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Phase Transition in External Fields (2nd Edition)

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A special issue of Crystals (ISSN 2073-4352). This special issue belongs to the section "Crystalline Metals and Alloys".

Deadline for manuscript submissions: closed (20 December 2023) | Viewed by 8523

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Dr. Andrew Kao

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Old Royal Naval College, University of Greenwich, Park Row, London SE109LS, UK
Interests: microstructure solidification; thermoelectric magnetohydrodynamics; numerical modelling
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Prof. Dr. Dmitri Alexandrov

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Laboratory of Multi-Scale Mathematical Modeling, Department of Theoretical and Mathematical Physics, Ural Federal University, 620000 Ekaterinburg, Russia
Interests: phase transitions; pattern formation; heat and mass transfer processes; nucleation; dendritic growth; physical kinetics; nonlinear physics; applied mathematics; geophysics; climate changes; volcanology; stochastic processes; materials science; mathematical modeling
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Dr. Liubov V. Toropova

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Otto-Schott-Institut für Materialforschung, Friedrich-Schiller-Universität Jena, 07743 Jena, Germany
Interests: applied mathematics; theoretical modeling; non-linear behavior; thermodynamics and kinetics of heat and mass transfer; materials science; phase transitions; dendrite growth
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Dr. Catherine Tonry

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Old Royal Naval College, University of Greenwich, Park Row, London SE109LS, UK
Interests: ultrasonics; electromagnetism; materials processing; numerical modelling
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Dear Colleagues,

The first volume of the Special Issue “Phase Transition in External Fields” (https://www.mdpi.com/journal/crystals/special_issues/externalfields_crystals) was an incredible success, with 18 papers published, and it is thus our pleasure to announce the second volume.

Topics included, but were not limited to, solidification, melting, condensation and evaporation in the presence of strong gravitational, acoustic, or electromagnetic (EM) fields. In a drive for improved materials or a better understanding of fundamental phenomena, the use of external fields has become widespread. Examples include the use of EM fields to levitate droplets of highly reactive metals to understand and measure key material properties, with experiments under microgravity conditions on board the International Space Station. The application of EM fields to melting, evaporation and solidification in casting or additive manufacturing is used to influence the microstructure.

Acoustic fields cause cavitation and refining microstructures, and strong gravitational fields can make materials denser, providing improved material properties in soft and condensed matter.

Both reviews and original research articles focusing on phase transition in external fields are welcome. It would give us great pleasure to invite you to participate in this Special Issue.

Dr. Andrew Kao
Prof. Dr. Dmitri Alexandrov
Dr. Liubov V. Toropova
Dr. Catherine Tonry
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Crystals is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

phase transition
external fields
solidification
phase field
melt treatment

Published Papers (10 papers)

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Research

14 pages, 10069 KiB

Open AccessArticle

Crystalline Microstructure, Microsegregations, and Mechanical Properties of Inconel 718 Alloy Samples Processed in Electromagnetic Levitation Facility

by Yindong Fang, Chu Yu, Nikolai Kropotin, Martin Seyring, Katharina Freiberg, Matthias Kolbe, Stephanie Lippmann and Peter K. Galenko

Crystals 2024, 14(3), 244; https://doi.org/10.3390/cryst14030244 - 29 Feb 2024

Viewed by 734

Abstract

The solidification of Inconel 718 alloy (IN718) from undercooled liquid is studied. The solidification kinetics is evaluated in melted and undercooled droplets processed using the electromagnetic levitation (EML) technique by the temperature–time profiles and solid/liquid (S/L) interface movement during recalescence. The kinetics is [...] Read more.

γ

-phase (the primary phase in IN718), the final crystalline microstructure (dendritic and grained), and the mechanical properties (microhardness) are strongly dependent on the initial undercooling

Δ T

at which the samples started to solidify with the originating

γ

-phase. Particularly, with the increase in undercooling, the secondary dendrite arm spacing decreases from 28 μm to 5 μm. At small and intermediate ranges of undercooling, the solidified droplets have a dendritic crystalline microstructure. At higher undercooling values reached in the experiment,

Δ T > 160

K (namely, for samples solidified with

Δ T = 170

K and

Δ T = 263

K), fine crystalline grains are observed instead of the dendritic structure of solidified drops. Such change in the crystalline morphology is qualitatively consistent with the behavior of crystal growth kinetics which exhibits the change from the power law to linear law at

Δ T \approx 160

K in the velocity–undercooling relationship (measured by the advancement of the recalescence front in solidifying droplets). Study of the local mechanical properties shows that the microhardness increases with the increase in the

γ^{″}

-phase within interdendritic spacing. The obtained data are the basis for testing the theoretical and computational of multicomponent alloy samples. Full article

(This article belongs to the Special Issue Phase Transition in External Fields (2nd Edition))

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10 pages, 534 KiB

Open AccessArticle

Wavy Ice Patterns as a Result of Morphological Instability of an Ice–Water Interface with Allowance for the Convective–Conductive Heat Transfer Mechanism

by Dmitri V. Alexandrov, Eugenya V. Makoveeva and Alina D. Pashko

Crystals 2024, 14(2), 138; https://doi.org/10.3390/cryst14020138 - 30 Jan 2024

Viewed by 602

Abstract

In this research, the wavy ice patterns that form due to the evolution of morphological perturbations on the water–ice phase transition interface in the presence of a fluid flow are studied. The mathematical model of heat transport from a relatively warm fluid to a cold wall includes the mechanism of convective–conductive heat transfer in liquid and small sinusoidal perturbations of the water–ice interface. The analytical solutions describing the main state with a flat phase interface as well as its small morphological perturbations are derived. Namely, the migration velocity of perturbations and the dispersion relation are found. We show that the amplification rate of morphological perturbations changes its sign with variation of the wavenumber. This confirms the existence of two different crystallization regimes with (i) a stable (flat) interfacial boundary and (ii) a wavy interfacial boundary. The maximum of the amplification rate representing the most dangerous (quickly growing) perturbations is found. The theory is in agreement with experimental data. Full article

(This article belongs to the Special Issue Phase Transition in External Fields (2nd Edition))

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11 pages, 2110 KiB

Open AccessArticle

The Degree of Metallic Alloys Crystallinity Formed under Various Supercooling Conditions

by Maxim V. Dudorov, Alexander D. Drozin, Roman S. Morozov, Vasiliy E. Roshchin and Dmitry A. Zherebtsov

Crystals 2024, 14(1), 48; https://doi.org/10.3390/cryst14010048 - 29 Dec 2023

Viewed by 712

Abstract

Amorphous metal alloys play an important role in the electrical industry. Studies show the presence of an insignificant proportion of crystals in alloys that are amorphous from the point of view of X-ray diffraction analysis. The crystals significantly affect the mechanical and magnetic properties of amorphous alloys. Therefore, within this work, a comprehensive approach has been developed to determine the degree of crystallinity of amorphous alloys based on theoretical and experimental methods. The study is based on the mathematical model of supercooled melt crystallization previously developed by the authors, which takes into account the patterns of crystal formation and their diffusion and diffusionless growth, taking into account the mutual influence of growing crystals on each other. The mathematical model also takes into account the melt cooling mode when producing amorphous ribbons by cooling the melt on a rotating copper drum. The calculation results have been verified by experiments based on the new technique developed by the authors for calorimetric studies of amorphous ribbons. The developed methodology allows us to determine not only the average fraction of the crystals in a ribbon, but also the patterns of crystal distribution along its thickness as well as the patterns of changes in the proportion of the crystals in ribbons depending on the melt cooling mode. Full article

(This article belongs to the Special Issue Phase Transition in External Fields (2nd Edition))

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12 pages, 2950 KiB

Open AccessFeature PaperArticle

Noise-Induced Defects in Honeycomb Lattice Structure: A Phase-Field Crystal Study

by Vladimir Ankudinov and Peter K. Galenko

Crystals 2024, 14(1), 38; https://doi.org/10.3390/cryst14010038 - 27 Dec 2023

Viewed by 776

Abstract

One of the classes of the kinetic phase-field model in the form of the two-mode hyperbolic phase-field crystal model (modified PFC model) is used for the study of the noise effect of the crystalline structure. Special attention is paid to the origin of the defect’s microstructure in the crystalline honeycomb lattice due to induced colored noise. It shows that the noise–time correlation coefficient

τ_{ζ}

, comparable to the diffusion time, enhances the grain boundary mobilities. Instead, a small spatial correlation coefficient,

λ_{ζ}

, close to the first lattice parameter of the honeycomb crystal, stabilizes the structure. The finite non-zero value of the relaxation time

τ

for the atomic flux significantly slows the local relaxation of the fluctuated field and leads to the grains’ fragmentation and formation of the disordered phases. The obtained results are applicable to the hexagonal atomic structures and, in particular, to honeycomb crystals, such as boron nitride, in which the lattice defects might be simulated through the induced colored noise. Full article

(This article belongs to the Special Issue Phase Transition in External Fields (2nd Edition))

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12 pages, 11493 KiB

Open AccessArticle

Novel High-Temperature Modification of Belomarinaite KNaSO₄: Crystal Structure and Thermal Order–Disorder Phase Transitions

by Andrey Shablinskii, Rimma Bubnova, Olga Shorets, Maria Krzhizhanovskaya, Sergey Volkov and Stanislav Filatov

Crystals 2024, 14(1), 27; https://doi.org/10.3390/cryst14010027 - 26 Dec 2023

Viewed by 714

Abstract

Belomarinaite KNaSO₄ (space group P3m1, a = 5.6072(3), c = 7.1781(4) Å and Z = 2) has been studied by high-temperature single crystal X-ray diffraction. The K and Na atoms are disordered, and M1(1c) and M2(1b) sites merge into an M1(2d)(K50%/Na50%) site with increasing temperature, and novel translationsgleiche phase transition of belomarinaite KNaSO₄ (P3m1 → P-3m1) was revealed at 123 °C. Then, the temperature increase leads to phase transition of

P \bar{3} m 1

-polymorph of KNaSO₄ to α-KNaSO₄ (P6₃/mmc) at 446 °C, and sodium and potassium atoms in K1(1a) and Na1(1b) sites merged into an M4(2a)(K50%/Na50%) site. Crystal structures of KNaSO₄ were refined at 300, 500 and 750 °C to R₁ = 0.057, 0.056 and 0.048, respectively. The BVS maps and bond-valence energy landscape (BVEL) have been calculated, and the probability of the Na⁺ migration has been predicted using structural data for belomarinaite at 25 °C. The Na⁺ ion migration can occur at 2.14 eV in the ab plane and 2.80 eV along the c axis at 25 °C. Full article

(This article belongs to the Special Issue Phase Transition in External Fields (2nd Edition))

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16 pages, 1970 KiB

Open AccessArticle

A Unified Empirical Equation for Determining the Mechanical Properties of Porous NiTi Alloy: From Nanoporosity to Microporosity

by Bulat N. Galimzyanov, Georgy A. Nikiforov, Sergey G. Anikeev, Nadezhda V. Artyukhova and Anatolii V. Mokshin

Crystals 2023, 13(12), 1656; https://doi.org/10.3390/cryst13121656 - 30 Nov 2023

Viewed by 1273

Abstract

The mechanical characteristics of a monolithic (non-porous) crystalline or amorphous material are described by a well-defined set of quantities. It is possible to change the mechanical properties by introducing porosity into this material; as a rule, the strength values decrease with the introduction of porosity. Thus, porosity can be considered an additional degree of freedom that can be used to influence the hardness, strength and plasticity of the material. In the present work, using porous crystalline NiTi as an example, it is shown that the mechanical characteristics such as the Young’s modulus, the yield strength, the ultimate tensile strength, etc., demonstrate a pronounced dependence on the average linear size

\bar{l}

of the pores. For the first time, an empirical equation is proposed that correctly reproduces the dependence of the mechanical characteristics on the porosity

ϕ

and on the average linear size

\bar{l}

of the pores in a wide range of sizes: from nano-sized pores to pores of a few hundred microns in size. This equation correctly takes into account the limit case corresponding to the monolithic material. The obtained results can be used directly to solve applied problems associated with the design of materials with the necessary combination of physical and mechanical characteristics, in particular, porous metallic biomaterials. Full article

(This article belongs to the Special Issue Phase Transition in External Fields (2nd Edition))

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12 pages, 3879 KiB

Open AccessArticle

Transport Properties of Equiatomic CoCrFeNi High-Entropy Alloy with a Single-Phase Face-Centered Cubic Structure

by Victor A. Bykov, Tatyana V. Kulikova, Ivan S. Sipatov, Eugene V. Sterkhov, Darya A. Kovalenko and Roman E. Ryltsev

Crystals 2023, 13(11), 1567; https://doi.org/10.3390/cryst13111567 - 02 Nov 2023

Viewed by 764

Abstract

The key thermophysical properties necessary for the successful design and use of CoCrFeNi alloy in thermophysical applications have been measured experimentally, and the results have been compared with literature values and results previously obtained for commercial Ni-Cr alloys and equiatomic CoCrFeNi alloy. In particular, the thermal diffusivity, coefficient of thermal expansion (CTE), and specific heat capacity were measured for the as-cast and homogenized equiatomic CoCrFeNi alloy over a temperature range allowing the thermal conductivity to be calculated up to 1173 K. The thermal conductivity and thermal diffusivity of the equiatomic CoCrFeNi alloy were found to deviate from monotonic behavior in the temperature range from 773 to 1100 K. Such a deviation was previously observed in the behavior of the temperature dependence of CTE and specific heat capacity of the equiatomic CoCrFeNi alloy. The non-linear behavior is primarily the result of order/disorder phenomena for the as-cast and homogenized sample, as well as non-equilibrium solidification under arc melting conditions for the as-cast sample. The measured data of thermophysical properties are provided for thermally differently treated samples, and it is shown that there is a difference in the behavior of the temperature dependences of CTE, thermal diffusivity, and heat capacity. Full article

(This article belongs to the Special Issue Phase Transition in External Fields (2nd Edition))

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11 pages, 3038 KiB

Open AccessArticle

Density Testing Method for Undercooling Solidification of High-Temperature Metal Melts

by Tongzhuang Niu, Junfeng Xu, Zhirui Yao, Zengyun Jian and Peter K. Galenko

Crystals 2023, 13(10), 1502; https://doi.org/10.3390/cryst13101502 - 16 Oct 2023

Viewed by 736

Abstract

There are numerous methods used for measuring the coefficient of thermal expansion of alloys and density change at low temperatures, but it is difficult to accurately measure the volume and density of high-temperature melts, particularly during the process of rapid volume change during material phase transformation. This article proposes a method for measuring and analysing the volume and density changes in high-temperature alloy melts using high-speed photography and computer MATLAB program image analysis technology, which includes the ordinary image threshold segmentation method, the elliptical fitting method, and the local dynamic threshold segmentation method. The ordinary image threshold segmentation method is best suited to samples with clear boundaries; the elliptical fitting method is the simplest and can be used to analyse samples with unclear boundaries; and the local dynamic threshold segmentation method is the most accurate and best suited to samples with unclear boundaries. These techniques will aid in understanding the variations in the volume and density of high-temperature melt samples during the phase transition process. Full article

(This article belongs to the Special Issue Phase Transition in External Fields (2nd Edition))

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14 pages, 3462 KiB

Open AccessArticle

Off-Eutectic Growth Model for Solidifying Alloy from an Undercooled State

by Junfeng Xu and Peter K. Galenko

Crystals 2023, 13(10), 1453; https://doi.org/10.3390/cryst13101453 - 29 Sep 2023

Viewed by 689

Abstract

Classical eutectic growth models are based on the use of eutectic composition. These models neglect the effect of primary phase formation, and their direct use in the rapid solidification process of off-eutectic (hypoeutectic and hypereutectic) alloys is absent. Combining the effect of the primary phase in the eutectic transformation and an off-eutectic composition, the solidification growth model is derived in the present work. The effect of the model and material parameters on solidification kinetics is discussed in comparison with experimental data. Computational results on the off-eutectic growth model show that the model agrees well with experimental data on the solidification kinetics of Ni–B and Ti–Si alloys. Full article

(This article belongs to the Special Issue Phase Transition in External Fields (2nd Edition))

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14 pages, 712 KiB

Open AccessArticle

Morphological/Dynamic Instability of Directional Crystallization in a Finite Domain with Intense Convection

by Eugenya V. Makoveeva, Irina E. Koroznikova, Alexandra E. Glebova and Dmitri V. Alexandrov

Crystals 2023, 13(8), 1276; https://doi.org/10.3390/cryst13081276 - 18 Aug 2023

Cited by 2 | Viewed by 823

Abstract

This study is devoted to the morphological/dynamic instability analysis of directional crystallization processes in finite domains with allowance for melt convection. At first, a linear instability theory for steady-state crystallization with a planar solid/liquid interface in the presence of convection was developed. We derived and analyzed a dispersion relation showing the existence of morphological instability over a wide range of wavenumbers. This instability results from perturbations arriving at the solid/liquid interface from the cooled wall through the solid phase. Also, we showed that a planar solid/liquid interface can be unstable when it comes to dynamic perturbations with a zero wavenumber (perturbations in its steady-state velocity). A branch of stable solutions for dynamic perturbations is available too. The crystallizing system can choose one of these branches (unstable or stable) depending of the action of convection. The result of morphological and dynamic instabilities is the appearance of a two-phase (mushy) layer ahead of the planar solid/liquid interface. Therefore, our next step was to analyze the dynamic instability of steady-state crystallization with a mushy layer, which was replaced by a discontinuity interface between the purely solid and liquid phases. This analysis showed the existence of dynamic instability over a wide range of crystallization velocities. This instability appears in the solid material at the cooled wall and propagates to the discontinuity interface, mimicking the properties of a mushy layer. As this takes place, at a certain crystallization velocity, a bifurcation of solutions occurs, leading to the existence of unstable and stable crystallization branches simultaneously. In this case, the system chooses one of them depending of the effect of the convection as before. In general, the crystallizing system may be morphologically/dynamically unstable when it comes to small perturbations arriving at the phase interface due to fluctuations in the heat and mass exchange equipment (e.g., fluctuations in the freezer temperature). Full article

(This article belongs to the Special Issue Phase Transition in External Fields (2nd Edition))

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