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Aggregation, Nucleation and Crystallization

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A special issue of Crystals (ISSN 2073-4352). This special issue belongs to the section "Industrial Crystallization".

Deadline for manuscript submissions: closed (30 June 2023) | Viewed by 18255

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Dr. Vesselin Tonchev

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Faculty of Physics, Sofia University, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria
Interests: modelling of crystal growth and instabilities; resulting in the formation of various patterns-fractals and dendrites, step bunching and/or meandering; the numerical approaches to these, such as Cellular Automata and Monte Carlo, etc.; classical models and methods from the statistical physics-diffusion, relaxation, percolation, transfer matrix; cloud condensation nuclei
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Dear Colleagues,

The idea behind this Special Issue’s vague title is not only to collect a maximum number of specialized and particular solutions, but to also eventually formulate a minimal number of principal problems.

When speaking of first-order phase transitions characterized by the co-existence of the two phases at the point of transition, it is the distance to the equilibrium measured as the chemical potential difference that drives the available modes of reaction, with the supersaturation sustained during the phase change or defined only in the beginning to follow the spontaneous reaction of the system. What are the principal reaction modes in either of the cases? Is it building aggregates to which arbitrary attachments are allowed and, thus, the rate of entropy production is not a factor of control, or building a well-ordered array of structural units in which each newly arriving one has a special place to build in - the kink position, which provides that the crystal can grow across orders of spatial scale(s) preserving its polygonised shape? When the system chooses between these two routes, from the very beginning or at a later stage? How do limiting factors, such as a slow material supply/slow kinetics, “shape” the growing morphologies along either of the routes?

As a researcher engaged mostly in numerical approaches, I have always been tempted to think that the modeler is a mediator between the theorists and experimentalists as, for the former, we can provide a further check of their fundamental results and, for the latter, we systematically build templates to compare the outcome of their work with the theories. In any case, well-thought-out methodologies, rich and exhaustive monitoring protocols, and their adequate visualization are the key to an accurate communication and, thus, to the resonance with a maximal audience.

How this Special Issue is presented by the end depends on the reaction of the different research communities, whether it will be an aggregate of papers with no apparent coherence or a well-ordered “low-entropy” collection of consistent works—our mission at the journal Crystals is to provide only the nucleus! In any case, we believe that the final result will shine as a beautiful, colorful crystal.

Dr. Vesselin Tonchev
Guest Editor

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Keywords

nucleation
aggregation
crystallization
growth modes
growth morphologies and the transitions between them

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Related Special Issue

Aggregation, Nucleation and Crystallization—Second Edition in Crystals

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Research

14 pages, 6484 KiB

Open AccessArticle

Heterogeneous Substrates Modify Non-Classical Nucleation Pathways: Reanalysis of Kinetic Data from the Electrodeposition of Mercury on Platinum Using Hierarchy of Sigmoid Growth Models

by Viktoria Kleshtanova, Vassil V. Ivanov, Feyzim Hodzhaoglu, Jose Emilio Prieto and Vesselin Tonchev

Crystals 2023, 13(12), 1690; https://doi.org/10.3390/cryst13121690 - 15 Dec 2023

Viewed by 1117

Abstract

Using a hierarchy of three sigmoid growth models with increasing complexity, i.e., number of parameters, we reanalyzed kinetic data for heterogeneous nucleation—the number of nuclei N(t) vs. time t—from archetypical experiments on the electrodeposition of mercury on platinum by I. Markov and E. Stoycheva, to obtain two scales: N_max and τ. The universal character of the studied phenomenon was revealed when replotting the original data as α ≡ N(t)/N_max vs. t/τ. Yet the simplest model, the recently introduced α₂₁ model which is aimed to describe diffusion-limited growth in 2D, α₂₁ = tanh²(2t/τ₂₁), fits all datasets with an R² ≥ 0.989. This can be rationalized by attracting the non-classical notion of two-step nucleation—the nuclei form in a metastable phase which, in this case, grows on the electrode surface. Beyond the universality, we find the dependence of the two obtained scales on the overvoltage, which is increased systematically from 83 to 88 mV to generate the six N(t) datasets for each of the two electrode types—planar and hemispherical. Surprisingly, for one of them, the planar electrode, there is a discontinuity in the dependence—an almost horizontal jump from 85 to 86 mV, while for the hemispherical electrode, τ decreases smoothly. Full article

(This article belongs to the Special Issue Aggregation, Nucleation and Crystallization)

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16 pages, 11095 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Nanocrystallization of Cu₄₆Zr_33.5Hf_13.5Al₇ Metallic Glass

by Jaskaran S. Saini, Tamara D. Koledin, Tittaya Thaiyanurak, Lei Chen, Melissa K. Santala and Donghua Xu

Crystals 2023, 13(9), 1322; https://doi.org/10.3390/cryst13091322 - 29 Aug 2023

Cited by 1 | Viewed by 2154

Abstract

The recently discovered Cu₄₆Zr_33.5Hf_13.5Al₇ (at.%) bulk metallic glass (BMG) presents the highest glass-forming ability (GFA) among all known copper-based alloys, with a record-breaking critical casting thickness (or diameter) of 28.5 mm. At present, much remains to be explored about this new BMG that holds exceptional promise for engineering applications. Here, we report our study on the crystallization behavior of this new BMG, using isochronal and isothermal differential scanning calorimetry (DSC), X-ray diffraction (XRD), and transmission electron microscopy (TEM). With the calorimetric data, we determine the apparent activation energy of crystallization, the Avrami exponent, and the lower branch of the isothermal time–temperature–transformation (TTT) diagram. With XRD and TEM, we identify primary and secondary crystal phases utilizing samples crystallized to different degrees within the calorimeter. We also estimate the number density, nucleation rate, and growth rate of the primary crystals through TEM image analysis. Our results reveal that the crystallization in this BMG has a high activation energy of ≈360 kJ/mole and that the primary crystallization of this BMG produces a high number density (≈10²¹ m⁻³ at 475 °C) of slowly growing (growth rate < 0.5 nm/s at 475 °C) Cu₁₀(Zr,Hf)₇ nanocrystals dispersed in the glassy matrix, while the second crystallization event further produces a new phase, Cu(Zr,Hf)₂. The results help us to understand the GFA and thermal stability of this new BMG and provide important guidance for its future engineering applications, including its usage as a precursor to glass–crystal composite or bulk nanocrystalline structures. Full article

(This article belongs to the Special Issue Aggregation, Nucleation and Crystallization)

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14 pages, 1945 KiB

Open AccessArticle

Nucleation Kinetics of Rare Earth Scandium Salt: An Experimental Investigation of the Metastable Zone Width

by Josia Tonn, Aishe Grotjohann, Christian Kocks and Andreas Jupke

Crystals 2023, 13(7), 1074; https://doi.org/10.3390/cryst13071074 - 8 Jul 2023

Cited by 1 | Viewed by 1210

Abstract

Scandium is a rare earth element that has been declared a critical raw material by the EU. Its availability is low but the demand for it is increasing. Bauxite residue presents a possible European source. A novel process to extract scandium from the residue incorporates anti-solvent crystallization, which delivers the scandium salt (NH₄)₃ScF₆ that can be calcined to ScF₃ for direct use in an aluminum alloy. However, this crystallization process produces small crystals in the single-digit micrometer scale, hindering solid–liquid separation. In order to facilitate the separation, the crystallization process needs to be better understood and controlled. Therefore, nucleation kinetics are investigated by measuring the metastable zone width (MSZW) with an optical endoscope probe inside a 300 mL stirred fed-batch crystallizer with varying operating parameters. To study the influence of mixing on the MSZW, the stirring rate, the antisolvent addition rate, and the dilution of the antisolvent before injection are varied. The latter is proven to widen the MSZW by a multiple. It could be confirmed that mixing times on different scales greatly influence the MSZW and the growth of the crystals in the process. With these results, the boundaries for operating parameters are studied in order to control the crystallization process and thus crystal growth. Full article

(This article belongs to the Special Issue Aggregation, Nucleation and Crystallization)

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24 pages, 4791 KiB

Open AccessArticle

Modeling Analysis of Melting and Crystallization Process of Mold Flux Based on the Image Processing Technology

by Jian Chen, Chengang Liang, Jiawei Chen and Qiangqiang Zhou

Crystals 2023, 13(4), 594; https://doi.org/10.3390/cryst13040594 - 31 Mar 2023

Cited by 1 | Viewed by 1562

Abstract

The aim of this paper is to obtain the image information based on a given image of mold flux and to obtain the features that can describe the dynamical difference. The melting and crystallization dynamics of the slag were analyzed using the autoregressive moving average (ARIMA) time series model and data fitting method. Firstly, the binary image of the digital region of the original image was obtained by image information processing and segmentation methods, the original image number was determined by comparing the similarity of the information matrices of the given and standard images. The standard number with the highest similarity was considered as the number of the original image, and MATLAB was used to solve the problem, the digital information in all the images was successfully extracted. Secondly, ten eigenvalues were extracted from the given image after removing the background, and three principal components were obtained by principal component analysis. Then, a scoring model was constructed based on the percentage of variance, and the comprehensive scores of the three principal components to analyze the melting and crystallization process of the mold flux. Finally, based on the above work, the dynamic relationship between temperature, time and the melting and crystallization process of the mold flux was investigated. Since the temperature is approximately linearly correlated with time, the problem was transformed into finding the relationship between the melting and crystallization process of the mold flux and time. The least squares method, polynomial fitting and other methods were used to derive the relationship function, the relationship between the melting and crystallization process of mold flux and temperature and time was quantitatively analyzed. Full article

(This article belongs to the Special Issue Aggregation, Nucleation and Crystallization)

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11 pages, 4353 KiB

Open AccessEditor’s ChoiceArticle

Control of Molecular Packing in Crystal and Electron Communication of Two Ferrocenyl Moieties across Chiral Isomannide or Isosorbide Bridge

by Valerio Zullo, Tianao Guo, Anna Iuliano and Mark R. Ringenberg

Crystals 2023, 13(3), 520; https://doi.org/10.3390/cryst13030520 - 18 Mar 2023

Viewed by 1516

Abstract

Intramolecular electronic communication between electrochemically active groups connected by a bridging moiety can be modified through small changes in the spatial disposition of the redox active moieties and/or by the nature of the central core. In this study, chiral bio-based compounds, namely isomannide and isosorbide, were employed as cheap and easy-to-functionalize chiral scaffolds to bridge two ferrocenyl electroactive moieties. The crystal structures of both bis-ferrocenyl diester complexes were studied and they showed that the chirality of the bridge results in an open or tight helical crystal packing. The electron communication between the two electroactive units in the mixed valent monocations was also investigated using electrochemistry (cyclic voltammetry and differential pulsed voltammetry), and spectroelectrochemistry in the UV-Vis NIR. A computational study through time-dependent DFT was also employed to gain greater insight into the results obtained. Full article

(This article belongs to the Special Issue Aggregation, Nucleation and Crystallization)

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13 pages, 4678 KiB

Open AccessArticle

Effect of Ultrasound-Assisted Freezing on the Crystal Structure of Mango Sorbet

by Anna Kamińska-Dwórznicka, Anna Kot, Ewa Jakubczyk, Magdalena Buniowska-Olejnik and Małgorzata Nowacka

Crystals 2023, 13(3), 396; https://doi.org/10.3390/cryst13030396 - 25 Feb 2023

Cited by 8 | Viewed by 2032

Abstract

In this study, the effect of ultrasound-assisted immersion freezing (UAF) of mango sorbet in comparison to conventional freezer freezing, on freezing course and created crystal structure, was studied. The scope of work included the preparation of a sorbet mixture prepared on the basis of frozen mango fruit with the addition of locust bean gum (LBG), guar gum and a commercial mix of carrageenan without the addition of stabilizers, and freezing it using a conventional freezer and ultrasound-assisted freezing equipment, with variable operating parameters (21.5 kHz and 40 kHz—continuous or chopped mode). Then, the freezing time and the crystal structure of the frozen samples (a microscopy analysis) were examined. US-assisted freezing reduced the time of the process for stabilized samples of the sorbet. It was also proven that, proper stabilization with the combination of US treatment results in the formation of favorable crystal structure. Stabilized sorbet subjected to US action at a frequency of 21.5 kHz in chopped mode was characterized by the most uniform crystal structure, consisting of crystals with the smallest diameters among all the tested samples; the equivalent diameter was 9 µm, while for the stabilized control it was 25 µm. Full article

(This article belongs to the Special Issue Aggregation, Nucleation and Crystallization)

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10 pages, 3097 KiB

Open AccessFeature PaperArticle

Atomic Mechanisms of Crystallization in Nano-Sized Metallic Glasses

by Donghua Xu, Zhengming Wang, Lei Chen and Tittaya Thaiyanurak

Crystals 2023, 13(1), 32; https://doi.org/10.3390/cryst13010032 - 25 Dec 2022

Cited by 2 | Viewed by 2562

Abstract

Understanding crystallization mechanisms in nano-sized metallic glasses (MGs) is important to the manufacturing and application of these new nanomaterials that possess a unique combination of structural and functional properties. Due to the two-dimensional projections and limited spatial and/or temporal resolutions in experiments, significant questions (e.g., whether nucleation takes place on the free surface or in a near-surface layer) regarding this subject remain under debate. Here, we address these outstanding questions using molecular dynamics simulations of crystallization in MG nanorods together with atomistic visualization and data analysis. We show that nucleation in the nano-sized MGs predominantly takes place on the surface by converting the high-energy liquid surface to a lower-energy crystal surface (the most close-packed atomic plane). This is true for all the nanorods with different diameters studied. On the other hand, the apparent growth mode (inward/radial, lateral or longitudinal) and the resulting grain structure are more dependent on the nanorod diameter. For a relatively big diameter of the nanorod, the overall growth rate does not differ much among the three directions and the resulting grains are approximately semispherical. For small diameters, grains appear to grow more in longitudinal direction and some grains may form relatively long single-crystal segments along the length of the nanorod. The reasons for the difference are discussed. The study provides direct atomistic insights into the crystallization mechanisms in nano-sized MGs, which can facilitate the manufacturing and application of these new advanced materials. Full article

(This article belongs to the Special Issue Aggregation, Nucleation and Crystallization)

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18 pages, 36883 KiB

Open AccessEditor’s ChoiceArticle

Determination of Crystal Growth Rates in Multi-Component Solutions

by Christoph Helfenritter and Matthias Kind

Crystals 2022, 12(11), 1568; https://doi.org/10.3390/cryst12111568 - 3 Nov 2022

Cited by 3 | Viewed by 3114

Abstract

Many solid forming processes involve crystallization from multi-component solutions. In order to predict final phase assemblages, multi-component phase transfer kinetics must be known. It is not sufficient to have the kinetics of only one crystallizing component in the presence of other entities; the kinetics of concurrent crystallizing components are of interest as well. However, methods for their determination are currently lacking. We propose a new method comprising desupersaturation measurements of a 150 µm film of supersaturated solution in contact with a planar crystalline substrate. We show that concentration measurement at a single point in the film is sufficient to retrieve the phase transfer kinetics. For this, we use a confocal micro-Raman spectroscope, which is able to distinguish between different components and has a high spatial resolution. We chose crystallization of

N a_{2} S O_{4}

and

N a_{2} C O_{3}

decahydrate from aqueous solution as our model system because of its well-known phase equilibrium. In binary experiments, we demonstrate the mode of operation and its ability to reproduce known kinetics from the literature. In ternary experiments, we successfully distinguish two courses of crystallization, the first of which is a preferential crystallization of one component and the second a simultaneous crystallization of both crystallizing components. In both cases, the parameters for simple power law kinetics are determined. If sodium carbonate decahydrate crystallizes while sodium sulfate remains in solution, the mean mass transfer coefficient is revealed to be

k_{g, C O_{3}} = 6 \times 10^{- 7} m s^{- 1}

, which is about an order of magnitude lower compared to binary crystallization. If sodium carbonate decahydrate crystallizes concurrently with sodium sulfate decahydrate, the crystallization kinetics are similar to binary cases. The other component tends to be significantly slower compared to its binary crystallization. Full article

(This article belongs to the Special Issue Aggregation, Nucleation and Crystallization)

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12 pages, 3586 KiB

Open AccessEditor’s ChoiceArticle

2D Monte Carlo Simulation of Cocrystal Formation Using Patchy Particles

by Bogdan Ranguelov and Christo Nanev

Crystals 2022, 12(10), 1457; https://doi.org/10.3390/cryst12101457 - 15 Oct 2022

Viewed by 1826

Abstract

Cocrystals of Active Pharmaceutical Ingredients (APIs) are an attractive therapeutic alternative to salt formations. However, due to the molecular scale processes involved, the earliest stages of cocrystal formation remain poorly understood. In this paper, some light is shed on the thermodynamics and kinetics of co-crystallization. Importantly, to mimic the molecular scale processes of cocrystal formation, we use 2D Monte Carlo simulations and a computational model with short-range attraction and a mixture of two types of patchy particles (PPs) monomers. Each type possesses four patches, grouped in two by two, and each couple of patches is characterized by its specific placement on the circumference of the monomer and corresponding patch strength (a strong and narrow or weak and wide interaction). The spatial placement of the patches on both PPs monomers (alternating periodically through 60 and 120 degrees and vice versa) selected by us shows the emergence of both rhombohedral (metastable) and trihexagonal (stable) Kagome-like structures. The Kagome-like structures are preceded by formation of two types of trimers involving strong bonds only, or mixed trimers of strong and weak bonds, the later serving as building blocks for the finally generated Kagome patchy cocrystal, after prolonged simulation times. The step-by step process governing the cocrystal formation is discussed in detail, concerning the temperature interval, concentrations of PPs, the specific patch geometry and patch anisotropy as well. It is to be hoped that an understanding of the mechanisms of co-crystallization can help to control practical cocrystal synthesis and the possible phase transformations. Full article

(This article belongs to the Special Issue Aggregation, Nucleation and Crystallization)

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