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Keywords = crystal-lattice symmetry

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9 pages, 3179 KB  
Article
Stability and Mechanical Properties for Al3-xCuxSc (x = 0–3) Compounds
by Tong-Hui Yao and Wenqiang Sun
Crystals 2026, 16(9), 566; https://doi.org/10.3390/cryst16090566 - 30 Aug 2026
Abstract
Recent research has shown that Cu atoms can incorporate into the L12−Al3Sc precipitates in Al-Cu-Sc alloys, forming Al3−xCuxSc compounds that serve as effective hydrogen traps. Nevertheless, the Cu-induced modifications to the stability and mechanical properties [...] Read more.
Recent research has shown that Cu atoms can incorporate into the L12−Al3Sc precipitates in Al-Cu-Sc alloys, forming Al3−xCuxSc compounds that serve as effective hydrogen traps. Nevertheless, the Cu-induced modifications to the stability and mechanical properties of these precipitates have not yet been systematically quantified. In this work, first-principles calculations are performed to systematically investigate the crystal structures, phase stability, elastic properties, and thermodynamic behavior of Al3−xCuxSc (x = 0, 1, 2, 3) compounds. Structural optimizations are carried out for all compositions, and the formation enthalpies, elastic constants, polycrystalline moduli, and Debye temperatures are derived from the computed total energies and stress–strain relationships. The calculations reveal that Al2CuSc and AlCu2Sc adopt tetragonal structures rather than the cubic L12-type symmetry found in Al3Sc and Cu3Sc, indicating a composition-driven structural transition. The formation enthalpy becomes progressively less negative with increasing Cu content, implying a reduction in thermodynamic driving force for compound formation. The computed elastic properties further show that Cu substitution decreases the bulk-to-shear modulus ratio and the Vickers hardness, while simultaneously enhancing the ductility of the material. Additionally, the Debye temperature exhibits a monotonic and rapid decrease from Al3Sc to Cu3Sc, reflecting a significant softening of the lattice vibrational spectra upon Cu alloying. These quantitative theoretical results provide a comprehensive basis for understanding the compositional dependence of the mechanical and thermal responses of Cu-modified Al3Sc precipitates. Full article
(This article belongs to the Section Inorganic Crystalline Materials)
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9 pages, 1167 KB  
Article
Strain Engineering of Second-Harmonic Generation and Symmetry Breaking in Few-Layer ε-InSe
by Danliang Zhang, Sihan Liu, Peiran Li, Qing Ye and Ying Chen
Nanomaterials 2026, 16(15), 964; https://doi.org/10.3390/nano16150964 - 6 Aug 2026
Viewed by 271
Abstract
ε-phase indium selenide (ε-InSe), a non-centrosymmetric van der Waals layered semiconductor, exhibits broken inversion symmetry in all layer numbers, giving rise to exceptional second-order nonlinear optical responses and holding great promise for nonlinear optoelectronic applications. The dynamic control of the nonlinear efficiency of [...] Read more.
ε-phase indium selenide (ε-InSe), a non-centrosymmetric van der Waals layered semiconductor, exhibits broken inversion symmetry in all layer numbers, giving rise to exceptional second-order nonlinear optical responses and holding great promise for nonlinear optoelectronic applications. The dynamic control of the nonlinear efficiency of ε-InSe is crucial for its engineering applications. However, the quantitative manipulation of second-harmonic generation (SHG) intensity and crystal symmetry in few-layer ε-InSe via strain engineering is still lacking. In this work, we systematically investigate the modulation of SHG intensity and angle-resolved SHG patterns in few-layer ε-InSe under uniaxial tensile strain. Using a home-built straining apparatus, we apply controlled tensile strain and measure the strain-dependent SHG responses. The experimental results demonstrate that the SHG intensity of few-layer ε-InSe shows a non-monotonic response to increasing tensile strain, first increasing and then decreasing. Concurrently, the sixfold symmetry of the SHG pattern is broken, confirming the significant strain-induced modulation of the lattice symmetry. This study provides a viable route for the design of flexible and tunable nonlinear optoelectronic devices based on ε-InSe. Full article
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18 pages, 5298 KB  
Article
Symm-CGNN: Symmetry-Information-Enhanced Crystal Graph Neural Network for High-Symmetry Point Band Gap Prediction
by Qihang Xu, Jian Wu, Xiuying Zhang and Sicong Zhu
Nanomaterials 2026, 16(14), 871; https://doi.org/10.3390/nano16140871 - 15 Jul 2026
Viewed by 386
Abstract
Accurately characterizing the anisotropic optoelectronic properties of crystals requires determining the band gaps at specific high-symmetry points in the Brillouin zone. Relying solely on the minimum band gap is insufficient. However, although Graph Neural Networks (GNNs) offer rapid property predictions, conventional models remain [...] Read more.
Accurately characterizing the anisotropic optoelectronic properties of crystals requires determining the band gaps at specific high-symmetry points in the Brillouin zone. Relying solely on the minimum band gap is insufficient. However, although Graph Neural Networks (GNNs) offer rapid property predictions, conventional models remain trapped in a local real-space paradigm, lacking the global symmetry information necessary to differentiate these high-symmetry energy states. To address this problem, we propose the Symmetry-Information-Enhanced Crystal Graph Neural Network (Symm-CGNN). It explicitly incorporates local atomic environments with global symmetry information, including space groups, crystal systems, material density and lattice constants. The evaluation is performed on a comprehensive dataset including 3D (Materials Project) and 2D (2DMatpedia). The results demonstrate that Symm-CGNN achieves an 18% reduction in Mean Absolute Error (MAE) for high-symmetry band gap prediction compared to the baseline Crystal Graph Convolutional Neural Networks (CGCNN). This approach bridges the representational gap between local atomic coordination and macroscopic symmetry. Consequently, it provides a robust and efficient machine-learning paradigm for the high-throughput screening of materials with anisotropic optoelectronic properties. Full article
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17 pages, 3941 KB  
Article
Strain-Engineered Electronic, Structural, and Optical Properties of FeS2 Monolayer: A First-Principles Study for Strain Sensor and Photovoltaic Applications in Flexible Electronics
by Yang Ping, Shuang Bao, Muhammad Naeem Tabassam, Hao Xu, Zhenzhou Zhang, Yinlong Pan, Heng Zhu, Saad Aslam and Naveed Ahmad
Micro 2026, 6(3), 46; https://doi.org/10.3390/micro6030046 - 23 Jun 2026
Viewed by 507
Abstract
Two-dimensional (2D) materials have emerged as a key platform for next-generation electronics due to their atomic thickness and tunable properties. Iron disulfide (FeS2), known as pyrite, with a bandgap of ~0.95 eV, is suitable for solar energy applications. However, its performance [...] Read more.
Two-dimensional (2D) materials have emerged as a key platform for next-generation electronics due to their atomic thickness and tunable properties. Iron disulfide (FeS2), known as pyrite, with a bandgap of ~0.95 eV, is suitable for solar energy applications. However, its performance is limited by defects in bulk crystals. Reducing FeS2 to a single layer eliminates bulk defects and enables strain engineering of the bandgap. In this study, First-principles density functional theory (DFT) calculations are performed using the CASTEP code and the PBEsol functional to examine the structural, electronic, and optical properties of a distorted 1T′-phase FeS2 monolayer. Full geometry optimization yields lattice parameters a′ = 17.594 Å, b′ = 3.20231 Å, c′ = 5.28091 Å, and Fe–S bond angles of ~75.8° and ~98.2°, confirming symmetry-breaking distortion. The monolayer is dynamically stable, showing no imaginary modes in the phonon dispersion, and remains structurally intact up to 1000 K in molecular dynamics simulations. The unstrained system has an indirect bandgap of 0.70 eV, with the valence band maximum at the Γ point (dominated by S-p states) and conduction band minimum near the X point (Fe-d states). Under mechanical strain (±4%), the bandgap decreases significantly: from 0.70 eV to 0.44 eV under +4% tensile strain along the y-axis, and to 0.53 eV under −4% compressive strain. Biaxial strain causes weaker modulation, reducing the gap to 0.66 eV (+4%) and 0.62 eV (−4%). Optical absorption exceeds 104 cm−1 for photon energies above the bandgap, with tensile strain causing redshifts and compressive strain inducing blueshifts. These findings demonstrate that 2D FeS2 is mechanically robust, electronically tunable, and optically active, making it a promising candidate material for flexible strain sensors and photovoltaic devices. This work is intended to motivate and inform future synthesis efforts. Full article
(This article belongs to the Section Microscale Materials Science)
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23 pages, 27419 KB  
Article
MgCr2O4 Nanospinel for Efficient Organic Dye Pollutants Degradation: A Comparison of Photocatalysis, Fenton-like, and Photo-Fenton-like Reactions
by Jordan Meireles, André Luiz Menezes de Oliveira, Marta Célia Dantas, Ana Paula de Moura, Ruth Herta Goldschmidt Aliaga Kiminami, Iêda Maria Garcia dos Santos and Sayonara Andrade Eliziário
Processes 2026, 14(12), 1856; https://doi.org/10.3390/pr14121856 - 8 Jun 2026
Viewed by 359
Abstract
MgCr2O4 nanospinel samples were synthesized using a modified Pechini method, followed by controlled calcination. The resulting materials were evaluated in terms of crystal structure, particle morphology, and optical and electronic properties. Their oxidative activity towards the degradation of organic dyes [...] Read more.
MgCr2O4 nanospinel samples were synthesized using a modified Pechini method, followed by controlled calcination. The resulting materials were evaluated in terms of crystal structure, particle morphology, and optical and electronic properties. Their oxidative activity towards the degradation of organic dyes was investigated via photocatalysis, Fenton-like, and photon-Fenton-like processes. Various analytical techniques were employed to characterize the samples, including X-ray diffraction (XRD) with Rietveld refinements, infrared (IR) spectroscopy, UV–Vis spectroscopy, colorimetry, and transmission and high-resolution transmission electron microscopy (TEM/HRTEM). Structural characterization revealed that MgCr2O4 crystallized after calcination at 600 °C, and Rietveld refinements confirmed cubic Fd-3m symmetry. IR spectra confirmed the short-range order through the presence of vibrational modes assigned to CrO62- octahedra. UV–Vis spectroscopy indicated mixed Cr valences (Cr3+/Cr6+) for samples calcined at temperatures below 900 °C, with Cr6+ eliminated at higher temperatures, confirmed by electron paramagnetic resonance (EPR) spectroscopy. This suggests that an oxidation reaction occurred due to oxygen vacancies in the lattice. Optical bandgap (Eg) increased with temperature. Samples calcined at low temperatures were dark green and became more saturated at temperatures above 900 °C, suggesting photoresponse to visible light, as indicated by the Eg values. The oxidative activity of the nanospinels in degrading the dyes methylene blue (MB) and rhodamine B (RhB) under visible light depended on the nature of the dye, the catalyst concentration, and the use of H2O2 in the process to improve the formation of hydroxyl radicals (•OH), as confirmed by photohydroxylation of terephthalic acid (TA). The highest degradation rate was observed in the photo-Fenton-like process, with 96% and 97% degradation of RhB and MB dyes in 60 min, reaching a kinetic rate constant (Kapp) of 0.055 min−1 and 0.051 min−1, respectively. This study highlights the importance of controlling various parameters to promote the formation of reactive oxygen species (ROS) required for oxidative degradation by nanospinels. Full article
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29 pages, 2156 KB  
Article
Structural and Mechanical Properties of Y2SiO5-Lu2SiO5 Solid Solutions from Ab Initio Calculations
by Alexander Platonenko, Marina Konuhova, Dmitry V. Bocharov and Anatoli I. Popov
Crystals 2026, 16(6), 377; https://doi.org/10.3390/cryst16060377 - 4 Jun 2026
Viewed by 594
Abstract
Y2SiO5 (YSO) and Lu2SiO5 (LSO) are orthosilicates used in photonic and scintillation applications. Isovalent substitution on the rare-earth sublattice in YSO–LSO solid solutions enables systematic tuning of lattice parameters and elastic properties without changing the underlying monoclinic [...] Read more.
Y2SiO5 (YSO) and Lu2SiO5 (LSO) are orthosilicates used in photonic and scintillation applications. Isovalent substitution on the rare-earth sublattice in YSO–LSO solid solutions enables systematic tuning of lattice parameters and elastic properties without changing the underlying monoclinic structural framework. A systematic ab initio study of structural, elastic, and vibrational properties of Ce-free YSO–LSO solid solutions is performed within density functional theory using a localized Gaussian-type orbital basis. Nine compositions spanning the full range from YSO to LSO with a Lu content step of 12.5% are investigated. A total of 76 symmetry-independent Y/Lu substitution patterns are explicitly constructed. For each configuration, full geometry optimization and calculation of second-order elastic constants are carried out using the stress–strain approach. Bulk, shear, and Young’s moduli, as well as Poisson’s ratio, are obtained using the Voigt, Reuss, and Hill averaging schemes. Sound velocities and Debye temperatures are derived from the Hill-averaged elastic moduli and density. The unit-cell volumes decrease smoothly with increasing Lu content and follow Vegard’s law, indicating uniform lattice contraction. The Hill-averaged bulk modulus increases from 92 GPa (YSO) to 115 GPa (LSO), the Young’s modulus rises from 151 to 180 GPa, and a strong directional anisotropy (ratio ∼2) is preserved across the entire series. The Debye temperature decreases monotonically from 518 K to 439 K, indicating that the increase in mass density outweighs the stiffening-induced tendency toward higher sound velocities. These results provide quantitative guidance for composition selection and stress management in LYSO-based crystal detectors. Full article
(This article belongs to the Section Inorganic Crystalline Materials)
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15 pages, 3200 KB  
Article
Ab Initio Study on the Structural, Mechanical, Vibrational and Thermal Properties of Norbergite-Structured Vanadium Borate (V3BO6)
by Sabit Korcak
Crystals 2026, 16(5), 329; https://doi.org/10.3390/cryst16050329 - 13 May 2026
Viewed by 425
Abstract
Vanadium borate (V3BO6) has recently been synthesized and identified as a promising material for use in energy storage applications, particularly as a potential anode for lithium-ion batteries. However, despite previous studies highlighting its electrochemical performance, a comprehensive understanding of [...] Read more.
Vanadium borate (V3BO6) has recently been synthesized and identified as a promising material for use in energy storage applications, particularly as a potential anode for lithium-ion batteries. However, despite previous studies highlighting its electrochemical performance, a comprehensive understanding of its intrinsic mechanical, thermal, and vibrational properties remains limited. The compound crystallizes in an orthorhombic phase with the Pnma (No. 62) space group. To explore its intrinsic physical characteristics, full geometry optimization of the unit cell and atomic positions was performed using density functional theory (DFT) within the CASTEP framework. The Perdew–Burke–Ernzerhof (PBE) functional under the generalized gradient approximation (GGA) was used to model exchange–correlation effects. A plane-wave cut-off of 408 eV and a 6 × 6 × 13 Monkhorst–Pack grid were employed to ensure numerical convergence. The optimized lattice constants (a = 9.9025 Å, b = 8.4751 Å and c = 4.5354 Å) are highly consistent with experimental data, which confirms the reliability of the computational approach adopted. The elastic behaviour was further investigated using the first-principles strain-energy method, yielding nine independent elastic constants consistent with orthorhombic symmetry. The calculated bulk and shear moduli, along with the anisotropy parameters, suggest that V3BO6 has a favourable balance of mechanical robustness and moderate ductility. A Vickers hardness of 10.95 GPa and a B/G ratio of approximately 1.93 corroborate these findings. Additional parameters, such as Poisson’s ratio, Debye temperature and average sound velocities, were derived to gain deeper insight into the material’s thermomechanical performance. These results provide a solid theoretical foundation for understanding the mechanical stability and potential anode suitability of V3BO6 in lithium-ion battery systems. Full article
(This article belongs to the Section Polycrystalline Ceramics)
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14 pages, 2255 KB  
Article
Mechanochemical Synthesis and Luminescent Properties of Pure and Dy-Doped SrMoO4 Crystalline Phases
by Maria Gancheva, Reni Iordanova, Iovka Koseva, Georgi Avdeev and Petar Ivanov
Inorganics 2026, 14(5), 133; https://doi.org/10.3390/inorganics14050133 - 12 May 2026
Viewed by 922
Abstract
The pure and xDy3+-doped SrMoO4 series (x = 0.5, 1.0, 1.5 and 2.0 at.%) were synthesized using a direct mechanochemical route. We found that a milling speed of 850 rpm and a milling time of 30 min result in a [...] Read more.
The pure and xDy3+-doped SrMoO4 series (x = 0.5, 1.0, 1.5 and 2.0 at.%) were synthesized using a direct mechanochemical route. We found that a milling speed of 850 rpm and a milling time of 30 min result in a complete chemical reaction at different concentrations of dopant ions. The phase formation, structural units, and optical properties of the obtained samples were investigated by XRD, IR, UV-Vis and PL analyses. It has been established that Dy2O3 mainly influences the lattice parameters, unit cell volumes, crystallite sizes, and microstrains. The symmetry of MoO4 groups was investigated using IR spectroscopy, and it showed that pure and Dy3+-doped SrMoO4 samples are built up of deformed structural units. The calculated optical band gap of the obtained crystal phases decreases with increasing concentrations of Dy3+ ions. The host SrMoO4 matrix shows broad blue emission centered at 430 nm under an excitation wavelength of 230 nm. All doped samples display a strong yellow emission at 570 nm, belonging to the 4F9/26H13/2 transition of Dy3+ ions. The highest luminescence intensity was observed when the concentration of the Dy3+ ion was 0.5 at.%. The mechanism of concentration quenching was mainly caused by the electric dipole–dipole interaction. The calculated CIE chromaticity coordinates of the doped samples fall in the yellow range. This study demonstrates that mechanochemical treatment is an appropriate route for the fast preparation of yellow phosphors. Full article
(This article belongs to the Section Inorganic Materials)
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18 pages, 19996 KB  
Article
Optical and Structural Properties of Co2+-Doped CsPbI3 Nanocrystals Embedded in Borosilicate Glass
by Wilson A. Silva, Éder V. Guimarães, Klever A. S. Costa, Nataly S. Moura, José F. Condeles, Raquel A. Domingues and Ricardo S. Silva
Nanomaterials 2026, 16(10), 580; https://doi.org/10.3390/nano16100580 - 8 May 2026
Viewed by 1394
Abstract
Co2+-doped CsPbI3 nanocrystals (NCs) (CsPbI3:xCo, x = 0, 5, and 10 mol%) were synthesized in situ within a borosilicate glass matrix by the fusion method followed by controlled thermal treatment at 500 °C for 6–24 h. Transmission electron [...] Read more.
Co2+-doped CsPbI3 nanocrystals (NCs) (CsPbI3:xCo, x = 0, 5, and 10 mol%) were synthesized in situ within a borosilicate glass matrix by the fusion method followed by controlled thermal treatment at 500 °C for 6–24 h. Transmission electron microscopy images showed quasi-spherical NCs with mean diameters of 4.9–7.1 nm. Energy-dispersive X-ray spectroscopy suggested cobalt incorporation within the nanocrystalline regions. X-ray diffraction patterns confirmed the exclusive stabilization of the cubic α-phase across all compositions, with systematic lattice contraction from a = 6.321 Å to a = 6.301 Å with increasing Co content, consistent with preferential B-site substitution of Pb2+ by Co2+. Transmittance measurements confirmed macroscopic optical transparency of all glass-NC composites after thermal treatment. The crystal field theory and Tanabe–Sugano analysis for d7 ions in tetrahedral (Td) symmetry yielded Δ = 5032 cm−1 and B = 725 cm−1 in the as-prepared state, evolving to Δ = 4428 cm−1 and B = 805 cm−1 after thermal treatment, confirming Td Co2+ coordination and significant metal–iodide covalency. CIE 1931 chromaticity analysis revealed tunable emission from deep-red coordinates to near-white-light regions, demonstrating potential for LED and single-material WLED phosphor applications. Long-term photoluminescence measurements demonstrated full preservation of α-phase excitonic emission after approximately 365 days under ambient conditions, establishing the robust phase stability of CsPbI3:xCo NCs embedded in borosilicate glass. Full article
(This article belongs to the Section Synthesis, Interfaces and Nanostructures)
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15 pages, 1474 KB  
Article
The Effect of Solid-Phase and Melt Synthesis Methods on Dipole Ordering and Ion Conductivity of the Polar α-Phase of Na3Fe2(PO4)3 Polycrystals
by A. S. Nogai, A. A. Nogai, E. A. Nogai, N. F. Zikrillaev, D. E. Uskenbaev, A. B. Utegulov and K. U. Muhamedrahimov
J. Compos. Sci. 2026, 10(5), 232; https://doi.org/10.3390/jcs10050232 - 27 Apr 2026
Viewed by 1048
Abstract
The article investigates the dielectric and conductive properties of the polar α-phase of Na3Fe2(PO4)3 polycrystals synthesized by solid-phase (sample type 1), melt (type 2), and melt-quenching (type 3) methods. To enable a rapid assessment of the [...] Read more.
The article investigates the dielectric and conductive properties of the polar α-phase of Na3Fe2(PO4)3 polycrystals synthesized by solid-phase (sample type 1), melt (type 2), and melt-quenching (type 3) methods. To enable a rapid assessment of the dielectric properties of the polar α-phase of Na3Fe2(PO4)3, the thermo-polarization mobility parameter μTp(T, E(ω)) was introduced. By studying the dielectric properties, it was concluded that the polar α-phase of type 1 samples consists of large and small dipoles and ordered sodium cations, which possess low values of μTp(T, E(ω)), indicating the presence of strong interaction forces between the crystal lattice and the cationic part of the polycrystal. Additional studies of the samples’ conductivity confirm this conclusion. Studies of the polar α-phase of Na3Fe2(PO4)3 in type 2 samples have established that their structure contains dipoles and sodium cations with higher values of μTr(T, E(ω)), and also exhibits higher conductivity than Type 1 samples. These data indicate a weakening of the interaction forces between the cationic and anionic components in type 2 polycrystals due to a partial increase in crystal symmetry. The results of studies of the polar α-phase of type 3 samples show that their structure contains dipoles and sodium cations with higher values of μTr(T, E(ω)), and also exhibits higher conductivity than type 2 samples. It is concluded that the structure of type 3 samples is characterized by weak interaction forces between the cationic and anionic parts as a result of an increase in the symmetry of the polar α-phase of Na3Fe2(PO4)3, caused by sharply graded temperature conditions during the synthesis of polycrystals. By studying the dielectric properties of cathode materials, it is possible to obtain information on the extent of interactions between the cationic and anionic components in polycrystals. It is, therefore, appropriate to use this approach when investigating a wide range of new dielectric and ion-conducting materials. Full article
(This article belongs to the Section Composites Applications)
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18 pages, 3674 KB  
Article
Stress-Modulated Structural and Electronic Evolution in Metals with Different Crystal Structures
by Shushan Hu and Gang Huang
Crystals 2026, 16(4), 267; https://doi.org/10.3390/cryst16040267 - 16 Apr 2026
Viewed by 585
Abstract
While macroscopic stress significantly impacts the performance of metallic components, the underlying atom–electron coupling mechanisms governed by distinct crystal symmetries remain insufficiently understood. To address this gap, this work systematically investigates the structural and electronic evolution of representative metallic materials under applied stress. [...] Read more.
While macroscopic stress significantly impacts the performance of metallic components, the underlying atom–electron coupling mechanisms governed by distinct crystal symmetries remain insufficiently understood. To address this gap, this work systematically investigates the structural and electronic evolution of representative metallic materials under applied stress. Experimentally, X-ray diffraction (XRD) revealed complex macroscopic residual stress distributions in cold rolled titanium alloy and silicon steel. Motivated by these engineering observations, first-principles density functional theory (DFT) calculations were conducted to uncover the underlying physical mechanisms. Specifically, the responses of face-centered cubic (FCC) aluminum and copper, body-centered cubic (BCC) iron, and hexagonal close-packed (HCP) titanium crystals were investigated under tension and compression using the RPBE functional. Stress-dependent elastic properties, density of states (DOS), band structures, and phonon spectra were calculated. Results show that tension softens all metals (Al becomes mechanically unstable), whereas compression stiffens their lattices. Electronically, tensile loading sharpens DOS peaks near the Fermi level and shifts conduction bands closer to it, whereas compression smooths DOS peaks and shifts bands away. Phonon analysis indicates Cu and Ti remain dynamically stable, while Al and Fe exhibit phonon mode softening under high tension. These stress-induced changes highlight crucial atom–electron coupling mechanisms, providing a theoretical basis for tailoring metallic performance via stress engineering. Full article
(This article belongs to the Section Crystalline Metals and Alloys)
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14 pages, 2836 KB  
Article
Effect of Silicon Addition on the Phase Symmetry and Microstructural Stability of High-Entropy Alloys During Heat Treatment
by Sheetal Kumar Dewangan
Symmetry 2026, 18(4), 589; https://doi.org/10.3390/sym18040589 - 30 Mar 2026
Cited by 1 | Viewed by 594
Abstract
This study investigates the role of silicon (Si) addition in governing the evolution of phase symmetry and microstructural stability in a high-entropy alloy (HEA) synthesized via powder metallurgy. Mechanically alloyed powders were consolidated through conventional sintering, followed by systematic heat treatment to examine [...] Read more.
This study investigates the role of silicon (Si) addition in governing the evolution of phase symmetry and microstructural stability in a high-entropy alloy (HEA) synthesized via powder metallurgy. Mechanically alloyed powders were consolidated through conventional sintering, followed by systematic heat treatment to examine symmetry-driven phase transformations. Particular attention is given to the symmetry relationship between body-centered cubic (BCC) and face-centered cubic (FCC) crystal structures and their compositional stabilization mechanisms. X-ray diffraction and microstructural analyses reveal that Si incorporation modifies lattice symmetry, promotes controlled phase transformation, and influences the balance between competing crystallographic phases. The addition of Si contributes to symmetry stabilization by reducing heterogeneity in lattice distortion and suppressing grain coarsening during thermal exposure. These findings demonstrate that compositional tuning can regulate structural symmetry and phase equilibrium in multicomponent alloy systems. The work provides insight into symmetry-controlled material design strategies for enhancing the thermal robustness and structural reliability of HEAs for high-temperature applications. Full article
(This article belongs to the Special Issue Symmetry Studies in Metals & Alloys)
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23 pages, 3133 KB  
Article
Rayleigh Bound States in the Continuum in Shallow Surface Relief Phononic Crystals
by Francesc Alzina
Crystals 2025, 15(12), 1030; https://doi.org/10.3390/cryst15121030 - 1 Dec 2025
Viewed by 716
Abstract
We present an investigation into the band structure of acoustic waves in surface phononic crystals (SPnC), which comprise a square lattice of shallow cylinders on a mechanically isotropic semi-infinite substrate, utilizing the finite element method (FEM). The introduction of crystal periodicity to the [...] Read more.
We present an investigation into the band structure of acoustic waves in surface phononic crystals (SPnC), which comprise a square lattice of shallow cylinders on a mechanically isotropic semi-infinite substrate, utilizing the finite element method (FEM). The introduction of crystal periodicity to the surface modifies Rayleigh modes from non-dispersive to dispersive, thereby enabling the transformation of these modes into radiative or leaky forms. This spatial dispersion may facilitate the emergence of bound states in the continuum (BIC) by providing conditions appropriate for closing the radiative channels. A symmetry-protected BIC appears at the Γ point only when the periodicity of the crystal extends in the two dimensions of the surface plane. The decoupling from the radiative channels is due to symmetry incompatibility. An accidental BIC emerges in both one- and two-dimensional SPnCs at finite wave vectors. The partial-wave model applied to the empty lattice approximation shows that the underlying mechanism giving rise to the emergence of the accidental BIC is related to the simultaneous fulfillment of the nullification condition of the transverse radiative channel amplitude and the dispersion equation. Furthermore, the presence of the accidental BIC is not compromised by structural alterations that preserve the crystal symmetry, with only its frequency being influenced. Full article
(This article belongs to the Section Crystal Engineering)
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11 pages, 2572 KB  
Article
Molecular-Scale Analysis of Barium Azide (Ba(N3)2) Under High Pressure: A Synchrotron X-Ray Diffraction Study on Azide Ion Rotation and Phase Transition
by Xiaoxin Wu, Wenhui Jiang, Jinwei Zhang, Yuxin Ding, Yang Liu, Yanqing Liu, Hongyang Zhu, Junkai Zhang and Jingshu Wang
Molecules 2025, 30(22), 4426; https://doi.org/10.3390/molecules30224426 - 16 Nov 2025
Viewed by 601
Abstract
This study presents a comprehensive investigation of the high-pressure behavior of barium azide Ba(N3)2 through synchrotron X-ray diffraction, revealing critical insights into its anisotropic compressibility and phase transitions under pressures up to 28 GPa. At ambient conditions, Ba(N3) [...] Read more.
This study presents a comprehensive investigation of the high-pressure behavior of barium azide Ba(N3)2 through synchrotron X-ray diffraction, revealing critical insights into its anisotropic compressibility and phase transitions under pressures up to 28 GPa. At ambient conditions, Ba(N3)2 crystallizes in a monoclinic structure (space group P21/m), exhibiting pronounced anisotropic compression with axial compressibility following the order b > a > c. The distinct compressibility arises from the arrangement of azide ions, where interlayer interactions along the b-axis dominate the response to pressure. A reversible phase transition (Phase I → Phase II) initiates at 2.6 GPa, characterized by a monoclinic-to-monoclinic transformation involving subtle symmetry changes driven by azide ion rotation and lattice plane slippage. Above 11.8 GPa, emergent diffraction peaks suggest a potential secondary transition, though the structure remains stable up to 28 GPa. These findings underscore the unique role of azide ion dynamics in governing structural stability and phase evolution in divalent azides, offering implications for their utility as precursors in polymeric nitrogen synthesis. Full article
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21 pages, 3742 KB  
Article
Stability of Higher-Order Skyrmion Crystals Under Competing Magnetic Anisotropies in D3d Systems
by Satoru Hayami
Crystals 2025, 15(11), 978; https://doi.org/10.3390/cryst15110978 - 13 Nov 2025
Viewed by 1480
Abstract
We investigate the stability of higher-order skyrmion crystals with large topological charges in the presence of crystal-dependent magnetic anisotropies. Focusing on the competition between two types of bond-dependent anisotropy allowed by D3d crystalline symmetry on a two-dimensional triangular lattice, we systematically [...] Read more.
We investigate the stability of higher-order skyrmion crystals with large topological charges in the presence of crystal-dependent magnetic anisotropies. Focusing on the competition between two types of bond-dependent anisotropy allowed by D3d crystalline symmetry on a two-dimensional triangular lattice, we systematically construct a low-temperature magnetic phase diagram using simulated annealing. Our analysis reveals that the stability of the higher-order skyrmion crystal with skyrmion number of two is strongly controlled by the relative sign of the bond-dependent anisotropy to the D3d-type anisotropy: a positive anisotropy, which favors spin oscillations perpendicular to the ordering wave vector, enhances its stability, whereas a negative anisotropy, favoring oscillations parallel to the ordering wave vector, suppresses it and instead stabilizes a topologically trivial double-Q state. We further examine the field evolution of these phases under an out-of-plane magnetic field and show that distinct types of skyrmion crystals with the skyrmion number of one emerge in the intermediate-field regime. These results highlight that the competition between different magnetic anisotropies in crystalline systems is a key factor governing the stability of both zero-field and field-induced skyrmion crystals. Full article
(This article belongs to the Section Inorganic Crystalline Materials)
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