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Article
Physical Sciences
Condensed Matter Physics

Pedro Schlottmann

Abstract: Fermion bound states in the core of a line-shaped vortex of a two-dimensional topological superconductor are investigated. The superconducting pairing potential, described in terms of elliptical coordinates, vanishes along a line defect with the two foci at the endpoints. The superconductivity is induced into a topological insulator via proximity effect with a type II s-wave superconductor. The spin and the momentum are perpendicularly locked by the strong spin-orbit coupling via Rashba interaction. A zero-energy Majorana state arises from the Berry phase together with a sequence of equally spaced fermion excitations. By solving the Bogoliubov-de Gennes equations using the method employed by Caroli, de Gennes and Matricon we calculate the energies, the wavefunctions and spin-polarization of the bound states. An analytic expression for the local density of states within the vortex is obtained.
Article
Physical Sciences
Condensed Matter Physics

Tung-Yuan Yung

,

Yi-Ching Huang

,

Kuan-Yi Lee

,

Chun-Min Wu

,

Wen-Hsien Li

Abstract: A spiral spin arrangement with a magnetic unit cell 28 times the size of nuclear one has been reported for the Fe spins below TN = 80 K in bilayered van der Waals gapped FeOCl. In this work, we used neutron magnetic diffraction and ac magnetic susceptibility to reveal a much-reduced magnetic unit cell of 4 times the size of nuclear one for the Fe spins below TN = 119 K, when 27% of non-magnetic Na were intercalated into the van der Waals gaps of FeOCl. X-ray emission spectra and X-ray absorption edge spectra reveal charge transfers from the intercalated Na into the Fe sites that reduce the Fe3+ into Fe2+ ions, giving a significantly larger Fe-O-Fe bond angle that largely strengthens the strength of antiferromagnetic superexchange (AFMSE) coupling over the competing ferromagnetic direct exchange (FMDE) coupling between the two neighboring Fe ions, driving to a higher degree of magnetic symmetry and a significantly higher Neel temperature for the Fe spins in Na0.27FeOCl.
Article
Physical Sciences
Condensed Matter Physics

Helena Cristina Vasconcelos

,

Telmo Eleutério

,

Maria Gabriela Meirelles

,

Reşit Özmenteş

Abstract: The morphology of solid surfaces encodes fundamental information about the physical mechanisms that govern their formation. Here, we reinterpret scanning electron microscopy (SEM) micrographs of oxide thin films as two-dimensional self-affine surfaces and analyze them using a multiscale statistical-physics framework that integrates spectral, multifractal, geometric, and topological descriptors. Fourier-based power spectral density (PSD) provides the spectral slope β and apparent Hurst exponent H, while multifractal scaling yields the information dimensions D_q, the singularity spectrum f(α), and its width Δα, which quantify scale hierarchy and intermittency. Lacunarity captures intermediate-scale heterogeneity, and Minkowski functionals—especially the Euler characteristic χ(θ)—probe connectivity and identify the onset of a percolation-like network structure. Two representative surfaces with contrasting morphologies are used as model systems: one exhibiting an anisotropic, porous, strongly multifractal structure with fragmented domains; the other showing a compact, nearly isotropic, and nearly monofractal organization. The porous regime displays steep PSD decay, broad multifractal spectra, and positive χ, consistent with a sub-percolated, diffusion-limited, Edwards–Wilkinson-like (EW-like) growth regime. Conversely, the compact regime exhibits gentler spectral slopes, narrower f(α), enhanced lacunarity at intermediate scales, and a χ(θ) zero-crossing indicative of a connectivity transition where a surface becomes a percolating network, consistent with a Kardar–Parisi–Zhang-like (KPZ-like) correlated growth regime. These results demonstrate that individual SEM micrographs encode quantitative fingerprints of nonequilibrium universality classes and topology-driven transitions from fragmented surfaces to connected networks, establishing SEM as a quantitative probe for testing theories of rough surfaces and kinetic growth in experimental thin-film systems.
Article
Physical Sciences
Condensed Matter Physics

João Oliveira

,

Bruna M. Silva

,

Tiago Rodrigues

,

Jorge A. Mendes

,

Manuel J. L. F. Rodrigues

,

Michael Belsley

,

Francis Leonard Deepak

,

Bernardo G. Almeida

Abstract:

Multiferroic BaTiO3 (BTO, piezoelectric)/CoFe2O4 (CFO, magnetostrictive) bilayer thin films were prepared by laser ablation on conductive Nb-doped SrTiO3 (100) substrates to investigate the influence of BTO layer thickness on their structural, microstructural, dielectric, and electrical (DC and AC) properties. X-ray diffraction confirmed the coexistence of the cubic spinel CoFe2O4 phase and the tetragonal ferroelectric BaTiO3 phase. The films exhibit preferred orientation, with CFO showing the [400] direction along the growth axis and BTO displaying (100)/(001) planes stacked parallel to it. The CFO unit cell is compressed along the growth direction, while BTO presents the ferroelectric distortion with a tetragonality ratio (c/a) slightly below, but close to, the bulk value. Second harmonic generation studies further verified the non-centrosymmetric ferroelectric nature of BTO at room temperature. The temperature-dependent dielectric permittivity was modeled using the Havriliak–Negami function with an additional conductivity term to extract relaxation dynamics, DC conductivity, Curie temperature (Tc), and activation energies. The Curie temperature increases with BTO thickness, approaching the bulk value for thicker layers. DC conductivity activation energies exhibit a change at Tc, from below 0.5 eV for T < Tc to above 0.5 eV for T > Tc, consistent with small-polaron tunneling. The AC conductivity follows a Jonscher-type frequency dependence with two power-law contributions reflecting the behavior of both layers. Temperature-dependent analysis of the power-law exponents reveals that small-polaron tunneling dominates conduction in BTO, while ion hopping between octahedral sites governs conduction in CFO. Underoxidation leads to a more complex transport regime in BTO, showing a transition from quantum-mechanical tunneling below Tc to correlated barrier hopping above it. By revealing how transport processes operate within multiferroic oriented bilayer systems, these findings advance our understanding of material interactions and pave the way for the design of innovative multifunctional platforms optimized for spintronic technologies.

Article
Physical Sciences
Condensed Matter Physics

Tarik Akan

,

Perihan Aksu

,

Recep Sahingoz

,

Feliks S Zaseev

,

Vladislav B. Zaalishvili

,

Tamerlan T Magkoev

Abstract:

A \( 5\,nm \) thick polycrystalline \( \mathrm{Ni_{81}Fe_{19}} \) film was sputter-deposited onto a circular 3-inch diameter, \( 390\,\mu m \) thick single-crystal wafer with \( \mathrm{SiO_2} \) surface layers. The magnetoresistance (MR) of the sample was analyzed as a function of the applied DC magnetic field and temperature using the Van der Pauw technique. Magnetic measurements were carried out over a temperature range of \( 25^{\circ}\mathrm{C} \) to \( 350^{\circ}\mathrm{C} \) using a Lake Shore Hall Effect Measurement System (HEMS). An external magnetic field ranging from \( +14$\,kG \) to \( -14$\,kG \) was applied at each temperature value to observe changes in resistance. Hall coefficients and resistance were obtained by applying current in both directions with different contact configurations.Machine learning techniques, including Random Forest Regression, were employed to predict magnetoresistivity beyond \( 350^{\circ}\mathrm{C} \) and estimate the Curie temperature (\( 570^{\circ}\mathrm{C} \)). This study highlights the potential of machine learning in accurately forecasting material properties beyond experimental limits, providing enhanced predictive models for the magnetoresistive behavior and critical temperature transitions of \( \mathrm{Ni_{81}Fe_{19}} \) [1–3].

Article
Physical Sciences
Condensed Matter Physics

Adrian Crisan

,

Alina M. Badea

,

Ion Ivan

,

Corneliu F. Miclea

,

Daniel N. Crisan

,

Armando Galluzzi

,

Massimiliano Polichetti

Abstract: Magnetic superconductor EuRbFe4As4 is a quite unique system in which macroscopic superconductivity and magnetic ordering coexist, with interesting interactions between Abrikosov vortices and Eu2+ spins that were investigated mostly by static (DC) magnetization measurements. Our aim is to study the dynamic interactions between the two sub-systems using AC susceptibility measurements in a wide range of temperatures and superimposed DC fields. In low DC fields, the magnetic transition at 15 K is clearly visible. We have observed very little difference between the AC susceptibility in different cooling regimes, but large difference for different field orientation. For field perpendicular to the superconducting planes, we have observed an anomalous dependence just below the critical temperature, which is absent in the parallel field orientation. We explained the anomaly by the interplay between the sample dimensions and the temperature dependence of the London penetration depth which may allow the paramagnetic Meissner phase to be detected in the susceptibility response.
Article
Physical Sciences
Condensed Matter Physics

Satoru Hayami

Abstract: We theoretically investigate multiple-Q instabilities in centrosymmetric hexagonal magnets, formulated as superpositions of independent six ordering wave vectors related by sixfold rotational and mirror symmetries. By employing a spin model that incorporates biquadratic interactions and an external magnetic field, we establish a comprehensive low-temperature phase diagram hosting single-Q, double-Q, triple-Q, and sextuple-Q states, as well as skyrmion crystals with topological charges of one and two. The field evolution of the magnetization, scalar spin chirality, and finite wave-vector magnetic amplitudes reveals a hierarchical buildup of multiple-Q order, accompanied by first-order transitions between topologically distinct and trivial phases. At large biquadratic coupling, all six symmetry-related ordering wave vectors coherently participate, giving rise to two sextuple-Q states under magnetic fields and to another spontaneous sextuple-Q state even at zero field. The latter zero-field sextuple-Q state represents a fully developed sixfold interference pattern stabilized solely by the biquadratic interaction, characterized by alternating skyrmion- and antiskyrmion-like cores with vanishing uniform scalar spin chirality. These findings establish a unified framework for understanding hierarchical multiple-Q ordering and demonstrate that the interplay between bilinear and biquadratic interactions under hexagonal symmetry provides a generic route to complex noncoplanar magnetism in centrosymmetric itinerant systems.
Article
Physical Sciences
Condensed Matter Physics

Aisen Ruslanovich Prokopiev

,

Nikolay Nikolaevich Loskin

,

Pavel Vasilievich Vinokurov

Abstract: The development of economical and scalable methods for synthesizing high-quality graphene remains a pivotal challenge in materials science. This study presents an efficient approach for synthesizing turbostratic graphene with micron-sized domains from an accessible bioprecursor – activated charcoal – using fast Joule heating. We demonstrate that ultra-rapid thermal annealing (~16.2 kJ/g, up to 3000 K) triggers a phase transition from amorphous carbon to a highly graphitized structure. Comprehensive characterization via SEM, AFM, Raman spectroscopy, and XRD revealed the formation of large flakes with lateral dimensions up to 1.5 µm and thicknesses ranging from 4 to 200 nm. Raman mapping further uncovered a heterogeneous structure with alternating regions exhibiting different degrees of interlayer coupling, characteristic of turbostratic stacking. The key feature of the material is its turbostratic layer stacking, confirmed by the combination of XRD data showing an interlayer distance of 3.436 Å and Raman spectra characteristic of decoupled graphene layers. The synthesized material exhibits excellent electrical transport properties, with a bulk resistivity of 0.51 Ω·cm – an order of magnitude lower than that of the initial charcoal. These findings highlight the potential of the developed method for producing electrode materials for energy storage devices and conductive composites.
Article
Physical Sciences
Condensed Matter Physics

Yawen Shen

,

Boyang Zhang

,

Pengcheng Ma

,

Qiujiao Du

,

Hongwu Yang

,

Pai Peng

,

Fengming Liu

Abstract: Controlling seismic wave propagation to protect critical infrastructure through metamaterials has emerged as a frontier research topic. The narrow bandgap and heavy weight of a resonant seismic metamaterial(SM) limit its application for securing buildings. In this research, we first develop a two-dimensional(2D) seismic metamaterial with gammadion-shaped chiral inclusions achieving a high relative bandgap width of 77.34%. And its effective mass density is investigated to clarify the generation mechanism of bandgap due to negative mass density between 12.53 - 28.33 Hz. Then, the gammadion-shaped pillars are introduced on a half-space to design a three-dimensional(3D) chiral SM to attenuate Rayleigh waves within a wider low-frequency range. Further, time-frequency analyses for real seismic waves and scaled experimental tests confirm the practical feasibility of the 3D SM. Compared with common resonant SMs, our chiral configurations offer a wider attenuation zone and lighter weight.
Brief Report
Physical Sciences
Condensed Matter Physics

Jakub M. Głuch

,

Michał Szot

,

Grzegorz Karczewski

Abstract:

Quantum dots (QDots) composed of the narrow-bandgap semiconductor PbTe were incorporated into the depletion region of p–n junctions based on wide-bandgap II–VI semiconductors (p-ZnTe/n-CdTe). The heterostructures were grown by molecular beam epitaxy (MBE) on semi-insulating GaAs (100) substrates. The depletion region was engineered by depositing 20 alternating thin layers of CdTe and PbTe, followed by thermal annealing under ultrahigh vacuum conditions. As revealed by cross-sectional scanning electron microscopy (SEM), the initially continuous PbTe layers transformed into arrays of zero-dimensional nanostructures—PbTe quantum dots (QDs). The formation of PbTe QDs in a CdTe matrix arises from the structural mismatch between the zinc blende and rock salt crystal structures of the two materials. Electron-beam-induced current (EBIC) measurements confirmed that the PbTe QDs are located within the depletion region between the p-ZnTe and n-CdTe layers. The resulting p-ZnTe/n-CdTe diodes containing PbTe QDs exhibit pronounced sensitivity to infrared radiation in the spectral range of 1–4.5 μm, with a peak responsivity of approximately 8 V/W at a wavelength of ~2.0 μm and a temperature of 200 K. The temperature dependence of the cutoff wavelength demonstrates that the infrared response originates from band-to-band optical transitions within the PbTe QDs. In addition, the devices show sensitivity to visible radiation, with a maximum responsivity of 20 V/W at 0.69 μm. These results demonstrate that wide-bandgap p–n junctions incorporating narrow-bandgap quantum dots can function as dual-wavelength (visible and infrared) photodetectors, with potential applications in two-color detection and infrared solar cells.

Article
Physical Sciences
Condensed Matter Physics

Alan Kenzhiyev

,

Viktor N. Kudiiarov

,

Alena A. Spiridonova

,

Daria V. Terenteva

,

Dmitrii B. Vrublevskii

,

Leonid A. Svyatkin

,

Dmitrii S. Nikitin

,

Egor B. Kashkarov

Abstract: The composite material MgH₂-EEWNi-Cr (20 wt. %) with a hydrogen content of 5.2 ± 0.1 wt. % is characterized by improved hydrogen interaction properties compared to the original MgH₂. The dissociation of the material occurs in three temperature ranges (86-117, 152-162, 281-351 °C), associated with a complex of effects consisting of changes in the specific surface area of the material, alterations in the crystal lattice during ball milling, and changes in the electronic structure in the presence of a Ni-Cr catalyst, based on first-principles calculations. The decrease in desorption activation energy (Ed = 65-96 ± 1 kJ/mol, ΔEd = 59-90 kJ/mol) is due to the catalytic effect of Ni-Cr, leading to a faster decomposition of the hydride phase. Based on the results of ABINIT calculations, Ni-Cr on the MgH₂ surface leads to a significant decrease in hydrogen binding energy (ΔEb = 60%) compared to pure magnesium hydride due to the formation of Ni–H and Cr–H covalent bonds, which reduces the degree of H–Mg ionic bonding. The results obtained allow us to expand our understanding of the mechanisms of hydrogen interaction with storage materials and the possibility of using these as mobile hydrogen storage and transportation materials.
Review
Physical Sciences
Condensed Matter Physics

Habib Rostaghi Chalaki

,

Ebenezer Seesi

,

Gene Yang

,

Mohammad El Loubani

,

Dongkyu Lee

Abstract: ABO3 perovskite oxides are a versatile class of materials whose surfaces and interfaces play essential roles in sustainable energy technologies, including catalysis, solid oxide fuel and electrolysis cells, thermoelectrics, and energy-relevant oxide electronics. The interplay between point defects and surface reconstructions strongly affects interfacial stability, charge transport, and catalytic activity under operating conditions. This review summarizes recent progress in understanding how oxygen vacancies, cation nonstoichiometry, and electronic defects couple to atomic-scale surface rearrangements in representative perovskite systems. We first revisit Tasker’s classification of ionic surfaces and clarify how defect chemistry provides compensation mechanisms that stabilize otherwise polar or metastable terminations. We then discuss experimental and theoretical insights into defect-mediated reconstructions on perovskite surfaces and how they influence the performance of energy conversion devices. Finally, we conclude with a perspective on design strategies that leverage defect engineering and surface control to enhance functionality in energy applications, aiming to connect fundamental surface science with practical materials solutions for the transition to sustainable energy.
Article
Physical Sciences
Condensed Matter Physics

Daniel Parejo

,

Andres Santos

Abstract: We derive an explicit analytic expression for the first quantum correction to the second virial coefficient of a $d$-dimensional fluid whose particles interact via the generalized Lennard-Jones $(2n,n)$ potential. By introducing an appropriate change of variable, the correction term is reduced to a single integral that can be evaluated in closed form in terms of parabolic cylinder or generalized Hermite functions. The resulting expression compactly incorporates both dimensionality and stiffness, providing direct access to the low- and high-temperature asymptotic regimes. In the special case of the standard Lennard-Jones fluid ($d=3$, $n=6$), the formula obtained is considerably more compact than previously reported representations based on hypergeometric functions. The knowledge of this correction allows us to determine the first quantum contribution to the Boyle temperature, whose dependence on dimensionality and stiffness is explicitly analyzed. Moreover, the same methodology can be systematically extended to obtain higher-order quantum corrections.
Article
Physical Sciences
Condensed Matter Physics

Israel Felner

,

Michael I. Oshtrakh

Abstract: Meteorites are mainly magnetic materials which contain Iron alloys. The large number of mete-orites requires their classification and they can be classified within different approaches. The most frequent and simple method (based on their iron content and magnetic properties), is to divide them, into main three groups: (i) stony, (ii) stony-iron and (iii) iron meteorites. Meteor-ites are usually named after the places in the world where they fell. In general, scientific articles on meteorites are published in specified related journals, which are read by selected specialists who are interested in them. Practically, these articles describe the meteorites’ com-position, crystal structures and their various phases and obviously their physical properties in-cluding magnetic properties. In recent years, our group managed to perform extensive meas-urements (including magnetic studies) on several dozens of meteorites. Following the above classification, we aim to present the magnetic behavior of seven typical representative meteorites form the three mentioned groups, all published in the past. This article is intended and directed to non-expert scientists, for whom meteorites are not in their research field. Generally speaking, any meteorite is composed of two parts: (1) magnetic components (mainly Fe-Ni-Co alloys) with magnetic transition temperatures well above or below room temperature, (2) various paramag-netic components. The ratio between the two parts determines the meteorite property and its classification. The dominant magnetic character of the first part may overshadow the second part's magnetic properties.
Article
Physical Sciences
Condensed Matter Physics

Valeriy Efimovich Arkhincheev

Abstract: This paper studies percolation transitions in a disordered L-C system composed of inductors and capacitors (non-dissipative reactive elements). These transitions occur between different percolating states, which are described by distinct constant values of effective conductivity. An exact approach, based on the rotational symmetry of two-dimensional DC equations, was employed. T A new type of topological transition was identified for non-dissipative systems. The characteristics of these transitions—topological invariants—are calculated.. These transi-tions may be considered a classical analog of quantum transitions, such as the Quantum Hall effect.
Article
Physical Sciences
Condensed Matter Physics

Alessandro Scirè

Abstract: This work unveils complex topological properties within a recent theoretical model concerning the interplay of positional and orientational order. The model features "complementary-spins" (c-spins), symbolic agents divided into two populations with contrasting positional and orien-tational interactions. The model is governed by a control parameter, a form of circular anisot-ropy that splits the c-spins natural rotational frequencies. For a given system size and for small anisotropy, uniform equilibrium patterns showing both positional and orientational regularity emerge, consistently with local stability predictions. For moderate anisotropy, the system de-velops complex topological point defects, driven by phase singularity and bistable with the uniform patterns. The defects are constituted by curled orientational textures embedding two c-spin loop trains that counter-rotate around the same center, exhibiting regular spacing, spin-momentum locking and dissipationless flow. These defect complexes are extremely robust to noise and capable of self-repair, and constitute a whole new class of non-equilibrium dissi-pative structures. These are in fact topological vortex states, classifiable by a two-valued topo-logical charge. For anisotropy values exceeding a local stability threshold, active turbulence (deterministic chaos) takes place and order is lost. A statistical analysis revealed the coexistence of a double phase transition at a critical parameter value: an "ordinary" symmetry-breaking transition associated with standard collective synchronization and a novel topological phase transition activating the vortex complexes. Quantitative boundaries in the parameter space have been evaluated, either analytically or numerically. Increasing system size enhances organiza-tional complexity, developing more intricate spin-momentum locked transport networks. Thanks to its self-organizational properties, this work provides a new tool to understand ro-bustness and morphogenesis in living systems.
Article
Physical Sciences
Condensed Matter Physics

Yue Liu

Abstract: The establishment of wave mechanics theory in microwave absorption research carries significance that transcends mere error correction. While refuting impedance matching theory eliminates false explanatory frameworks, the deeper contribution of wave mechanics theory lies in fundamentally redirecting research methodology and objectives. This essay argues that the true value of wave mechanics theory emerges not from what it negates—the impedance matching framework, the treatment of return loss (RL) as material property, the attribution of film thickness effects to material structure—but from what it enables: a reoriented research paradigm that investigates optimal relationships between complex permittivity, complex permeability, frequency response characteristics, and microwave absorption performance. The profound contribution of wave mechanics theory is methodological: it transforms microwave absorption research from a descriptive cataloging of material structures into a rigorous investigation of how material composition and structural design influence the frequency response characteristics of electromagnetic properties. This reorientation represents the genuine theoretical advancement that the field requires.
Article
Physical Sciences
Condensed Matter Physics

Xiuqing Huang

Abstract: Explaining the Josephson effect with a classical, non-wavefunction theory has long been a challenge in condensed matter physics. Based on the superconductivity theory of real-space localized electron-hole pair symmetry breaking, this paper uses the fine-structure constant α to demonstrate that the elementary charge e, a quantity with intrinsic material properties, is more suitable as a quantum constant than Planck's constant h. The new mechanism unifies electric dipoles, capacitance, magnetic flux, displacement current and magnetic monopoles, providing a reliable explanation for the physical origins of flux quantization and the quantum Hall effect. It clarifies that the Josephson junction is essentially a microcapacitor, and the Josephson effect is inherently a microelectronic circuit phenomenon. Without invoking wavefunctions or the hypothesis of Cooper pair quantum tunneling, the DC and AC Josephson current equations are derived analytically, with results in perfect agreement with experimental observations. This study offers a novel perspective on the nature of the Josephson effect. Meanwhile, it signifies that the discovery of magnetic monopoles and the realization of the mathematical perfect symmetry of Maxwell's equations are bound to bring a paradigm shift to the entire field of physics.
Article
Physical Sciences
Condensed Matter Physics

Satoru Hayami

Abstract: We theoretically investigate topological transitions between coplanar and noncoplanar magnetic states in centrosymmetric itinerant magnets on a square lattice. A canonical effective spin model incorporating bilinear and biquadratic exchange interactions at finite wave vectors is analyzed to elucidate the emergence of multiple-Q magnetic orders. By taking into account high-harmonic wave-vector interactions, we demonstrate that a coplanar double-Q spin texture continuously evolves into a noncoplanar triple-Q state carrying a finite scalar spin chirality. The stability of these multiple-Q states is examined using simulated annealing as a function of the relative strengths of the high-harmonic coupling, the biquadratic interaction, and the external magnetic field. The resulting phase diagrams reveal a competition between double-Q and triple-Q states, where the noncoplanar triple-Q phase is stabilized through the cooperative effect of the high-harmonic and biquadratic interactions. Real-space spin textures, spin structure factors, and scalar spin chirality distributions are analyzed to characterize the distinct magnetic phases and the topological transitions connecting them. These findings provide a microscopic framework for understanding the emergence of noncoplanar magnetic textures driven by the interplay between two- and four-spin interactions in centrosymmetric itinerant magnets.
Article
Physical Sciences
Condensed Matter Physics

Ilya S. Sugonyako

,

Danila V. Tarov

,

Elena A. Korznikova

,

Gulnara R. Khalikova

,

Alexander S. Semenov

,

Konstantin V. Kukudzhanov

,

Sergey V. Dmitriev

Abstract: A 1.13 mm long fatigue crack in a 09G2S steel plate was completely healed using pulsed current treatment. The following pulsed current parameters were used: number of pulses – 6, pulse duration – 10-4 s, capacitor voltage increased from pulse to pulse in the range of 200÷250 V, maximum current density – 103÷1.25×103 A/mm2. To under-stand the healing mechanism, microstructural studies were performed using a scan-ning electron microscope near the healed crack and microhardness measurements in this area. The area near the healed crack can be roughly divided into three zones: the melting zone (MZ), the heat-affected zone (HAZ), and the base metal zone (BMZ). In the MZ, as a result of strong heating due to the current pulse, melting and subsequent quenching due to rapid cooling occurred, forming a lamellar martensite structure characterized by increased microhardness. In the HAZ, as a result of Joule heat release in an area previously unevenly deformed during fatigue testing, primary recrystalliza-tion occurred, forming a heterogeneous structure with ferrite grains of varying sizes and orientations. Moreover, the grain size in the HAZ was significantly smaller than in the BMZ. It is also worth noting that after healing, defects associated with the dis-placement of impurities by the crystallization front toward the crack were detected in the MZ.

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