single largest percolation cluster by attachment of smaller clusters and newly formed crystalline atoms upon further annealing. We find that only one third of the ‘naturally quenched-in’ crystalline atoms remains stable and participates in the crystallization process. Free surface effects on structure and crystallization is also found and discussed.

Phase transition of syndiotactic polypropylene in electrospun nanofibers during progressive heating

By means of high-temperature electrospinning process, syndiotactic polypropylene (sPP) nanofibers with an average diameter of 127 nm were obtained using a rotating disc as a collector. The aligned fibers were subjected to progressive heating for fiber melting. During heating, structural evolution of the sPP nanofibers was investigated in situ by means of two-dimensional wide-angle and small-angle X-ray scattering with synchrotron radiation sources. It was found that the as-spun fibers consist of the antichiral form I (9 %), mesophase (31 %), and amorphous phase (60 %), in the absence of isochiral form II. Upon heating, the mesophase started to melt and completely disappeared at 90 °C. The melting of the mesophase directly produced amorphous chains at 35–60 °C, and brought up the isochiral form II at low temperatures (60–70 °C), as well as the antichiral form I at high temperatures (70–110 °C). These events were in accordance with the DSC heating curve, which exhibited a small endotherm centered at 52 °C for the mesophase melting, followed by a shallow and broad exotherm associated with two phase-transition events, i.e., the crystal reorganization and the crystallization of supercooled liquid. The former is likely due to the solid–solid transition of meso→II phase as suggested by Lotz et al. (Macromolecules 31:9253, 1998), and the latter is relevant with crystallization of amorphous chains to develop the thermodynamic stable form I phase at high temperatures.

Toward Better Understanding Crystallization of Supercooled Liquids under Compression: Isochronal Crystallization Kinetics Approach

In this paper, we present dielectric studies on the effect of different thermodynamic conditions on the physical stability of van der Waals glass-forming material of pharmaceutical interest, indomethacin. By maintaining isochronal condition during measurements, we were able to control the kinetic factor of the crystallization process and untangle purely thermodynamic effects on crystallization from kinetic ones. This cannot be achieved by any other experimental attempt performed at atmospheric pressure. Along with experimental studies, crystallization of supercooled indomethacin under pressure was described theoretically. We have demonstrated within the studied pressure range (0.1–220 MPa) that one should expect an increase of thermodynamic driving force, decrease in melt/crystal interface energy, and critical nuclei size. Therefore, an experimentally observed increase in the overall crystallization rate under isochronal conditions can be exclusively rationalized as due to variations of the thermodynamic factor.

Size of a crystal nucleus in the isothermal crystallization of supercooled liquid

We present an alternative to classical nucleation theory (CNT). We introduce a size-dependent surface energy into the total Gibbs free-energy of formation of a crystal (ΔG). We consider the free-energy in the core part of the total volume of crystal and the free-energy in the surface-layer part of it, separately, for the evaluation of ΔG. As a result, we present an explicit model to evaluate a characteristic size of an initial nucleus that differs from the critical nucleus of CNT, but whose temperature dependence agrees well with that reported for the temperature dependency initial fold length of isotactic polystyrene and polyethylene in the literature. Our model has fitted the experimental data in the literature with only one adjustable parameter that is defined as nucleation constant. The nucleation constant is the Gibbs free-energy difference between the crystal and supercooled liquid phases for the volume of initial nucleus. We also present an expression to approximate the evolution of free-energy in the surface-layer part of crystal during the crystal growth.

The microscopic pathway to crystallization in supercooled liquids.

Despite its fundamental and technological importance, a microscopic understanding of the crystallization process is still elusive. By computer simulations of the hard-sphere model we reveal the mechanism by which thermal fluctuations drive the transition from the supercooled liquid state to the crystal state. In particular we show that fluctuations in bond orientational order trigger the nucleation process, contrary to the common belief that the transition is initiated by density fluctuations. Moreover, the analysis of bond orientational fluctuations shows that these not only act as seeds of the nucleation process, but also i) determine the particular polymorph which is to be nucleated from them and ii) at high density favour the formation of fivefold structures which can frustrate the formation of crystals. These results can shed new light on our understanding of the relationship between crystallization and vitrification.

In situ Observation of Supercooled Liquid–Crystal Phase Transition in Glassy Ferroelectric LaBGeO5

Inelastic light scattering was observed in situ from glassy ferroelectric LaBGeO5, which crystallizes the stillwellite-type stoichiometric phase, in the glass–supercooled liquid (SCL) and subsequent SCL–crystal phase transition regimes. The dynamics of the planar BO3 unit in the crystal growth period of the crystallization process was clarified through in situ observation.