Nucleation Theory Research Articles

Microscopic mechanism of water-assisted diffusional phase transitions in inorganic metal halide perovskites.

The stability of perovskite materials is profoundly influenced by the presence of moisture in the surrounding environment. While it is well-established that water triggers and accelerates the black-yellow phase transition, leading to the degradation of the photovoltaic properties of perovskites, the underlying microscopic mechanism remains elusive. In this study, we employ classical molecular dynamics simulations to examine the role of water molecules in the yellow-black phase transition in a typical inorganic metal halide perovskite, CsPbI3. We have demonstrated, through interfacial energy calculations and classical nucleation theory, that the phase transition necessitates a crystal-amorphous-crystal two-step pathway rather than the conventional crystal-crystal mechanism. Simulations for CsPbI3 nanowires show that water molecules in the air can enter the amorphous interface between the black and yellow regions. The phase transition rate markedly increases with the influx of interfacial water molecules, which enhance ion diffusivity by reducing the diffusion barrier, thereby expediting the yellow-black phase transition in CsPbI3. We propose a general mechanism through which solvent molecules can greatly facilitate phase transitions that otherwise have prohibitively high transition energies.

Evaluation of transition rates from nonequilibrium instantons

Equilibrium rate theories play a crucial role in understanding rare, reactive events. However, they are inapplicable to a range of irreversible processes in systems driven far from thermodynamic equilibrium like active and biological matter. Here we develop an efficient numerical method to compute the rate constant of rare nonequilibrium events in the weak-noise limit based on an instanton approximation to the stochastic path integral and illustrate its wide range of application. We demonstrate excellent agreement of the instanton rates with numerically exact results for a particle under a nonconservative force. We also study phase transitions in an active field theory. We elucidate how activity alters the stability of the two phases and their rates of interconversion in a manner that can be well described by modifying classical nucleation theory. Published by the American Physical Society 2024

What will be the Euclidean dimension of an Ising ferromagnetic cubic shell?

The equilibrium and nonequilibrium properties of an Ising ferromagnetic cubic shell have been extensively studied by Monte Carlo simulation using Metropolis single spin flip algorithm. Although, geometrically the Euclidean dimension of the cubical shell is three, interestingly, the Ising ferromagnetic cubic shell undergoes ferromagnetic phase transition at a temperature which is very close to that for two-dimensional Ising ferromagnet. Surprisingly, the Ising ferromagnetic cubic shell shows a strange (neither exponential nor stretched exponential) kind of relaxation behaviour, instead of exponential relaxation as usually observed in the two dimensional Ising ferromagnet. The metastable lifetime of a ferromagnetic Ising cubical shell is studied as a function of the applied magnetic field. Here also, the cubic shell behaves more likely a two-dimensional object as found from statistical analysis and comparison with Becker-Döring prediction of classical nucleation theory.

Modeling of the perovskite nickelate SmNiO3 nucleation from amorphous thin films: A Volmer's thermodynamical approach

We present a thermodynamical model based on Volmer's nucleation theory adapted to the case of the perovskite nickelate SmNiO3 crystallization (SNO) from an amorphous (aSNO) thin film. This amorphous phase is synthesized via reactive magnetron sputtering and then subsequently annealed in air at temperatures between 725 and 925 K to crystallize it. This model allows to predict the theoretical nucleation rate of the crystallized perovskite phase according to the annealing temperature, the type of the nucleation (homogeneous and heterogeneous mechanisms) and to estimate some physical and thermodynamical data related to this transformation. A theoretical evaluation of the nucleation rate shows that the optimum temperature for crystallization is close to 800 K for which the nucleation rate can reach 1021 m-3.s-1 if considering both homogeneous and heterogeneous nucleation mechanisms. As the annealing temperature moves away from 800 K, the theoretical nucleation rate drops drastically, as observed experimentally by X-ray Diffraction (XRD) when we annealed 200 nm thick aSNO films. The good agreement between the presented model and the experimental crystallization results allows us to numerically evaluate some physical parameters not yet reported to date in the literature for SNO perovskites such as the surface energy between the amorphous and the crystallized SNO phases, the strain energy when the crystallization occurs and the enthalpy associated with crystallization.

Numerical simulation of a two-dimensional Blume-Capel ferromagnet in an oscillating magnetic field with a constant bias

We perform a numerical study of the kinetic Blume-Capel (BC) model to find if it exhibits the metamagnetic anomalies previously observed in the kinetic Ising model for supercritical periods [P. Riego , ; G. M. Buendía , ]. We employ a heat-bath Monte Carlo (MC) algorithm on a square lattice in which spins can take values of ±1,0, with a nonzero crystal field, subjected to a sinusoidal oscillating field in conjunction with a constant bias. In the ordered region, we find an equivalent hysteretic response of the order parameters with its respective conjugate fields between the kinetic and the equilibrium model. In the disordered region (supercritical periods), we observed two peaks, symmetrical with respect to zero bias, in the susceptibility and scaled variance curves, consistent with the numerical and experimental findings on the kinetic Ising model. This behavior does not have a counterpart in the equilibrium model. Furthermore, we find that the peaks occur at higher values of the bias field and become progressively smaller as the density of zeros, or the amplitude of the oscillating field, increases. Using nucleation theory, we demonstrate that these fluctuations, as in the Ising model, are not a critical phenomenon, but that they are associated with a crossover between a single-droplet (SD) and a multidroplet (MD) magnetization switching mechanism. For strong (weak) bias, the SD (MD) mechanism dominates. We also found that the zeros concentrate on the droplets' surfaces, which may cause a reduced interface tension in comparison with the Ising model [M. Schick , ]. Our results suggest that metamagnetic anomalies are not particular to the kinetic Ising model, but rather are a general characteristic of spin kinetic models, and provide further evidence that the equivalence between dynamical phase transitions and equilibrium ones is only valid near the critical point. Published by the American Physical Society 2024

Unveiling exotic multi-scale microstructure transformation and crack formation mechanisms in eutectic ceramic composite by laser powder bed fusion

Laser powder bed fusion (LPBF) represents an advanced and versatile technology. Exploiting its distinctive advantages for direct and rapid fabrication of complex-structured melt-grown oxide eutectic ceramic composite represents a pioneering yet challenging endeavor. In this work, LPBF is creatively employed to fabricate turbine blade-shaped, in-situ ternary eutectic ceramic composite. Through the integration of experimental procedures, Finite element method (FEM) simulations, and numerical analyses, an innovative design and manufacturing of oxide eutectic ceramic composites have been successfully established. Comprehensive FEM simulations, with detailed interface characteristic analysis, have revealed macro-scale cracks induced by intense maximum principal stress, and micro-cracks stemming from significant interfacial energy disparities among the three constituent phases. The applications of rapid solidification and nucleation theories have facilitated profound insights into the formation mechanisms of multi-scale exotic microstructures, including top-layer coarse dendrites, rosette-like spherical internally grown eutectic colony within layers, and columnar eutectic colonies with ultra-fine lamellar eutectic structures. Micro-mechanical property testing reveals enhanced performance in the inter-layer ultra-fine lamellar eutectic structure, which is attributed to a refined eutectic spacing of approximately 61 nm, coupled with distinct and robust bonding interfaces. These groundbreaking achievements, focusing on the processing-microstructure-property relationship in the fabrication of gas turbine blade-shaped solidified eutectic ceramic composite using LPBF, provide invaluable theoretical insights and data. This knowledge is crucial for the LPBF production of high-temperature structural materials, highlighting its significant potential applications in fields of aerospace and mechanical engineering.

Precision Seismicity of the San Andreas Fault System in Central California: Insights into Active Tectonics and Earthquake Physics

Since the late 1960s, seismicity of the San Andreas Fault system in central California has been under intense observation by U. S. Geological Survey’s Northern California Seismic Network (NCSN). Designed to provide accurate focal depth control and a low magnitude of catalog completeness, the network maps fault, both large and small across the full breadth of this 400-kilometer-long portion of the plate boundary, including many that are known only from their seismicity. Beginning in 1984, with the advent of routine digital recording, new opportunities were created to significantly enhance the spatial resolution of seismicity. This led to the co-evolution of method that take full advantage of digital waveforms and new insights into the nature of seismicity and faults. Collectively referred to as precision seismicity, discoveries included repeating earthquakes and highly organized and stable distributions of seismicity on major faults. Long term observation of seismicity before and after the six largest earthquakes over the last half-century underscore the outstanding challenges for earthquake predictability and theories of earthquake nucleation.

Modeling phase separation in solids beyond the classical nucleation theory: Application to FeCr.

Despite a large amount of work being devoted to study the phase separation in solids, the underlying physical mechanism responsible for such diffusive first-order phase transitions remains difficult to model outside the spinodal regime, i.e., in the nucleation and growth regime. This work presents an alternative of the classical nucleation theory for modeling phase separation in this regime, even for systems far from the solubility limit, i.e., for high degree of meta-stability where the classical nucleation theory does not hold. This method then allows a direct comparison between simulations and experiments always performed in solids with a high degree of meta-stability.

High-speed Ta2O5-based threshold switching memristor for LIF neurons

Due to their high similarity to biological ion channels, low power consumption, small footprint, and the fact that they do not require reset circuits, threshold switching memristors have been intensively studied for simulating neurons in neuromorphic chips. Switching speed is one of the key challenges which limit the application of threshold switching memristors in chips. In this study, Ta2O5 threshold switching memristors with high switching speeds were prepared by doping with silver. The results show that 14 wt. % Ag doped Ta2O5 threshold switching memristors exhibit excellent bi-directional threshold switching performance, featuring fast switching speeds (<20 ns, <18 ns), low leakage currents (<10 pA), and high switching ratio (>107). According to the field nucleation theory, the rapid switching speed can be attributed to the low nucleation energy (0.26 eV) of silver within the Ta2O5 matrix, which is achieved by incorporating 14 wt. % Ag during the doping process. Based on Pspice, a LIF (leaky integrate-and-fire) neuron based on the silver nanoparticles doped Ta2O5 threshold switching memristors is built, and its firing function has been simulated. The results show that the LIF neuron with a short switching time is able to excite pulse spiking with high frequencies. These results demonstrated that the silver nanoparticles doped Ta2O5-based threshold switching memristors hold significant potential for constructing high-speed artificial neural networks.

On the theory of the nucleation of gas bubbles at grain boundaries and incoherent inclusions

On the base of the critical analysis of two-dimensional models of the nucleation of gas filled bubbles at grain boundaries of helium-implanted specimens under the action of tensile stresses, a new model is developed within the framework of the Reiss theory of homogeneous nucleation in binary systems. This approach considers that gas bubbles are formed as a result of agglomeration in a binary system of vacancies and gas atoms at grain boundaries, avoiding significant simplifications of previous models based on the classical nucleation theory for single-component (unary) systems. The new model is extended to consider the nucleation of Xe bubbles at grain boundaries in UO2 under irradiation conditions and can be used for numerical analysis of experimental observations after the foreseen implementation in a fuel performance code. A similar approach can be applied to the nucleation and growth of gas bubbles on incoherent inclusions, such as those observed in irradiated ODS steels.

Development of an advanced hydride reorientation model for Zircaloy cladding and its experimental validation

Hydride reorientation, which occurs under hoop stress during cooling, stands out as a primary mechanism for material degradation in spent fuel management. The radial hydride fraction (RHF) is strongly involved in the mechanical integrity of cladding, highlighting the necessity for a robust modeling framework for quantitative analysis. However, the predictability of previous thermodynamic models for hydride reorientation in reactor-grade Cold Worked Stress Relieved (CWSR) Zircaloy has been hindered due to the intricate nature of hydride reorientation and the difficulties in characterizing microstructures. Recent successful EBSD characterization of reactor-grade CWSR Zircaloy have revealed valuable insights into microstructural characteristics of hydrides, enabling advancements in the modeling framework of hydride reorientation. This study aims to develop a thermodynamic model specifically focused on predicting the RHF. The developed thermodynamic model, based on classical nucleation theory, integrates aforementioned microstructural findings, combined with the Hydride-Nucleation-Growth-Dissolution (HNGD) model to capture transient precipitation behavior during cooling. Extensive experimental validations demonstrate enhanced predictability of the model. Additionally, the study examines the sensitivities of hydride reorientation to hydrogen concentration, applied stress, and cooling rate. It also provides predictions on reorientation behavior for engineering implications such as extension of wet storage, matrix hardening, recrystallization, and thermal cycling, supported by plausible explanations rooted in the underlying physical mechanisms elucidated through the model.

Numerical simulations of freezing behaviors of water droplets impacting cold hydrophobic surfaces

Freezing, as a prominent phase transition phenomenon, occurs frequently in nature and industry. This study employs a combination of the Volume of Fluid(VOF) model, solidification model, and a dynamic contact angle model to simulate the dynamics and solidification process of droplets impacting supercooled surfaces. Two distinct freezing morphologies, central-concave and central-convex, are observed. These different morphologies are attributed to the competition between the time scales associated with droplet impact dynamics and solidification (retraction time tr and solidification time tf,p). Thus, we propose a scaling law to predict the occurrence of different morphologies: when tr < tf,p, the final freezing morphology exhibits a central-convex shape, while when tr > tf,p, it exhibits a central-concave shape. In order to explore effects of nucleation on solidification, the classical nucleation theory is adopted to determine the nucleation time, and thus the freezing behaviors can be well captured. Furthermore, we examine the effect of volume expansion during phase transition on the freezing behaviors, and find that the increase in freezing time due to volumetric expansion can be well predicted by the scaling law tf ∼ Δ(H2)/ΔT.

Crystallization Kinetics of Tacrolimus Monohydrate in an Ethanol–Water System

Nucleation and growth during the crystallization process are crucial steps that determine the crystal structure, size, morphology, and purity. A thorough understanding of these mechanisms is essential for producing crystalline products with consistent properties. This study investigates the solubility of tacrolimus (FK506) in an ethanol–water system (1:1, v/v) and examines its crystallization kinetics using batch crystallization experiments. Initially, the solubility of FK506 was measured, and classical nucleation theory was employed to analyze the induction period to determine interfacial free energy (γ) and other nucleation parameters, including the critical nucleus radius (r*), critical free energy (∆G*), and the molecular count of the critical nucleus (i*). Crystallization kinetics under seeded conditions were also measured, and the parameters of the kinetic model were analyzed to understand the effects of process states such as temperature on the crystallization process. The results suggested that increasing temperature and supersaturation promotes nucleation. The surface entropy factor (f) indicates that the tacrolimus crystal growth mechanism is a two-dimensional nucleation growth. The growth process follows the particle size-independent growth law proposed by McCabe. The estimated kinetic parameters reveal the effects of supersaturation, temperature, and suspension density on the nucleation and growth rates.

Modeling and Experimental Validation of Cell Morphology in Microcellular-Foamed Polycaprolactone.

This study investigates the modeling and experimental validation of cell morphology in microcellular-foamed polycaprolactone (PCL) using supercritical carbon dioxide (scCO2) as the blowing agent. The microcellular foaming process (MCP) was conducted using a solid-state batch foaming process, where PCL was saturated with scCO2 at 6 to 9 MPa and 313 K, followed by depressurization at a rate of -0.3 and -1 MPa/s. This study utilized the Sanchez-Lacombe equation of state and the Peng-Robinson-Stryjek-Vera equation of state to model the solubility and density of the PCL-CO2 mixture. Classical nucleation theory was modified and combined with numerical analysis to predict cell density, incorporating factors such as gas absorption kinetics, the role of scCO2 in promoting nucleation, and the impact of depressurization rate and saturation pressure on cell growth. The validity of the model was confirmed by comparing the theoretical predictions with experimental and reference data, with the cell density determined through field-emission scanning electron microscopy analysis of foamed PCL samples. This study proposes a method for predicting cell density that can be applied to various polymers, with the potential for wide-ranging applications in biomaterials and industrial settings. This research also introduces a Python-based numerical analysis tool that allows for easy calculation of solubility and cell density based on the material properties of polymers and penetrant gases, offering a practical solution for optimizing MCP conditions in different contexts.

Nanoscale inhomogeneities in undercooled benzoic acid: A molecular dynamics study

The dynamics of undercooled organic liquids is very complex and still far from being fully understood. A major problem is the lack of general algorithms to recognize nanoscale inhomogeneities that exploit different inner structures with respect to the bulk liquid. We show that a geometry-independent energy criterion, coupled with the requirement that the cluster must survive for times longer than thermal fluctuations, can be consistently used to individuate persistent and recognizable (meta)stable inhomogeneities or, possibly, subcritical clusters in benzoic acid. The algorithm applies to all organic liquids, regardless of their ability to form hydrogen bonds. We show that undercooled benzoic acid becomes granular with respect to the thermodynamically stable liquid, hosting medium size inhomogeneities composed of up to 17 molecules for durations on the order of hundreds of picoseconds. These correlate with the predicted increase of density and viscosity upon undercooling. Most important, the inner structure of these inhomogeneities is intermediate between the liquid and the crystal. Stacking interactions, analogue to those present in the crystal, begin to develop in the largest persistent clusters. The pros and cons of the method are discussed in the context of non-classical nucleation theories.

Metastable water at several compression rates and its freezing kinetics into ice VII

Water can be dynamically over-compressed well into the stability field of ice VII. Whether water then transforms into ice VII, vitreous ice or a metastable novel crystalline phase remained uncertain. We report here the freezing of over-compressed water to ice VII by time-resolved X-ray diffraction. Quasi-isothermal dynamic compression paths are achieved using a dynamic-piezo-Diamond-Anvil-Cell, with programmable pressure rise time from 0.1 ms to 100 ms. By combining the present data set with those obtained on various ns-dynamical platforms, a complete evolution of the solidification pressure of metastable water versus the compression rate is rationalized within the classical nucleation theory framework. Also, when crystallization into ice VII occurs in between 1.6 GPa and 2.0 GPa, that is in the stability field of ice VI, a structural evolution over few ms is then observed into a mixture of ice VI and ice VII that seems to resolve apparent contradictions between previous results.

Cluster-dynamics-based parameterization for sulfuric acid–dimethylamine nucleation: comparison and selection through box and three-dimensional modeling

Abstract. Clustering of gaseous sulfuric acid (SA) enhanced by dimethylamine (DMA) is a major mechanism for new particle formation (NPF) in polluted atmospheres. However, uncertainty remains regarding the SA–DMA nucleation parameterization that reasonably represents cluster dynamics and is applicable across various atmospheric conditions. This uncertainty hinders accurate three-dimensional (3-D) modeling of NPF and the subsequent assessment of its environmental and climatic impacts. Here we extensively compare different cluster-dynamics-based parameterizations for SA–DMA nucleation and identify the most reliable one through a combination of box model simulations, 3-D modeling, and in situ observations. Results show that the parameterization derived from Atmospheric Cluster Dynamic Code (ACDC) simulations, incorporating the latest theoretical insights (DLPNO-CCSD(T)/aug-cc-pVTZ//ωB97X-D/6-311++G(3df,3pd) level of theory) and adequate representation of cluster dynamics, exhibits dependable performance in 3-D NPF simulation for both winter and summer conditions in Beijing and shows promise for application in diverse atmospheric conditions. Another ACDC-derived parameterization, replacing the level of theory with RI-CC2/aug-cc-pV(T+d)Z//M06-2X/6–311++G(3df,3pd), also performs well in NPF modeling at relatively low temperatures around 280 K but exhibits limitations at higher temperatures due to inappropriate representation of SA–DMA cluster thermodynamics. Additionally, a previously reported parameterization incorporating simplifications is applicable for simulating NPF in polluted atmospheres but tends to overestimate particle formation rates under conditions of elevated temperature (&gt;∼300 K) and low-condensation sink (&lt;∼3×10-3 s−1). Our findings highlight the applicability of the new ACDC-derived parameterization, which couples the latest SA–DMA nucleation theory and holistic cluster dynamics, in 3-D NPF modeling. The ACDC-derived parameterization framework provides a valuable reference for developing parameterizations for other nucleation systems.

Incubation of Amyloidogenic Peptides in Reverse Micelles Allow Active Control of Oligomer Size and Study of Protein-Protein Interactions.

Studies of the structure and dynamics of oligomeric aggregates of amyloidogenic peptides pose challenges due to their transient nature. This concept article provides a brief overview of various nucleation mechanisms with reference to the classical nucleation theory and illustrates the advantages of incubating amyloidogenic peptides in reverse micelles (RMs). The use of RMs not only facilitates size regulation of oligomeric aggregates but also provides an avenue to explore protein-protein interactions among the oligomeric aggregates of various amyloidogenic peptides. Additionally, we envision the feasibility of preparing brain tissue-derived oligomeric aggregates using RMs, potentially advancing the development of monoclonal antibodies with enhanced potency against these pathological species in vivo.

Metastable zone width and nucleation kinetics of vanillyl alcohol crystallization in various solvents

In this study, linear cooling batch crystallization of vanillyl alcohol using a laser power system was carried out to experimentally measure the metastable zone widths of vanillyl alcohol in selected solvents (ethanol, 2-propanol, and methyl cyanide) at various saturated temperatures (40, 50, and 60 °C), cooling rates (0.5, 1, 1.5, and 2 °C/min), and agitation speeds (300, 400 rpm). Besides, the sonocrystallization of vanillyl alcohol in ethanol was conducted for measuring MSZW at a various ultrasonic amplitudes (0 %, 25 %, 50 %, and 100 %) at a fixed temperature of 40 °C, cooling rate of 1 °C/min, and agitation speed of 300 rpm. For all three solvents, the MSZW decreases with saturation temperature, while it increases with cooling rate, and this trend doesn’t change for different agitation speeds. Three models—the self-consistent Nývlt-like model, the classical 3D nucleation theory model, and the simplified linear integral model based on classical nucleation theory (CNT)—were employed to estimate the nucleation kinetic parameters for vanillyl alcohol in three solvents. The goodness fit of the models were checked by the coefficient of determination (R-squared). The R-squared values reflected a very good fit between the experimental and predicted values and implied that the models are reliable to estimate nucleation kinetic parameters. Additionally, the interfacial energy between vanillyl alcohol and the solvents was observed to decrease with increasing temperature. Overall, the results indicate that a low nucleation order and low interfacial energy suggest weak solute–solvent interactions, making nucleation easier in the following order: methyl cyanide > ethanol > 2-propanol.

A microscopic approach to crystallization: Challenging the classical/non-classical dichotomy.

We present a fundamental framework for the study of crystallization based on a combination of classical density functional theory and fluctuating hydrodynamics that is free of any assumptions regarding order parameters and that requires no input other than molecular interaction potentials. We use it to study the nucleation of both droplets and crystalline solids from a low-concentration solution of colloidal particles using two different interaction potentials. We find that the nucleation pathways of both droplets and crystals are remarkably similar at the early stages of nucleation until they diverge due to a rapid ordering along the solid pathways in line with the paradigm of "non-classical" crystallization. We compute the unstable modes at the critical clusters and find that despite the non-classical nature of solid nucleation, the size of the nucleating clusters remains the principle order parameter in all cases, supporting a "classical" description of the dynamics of crystallization. We show that nucleation rates can be extracted from our formalism in a systematic way. Our results suggest that in some cases, despite the non-classical nature of the nucleation pathways, classical nucleation theory can give reasonable results for solids but that there are circumstances where it may fail. This contributes a nuanced perspective to recent experimental and simulation work, suggesting that important aspects of crystal nucleation can be described within a classical framework.