Morphology,Growth Rate,and Lamellar Thickness of Polymer Crystals

At high supercoolings, isotactic polystyrene and polybutene-1 have a rounded crystal shape, suggesting kinetic roughening. Still, the growth rates of these polymer crystals show the supercooling dependence derived for nucleation controlled growth. On the other hand, isotactic poly-4-methylpentene-1 1,4 trans-polybutadiene at higher crystallization temperatures and polyethylene at high pressures show a rounded crystal shape: thermal roughening. Again, the growth rate is described by the nucleation theory. On the basis of these observations, we propose a crystallization kinetics taking account of the entropic barrier that was originally proposed by Sadler.     

The activation energy of crystallization of amorphous Fe40Ni40P14B6

The isothermal crystallization of Fe₄₀Ni₄₀P₁₄B₆ (Metglas 2826) has been studied by transmission electron microscopy, using static observations of partially crystallized ribbons at room temperature and in situ dynamic registration of the crystallization process at elevated temperatures. At all temperatures crystallization takes place by the nucleation and growth of individual crystals. Analysis of the transformation kinetics allowed to determine the nucleation rates and the activation energy for crystal growth. The growth velocity of the crystal phase was found to be controlled by the diffusion coefficient of phosphorus in this alloy withD ₀=2.5×10^10±1cm{swu2}/s andQ=(3.4±0.15)eV.     

The kinetics of solidification of Al-Si eutectic alloys under high pressure

Abstract

The kinetics of crystallization of eutectic alloys Al_100-xSi_x (χ=12, 18, 26 at.%) was investigated under pressures p=0.5, 2.5, 4.5 GPa. The values of supercooling and average grain size of silicon crystals were determined for alloys quenched from melt under different pressures with the cooling rate 10³ K/s. The data obtained were used to evaluate quantitatively the pressure dependences of surface tension (between melt and crystal) and activation energy of crystal growth which, in turn, have made it possible to determine the relative change of nucleation frequency and of the rate of crystal growth with pressure.

The possibility is shown, based on the investigation of mechanical properties of the samples obtained under high pressure, for improving the strength and the plasticity of A1-Si alloys by means of high pressure-high temperature treatment.     

Study of precipitation in NaCl:Pb2+ by light scattering and ultramicroscopy

The formation and dissolution behaviour of precipitates in NaCl : Pb²⁺ single crystals is studied by light scattering and ultramicroscopy. Measurements of Rayleigh ratio together with ultramicroscopic observations during isochronal annealing indicate the presence of two types of precipitates in as-grown crystals. Isochronal annealing after suitable thermal and thermomechanical treatments shows that precipitates of first type (I) which form and dissolve at lower temperatures, are due to homogeneous nucleation. Precipitates of the second category (II) which form and dissolve at higher temperatures are aligned along crystallographic directions and have their origin in stress-assisted processes. Isothermal annealing has been used to study the dissolution kinetics of the precipitated fraction, and it is found that the kinetics is of first order. The enthalpy of solution is determined from a study of the temperature dependence of the kinetic rate constant, in conjunction with available information on the migration energy of Pb²⁺ in NaCl. The enthalpy so deduced is in good agreement with the value as usually obtained from the concentration dependence of the dissolution temperature.     

New developments on size-dependent growth applied to the crystallization of sucrose

The effect of crystal size on the growth rate of sucrose (C₁₂H₂₂O₁₁) at 40 °C is investigated from a theoretical and an experimental point of view. Based on new perspectives resulting from the recently introduced spiral nucleation model [P.M. Martins, F. Rocha, Surf. Sci. 601 (2007) 3400], crystal growth rates are expressed in terms of mass deposition per time and crystal volume units. This alternative definition is demonstrated to be size-independent over the considered supersaturation range. The conventional overall growth rate expressed per surface area units is found to be linearly dependent on crystal size. The advantages of the “volumetric” growth rate concept are discussed. Sucrose dissolution rates were measured under reciprocal conditions of the growth experiments in order to investigate the two-way effect of crystal size on mass transfer rates and on the integration kinetics. Both effects are adequately described by combining a well-established diffusion-integration model and the spiral nucleation mechanism.     

On the homogeneous nucleation and propagation of dislocations under shock compression

The dynamic response of crystalline materials subjected to extreme shock compression is not well understood. The interaction between the propagating shock wave and the material’s defect occurs at the sub-nanosecond timescale which makes in situ experimental measurements very challenging. Therefore, computer simulation coupled with theoretical modelling and available experimental data is useful to determine the underlying physics behind shock-induced plasticity. In this work, multiscale dislocation dynamics plasticity (MDDP) calculations are carried out to simulate the mechanical response of copper reported at ultra-high strain rates shock loading. We compare the value of threshold stress for homogeneous nucleation obtained from elastodynamic solution and standard nucleation theory with MDDP predictions for copper single crystals oriented in the [0 0 1]. MDDP homogeneous nucleation simulations are then carried out to investigate several aspects of shock-induced deformation such as; stress profile characteristics, plastic relaxation, dislocation microstructure evolution and temperature rise behind the wave front. The computation results show that the stresses exhibit an elastic overshoot followed by rapid relaxation such that the 1D state of strain is transformed into a 3D state of strain due to plastic flow. We demonstrate that MDDP computations of the dislocation density, peak pressure, dynamics yielding and flow stress are in good agreement with recent experimental findings and compare well with the predictions of several dislocation-based continuum models. MDDP-based models for dislocation density evolution, saturation dislocation density, temperature rise due to plastic work and strain rate hardening are proposed. Additionally, we demonstrated using MDDP computations along with recent experimental reports the breakdown of the fourth power law of Swegle and Grady in the homogeneous nucleation regime.     

Investigation of the activation-parameters of low-temperature slip in cubic metals

The macroscopic critical resolved shear stress (CRSS)τ of 9 body-centred cubic (BCC) and 5 face-centred cubic (FCC) metals has been found to vary with temperatureT in the range 0 to 300 K as given by: lnτ=A − BT, whereA andB are positive constants. Theτ−T data have been analysed within the framework of a kink-pair nucleation (KPN) model of plastic flow in crystals. The microscopic parameters of the unit activation process of yielding, e.g. the initial length of the glide dislocation segment, the critical height of the kink-pair nucleated in it, the activation volume associated with the CRSS, and the binding energy per interatomic spacing along the glide dislocation in the slip plane etc., have been evaluated. A consistent picture of the dislocation kinetics involved in the yielding of BCC and FCC metals emerges, which is adequately described by the KNP model of plastic flow in crystals.     

Coherent kinetic control over crystal orientation in macroscopic ensembles of polymer nanorods and nanotubes

We show that the crystal orientation in polymer nanotubes and nanorods inside porous templates is controlled by the kinetics of nucleation and growth under 2D confinement. Two clear limiting cases are identified: In separated nanostructures, any crystal orientation allowing the growth of lamellar crystals along the pores appears statistically. If a bulklike surface film connects the nanostructures, macroscopic arrays with uniform crystal orientation are obtained, in which the dominant growth direction of the crystals is aligned with the long axes of the pores of the template.     

Determination of the colloidal crystal nucleation rate density

Colloidal suspensions of charged latex microspheres in water exhibit liquid-like or crystalline ordering depending on particle interaction and concentration. By virtue of large particle spacing and slow dynamics, colloidal systems offer a unique opportunity to study interfacial structure and dynamics. This paper presents the first reported experimental study of the nucleation rate density, c, of an nonequilibrium (supercooled) colloidal liquid to colloidal crystal first order phase transition. Local and global observations of colloidal crystals growing from a metastable colloidal liquid were used to determine c. Microscopic local observations revealed homogeneous nucleation and constant interface velocity growth of quasispherical crystallites in the bulk and heterogeneous nucleation of a crystalline sheet with lower growth velocity at the cell wall. Complementary global observations of the recrystallization transition made by measuring the time dependence of the suspension transparency (the fraction of transmitted laser light) determined c by fitting this curve to a model based on an extension of Avrami's theory of crystallization.     

Laser-induced preferential domain nucleation in hafnium-doped congruent lithium niobate crystal

The focused visible laser-induced preferential domain nucleation effect is investigated in 3 mol% hafnium-doped congruent lithium niobate crystal. The local phase variation is in-situ monitored during laser-induced preferential domain nucleation. The variations of phase distributions are reconstructed by digital holographic interferometry. The nucleation field decreases exponentially with increasing irradiation intensity. The space charge field along the z direction is thought to be an important mechanism for the laser-induced preferential domain nucleation. Laser-induced hafnium-doped congruent lithium niobate crystals appear to be a promising candidate for further development of ferroelectric domain engineering.     

Phase diagrams and kinetics of phase transitions in protein solutions

The phase behavior of proteins is of interest for fundamental and practical reasons. The nucleation of new phases is one of the last major unresolved problems of nature. The formation of protein condensed phases (crystals, polymers, and other solid aggregates, as well as dense liquids and gels) underlies pathological conditions, plays a crucial role in the biological function of the respective protein, or is an essential part of laboratory and industrial processes. In this review, we focus on phase transitions of proteins in their properly folded state. We first summarize the recently acquired understanding of physical processes underlying the phase diagrams of the protein solutions and the thermodynamics of protein phase transitions. Then we review recent findings on the kinetics of nucleation of dense liquid droplets and crystals. We explore the transition from nucleation to spinodal decomposition for liquid-liquid separation and introduce the new concept of solution-to-crystal spinodal. We review the two-step mechanism of protein crystal nucleation, in which mesoscopic metastable protein clusters serve as precursors to the ordered crystal nuclei. The concepts and mechanisms reviewed here provide powerful tools for control of the nucleation process by varying the solution thermodynamic parameters.     

Direct Observation of Crystallization of Polybutene-1 Under Low Shear Rate Flow

The isothermal crystallization process of polybutene-1 melt under shear flow was investigated with an optical microscope and a device (shear flow direct observation system, SF-DOS) newly developed by our group. The nucleation rate and growth rate of polybutene-1 were studied under slow shear rates (0–0.1 s^?1) at high crystallization temperature (102–108°C) with the SF-DOS. The nucleation remains heterogeneous. The number of nuclei after long times increased and induction time decreased by increasing the shear rate. Anisotropic and distorted spherulites were observed under shear flow, while the spherulites in the static condition were isotropic. It was clearly observed that the spherulites were rotating under shear. The average growth rates were enhanced by increasing shear rates, which acts as the main factor affecting the overall crystallization kinetics. Finally, the crystallization kinetics were analyzed on the basis of the secondary nucleation theory of Hoffman and Lauritzen. Even under very low shear rates, the product of lateral‐surface free energy σ _s and fold-surface free energy σ _e was found to be reduced as shear rate increased.     

On the problem of the consistency of the high-temperature precipitation model with the classical nucleation theory

The adequacy of the model of high-temperature precipitation in dislocation-free silicon single crystals to the classical theory of nucleation and growth of second-phase particles in solids has been considered. It has been shown that the introduction and consideration of thermal conditions of crystal growth in the initial equations of the classical nucleation theory make it possible to explain the precipitation processes occurring in the high-temperature range and thus extend the theoretical basis of the application of the classical nucleation theory. According to the model of high-temperature precipitation, the smallest critical radius of oxygen and carbon precipitates is observed in the vicinity of the crystallization front. Cooling of the crystal is accompanied by the growth and coalescence of precipitates. During heat treatments, the nucleation of precipitates starts at low temperatures, whereas the growth and coalescence of precipitates occur with an increase in the temperature. It has been assumed that the high-temperature precipitation of impurities can determine the overall kinetics of defect formation in other dislocation-free single crystals of semiconductors and metals.     

A crystal plasticity finite element model for flow stress anomalies in Ni3Al single crystals

This paper presents a dislocation density-based non-Schmid constitutive model to address the anomalous thermo-mechanical behaviour of the L1₂ intermetallic single-crystal Ni₃Al. Ni₃Al is used as a strengthening precipitate (γ′ phase) in Ni-based superalloys. Addressing such anomalous behaviour by accounting for temperature-dependent flow stress and hardening evolution, as well as orientation-dependent tension–compression asymmetry, is necessary for modelling superalloys across a range of temperatures. While hardening in cube-slip systems results from statistically stored dislocations (SSDs), hardening in octahedral slip systems is due to both SSDs and cross-slip dislocations (CSDs). The constitutive model incorporates hardening evolution due to SSDs and CSDs. Experimental data for Ni₃Al-type single crystals, available in the literature, are used to calibrate material parameters. Subsequently, results of crystal plasticity FEM simulations are compared with experimental data for several orientations under constant strain rate and creep loading conditions for a wide range of temperatures. The model is able to correctly predict the response of L1₂ intermetallic single crystals including features of anomalous flow stress and non-Schmid yield behaviour.     

大颗粒立方氮化硼单晶的合成

 在Mg-B-N体系中通过控制立方氮化硼晶体的成核率及生长速度，在4.5~6.0 GPa、1 500~1 900 ℃的高压高温条件下，在几分钟时间内，成功地获得了粒径达毫米量级的立方氮化硼单晶体，其最大单晶粒径达1.6 mm。研究了该体系中立方氮化硼单晶的生长特性，讨论了该种单晶体在Mg-B-N体系中的生长机制。     

X-Ray kinetic study of glassy crystal formation in adamantane derivatives: TTT curves and crystal size effect

Abstract

The kinetics of polymorphic solid-state transformation in mixed adamantane compounds (CN_1?x Cl _x ADM: x = 0 and x = 0.25) have been studied by X-ray scattering. The classical form of the time-temperature-transformation TTT curves has been directly observed for the first time for the ordering supercooled plastic phases. For both compounds a considerable effect of crystal size on the kinetics has been observed. For x = 0.25 it leads to a continuous transition from Avrami to nucleation behaviour. These observations help us to understand the factors controlling nucleation and growth as well as to establish better operating conditions in order to form a glassy crystal.     

A phase-field/Monte-Carlo model describing organic crystal growth from solution

In this paper work we present a phase-field/Monte-Carlo hybrid algorithm for the simulation of solutal growth of organic crystals. The algorithm is subsequently used for an investigation of diffusion effects on the growth mechanisms. This method combines a two-scale phase-field model of the liquid phase epitaxial growth and a Monte-Carlo algorithm of the 2D nucleation and thus is faster than previous purely Monte Carlo simulations of crystal growth. The inclusion of supersaturation and diffusion in the method allows the study of crystal growth under various growth conditions. Parameters used in the hybrid algorithm are bound to the energetic parameters of crystal faces, which can be estimated from a detailed study of the actual crystal structure based on a connected nets analysis, which allows the prediction of the shape and morphology of real crystals. The study of the diffusion effect is carried out based on an example of a hydroquinone crystal, which grows from the water solution at various supersaturations. The dependencies of the growth rate and the nucleation rate on the supersaturation indicate the change of the growth mechanism from spiral growth to 2D nucleation. The difference in the growth rate for various faces is in agreement with the crystal morphologies derived from the attachment energy method and observed experimentally. The main result of the simulation is the evaluation of engineering limits for choosing appropriate external process conditions.     

Precise in situ study of the kinetics of pressure-induced phase transition in CaF<Subscript>2</Subscript> including initial transformation stages

The kinetics of room-temperature phase transition in fluorite (CaF₂) single crystals under hydrostatic pressure up to 9 GPa was studied in situ by means of strain gauge compressibility measurements. Initial stages of the pressure-induced first-order phase transition kinetics (corresponding to less than 1% content of the new phase) were studied for the first time. In a broad range of concentrations of the new phase (5–20%), the transformation kinetics is well described within the framework of the classical Kolmogorov-Avrami-Mehl-Johnson model. The laws governing the initial and late stages of the transformation are more complicated and do not conform to the classical model. The initial stages involve avalanche growth in the nucleation rate corresponding to giant values of the Avrami exponent (n ≈ 20). At large concentrations of the new phase (above 30%), the transformation rate significantly decreases (saturation) as a result of the formation of a rigid cellular structure of the new phase.     

Size effects under plastic deformation of microcrystals and nanocrystals

A theoretical analysis of size effects in plastically deformed crystals with transverse sizes in micro and nanometer ranges has been performed in the framework of the dislocation-kinetic approach. The analysis is based on the evolution equation of the dislocation density in these crystals and takes into account the generation of dislocations from surface dislocation sources and the escape of dislocations from the crystal through the crystal surface. It has been established that the generation of dislocations from the sources leads to a strong strain hardening of the crystal and that the escape of dislocations through the crystal surface results in a fast equilibration of these two kinetic processes. As a result, there occurs a strong “exhaustion” of strain hardening of thin crystals at the early stage of their plastic deformation in accordance with experiments. According to the theory, the flow stresses σ and transverse sizes D of microcrystals and nanocrystals are related by the expressions σ ∼ D ⁻ⁿ (n = 0.625–1.0), which are in agreement with the experiment.