Critical Nucleus Size Research Articles

Exploring the crystallization path of lithium disilicate through metadynamics simulations

Understanding the crystallization mechanism in silica-based materials is of paramount importance to comprehend geological phenomena and to design novel materials for a variety of technological and industrial applications. In this work, we show that metadynamics simulations can effectively overcome a large energy barrier to crystallize from viscous oxide glass melts and can be used to identify the melt-to-crystal transition path of the lithium disilicate system. The accelerated atomistic simulation revealed of a two-step mechanism of the nanoscale crystal formation. First, a partially layered silica embryo appeared, and then a more ordered crystalline layer with size larger than the critical nucleus size was formed. Subsequently, lithium ions piled up around the silicate layer and triggered stacking of adjacent silicate layers, which eventually built a perfect crystal. Contrarily to previous hypotheses, no lithium metasilicate crystal was observed as a precursor of the homogeneous crystallization of lithium disilicate.

Assessment of the classical nucleation theory in supercooled nickel by molecular dynamics

In this work, we performed a thorough study of crystal nucleation rates in supercooled liquid (SCL) nickel by comparing molecular dynamics (MD) simulation results, theoretical calculations, and experimental data. Our aim was to assess the validity of the most used theoretical framework, the Classical Nucleation Theory (CNT), in describing homogeneous nucleation in a deeply supercooled liquid. To this end, we carried out MD simulations using an embedded atom interaction potential, which describes quite well the melting point, Tm, the enthalpy of fusion, Δh, and the liquid density, ρl, of our model material. We then determined the critical nucleus size and the diffusion coefficient in the temperature range from 0.68 to 0.80Tm. By combining the physical properties obtained from our MD simulations and the calculated crystal-liquid free energy difference, we compared the CNT predictions with the nucleation rates obtained directly via brute force MD simulations on a system with 4 million atoms. We found an excellent agreement between the theoretically calculated nucleation rates and the values obtained by MD simulations. Moreover, the CNT prediction for the nucleation rate agrees with experimental data at 1350 K. Our results confirm that the CNT is indeed a powerful tool to describe the nucleation kinetics in supercooled liquids.

Uncover cooling rate and temperature dependent on nucleation behavior of nicotinic acid

As the first step of the crystallization process, nucleation has always been a hot spot in the industry to track research, and it can provide people with new ideas for a better understanding of the crystallization process. In order to explore the nucleation behavior of nicotinic acid (NA) during the cooling crystallization process, we used the polythermal method to measure the metastable zone widths (MSZWs) of NA in ethanol. By analyzing Nývlt’s model, we find that the cooling rate and MSZW follow a reasonable linear relationship and calculate a nucleation order m < 4, which demonstrates the transient nucleation mechanism. Then the value of the surface roughness factor f is calculated, which indicates that continuous growth will occur at the crystal interface. The self-consistent Nývlt's-like model embeds the effect of saturation temperature on the MSZW, which proves to be a better fit. Furthermore, the modified Sangwal model provides a basis for further analysis of the nucleation behavior, from which we can obtain the critical nuclei size and the critical Gibbs free energy. Besides, we explore the relationship between γ and the driving force. We can conclude that temperature and driving force jointly affect the MSZW and the nucleation rate.

Identification of critical nuclei in the rapid solidification via configuration heredity

The identification and characterization of critical nuclei is a long-standing issue in the rapid solidification of metals and alloys. An ambiguous description for their sizes and shapes used to lead to an overestimation or underestimation of homogeneous nucleation rates in the framework of classical nucleation theory (CNT). In this paper, a unique method able to distinguish the critical nucleus from numerous embryos is put forward on the basis of configuration heredities of clusters during rapid solidifications. As this technique is applied to analyze the formation and evolution of various fcc-Al single crystal clusters in a large-scale molecular dynamics simulation system, it is found that the size n c and geometrical configuration of critical nuclei as well as their liquid–solid interfacial structure can be determined directly. For the present deep super-cooled system with an undercooling of , the average size of critical nuclei is demonstrated to be , but most of which are non-spherical lamellae. Also, their liquid–solid interfaces are revealed to be not an fcc-liquid duplex-phase interface but an fcc/hcp-liquid multi-phase structure. These findings shed some lights on the CNT, and a good agreement with previous simulations and experiments in indicates this technique can be used to explore the early-stage of nucleation from atomistic levels.

Follow-up ultrasonic vibration assisted laser welding dissimilar metals for nuclear reactor pump can end sealing

A novel follow-up ultrasonic vibration assisted welding process was proposed to reduce the common defects in laser welding of dissimilar metals for nuclear reactor pump can end sealing, such as unmixed zone, precipitated phase, and uneven element distribution. The influences of ultrasonic vibration on morphology, microstructure and property of C-276/304 laser-welded joint was analyzed. The results indicated that, the most significant ultrasonic vibration at welding position was achieved at parameters of 25 N pressing force and 13 mm distance from ultrasonic action point to welding position. By the application of follow-up ultrasonic vibration, the width of unmixed zone was reduced and the macro element distribution was homogenized due to the enhancement of molten convection. The average grain radius was refined from 1.03 μm to 0.55 μm because acoustic pressure in the molten pool reduced critical nucleus size rk and caused grain fragmentation. The higher diffusion coefficient and cooling rate caused by ultrasonic vibration suppressed element segregation, and thus the amount of precipitated phase decreased from 2.15% to 0.62%, which finally improved the intergranular corrosion resistance of weld metal. The load capacity of weld joint was improved by 12.6%, and the micro-hardness of weld metal was also increased, attributing to the grain refinement strengthening. The follow-up ultrasonic vibration process proposed in this paper provided an efficient, convenient and widely applicable process for laser seal welding of dissimilar metals for nuclear reactor pump can end sealing with higher qualities.

Competing nucleation of single- and double-layer Guinier\u2013Preston zones in Al\u2013Cu alloys

Solid-state precipitation is a key heat-treatment strategy for strengthening engineering alloys. Therefore, predicting the precipitation process of localized solute-rich clusters, such as Guinier–Preston (GP) zones, is necessary. We quantitatively evaluated the critical nucleus size and nucleation barrier of GP zones in Al–Cu alloys, illustrating the precipitation preferences of single-layer (GP1) and double-layer (GP2) GP zones. Based on classical nucleation theory using an effective multi-body potential for dilute Al–Cu systems, our model predicted GP1 and GP2 precipitation sequences at various temperatures and Cu concentrations in a manner consistent with experimental observations. The crossover between formation enthalpy curves of GP1 and GP2 with increasing cluster size determines the critical conditions under which GP2 zones can nucleate without prior formation of GP1 zones. This relationship reflects competing interactions within and between clusters. The results illustrate the underlying mechanisms of competing nucleation between zones, and provide guidance for tailoring aging conditions to achieve desired mechanical properties for specific applications.

Anormal Thermal History Effect on the Structural Dynamics of Probucol Infiltrated into Porous Alumina

Herein, broadband dielectric (BDS) and Fourier transform infrared spectroscopy (FTIR), together with differential scanning calorimetry (DSC) and X-ray diffraction (XRD), were applied to study the molecular dynamics, molecular interactions as well as physical stability of an amorphous Active Pharmaceutical Ingredient (API)—probucol (PRO)—infiltrated into anodic aluminum oxide (AAO) membranes of pore size, d ∼ 10–160 nm. Interestingly, the behavior of examined substance strongly depends on the applied thermal protocol. Remarkably, for the first time, we observed that the structural dynamics of the slowly cooled PRO under confinement is significantly enhanced when compared to that of the quenched material. This unusual behavior was interpreted as a result of surface-induced effects (including the formation of well-resolved interfacial H-bonded layer and adsorption–desorption processes near the interface) that are magnified by the extremely high sensitivity to density fluctuation of studied PRO, reflected in the enormous pressure coefficient of the glass transition temperature dTg/dp = 427 K/GPa. In fact, FTIR investigations revealed that PRO tends to self-associate under confinement and forms a strongly bonded interfacial layer, which controls the variation in the structural dynamics of core molecules. Finally, we observed that the tendency to crystallize of confined API is reduced with respect to the bulk, even though the critical size of PRO nuclei (rc ∼ 3 nm) is significantly lower than the smallest examined pore size. Nevertheless, after few weeks of storage, the investigated substance crystallized in larger pores, while it remained stable in the nanochannels of d = 10 nm. A combination of XRD and DSC measurements indicated that the infiltrated PRO forms two polymorphs, the stable form I (dominating in bulk) and unstable form II (prevailing under confinement). That means that porous matrices might be used to obtain and maintain prolonged stability of unstable polymorphic forms of API.

Modeling of Al and Ga Droplet Nucleation during Droplet Epitaxy or Droplet Etching.

The temperature dependent density of Al and Ga droplets deposited on AlGaAs with molecular beam epitaxy is studied theoretically. Such droplets are important for applications in quantum information technology and can be functionalized e.g., by droplet epitaxy or droplet etching for the self-assembled generation of quantum emitters. After an estimation based on a scaling analysis, the droplet densities are simulated using first a mean-field rate model and second a kinetic Monte Carlo (KMC) simulation basing on an atomistic representation of the mobile adatoms. The modeling of droplet nucleation with a very high surface activity of the adatoms and ultra-low droplet densities down to 5 × 10 cm is highly demanding in particular for the KMC simulation. Both models consider two material related model parameters, the energy barrier for surface diffusion of free adatoms and the energy barrier for escape of atoms from droplets. The rate model quantitatively reproduces the droplet densities with = 0.19 eV, = 1.71 eV for Al droplets and = 0.115 eV for Ga droplets. For Ga, the values of are temperature dependent indicating the relevance of additional processes. Interestingly, the critical nucleus size depends on deposition time, which conflicts with the assumptions of the scaling model. Using a multiscale KMC algorithm to substantially shorten the computation times, Al droplets up to 460 °C on a 7500 × 7500 simulation field and Ga droplets up to 550 °C are simulated. The results show a very good agreement with the experiments using = 0.19 eV, = 1.44 eV for Al, and = 0.115 eV, = 1.24 eV ( 300 °C) or = 1.24 + 0.06 (T[°C] − 300)/100 eV ( °C) for Ga. The deviating is attributed to a re-nucleation effect that is not considered in the mean-field assumption of the rate model.

Anomalous Behavior in the Nucleation of Ice at Negative Pressures.

Ice nucleation is a phenomenon that, despite the relevant implications for life, atmospheric sciences, and technological applications, is far from being completely understood, especially under extreme thermodynamic conditions. In this work we present a computational investigation of the homogeneous ice nucleation at negative pressures. By means of the seeding technique we estimate the size of the ice critical nucleus N_{c} for the TIP4P/Ice water model. This is done along the isotherms 230, 240, and 250K, from positive to negative pressures until reaching the liquid-gas kinetic stability limit (where cavitation cannot be avoided). We find that N_{c} is nonmonotonic upon depressurization, reaching a minimum at negative pressures in the doubly metastable region of water. According to classical nucleation theory we establish the nucleation rate J and the surface tension γ, revealing a retracing behavior of both when the liquid-gas kinetic stability limit is approached. We also predict a reentrant behavior of the homogeneous nucleation line. The reentrance of these properties is related to the reentrance of the coexistence line at negative pressure, revealing new anomalies of water. The results of this work suggest the possibility of having metastable samples of liquid water for long times at negative pressure provided that heterogeneous nucleation is suppressed.

Homogeneous nucleation in a Poiseuille flow

Nucleation in a dynamical environment plays an important role in the synthesis and manufacturing of quantum dots and nanocrystals. In this work, we investigate the effects of fluid flow (low Reynolds number flow) on the homogeneous nucleation in a circular microchannel in the framework of the classical nucleation theory. The contributions of the configuration entropy from the momentum-phase space and the kinetic energy and strain energy of a microcluster are incorporated in the calculation of the change of the Gibbs free energy from a flow state without a microcluster to a flow state with a microcluster. An analytical equation is derived for the determination of the critical nucleus size. Using this analytical equation, an analytical solution of the critical nucleus size for the formation of a critical liquid nucleus is found. For the formation of a critical solid nucleus, the contributions from both the kinetic energy and the strain energy are generally negligible. We perform numerical analysis of the homogeneous nucleation of a sucrose microcluster in a representative volume element of an aqueous solution, which flows through a circular microchannel. The numerical results reveal the decrease of the critical nucleus size and the corresponding work of formation of a critical nucleus with the increase of the distance to axisymmetric axis for the same numbers of solvent atoms and solute atoms/particles.

Nucleation rate in the two dimensional Ising model in the presence of random impurities.

Nucleation phenomena are ubiquitous in nature and the presence of impurities in every real and experimental system is unavoidable. Yet numerical studies of nucleation are nearly always conducted for entirely pure systems. We have studied the behaviour of the droplet free energy in two dimensional Ising model in the presence of randomly positioned static and dynamic impurities. We have shown that both the free energy barrier height and critical nucleus size monotonically decreases with increasing the impurity density for the static case. We have compared the nucleation rates obtained from the Classical Nucleation Theory and the Forward Flux Sampling method for different densities of the static impurities. The results show good agreement. In the case of dynamic impurities, we observe preferential occupancy of the impurities at the boundary positions of the nucleus when the temperature is low. This further boosts enhancement of the nucleation rate due to lowering of the effective interfacial free energy.

Crystallization of FCC and BCC Liquid Metals Studied by Molecular Dynamics Simulation

The atomic structure variations on cooling, vitrification and crystallization processes in liquid metals face centered cubic (FCC) Cu are simulated in the present work in comparison with body centered cubic (BCC) Fe. The process is done on continuous cooling and isothermal annealing using a classical molecular-dynamics computer simulation procedure with an embedded-atom method potential at constant pressure. The structural changes are monitored with direct structure observation in the simulation cells containing from about 100 k to 1 M atoms. The crystallization process is analyzed under isothermal conditions by monitoring density and energy variation as a function of time. A common-neighbor cluster analysis is performed. The results of thermodynamic calculations on estimating the energy barrier for crystal nucleation and a critical nucleus size are compared with those obtained from simulation. The differences in crystallization of an FCC and a BCC metal are discussed.

Molecular dynamics simulations of spontaneous and seeded nucleation and theoretical calculations for zinc selenide

Understanding and controlling the liquid to crystal transformation is a central topic for numerous natural phenomena and technological applications. However, the microscopic mechanism of crystal nucleation is still elusive, which leads to strong controversies regarding the ability of the most used model, the Classical Nucleation Theory (CNT), to describe nucleation rates in supercooled liquids. In this work, we were able to deeply supercool Zinc Selenide (ZnSe), and determine spontaneous homogeneous steady-state nucleation rates, JMD, by MD simulations using the mean lifetime method. At moderate supercoolings, where the nucleation rates are much smaller, we used the seeding method to compute the nucleation rates by the CNT formalism, JCNT, without any fitting parameter, using the physical properties obtained by MD simulations: the melting temperature, Tm, density, melting enthalpy, diffusion coefficient, D+, and the critical nucleus size, N∗, combined with two expressions for the thermodynamic driving force, Δμ. The values of interfacial free energy, γ, calculated by the CNT expression using the MD simulation data, via both the seeding method and the mean lifetime method at moderate and deep supercoolings show a weak temperature dependence, which is in line with the Diffuse Interface Theory. The extrapolated values of γ, from the spontaneous nucleation regime to the seeding nucleation region cover the range of values of γ calculated via the seeding method and the CNT formalism. Finally, the JCNT extrapolated from moderate supercoolings to deep supercoolings are in good agreement with the JMD. These results confirm the validity of the CNT.

Термодинамическая вероятность образования твердых растворов FexPb1−xS гидрохимическим осаждением

Analysis of the literature showed that narrow-gap lead sulfide PbS (0.4 eV at 300 K), due to its unique properties, has found wide application in such devices as photodetectors with a wide (from infrared to ultraviolet) radiation range, solar energy converters, chemical sensors, temperature sensors, flame detectors, etc. Doping of lead sulfide with various metal ions can affect the bandgap, and hence expand the scope of its application. Of particular interest is the preparation of thin film solid solutions in the PbS – FeS system, which can lead to the appearance of ferromagnetism in lead sulfide. To obtain doped films of lead sulfide and solid solutions based on it, the method of chemical deposition from aqueous media is considered promising, which, in addition to its cost-effectiveness and simplicity of the process, allows one to determine in advance the areas of formation of the semiconducting metal chalcogenides of interest. The analysis of ionic equilibria in the systems "PbAc2 – FeCl2 – Na3Cit – NH4OH – N2H4CS", "PbAc2 – FeCl2 – NaAc – NH4OH – N2H4CS "and " PbAc2 – FeCl2 – Na2С2О4 – NH4OH – N2H4CS "made it possible to reveal predominantly forms of metals in a given pH range. To assess the conditions for the deposition of the main and impurity phases by thermodynamic calculations taking into account the sizes of critical nuclei, the boundary conditions and regions of the formation of FeS, PbS, Fe(OH)2, Pb(OH)2 in the reaction systems under study were found. It is shown that the most promising for the preparation of the three-component PbFeS compound, which does not contain impurity phases of lead and iron hydroxides, is the reaction system "PbAc2 – FeCl2 – Na3Cit – NH4OH – N2H4CS". The possibility of obtaining PbS: Fe films with a uniform iron distribution of ~ 0.5 at.% and deviation from stoichiometry towards Pb deficiency (47.7 at.%) and S excess (50.7 at.%) was experimentally demonstrated.

Unraveling nucleation pathway in methane clathrate formation

Methane clathrates are widespread on the ocean floor of the Earth. A better understanding of methane clathrate formation has important implications for natural-gas exploitation, storage, and transportation. A key step toward understanding clathrate formation is hydrate nucleation, which has been suggested to involve multiple evolution pathways. Herein, a unique nucleation/growth pathway for methane clathrate formation has been identified by analyzing the trajectories of large-scale molecular dynamics (MD) simulations. In particular, ternary water-ring aggregations (TWRAs) have been identified as fundamental structures for characterizing the nucleation pathway. Based on this nucleation pathway, the critical nucleus size and nucleation timescale can be quantitatively determined. Specifically, a methane hydration layer compression/shedding process is observed to be the critical step in (and driving) the nucleation/growth pathway, which is manifested through overlapping/compression of the surrounding hydration layers of the methane molecules, followed by detachment (shedding) of the hydration layer. As such, an effective way to control methane hydrate nucleation is to alter the hydration layer compression/shedding process during the course of nucleation.

Combined effect of weak electric field and ions on critical water cluster: Insight from molecular dynamics simulation

The effects of ion and electric field on the vapor–liquid transition of water, are studied by using the optimal point charge (OPC) water model in this paper. A canonical Molecular Dynamics (MD) simulation approach, which calculates equilibrium time and the number of water molecules in the clusters, is employed to study the factors affecting the nucleation of water molecules. In addition, Quantum Mechanics (QM) method is adopted to calculate the hydration free energy of ions as a supplement. The results demonstrate that the ion has a significant promoting effect on vapor–liquid nucleation below the critical nucleus size (1–3 nm). However, as the cluster grows, the ion will no longer promote cluster growth, due to electrostatic shielding effect from the aggregated water molecules. When a weak uniform electric field (less than 0.1 V/nm) is applied, the promotion of the ion reappears. According to the trajectory analysis of ion in the water droplet, we believe that the electric field changes the relative position of ions in the droplets, thus weakening the shielding of water molecules. It is further demonstrated by a proposed novel statistical method, which provides an alternative, visualized and effective approach to evaluate the promotion effect in similar analyses, compared to radial distribution function.

Effect of Mg Treatment on the Nucleation and Ostwald Growth of Inclusions in Fe-O-Al-Mg Melt.

This study aimed to investigate the effect of Mg treatment on the nucleation and ostwald growth of inclusions. Deoxidized experiments with Al (0.05%Al) and Al-Mg (0.05%Al + 0.03%Mg) were carried out at 1873 K, and the composition, number, and size of inclusions were studied as a function of holding time. Homogeneous nucleation theory and ostwald ripening were utilized to calculate the nucleation rate, the critical size of nuclei, and coarsening rate of inclusions. The results show that small inclusions were more easily found in the steels with Al-Mg complex deoxidation, and the number of inclusions with Al-Mg complex deoxidation is larger at an early stage of deoxidation. The critical size of nuclei increases in the order of MgAl2O4 (0.3–0.4 nm) < Al2O3 (0.4–0.6 nm), and the nucleation rate increases in the order of Al2O3 (1100 cm−3 s−1) < MgAl2O4 (1200 cm−3s−1), which is consistent with the experimental results. Moreover, the coarsening rate of MgAl2O4 inclusions was smaller than Al2O3 inclusions in both the value of kd(cal.) from ostwald growth and the value of kd(obs.) from inclusion size. The effect of Mg addition on coarsening of inclusion was analyzed and their mechanism was discussed based on ostwald ripening theory and Factsage calculation.

Competitive Nucleation Mechanism for CsPbBr3 Perovskite Nanoplatelet Growth.

We analyze nucleation-controlled nanocrystal growth in a solution containing surface-binding molecular ligands, which can also nucleate compact layers on the crystal surfaces. We show that, if the critical nucleus size for ligands is larger and the nucleation barrier is lower than those for crystal atoms, the ligands nucleate faster than the atoms on relatively wide crystal facets but much slower, if at all, on narrow facets. Such competitive nucleation of ligands and atoms results in ligands covering predominantly wider facets, thus excluding them from the growth process, and acts as a selection mechanism for the growth of crystals with narrower facets, the so-called nanoplatelets. The theory is confirmed by Monte Carlo simulations and validated experimentally for CsPbBr3 nanoplatelets grown from solution. We find that the anisotropic crystal growth is controlled by the growth temperature and the strength of surface bonding for the passivating molecular ligands.

Energetics of heterogeneous Mg [formula omitted] deformation twinning migration using an atomistically informed phase-field model

We have constructed an atomistically informed phase-field model for the quantitative energetic analysis of phase transformations. In our model, to describe the general phase transformation with a non-linear correlation between displacive and diffusive modes, we have defined two order parameters, γ and ϕ, which describe the lattice distortion (displacive mode) and shuffling (diffusive mode), respectively. Our method provides a way to introduce the energetics from atomistic simulations to the phase-field model, describes γ and ϕ in an atomic model, and derives phase-field parameters from the free energy calculated by atomistic simulation. As an application of our model, we used the energetics obtained from atomistic simulations using a density functional theory potential, and we calculated the free energy change during the heterogeneous {101¯2} twin migration of hexagonally close-packed (HCP) Mg, which can be considered as a lattice distortion and shuffling mixed phase transformation, by combining our phase-field model with the nudged elastic band method. The activation energy, and the critical nucleus size of the heterogeneous {101¯2} twin migration under a set stress were derived. The critical c-axis tensile stress (athermal stress), at which the activation energy becomes zero, is consistent with the experimental yield stress of {101¯2} for the twinning deformation of HCP Mg nanopillars in tensile tests. The critical nucleus size of the heterogeneous {101¯2} twin migration is on the range of nanometers under several hundred megapascals stress, which is consistent with the experimental observation of nanotwins.

Ultrasound-assisted intensified crystallization of L-glutamic acid: Crystal nucleation and polymorph transformation.

In this paper, the crystallization of L-glutamic acid with application of ultrasound was explored in detail, including the process of nucleation, polymorphic control and polymorphic transformation. The induction time and metastable zone widths (MSZWs) were measured with and without ultrasound during the nucleation process. The induction time and MSZWs were decreased by ultrasound and the induction time was further decreased by higher ultrasonic power. The calculated nucleation parameters (such as interfacial energy, critical nucleus size and critical Gibbs energy) showed an obvious decrease in the presence of ultrasound, indicating that the nucleation was enhanced with application of ultrasound. By adjusting the ultrasonic power in the quench cooling process, the difference in nucleation temperatures would determine the distribution of polymorphs. In further, the polymorphic transformation was investigated quantitatively, and to the best of our knowledge, it was the first time to study the transformation kinetics with ultrasound using Avrami-Erofeev model. In the transformation process, the crystallization mechanism of the stable form was modified by ultrasound. The ultrasound eliminated the nucleation element in the rate-limiting step and facilitated the crystal growth of stable form. Thus, the ultrasound has a profound influence on L-glutamic acid crystallization.