Characterization of crystal growth using a spiral nucleation model

Classical concepts of two-dimensional nucleation and spiral growth are used together with recent findings on the dynamics of dislocation spirals to derive a new crystal growth model. Initial growth nuclei result from the organization of adsorbed molecules in spirals around surface dislocations. The energetic barrier for the activation of the spiral nuclei is considerably lower than the admitted by classical two dimensional nucleation models. Stable nuclei evolve into bigger growth hillocks in supersaturated media through the incorporation of adsorbed units into their steps. The displacement velocity of steps during solution and vapour growth is calculated by different kinetic approaches, taking into consideration the distinct role of surface diffusion in each process, and avoiding known limitations of conventional theories. A generalized expression is obtained relating the crystal growth rate with main variables such as supersaturation, temperature, crystal size, surface topology and interfacial properties. At the end of the paper, the crystallization kinetics of sucrose measured at 40 °C is interpreted in the light of the new perspectives resulting from the proposed model. The application example illustrates how to estimate interfacial and topological properties from the experimental crystal growth results.     

非晶一次晶化过程微观组织演化和生长动力学的相场法研究

在晶化物理模型中添加扩散系数对晶化过程的影响, 采用相场方法研究初始形核率和初始形核半径对一次晶化过程中微观组织和生长动力学的影响。结果表明: 随着初始形核率的增加, 相同时间内非晶一次晶化的晶粒数量逐渐增加, 晶粒尺寸逐渐减小。晶化分数随着演化时间和初始形核率的增加逐渐增大, 初始形核率越大, 相同演化时间内的晶化分数越高。不同初始形核半径情况下, 非晶一次晶化过程中的晶粒数量和尺寸随着演化时间的增加基本保持不变。晶化分数随着演化时间的增加而增大。不同初始形核率和初始形核半径情况下所对应的生长指数均小于1, 表明初始形核率和初始形核半径对晶化方式无影响, 均为一次晶化。改变初始形核率和初始形核半径可调控一次晶化微观组织结构, 而晶粒尺寸及晶化分数直接关系到合金性能。     

无容器过程中Pd-Ni-P系合金的过冷及金属玻璃形成

在1.2m落管中对Pd_43.5Ni_43.5P₁₃和Pd₄₀Ni₄₀P₂₀合金进行了无容器过冷实验。通过在落管中充以不同的惰性气体,从而调节过冷液滴的散热条件,研究了冷却速率对于Pd₄₀Ni₄₀P₂₀合金的玻璃形成、晶体成核和长大的影响。确定了在落管中形成玻璃的临界冷却速率。此外,液滴下落以前的初始温度也与玻璃形 关键词：     

Effect of ultrasound on the kinetics of anti-solvent crystallization of sucrose

The effect of ultrasound on the kinetics of anti-solvent crystallization of sucrose was studied. The influence of temperature, stirring rate, supersaturation and ultrasonic power on the anti-solvent crystallization of sucrose was investigated. The relationship between infrared spectral characteristic band of sucrose and supersaturation was determined with an online reaction analyzer. The crystal size distribution of sucrose was detected by a laser particle-size analyzer. Ultrasound accelerated the crystallization process, and had no impact on the crystal shape. Abegg, Stevens and Larson model was fitted to the experimental data, and the results were the following: At 298.15 K, the average size of crystals was 133.8 μm and nucleation rate was 4.87 × 10⁹ m⁻³·s⁻¹ without ultrasound. In an ultrasonic field, the average size was 80.5 μm, and nucleation rate was 1.18 × 10¹¹ m⁻³·s⁻¹. Ultrasound significantly reduced the average size of crystals and improved the nucleation rate. It was observed that the crystal size decreased with the increase of stirring rate in silent environment. When the stirring rate increased from 250 to 400 rpm, the average size decreased from 173.0 to 132.9 μm. However, the stirring rate had no significant impact on the crystal size in the ultrasonic field. In addition, the activation energy of anti-solvent crystallization of sucrose was decreased, and the kinetic constant of nucleation rate was increased due to the effect of ultrasound. In the ultrasonic field, the activation energy was reduced from 20422.5 to 790.5 J·mol⁻¹, and the kinetic constant was increased from 9.76 × 10² to 8.38 × 10⁸.     

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.     

Growth and size control in anti-solvent crystallization of glycine with high frequency ultrasound

Antisolvent crystallization of glycine was performed under ultrasonic irradiation of 1.6 MHz. The irradiation enhanced both the growth of α-glycine crystal and the uniformity in the crystal size. The degree of both enhancement effects increased with increasing ultrasonic power. While under the irradiation of 20 kHz ultrasound, no growth enhancement was observed, but the crystal size reduced as was reported in the literature. To elucidate the mechanism of growth enhancement, another experiment was designed and conducted to avoid the effect of nucleation from the sonocrystallization. The result suggests that the ultrasound enhances the incorporation of microcrystals to larger crystals. Probably, the collision between solid particles is intensified by the disturbance characterized by the high frequency ultrasound. The crystal growth was modeled with an apparent reaction of microcrystal and larger crystal. The result of the growth experiment was successfully predicted with a rate equation for pseudo first order reaction with a single parameter of rate constant. The rate constant linearly increased with the ultrasonic power. The analysis enables quantitative evaluation of the ultrasonic effect on the crystal growth.     

Energetics of Ge nucleation on SiO2 and implications for selective epitaxial growth

We have measured the time evolution of Ge nucleation density on SiO₂ over a temperature range of 673–973 K and deposition rates from 5.1 × 10¹³ atoms/cm² s (5 ML/min) to 6.9 × 10¹⁴ atoms/cm² s (65 ML/min) during molecular beam epitaxy. The governing equations from mean-field theory that describe surface energetics and saturation nucleation density are used to determine the size and binding energy of the critical Ge nucleus and the activation energy for Ge surface diffusion on SiO₂. The critical nucleus size is found to be a single Ge atom over substrate temperatures from 673 to 773 K, whereas a three-atom nucleus is found to be the critical size over substrate temperatures from 773 to 973 K. We have previously reported 0.44 ± 0.03 eV for the Ge desorption activation energy from SiO₂. This value, in conjunction with the saturation nucleation density as a function of substrate temperature, is used to determine that the activation energy for surface diffusion is 0.24 ± 0.05 eV, and the binding energy of the three-atom nucleus is 3.7 ± 0.1 eV. The values of the activation energy for desorption and surface diffusion are in good agreement with previous experiments of metals and semiconductors on insulating substrates. The small desorption and surface diffusion activation barriers predict that selective growth occurring on window-patterned samples is by direct impingement of Ge onto Si and ready desorption of Ge from SiO₂. This prediction is confirmed by the small integral condensation coefficient for Ge on SiO₂ and two key observations of nucleation behavior on the window-patterned samples. The first observation is the lack of nucleation exclusion zones around the windows, and second is the independence of the random Ge nucleation density on patterned versus unpatterned oxide surfaces. We also present the Ge nucleation density as a function of substrate temperature and deposition rate to demarcate selective growth conditions for Ge on Si with a window-patterned SiO₂ mask.     

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.     

Analysis of ferroelectric switching in sodium nitrite:poly(vinyl alcohol) nanocomposite films

The Fourier transform infrared (FTIR) spectra and switching current response in sodium nitrite:poly(vinyl alcohol) nanocomposite films have been studied as a function of composition of NaNO₂. The switching current data fitted well to infinite-grain model (IGM) in the region t<t _s and to finite-grain model (FGM) in the region t≥t _s . The microscopic parameters like the dimensionality, the domain wall velocity, and the nucleation rate have been evaluated which provide more physical insight of the switching phenomena in the composite films. The polarization current and nucleation rate are optimum in 50 wt.% composite film and have been discussed in terms of grain size and strain variations with the composition. The effect of applied field and pulse width variation on the switching behavior of 50 wt.% composition has also been studied. The exponential field dependence of the domain wall velocity and the nucleation rate indicate that nucleation mechanism is responsible for switching phenomena in the composite films. The writing pulse width affects significantly on the switching behavior of the composite films.     

Molecular dynamics simulation of homogeneous nucleation of KBr cluster

We perform molecular dynamics simulations to study the homogeneous nucleation in the freezing of molten potassium bromide clusters. The nucleation rates tend to decrease with increasing cluster size and temperature. The solid-liquid interfacial free energy σ_sl of 42.4-52.3 mJ/m² is close to the values predicted by Turnbull's relation and comparable to the experimental observation by Buckle and Ubbelohde. It is interesting to find that there is no cluster size effect on the critical nucleus size. Critical nucleus sizes inferred from classical nucleation theory are of 6.5-20.7 K⁺Br⁻ ionic pairs in the temperature range of 400-600 K. The critical nucleus size at bulk MD freezing temperature obtained by extrapolation is about 45 K⁺Br⁻ ionic pairs, which is comparable to the experimental value of NaCl.     

A poor man's interpretation of the Nozières-Gallet effect

Summary An interpretation of the effect proposed theoretically by Nozières and Gallet (and experimentally observed in⁴He), according to which the growth ratev of a crystal surface just below the roughening temperatureT _R is approximately linear in the disequilibrium Δμ, is given in terms of the properties of the nucleation process in the presence of a characteristic length l. The physical meaning ofl is the distance over which information can propagate on the surface before a new layer is formed. The nucleation barrier is lowered, because the size of a critical nucleus cannot exceedl, the latter being in turn proportional tov ^−1/2. A self-consistency condition ensues. The effect takes place when the correlation length ξ, which diverges atT _R, becomes comparable tol. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Effect of Ni on growth kinetics,microstructural evolution and crystal structure in the Cu(Ni)–Sn system

Abstract

The role of Ni addition in Cu on the growth of intermetallic compounds in the Cu–Sn system is studied based on microstructure, crystal structure and quantitative diffusion analysis. The diffraction pattern analysis of intermetallic compounds indicates that the presence of Ni does not change their crystal structure. However, it strongly affects the microstructural evolution and diffusion rates of components. The growth rate of (Cu,Ni)₃Sn decreases without changing the diffusion coefficient because of the increase in growth rate of (Cu,Ni)₆Sn₅. For 3 at.% or higher Ni addition in Cu, only the (Cu,Ni)₆Sn₅ phase grows in the interdiffusion zone. The elongated grains of (Cu,Ni)₆Sn₅ are found when it is grown from (Cu,Ni)₃Sn. This indicates that the newly formed intermetallic compound joins with the existing grains of the phase. On the other hand, smaller grains are found when this phase grows directly from Cu in the absence of (Cu,Ni)₃Sn indicating the ease of repeated nucleation. Grain size of (Cu,Ni)₆Sn₅ decreases with further increase in Ni content, which indicates a further reduction of activation barrier for nucleation. The relations for the estimation of relevant diffusion parameters are established considering the diffusion mechanism in the Cu(Ni)–Sn system, which is otherwise impossible in the phases with narrow homogeneity range in a ternary system. The flux of Sn increases, whereas the flux of Cu decreases drastically with the addition of very small amount of Ni, such as 0.5 at.% Ni, in Cu. Analysis of the atomic mechanism of diffusion indicates the contribution from both lattice and grain boundary for the growth of (Cu,Ni)₆Sn₅ phase.     

Effect of Interfacial Structure on Crystallization Behavior of Polypropylene/Polyolefin Elastomer/Barium Sulfate Ternary Composites

In this paper, interfacial structure induced development of crystallization behavior of polypropylene (PP)/polyolefin elastomer (POE)/barium sulfate (BaSO₄) ternary composites was studied by DSC. Two kinds of PP (copolymer and homopolymer) were used. The compatibility between PP and POE had a distinct influence on nucleation and crystal growth of PP in PP/POE binary composites. The crystallization rate of PP homopolymer increased because of the heterogeneous nucleation by POE, while the crystallinity of PP homopolymer decreased because of an inhibition effect of the hexane side chains in POE. BaSO₄ particles acted as heterogeneous nucleating agents of PP in ternary composites. The dispersion of BaSO₄, controlled by interfacial design, had a distinct influence on the nucleation activity of BaSO₄ in ternary composites. Interfacial structure had the same effect on nucleation activity of BaSO₄ particles and crystallization rate of PP matrix in PP copolymer ternary composites as those in PP homopolymer ternary composites.     

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.     

Growth kinetics of polymer crystals in bulk

Temperature-dependent measurements of spherulite growth rates carried out for i-polystyrene, poly(ε -caprolactone) and linear polyethylene show that the controlling activation barrier diverges at a temperature which is 14K, 22K and 12K, respectively, below the equilibrium melting points. We discuss the existence of such a “zero growth temperature” T _zg in the framework of a recently introduced thermodynamic multiphase scheme and identify T _zg with the temperature of a (hidden) transition between the melt and a mesomorphic phase which mediates the crystal growth. The rate-determining step in our model of crystal growth is the attachment of chain sequences from the melt onto the lateral face of a mesomorphic layer at the growth front. The necessary straightening of the sequence prior to an attachment is the cause of the activation barrier. A theory based on this view describes correctly the observations. With a knowledge of T _zg it is possible to fully establish the nanophase diagram describing the stability ranges of crystalline and mesomorphic layers in a melt. An evaluation of data from small-angle X-ray scattering, calorimetry and optical growth rate measurements yields heats of transition and surface free energies of crystals and mesophase layers, as well as the activation barrier per monomer associated with the chain stretching. According to the theory, the temperature dependence of the crystallization rate is determined by both the activation energy per monomer and the surface free energy of the preceding mesomorphic layer. Data indicate that the easiness of crystallization in polyethylene is first of all due to a particularly low surface free energy of the mesomorphic layer.     

Attainment of growth stability through the widening of Ostwold–Mier's zone width: A novel technique

A novel method has been found to enhance the metastable zone width of solutions in their supersaturated region in order to grow large size crystals at a faster rate under stabilized conditions. In which, the incorporation of a small quantity of ethylinediamine tetra acetic acid (EDTA) and hydrogen peroxide (H₂O₂) a well-known chelating agents, enhances Ostwold–Mier's metastable zone width significantly due to their chelating action. Also this incorporation reduces the secondary nucleation rate and enhances the growth rate of the crystal. Powder X-ray diffraction, Fourier transform infrared (FTIR), UV–visible–NIR studies for the grown crystal reveal that EDTA and H₂O₂ addition do not affect the crystalline quality. This concept has been realized with barium nitrate Ba(NO₃)₂, a potential SRS crystal. The complexation also promotes the growth rate leading to a rapid growth with high crystalline quality.     

冷却速率对温敏聚N-异丙基丙烯酰胺胶体结晶过程的影响

冷却速率对结晶过程具有重要的影响. 本文采用温敏poly-N-isopropylacrylamide (PNIPAM) 胶体晶体体系实时观察了冷却速率对结晶晶粒尺寸的影响. 通过高倍透射明场观察和Bragg衍射观察研究连续冷却下的晶粒形核和生长实时演化过程, 发现随着冷却速率的增加, PNIPAM胶体晶体晶粒尺寸不断减少. 晶粒尺寸与冷却速率符合幂指数关系, 与金属体系具有相似的演化规律.     

Quark matter nucleation in hot hadronic matter

We study the quark deconfinement phase transition in hot β-stable hadronic matter. Assuming a first order phase transition, we calculate the enthalpy per baryon of the hadron–quark phase transition. We calculate and compare the nucleation rate and the nucleation time due to thermal and quantum nucleation mechanisms. We compute the crossover temperature above which thermal nucleation dominates the finite temperature quantum nucleation mechanism. We next discuss the consequences for the physics of proto-neutron stars. We introduce the concept of limiting conversion temperature and critical mass M_cr for proto-hadronic stars, and we show that proto-hadronic stars with a mass M<M_cr could survive the early stages of their evolution without decaying to a quark star.     

超薄膜多中心生长过程的计算机模拟

利用计算机模拟了不同的允许扩散步数下超薄膜的多中心分形生长和团状生长现象,研究了成核及长大的动力学过程．分形生长时分形维数随团簇大小的增大而增加．分形生长和团状生长时成核率随扩散步数的增大而减小,随时间的增大而急速下降．团簇长大过程可用团簇大小S和生长时间t-t₀的幂函数(t-t₀)^κ描述．由于团簇间的分流作用,生长指数κ比经典理论值1略小,并且存在着非线性现象,即长得较大的团簇的生长指数Κ也较大. 关键词：     

Crystallization Kinetics of Lamellar Crystals Confined in Polymer Thin Films

We used dynamic Monte Carlo simulations to investigate the crystallization kinetics of flat-on lamellar polymer crystals in variable thickness films. We found that the growth rates linearly reduced with decreasing film thickness for the films thinner than a transition thickness d_t , while they were constant for the films thicker than d_t . Moreover, the mean stem lengths (crystal thickness) we calculated decreased with film thickness in a similar way to the growth rates, and the intramolecular crystallinities we calculated confirmed the film thickness dependence of the crytsal thickness. Besides, the crystal melting rates in thin films were calculated and increased with decreasing film thickness. We proposed a new interpretation on the film thickness dependence of the crystal growth rate in thin films, suggesting that it is dominated by the crystal thickness in terms of the driving force term (l–l _min) expressed by Sadler, rather than the chain mobility based on experiments. The crystal thickness can determine whether a crystal grows or melts in a thin film at a fixed temperature, indicating the reversibility between the crystal growth and melting.