Nucleation Parameters Research Articles

Application of an Instability‐Based Fracture Model for Prediction of Crack Initiation in Modified 9Cr–1Mo Steel

ABSTRACTDuctile fracture of modified 9Cr–1Mo steel was investigated using smooth and notched bar tension tests. Round and flat notched specimens with varying notch acuity ratio were used to investigate the influence of stress state on the fracture strain. Simulations of the experiments were performed using the extended finite element method, together with an instability‐based crack initiation criterion based on the micromechanics of void coalescence. The parameters in the plasticity model were determined using smooth bar tension tests, whereas the void nucleation parameters were calibrated from experiments on a shallow‐notched specimen. Subsequently, the load–deflection responses and strain to crack initiation have been predicted for round and flat notched specimens with various notch acuities, and central notched specimens with notches oriented at various angles to the loading axis. Using a single set of parameters, the model was able to quantitatively predict fracture in different specimen geometries encompassing a range of stress states.

Electrochemical Properties of CeCl3 by Fitting Cyclic Voltammetry Data to a Kinetic Model Accounting for Adsorption and Nucleation

Due to the co-deposition phenomenon of actinides and rare Earth elements in the electrorefining process, understanding the electrochemical properties of rare Earth elements is crucial for element separation in spent nuclear fuel reprocessing. In this paper, a kinetic model for electrorefining is established to cover the adsorption and nucleation mechanisms occurring on the electrode surface. The study simulates the cyclic voltammetry of cerium (Ce) in molten LiCl-KCl at a temperature of 773 K, with varying scan rates and concentrations, using the model. The electrochemical properties of Ce are deduced by fitting the experimental voltammetry data. The model is validated by comparing derived properties with those from experimental data. Notably, the diffusion coefficient and apparent potential obtained from the model agree well with those obtained experimentally. Finally, the effects of adsorption and nucleation parameters on the behaviors of Ce were explored.

On the calibration of thermo-microstructural simulation models for Laser Powder Bed Fusion process: Integrating physics-informed neural networks with cellular automata

Computational thermo-microstructural modeling has become a powerful tool for understanding the process-microstructure linkage in the Laser Powder Bed Fusion (PBF-LB) technique. Developing models that accurately represent experimental results requires properly calibrating non-measurable model parameters through computationally intensive inverse analysis. This study details the calibration of a thermo-microstructural model based on observations from single-track PBF-LB experiments for Hastelloy X (HX) alloy. The calibration framework integrates physics-informed neural networks (PINNs) for thermal analysis and cellular automata (CA) for microstructure simulation. Initially, a PINNs model is trained in an unsupervised fashion and validated against finite element simulation results to serve as a parametric solution for predicting single-track temperature profiles and melt pool dimensions under various PBF-LB process settings and heat source parameters. Due to the high computational efficiency of the PINNs model and its ability to provide high-order derivatives through automatic differentiation, the model can be effectively used in the inverse calibration of the heat source parameters in the thermal model based on experimentally measured melt pool dimensions. The calibrated thermal model then supplies temperature data for subsequent CA microstructure modelling, where the nucleation parameters and the temperature dependence of the grain growth rate need to be determined. In addition, this study thoroughly discusses the challenges in calibrating the microstructural model, particularly based on experimental observations from single PBF-LB tracks. Ultimately, it identifies the optimal CA parameter set capable of representing the experimentally observed microstructures of PBF-LB HX under five different process conditions.

Initial Stages of Electrocrystallization of Coatings with Tin and Tin-Copper and Tin-Copper-Ultradisperse Diamond Alloys

The need of modern microelectronics in the development of technological processes for the formation of nanostructured layers puts forward the necessity of understanding the mechanisms of nucleation and growth of deposits. The article considers the features of the initial stages of electrocrystallization of coatings with tin and tin-copper and tin-copper-ultradisperse diamond alloys. The kinetic regularities of electrode processes were studied by the voltammetry method. Based on the experimental data, the nucleation parameters (nucleation energy, effective interphase surface energy, radius and volume of the nucleus) were calculated. SEM images were obtained and the features of the roughness of the coating surfaces after deposition for 10, 20, 30 and 60 s were studied. It was found that co-deposition of tin-copper alloys and tin-copper-ultradisperse diamond particles increases the value of the limiting current from 2.8 · 10–2 to 5.0 · 10–2 A/cm2. With an increase in electrocrystallization over-voltage, the rate of nucleation increases and their size decreases, while fine-grained and dense deposits are formed. With an increase in the deposition duration, crystallites grow and gradually coalesce with each other, the value of the equivalent diameter of the grain coatings increases, respectively, for: Sn – from 1 ⋅ 10–6 to 4 ⋅ 10–6 m, Sn-Cu – from 0.3 ⋅ 10–6 to 1.3 ⋅ 10–6 m, Sn-Cu-ultradispersed diamond – from 0.9 ⋅ 10–6 to 1.4 ⋅ 10–6 m. The established patterns make it possible to control the structure of the coatings and obtain deposits with specified properties. The presented results may be of interest to specialists involved in the formation of solderable galvanic coatings.

An analysis of the synthesis, crystal structure, optical, spectroscopic, mechanical, self-focusing, and third-order nonlinear optical properties of Kojic acid single crystals

A single, excellent crystal of Kojic acid (KA) was developed utilising the traditional approach of gradual evaporation in a solution-growing procedure. A variety of characterisation techniques were utilised to evaluate the characteristics of the crystals generated. Single crystal x-ray diffraction (SXRD) was utilised to identify the crystal structure. The crystalline arrangement of the KA crystal was confirmed using a powder x-ray diffraction (PXRD) analysis. Experiments with UV–vis spectrometers revealed that the KA crystal has a lower wavelength at which it blocks UV light but has outstanding light transmission throughout the visible spectrum. The KA single crystal has an energy band gap (Eg) of 2.5 eV. The Z-scan method was used to examine the third order susceptibility, nonlinear refraction, and nonlinear absorption coefficient of the synthesised KA crystal. The dielectric characteristics and AC conductivity were examined, with a particular emphasis on their connection to resistance at room temperature. The presence of appreciable levels of kojic acid was confirmed by energy-dispersive spectrometry. The crystal’s thermal behaviour was investigated using differential thermal analysis (DTA) and thermogravimetric (TG) methods. The nucleation parameters and controlled nucleation rate were calculated using normal theoretical research methods.

Experimental and CFD Analysis of Hydrodynamics in Dual-Impeller Crystallizer at Different Off-Bottom Clearances

Producing tailor-made crystals demands knowledge of the influence of hydrodynamics and nucleation kinetics. In this paper, the hydrodynamic conditions in a dual-impeller crystallizer and their influence on the key nucleation parameters of the batch cooling crystallization of borax at different impeller off-bottom clearances were investigated. Two different impeller configurations were used—a dual pitched-blade turbine (2 PBT) and a dual straight-blade turbine (2 SBT). Hydrodynamics was analyzed in depth based on the developed computational fluid dynamics model. The experimental results on mixing time and power input were used to validate the numerical model. The results show that the properties of the final product are affected by the impeller position in both dual-impeller configurations. An increase in the impeller off-bottom clearance in both systems results in a decrease in the mean crystal size. The hydrodynamic conditions generated at C/D = 1 in the 2 PBT impeller system and at C/D = 0.6 in the 2 SBT impeller system favored an earlier onset of nucleation compared to other impeller positions. It was found that the eddy dissipation rate and the Kolmogorov length scale correlate highly with the mean crystal size, suggesting that the size is affected by the shear stress in the vessel, rather than the overall convective flow.

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.

A study of tin electrodeposition from ethaline: The electrode material effect

AbstractThis article studies the influence of electrode material on tin (Sn) electrodeposition from deep eutectic solvent. The Sn electrodeposition from ethaline‐based electrolyte onto glassy carbon (GC) and Pt substrates has been studied using cyclic voltammetry and chronoamperometry. The patterns and parameters of Sn nucleation and growth processes have been determined by means of Scharifker and Hills and Scharifker–Mostany models. Results show that Sn nucleation onto GCE follows instantaneous 3D nucleation, while in the case of PtE, it is controlled by adsorption, instantaneous 3D nucleation, and residual water reduction. The growth mechanism is diffusion‐controlled for both electrodes. The parameters of Sn electrodeposition onto GCE and PtE such as diffusion coefficient (D), nucleation rate (A), and active site density of Sn nuclei (No) are evaluated. The results showed that A and No increase linearly as the deposition potential is displaced towards more electronegative values while D is almost unchanged, regardless of the involved working electrode. The morphology and the structure of the electrodeposited Sn are also discussed based on scanning electron microscopy, X‐ray diffraction, and energy‐dispersive X‐ray spectroscopy investigations.

The corrosion performance for ultrafine WC-12Co processed by heat treatments in different pH solutions

The corrosion performance of WC-12Co after different post heat treatments (1100 °C, 1100 °C + 400 °C, 1100 °C + 500 °C, 1100 °C + 600 °C), were tested in 0.05 M H2SO4, 0.1 M Na2SO4, and 0.1 M NaOH. Heat treatments influence the corrosion performance of WC-12Co in acidic and neutral environments. However, the corrosion properties for WC-12CO in alkaline solutions are independent of the heat treatments. W and C diffuse to Co from the quenching process, dramatically improving corrosion resistance, with higher annealing temperature slightly reduces the corrosion performance. The rank of corrosion nucleation parameter tested by EIS and potentio-dynamic polarisation, with the corrosion expansion rate measured by potentio-static polarisation at +0.2 VSCE, + 0.5 VSCE, and + 0.8 VSCE for 30 min are not the same. The corrosion mechanism tested in different pH values is analysed using SEM, XPS, and DFT calculations.

Differential scanning calorimetry of proteins and Zimm–Bragg model in water

Differential Scanning Calorimetry (DSC) is a regular and powerful tool to measure the specific heat profile of various materials. Hydrogen bonds play a crucial role in stabilizing the three-dimensional structure of proteins. Naturally, information about the strength of hydrogen bonds is contained in the measured DSC profiles. Despite its obvious importance, there is no approach that would allow the extraction of such information from the heat capacity measurements. In order to connect the measured profile to microscopic properties of a polypeptide chain, a proper model is required to fit. Using recent advances in the Zimm–Bragg (ZB) theory of protein folding in water, we propose a new and efficient algorithm to process the DSC experimental data and to extract the H-bonding energy among other relevant constants. Thus, for the randomly picked set of 33 proteins, we have found a quite narrow distribution of hydrogen bonding energies from 1 to 8 kJ/mol with the average energy of intra-protein hydrogen bonds h¯=4.2±1.5 kJ/mol and the average energy of water–protein bonds as hps¯=3.8±1.5 kJ/mol. This is an important illustration of a tiny disbalance between the water–protein and intraprotein hydrogen bonds. Fitted values of the nucleation parameter σ belong to the range from 0.001 to 0.01, as expected. The reported method can be considered as complementary to the classical two-state approach and together with other parameters provides the protein–water and intraprotein H-bonding energies, not accessible within the two-state paradigm.

Modelling grain refinement under additive manufacturing solidification conditions using high performance cellular automata

Despite increasing applications of additively manufactured parts, they still suffer from anisotropic mechanical properties and can experience cracking due to coarse columnar grain structures induced by metal 3D printing. Microstructural control is promising avenue to overcome these challenges, but requires deeper understanding of factors controlling solidification, particularly regarding grain refinement. Addressing this gap, this study explores grain refinement in Al-Cu alloys with a process-microstructure linking cellular automata-finite difference (CAFD) approach supported by single-track laser surface remelting (LSR) experiments. To enhance the understanding of nucleation behaviour in alloys under additive manufacturing solidification conditions, this research analyses the influence of nucleation parameters on the post-LSR microstructures. Additionally, this study explores the computational dimensions of microstructure modelling, testing CA mesh sensitivity effects and benchmarking our CAFD models on two high-performance computing platforms. The CAFD model captures well the key microstructural features observed in LSR Al-Cu alloys with and without grain refiner addition. It is shown that the maximum nucleation density has a significant effect on the final microstructure, resulting in different proportions of coarse columnar grains resulting from epitaxial solidification, newly nucleated thin columnar grains, and equiaxed grains.

An integral model for determining the temperature-dependent interfacial energy and pre-exponential factor during the metastable zone width cooling process

By incorporating a temperature-dependent function of interfacial energy and a temperature-dependent pre-exponential factor inversely proportional to the solution viscosity, an integral model was developed according to classical nucleation theory to retrieve the nucleation parameters from the metastable zone width (MSZW) data. The developed model was applied to determine the temperature-dependent interfacial energy and pre-exponential factor during the cooling process from the MSZW data for phenacetin in ethanol experimentally measured in this work. For comparison, the interfacial energy and pre-exponential factor for phenacetin in ethanol at various operating temperatures were determined from the induction time data based on the conventional method. The results indicated that the temperature-dependent interfacial energy and pre-exponential factor for phenacetin in ethanol obtained from the MSZW data based on the developed model were consistent with those obtained from the induction time data based on the conventional method.

Methanol-water manipulated polymorphic nucleation of L-Ornithine-L-Aspartate

Screening for a suitable polymorph is crucial in pharmaceutical engineering. Here we reported the polymorphic nucleation of L-Ornithine-L-Aspartate (LOLA) in a methanol–water binary solvent. A new metastable form named monohydrate was discovered, which was found affected the nucleation of LOLA anhydrate. The antisolvent crystallization experiments showed that when the molar fraction of methanol was less than 0.387 or more than 0.448, the anhydrate LOLA nucleated, while it was between 0.390–0.416, the monohydrate appeared. Specifically, the isolated water molecules were the key parameter for polymorphic nucleation of LOLA. When methanol was less or more, it was insufficient to break the water hydrogen bonding network or enough to form methanol–water network, both could cause less isolated water, thus the anhydrate nucleated. On the contrary, when the methanol content was 0.390–0.416, methanol molecules could occupy some spatial sites in the water network resulting in more isolated water, thus the monohydrate appeared.

A two-scale approach for assessing the role of defects in fatigue crack nucleation in metallic structures

Metal structures often exhibit macroscopic defects from which cracks can nucleate during cyclic loading. The current work presents a two-scale approach to enable the prediction of crack nucleation from such defects by taking into account local microstructure features. The geometrical description of the defect and associated non-homogeneous strain fields are modeled using a macroscale model which employs a continuum elastoplastic material model for cyclic deformation. The cyclic deformation of the microstructure near the defect is modeled using a mesoscale model which employs a crystal plasticity material model and uses multiple realizations to address the statistical microstructure variability. The boundary conditions of the mesoscale model are extracted from the macroscale model. By simulating the deformation of the microstructure using the strain fields near the defect and by introducing a fatigue indicator parameter for crack nucleation, along with the weakest-link based upscaling methodology, the developed approach enables the prediction of the distribution of crack nucleation life. The approach is used for analyzing different defects for crack nucleation by considering local grain orientations. The predictions are shown to not only capture phenomena such as scatter, size effects, etc. qualitatively, but also agree with a classical engineering approach and experimentally reported data sets quantitatively.

A Numerical Hydration Model to Predict the Macro and Micro Properties of Cement–Eggshell Powder Binary Blends

This study aims to propose a hydration kinetic model for the cement–eggshell powder binary system and predict the performance development of composite concrete through this model. The specific content and results of the model are as follows. First, based on the cumulative hydration heat of the cement and eggshell powder binary system in the first seven days, the parameters of the cement hydration model and the eggshell powder nucleation parameter are calibrated. These parameters remain constant regardless of the mix ratio. Secondly, the hydration heat of the cement–eggshell powder binary system over 28 days is calculated using the hydration model. The results show that at 28 days, for specimens with 0%, 7.5%, and 15% eggshell powder substitution, the cement hydration degrees are 0.832, 0.882, and 0.923, respectively. The hydration heat per gram of cement is 402.69, 426.88, and 446.73 J/g cement, respectively, while the hydration heat per gram of binder is 402.69, 394.86, and 379.72 J/g binder, respectively. Additionally, the hydration model is used to calculate the chemically bound water and calcium hydroxide content of the cement–eggshell powder binary system. At 28 days, for samples with 0%, 7.5%, and 15% eggshell powder, the chemically bound water content is 0.191, 0.188, and 0.180 g/g binder, respectively, and the calcium hydroxide content is 0.183, 0.179, and 0.173 g/g binder, respectively. Finally, a power function is used to regress the calculated hydration heat with experimentally measured compressive strength and surface electrical resistivity. The correlation coefficients for compressive strength and surface electrical resistivity are 0.8474 and 0.9714, respectively. This is because the strength weak point effect of eggshell powder has minimal impact on hydration heat and surface electrical resistivity experiments but significantly affects the strength experiment.

Uncovering grain and subgrain microstructure at the scale of additive manufacturing melt tracks with a scalable cellular automaton solidification model

Metal additive manufacturing, characterized by rapid solidification, yields refined grains with a distinctive cellular subgrain microstructure that plays a pivotal role in determining material properties. Due to the significant computational expense demanded to simulate the required physics with submicron spatial resolution, their numerical simulations have been limited to proof-of-concept studies to either 2D or small subregions of a melt pool. In this study, an open-source, scalable, solidification code, muMatScale, based on the cellular automaton method, has been developed to predict the grain and the underlying subgrain microstructure over an entire melt pool. The model incorporates flexible parallelization schemes, utilizing MPI and OpenMP GPU Offloading, in addition to appropriate multi-physics specific to non-equilibrium rapid solidification in AM. The impact of nucleation parameters on grain microstructures was investigated with a focus on grain size variations and morphology transitions. With selected nucleation parameters, the simulation predicted the grain size, subgrain morphology, crystallographic orientation, and microsegregation aligned with experimental measurements. The model demonstrates that epitaxial grain growth is a dominant factor at the melt pool boundary, influencing grain size variation under different grain sizes in the build plate while maintaining consistent primary dendrite arm spacing under identical thermal conditions. The highly efficient numerical model enables large-scale simulations with a spatial resolution of 100 nm or less, unveiling unprecedented insights into thermal and solutal diffusion driven grain growth, and the subgrains with microsegregation within grains in 3D across scales. muMatScale will enable the linking of submicron length-scale microstructure to part-level material behavior by investigating fundamental solidification problems at the intercellular scale in many-track and many-layer builds.

Elucidating the influence of electrolyte additives on iron electroplating performance

Iron electroplating is great interest for multiple large-scale industrial and emerging energy applications, such as all-iron redox flow batteries. However, the process efficiency and material lifetime are limited by the poorly understood plating process and the presence of competitive reactions. In this work, we propose a methodology to deconvolute the nucleation parameters of iron plating via a suite of electrochemical techniques, spectroscopy, and analytical models, coupled with microscopic and crystallographic techniques. We perform a systematic analysis with iron-based electrolytes to deconvolute the simultaneous plating and hydrogen evolution reactions, and investigate an array of additives to tune electroplating descriptors. We find that all additives studied are able to regulate the plating process and that highly stable iron-complexes based on buffers, such as iron-borates or -citrates deliver greater overall electroplating performance. These additives show superior selectivity, with improvements in faradaic efficiencies from 60 % to ∼90 % due to the balanced effects of enhanced nucleation and side reaction suppression. Herewith, the aim of this study is to bridge the knowledge gap between the role of additives, kinetics and efficiency of the electrodeposition reaction, and their interplay defining the quality of the resulting plated layers.

Nucleation behaviors of p-coumaric acid in four solvents from induction time and metastable zone width: experiments and simulations

The study of nucleation behaviors during crystallization is important for understanding the drug crystallization process. The induction time of p-coumaric acid (p-CA) was measured in four solvents at various levels of supersaturation. The kinetic parameters of nucleation (interfacial energy, critical nucleation radius, and critical Gibbs free energy) were estimated using the classical nucleation theory (CNT). The results showed that the nucleation difficulty of p-CA in the four solvents was in the order of ethyl acetate > acetone > ethanol > methanol. In addition, the metastable zone width (MSZW) of p-CA was determined in four solvents. The nucleation behaviors of p-CA were further expounded using self-consistent Nývlt-like model and modified Sangwal’s model. The results were consistent with those of CNT. To further reveal the impact of interactions between solvent and solute molecules on the nucleation behaviors of p-CA, molecular electrostatic potential surfaces (MEPs), Hirshfeld Surfaces (HS), and the radial distribution function (RDF) were performed. The investigation revealed that the intensity of solvent–solute interactions depended primarily on the strength of hydrogen bonding interactions. The RDF results showed that the magnitude of hydrogen bonding interactions of p-CA in the four solvents was in the following order: ethyl acetate > acetone > ethanol > methanol. As the hydrogen bonding interactions between p-CA and solvent molecules became stronger, the dissociation of solute molecules from solvent molecules became more difficult, leading to a wider MSZW and a lower nucleation rate.

Controlled epitaxy and patterned growth of one-dimensional crystals via surface treatment of two-dimensional templates

Mixed-dimensional van der Waals (vdW) heterostructures offer promising platforms for exploring interesting phenomena and functionalities. To exploit their full potential, precise epitaxial processes and well-defined heterointerfaces between different components are essential. Here, we control the growth of one-dimensional (1D) vdW microwires on hexagonal crystals via plasma treatment of the growth templates. AgCN serves as a model 1D system for examining the dependence of the nucleation and growth parameters on the surface treatment conditions and substrate types. The oxygen-plasma-treated transition metal dichalcogenides form step edges mediated by formation of surface metal oxides, leading to robust AgCN epitaxy with an enhanced nucleation density and low horizontal growth rates. Monte Carlo simulations reproduce the experimentally observed growth behaviors and unveil the crucial growth parameters, such as surface diffusivity. The plasma treatment results in distinct effects on graphite and hexagonal boron nitride templates, which undergo plasma-induced amorphization and deactivation of the AgCN vdW epitaxy. We achieve the selective growth of AgCN microwires on graphite using the deactivated vdW epitaxy. This study offers significant insights into the impact of surface treatment on 1D vdW epitaxy, opening avenues for controlled fabrication of mixed-dimensional vdW heterostructures.

Mechanistic modeling of twin screw wet granulation for pharmaceutical formulations: Calibration, sensitivity analysis, and model-driven workflow

Wet granulation, a particle size enlargement process, can significantly enhance the critical quality attributes of powders and improve the ability to form tablets in pharmaceutical manufacturing. In this study, a mechanistic-based population balance model is applied to twin screw wet granulation. This model incorporated a recently developed breakage kernel specifically designed for twin screw granulation, along with nucleation, layering, and consolidation. Calibration and validation were performed on Hydrochlorothiazide and Acetaminophen formulations, which exhibit different particle size and wettability characteristics. Utilizing a compartmental experimental dataset, a comprehensive global sensitivity analysis identified critical inputs impacting quality attributes. The study revealed that the nucleation rate process model, effectively represented particle size distributions for both formulations. Adjustments to nucleation and breakage rate parameters, influenced by material properties and screw configuration, improved the model’s accuracy. A model-driven workflow was proposed, offering step-by-step guidelines and facilitating PBM model usage, providing essential details for future active pharmaceutical ingredient (API) formulations.