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17 pages, 4942 KB  
Article
Phase Stability and Competing Crystal Structures in the Formation of the Intermetallic Compounds Cu5As2 and Cu5(As,Sb)2
by Marianne Mödlinger, Alessia Provino, Pavlo Solokha, Serena De Negri, Antonio Bianco, Cristina Bernini and Pietro Manfrinetti
Solids 2026, 7(3), 24; https://doi.org/10.3390/solids7030024 - 1 May 2026
Abstract
An experimental investigation of the Cu-As-Sb ternary system in the Cu-rich region led to the identification of a new intermetallic phase, Cu5(As,Sb)2. The compound crystallizes in the orthorhombic Mg5Ga2-type structure (oI28, Ibam), [...] Read more.
An experimental investigation of the Cu-As-Sb ternary system in the Cu-rich region led to the identification of a new intermetallic phase, Cu5(As,Sb)2. The compound crystallizes in the orthorhombic Mg5Ga2-type structure (oI28, Ibam), analogous to the binary parent phase Cu5As2, with lattice parameters a = 5.968–5.977(1) Å, b = 11.550–11.565(3) Å, c = 5.530–5.573(3) Å. Similar to the parent Cu5As2 phase, the ternary compound forms with slight Cu under stoichiometry and exhibits a limited compositional range, with no continuous solid solubility between the binary and ternary phases. The phase formation, compositional stability, and decomposition behavior were systematically studied using a combination of powder and single-crystal X-ray diffraction (XRD, including Rietveld refinement), metallographic analysis with optical and scanning electron microscopy with energy-dispersive X-ray spectroscopy (LOM, SEM-EDXS), electron backscatter diffraction (EBSD) and thermal analysis (DTA, DSC). The results reveal that Cu5(As,Sb)2 is a high-temperature phase forming peritectically at 650–635 °C and stable only within a limited temperature interval. No continuous solid solubility exists between the ternary compound and the parent binary phase Cu5As2. Its formation occurs in strong competition with that of two other close neighboring solid-solution compounds, [Cu3−x(As1−ySby) (Cu3P-type; hP24, P63cm) and Cu3−x(As,Sb) (Cu9TeSb2-type; cP32, Pm−3n)], reflecting a complex interplay between composition, solubility ranges and thermal history. No evidence for the existence of high-temperature (HT) and low-temperature (LT) polymorphic phases was found for either the binary compound Cu5As2 or the ternary compound Cu5(As,Sb)2. Electrical resistivity measurements on a quenched sample indicate metallic behavior. These findings provide new insight into phase stability and structure–property relationships in Cu-As-Sb alloys and contribute to the understanding of competing intermetallic phases in this system. Full article
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12 pages, 4381 KB  
Article
High-Field Measurements of CoP and Elemental Combinatorics in the MnP-Type Family
by Daniel J. Campbell, John Collini, Kefeng Wang, Limin Wang, Brandon Wilfong, David Graf, Efrain E. Rodriguez and Johnpierre Paglione
Crystals 2026, 16(5), 299; https://doi.org/10.3390/cryst16050299 - 1 May 2026
Abstract
The MnP family of binary compounds presents an intriguingly simple platform to mix-and-match elemental components. Replacement on the transition metal or pnictogen site can alter magnetism, electronic correlations, and electrical properties. Here we report low-temperature properties of CoP, including measurements at magnetic fields [...] Read more.
The MnP family of binary compounds presents an intriguingly simple platform to mix-and-match elemental components. Replacement on the transition metal or pnictogen site can alter magnetism, electronic correlations, and electrical properties. Here we report low-temperature properties of CoP, including measurements at magnetic fields exceeding 30 T, revealing de Haas–van Alphen oscillations and a nearly two orders of magnitude increase in resistance. When viewed together with prior work, it is possible to put together a global picture of the role of different atoms in variations in magnetic ordering, lattice coherence, and topological band structure features in this material family. Full article
(This article belongs to the Section Crystalline Metals and Alloys)
24 pages, 2444 KB  
Article
Structural and Morphological Evaluation of Air-Processed Cs3Sb2I9 Perovskite Thin Film in Ambient Conditions
by Pranta Barua, Kannoorpatti Krishnan and Naveen Kumar Elumalai
Energies 2026, 19(9), 2196; https://doi.org/10.3390/en19092196 - 1 May 2026
Abstract
The ambient stability of ambient-processed lead-free perovskite absorbers remains a critical challenge toward scalable, eco-friendly photovoltaics. Herein, we systematically investigate the time-dependent structural and morphological evolution of drop-cast ambient-processed Cs3Sb2I9 thin films, being a potential non-toxic and stable [...] Read more.
The ambient stability of ambient-processed lead-free perovskite absorbers remains a critical challenge toward scalable, eco-friendly photovoltaics. Herein, we systematically investigate the time-dependent structural and morphological evolution of drop-cast ambient-processed Cs3Sb2I9 thin films, being a potential non-toxic and stable solar absorber candidate (energy bandgap ~2 eV) for solar cells, stored under uncontrolled ambient condition (~60% Relative humidity) for 28 days. Sequential X-ray diffraction (XRD) and surface morphology analyses using scanning electron microscope (SEM) reveal that the films preserve their trigonal P3̅m1 phase throughout aging, confirming phase stability. Moderate moisture exposure may induce partial recrystallization and subtle structural reorganization, possibly including minor c-axis realignment, leading to reduced lattice strain and improved crystallite coherence. Even after prolonged aging, no secondary phases or micro-cracks are detected, underscoring the slow degradation kinetics and robust Sb–I bonding that stabilize the layered [Sb2I9]3− dimers. The late-stage increase in diffraction intensity and partial recovery of crystallographic parameters could indicate transient structural reorganization, potentially associated with moisture-mediated reordering within an overall degradation pathway. These observations suggest some degree of morphological persistence and structural tolerance of Cs3Sb2I9 under ambient conditions, rather than complete stability. This behavior offers useful insights into ambient processing and the long-term reliability of lead-free perovskite photovoltaics. Full article
(This article belongs to the Section A2: Solar Energy and Photovoltaic Systems)
13 pages, 4687 KB  
Article
Non-Close-Packed Isotropic Responsive Magnetic Photonic Crystal Microspheres
by Lejian Zhao, Jie Zhu, Maocheng Sun, Wei Luo, Huiru Ma and Jianguo Guan
Nanomaterials 2026, 16(9), 556; https://doi.org/10.3390/nano16090556 - 1 May 2026
Abstract
Magnetic photonic crystal microspheres (MPCMs) have emerged as a versatile platform for intelligent sensing and display applications, owing to their integration of magnetic actuation with structural coloration. However, their practical implementation is limited by a fundamental structural constraint: most reported MPCMs adopt anisotropic [...] Read more.
Magnetic photonic crystal microspheres (MPCMs) have emerged as a versatile platform for intelligent sensing and display applications, owing to their integration of magnetic actuation with structural coloration. However, their practical implementation is limited by a fundamental structural constraint: most reported MPCMs adopt anisotropic architectures, resulting in angle-dependent optical responses that require continuous magnetic alignment to maintain uniform coloration. Herein, we propose a different structural paradigm based on non-close-packed, optically isotropic MPCMs. Driven by electrostatic repulsion in solutions, monodisperse Fe3O4@tannic acid (TA) core–shell nanoparticles spontaneously assemble into non-close-packed amorphous colloidal arrays, also known as photonic glasses, which are subsequently immobilized within stimuli-responsive polymer networks via emulsification-assisted thermal polymerization. By integrating poly(2-hydroxyethyl methacrylate-co-N-vinylpyrrolidone) (HEMA–NVP) or poly(N-isopropylacrylamide) (PNIPAM) as responsive matrices, the resulting MPCMs exhibit sensitive solvent- or thermo-dependent optical responses. Crucially, structural isotropy ensures angle-independent coloration, eliminating the need for continuous magnetic alignment during optical readout. As evidenced by the unchanged structural color and reflection peak under various magnetic field orientations, this design effectively decouples optical sensing from magnetic actuation. The intrinsic free volume of the non-close-packed architecture allows for isotropic lattice expansion and contraction, leading to broad spectral tunability. Collectively, this work establishes a promising design framework for magnetic photonic microsensors. Full article
(This article belongs to the Section Nanophotonics Materials and Devices)
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34 pages, 485 KB  
Article
Area Law for the Entanglement Entropy of Free Fermions in Nonrandom Ergodic Field
by Leonid Pastur and Mira Shamis
Entropy 2026, 28(5), 509; https://doi.org/10.3390/e28050509 - 1 May 2026
Abstract
The paper deals with the asymptotic behavior of a widely used correlation characteristic in large quantum systems. The correlation is quantum entanglement, the characteristic is entanglement entropy, and the system is an ideal gas of lattice fermions. If the one-body Hamiltonian of fermions [...] Read more.
The paper deals with the asymptotic behavior of a widely used correlation characteristic in large quantum systems. The correlation is quantum entanglement, the characteristic is entanglement entropy, and the system is an ideal gas of lattice fermions. If the one-body Hamiltonian of fermions is an ergodic finite difference operator with an exponentially decaying spectral projection, then the large-block form of the entanglement entropy is the so-called area law. However, the only class of one-body Hamiltonians for which this spectral condition was verified consists of discrete Schrödinger operators with random potential. In this paper, we prove the area law for several classes of Schrödinger operators whose potentials are ergodic but not random. We begin with quasiperiodic and limit-periodic operators and then move to a highly non-trivial case of potentials generated by subshifts of finite type. These arose in the theory of dynamical systems when studying chaotic phenomena. The corresponding asymptotic study requires involved spectral analysis, which therefore constitutes the bulk of the paper. Specifically, we prove uniform localisation of the eigenfunctions for the Maryland model and exponential decay of the eigenfunction correlator for various models. We believe these properties are of significant independent interest. Full article
(This article belongs to the Section Quantum Information)
22 pages, 9153 KB  
Article
Orbital-Driven Stability and Multifunctional Response in XYO3 (X = Nb, Ta; Y = Ag, Au) Cubic Perovskites: A First-Principles Study
by Łukasz Szeleszczuk, Katarzyna Mądra-Gackowska and Marcin Gackowski
Appl. Sci. 2026, 16(9), 4429; https://doi.org/10.3390/app16094429 - 1 May 2026
Abstract
Designing stable and multifunctional perovskite materials with tunable electronic and optical properties is crucial for advancing next-generation optoelectronic and high-temperature applications. In this study, the structural, electronic, optical, mechanical, and thermal properties of XYO3 (X = Nb, Ta; Y = [...] Read more.
Designing stable and multifunctional perovskite materials with tunable electronic and optical properties is crucial for advancing next-generation optoelectronic and high-temperature applications. In this study, the structural, electronic, optical, mechanical, and thermal properties of XYO3 (X = Nb, Ta; Y = Ag, Au) cubic perovskites were systematically investigated using density functional theory (DFT). Each compound crystallized into a cubic perovskite structure and was found to be both thermodynamically and dynamically stable. Hybrid functional (HSE06) calculations indicate semiconducting behavior with band gaps of 1.885 eV (NbAgO3), 1.298 eV (NbAuO3), 3.074 eV (TaAgO3), and 1.801 eV (TaAuO3). The density-of-state analysis reveals strong hybridization between the O-2p and Nb/Ta-d orbitals, which hints at mixed ionic/covalent bonding. Optical properties exhibit large absorption coefficients (about 106 cm−1) in the ultraviolet range and at lower reflectivity, especially of NbAgO3 and TaAgO3, indicating efficient light absorption. NbAgO3 and NbAuO3 possess moderate direct band gaps, making them suitable for optoelectronic and photovoltaic applications, whereas the wide bandgap of TaAgO3 is beneficial in ultraviolet optoelectronic devices. Mechanical analysis confirms the ductile nature of all compounds, with TaAuO3 exhibiting the highest ductility. Thermal analysis indicates that NbAgO3 and TaAgO3 exhibit higher lattice rigidity and thermal conductivity, but NbAuO3 and TaAuO3 are more anharmonic and have higher thermal expansion. Overall, these results demonstrate the multifunctional potential of XYO3 perovskites for applications in optoelectronics, photovoltaics, ultraviolet devices, flexible electronics, and high-temperature environments. Full article
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29 pages, 8655 KB  
Review
Multidisciplinary Breakthroughs in Short-Fiber Composites—Properties, Microstructure, Topology Optimization and Embedded Elements
by Evgenii I. Kurkin, Vladislava O. Chertykovtseva and Andrey V. Sedelnikov
Technologies 2026, 14(5), 275; https://doi.org/10.3390/technologies14050275 - 1 May 2026
Abstract
Short-fiber-reinforced composite materials are increasingly being used in a wide variety of fields, including medicine, the automotive industry, and aviation. This growing demand has driven the development of new manufacturing technologies, numerical modeling and topology optimization methods, and techniques for assessing the internal [...] Read more.
Short-fiber-reinforced composite materials are increasingly being used in a wide variety of fields, including medicine, the automotive industry, and aviation. This growing demand has driven the development of new manufacturing technologies, numerical modeling and topology optimization methods, and techniques for assessing the internal structure of such products, among others. This review provides a comprehensive examination of the characteristics and mechanical properties of short-fiber-reinforced composite materials, focusing on the key aspects of their design and manufacturing processes. We analyze the consideration of anisotropy in material modeling, the methods for the non-destructive testing of material structure, and the multidisciplinary approach to product design. The review also addresses advanced design techniques, including topology optimization and bimaterial optimization for designing products with embedded lattice structures, as well as adhesion modeling. In contrast to existing reviews, this work presents an overview of multidisciplinary studies dedicated to all stages of designing and manufacturing structures from short-fiber-reinforced composites, unifying the engineering pipeline from material property and molding modeling to topology-optimized design and static analysis under operation loads. Full article
(This article belongs to the Section Innovations in Materials Science and Materials Processing)
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30 pages, 11635 KB  
Article
A Traffic-Density-Aware, Speed-Adaptive Control Strategy to Mitigate Traffic Congestion for New Energy Vehicle Networks
by Chia-Kai Wen and Chia-Sheng Tsai
World Electr. Veh. J. 2026, 17(5), 241; https://doi.org/10.3390/wevj17050241 - 30 Apr 2026
Abstract
The rising market penetration of new energy vehicles (NEVs) is transforming urban traffic into a heterogeneous mix of battery electric (BEVs), hybrid electric (HEVs), and conventional fuel vehicles (FVs). For analytical brevity, traditional internal combustion engine vehicles (ICEVs) are hereafter referred to as [...] Read more.
The rising market penetration of new energy vehicles (NEVs) is transforming urban traffic into a heterogeneous mix of battery electric (BEVs), hybrid electric (HEVs), and conventional fuel vehicles (FVs). For analytical brevity, traditional internal combustion engine vehicles (ICEVs) are hereafter referred to as ‘fuel vehicles (FVs)’ in the discussion of New Energy Vehicle (NEV) networks. This research investigates the efficacy of centralized coordination for NEVs within a localized region, as opposed to individualized speed control, in enhancing the mitigation of traffic congestion. Evaluating traffic efficiency and decarbonization strategies in such settings often requires extensive random sampling and Monte Carlo simulations over a large set of parameter combinations. However, conventional microscopic traffic simulators (e.g., SUMO), which rely on fine-grained modeling of vehicle dynamics and signal control, incur prohibitive computational time when scaled to large networks and numerous experimental scenarios. In this study, battery electric vehicles and hybrid electric vehicles are designed as density-aware vehicles, whose movement speed is adaptively adjusted according to the regional traffic density in their vicinity and the control parameter β. In contrast, fuel vehicles adopt a stochastic movement speed and, together with other vehicle types, exhibit either movement or stoppage in the lattice environment. This density-driven speed-adaptive control and lattice arbitration mechanism is intended to reproduce, in a simplified yet extensible manner, changes in mobility and traffic-flow stability under high-density traffic conditions. The simulation results indicate that, under the same Manhattan road network and vehicle-density conditions, tuning the β parameter of new energy vehicles to reduce their movement speed in high-density areas and to mitigate abrupt position changes can suppress traffic-flow oscillations, delay the onset of the congestion phase transition, and promote spatial equilibrium of traffic flow. Meanwhile, this study develops simplified energy-consumption and carbon emission models for battery electric vehicles, hybrid electric vehicles, and fuel vehicles, demonstrating that incorporating a speed-adaptive density strategy into mixed traffic flow not only helps alleviate abnormal congestion but also reduces potential energy use and carbon emissions caused by congestion and stop-and-go behavior. From a sensing and practical perspective, the proposed framework assumes that future connected and autonomous vehicles (CAVs) can estimate vehicle states and local traffic density through GNSS–IMU multi-sensor fusion and V2X communications, indicating methodological consistency between the proposed model and real-world CAV sensing capabilities and making it a suitable and effective experimental platform for investigating the relationships among new energy vehicle penetration, density-control strategies, and carbon footprint. Full article
(This article belongs to the Section Automated and Connected Vehicles)
14 pages, 1372 KB  
Article
Mineralogical Characteristics and Fluorescent Properties of Yellow and Pink Calcite
by Qiuli Yan, Wenkai Liang and Qingfeng Guo
Crystals 2026, 16(5), 297; https://doi.org/10.3390/cryst16050297 - 30 Apr 2026
Abstract
Yellow and pink calcite samples from the Huanggangliang and Xilingol mining areas in Inner Mongolia were investigated to elucidate the relationships among chemical composition, unit-cell parameters, coloration, and luminescence. Electron probe micro-analysis, laser ablation inductively coupled plasma mass spectrometry, X-ray diffraction, infrared spectroscopy, [...] Read more.
Yellow and pink calcite samples from the Huanggangliang and Xilingol mining areas in Inner Mongolia were investigated to elucidate the relationships among chemical composition, unit-cell parameters, coloration, and luminescence. Electron probe micro-analysis, laser ablation inductively coupled plasma mass spectrometry, X-ray diffraction, infrared spectroscopy, Raman spectroscopy, UV-Vis absorption spectroscopy, and photoluminescence measurements show that samples of yellow and pink calcite differ significantly in impurity incorporation and optical behavior. Yellow calcite is relatively enriched in Mg and rare earth elements, especially Y and Ce, whereas pink calcite contains markedly higher Mn and Fe contents. The pink calcite has smaller lattice parameters and unit-cell volume, consistent with greater substitution of Ca2+ by smaller-radius cations. Spectra reveal that the pink coloration is mainly related to Mn-associated absorption bands at 402 and 527 nm, whereas the yellow color is attributed to weak impurity- and defect-related absorption. Under ultraviolet excitation, yellow calcite exhibits a broad blue–white emission centered at ~470 nm, whereas pink calcite shows an intense orange–red emission near 625 nm characteristic of Mn2+. Variable-temperature photoluminescence further demonstrates that the pink calcite has higher thermal stability, with a thermal-quenching activation energy of 0.218 eV, compared with 0.074 eV for the yellow calcite. These results demonstrate that trace element incorporation plays a key role in regulating the coloration and luminescence of calcite and provide useful insight into the optical behavior of carbonate minerals. Full article
16 pages, 2029 KB  
Article
Engineering Flow Anisotropy in Additively Manufactured Lattices via Patterned Unit Cell Symmetry
by Ian R. Woodward, Dominic J. Hoffman and Catherine A. Fromen
J. Compos. Sci. 2026, 10(5), 246; https://doi.org/10.3390/jcs10050246 - 30 Apr 2026
Abstract
Additively manufactured lattice structures have become a staple of optimized structural parts and are increasingly common in biomedical and chemical applications that require consideration of flow through porous architectures. However, design principles governing transport performance trail those established for mechanical optimization. Here, we [...] Read more.
Additively manufactured lattice structures have become a staple of optimized structural parts and are increasingly common in biomedical and chemical applications that require consideration of flow through porous architectures. However, design principles governing transport performance trail those established for mechanical optimization. Here, we introduce two complementary design frameworks that modify symmetry at both the unit cell and part scales to systematically tune internal transport. These approaches are further extended into patterned lattice structures, where multiple unit cell designs can be combined in one, two, or three dimensions to further regulate the internal flow. We find that identical global lattice geometries can arise from different unit cell basis and voxel plane orientations, with minimal changes in bulk geometric properties. Yet in parts with diameters of 12–35 mm, hydraulic diameters of 1–4 mm, and porosities ~80%, these design selections significantly affect the hydraulic tortuosity and fluid transport behavior. We further demonstrate performance from select designs that yield a new class of anisotropic lattices with strong sensitivity to flow direction that is tuned by the projected area perpendicular to flow. Collectively, these symmetry-informed, multi-order combinatorial design approaches enable predictable, direction-dependent transport design and expand the functional potential of lattice architectures across disciplines. Full article
(This article belongs to the Special Issue Lattice Structures)
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19 pages, 5266 KB  
Article
Synthesis and Perspectives of Oriented Growth of Double-Perovskite Cs2SnI6 in the Presence of Antimony
by Shodruz T. Umedov, Anastasia V. Grigorieva, Egor V. Latipov, Alexander V. Dzuban, Alexander V. Knotko and Andrei V. Shevelkov
Nanomaterials 2026, 16(9), 553; https://doi.org/10.3390/nano16090553 - 30 Apr 2026
Abstract
Vacancy-ordered double-perovskite Cs2SnI6 is known to be a good candidate for perovskite photovoltaics, as it is a light harvesting material which has potential both as an individual compound and as a component of a composite material. The compound is interesting [...] Read more.
Vacancy-ordered double-perovskite Cs2SnI6 is known to be a good candidate for perovskite photovoltaics, as it is a light harvesting material which has potential both as an individual compound and as a component of a composite material. The compound is interesting due to being free of atom sites in B cationic positions, making the lattice “breathable” and giving it optoelectronic characteristics that vary with dopants. Here, antimony was examined as a possible heterovalent dopant with an ionic radius larger than that of Sn4+. In practice, it has been found that most of the materials are composites of Cs2SnI6 and Cs3Sb2I9 phases. In the CsI–SnI4–SbI3 phase triangle, the melt crystallization process produced a layered (111)-oriented microstructure of crystallites with an increasing percentage of antimony. Two-dimensional perovskite materials look more promising in the decomposition of a solid solution to Cs2SnI6 and Cs3Sb2I9 phases than in heterophase nucleation. The observed effect of (111)-oriented growth could be translated to other inorganic halides to form new oriented films or single crystals of perovskite materials. Diffuse reflectance spectroscopy showed an additional absorption shoulder in the NIR region for all groups of compounds, most likely induced by point defects in I sublattices of Cs2SnI6. Expanding the Cs2SnI6 absorption range to the NIR region could lead to new perspectives for its application. Full article
(This article belongs to the Section Synthesis, Interfaces and Nanostructures)
12 pages, 10929 KB  
Article
Insights on Structural, Mechanical and Thermal Properties of High-Entropy Perovskite Oxide (Ca0.2Sr0.2Ba0.2La0.2Pb0.2)TiO3 from First-Principles Calculations
by Lin Shao, Shuaiqi Liu, Pingying Tang and Riwen Ji
Materials 2026, 19(9), 1845; https://doi.org/10.3390/ma19091845 - 30 Apr 2026
Abstract
High-entropy perovskite oxides attract considerable attention due to their outstanding properties and extensive applications. In this work, the lattice distortion and the mechanical, thermal and electronic structure properties of high-entropy (Ca0.2Sr0.2Ba0.2La0.2Pb0.2)TiO3 (CSBLPT) [...] Read more.
High-entropy perovskite oxides attract considerable attention due to their outstanding properties and extensive applications. In this work, the lattice distortion and the mechanical, thermal and electronic structure properties of high-entropy (Ca0.2Sr0.2Ba0.2La0.2Pb0.2)TiO3 (CSBLPT) are investigated through first-principles calculations. The results suggest that the influence of O atoms on lattice distortion is predominant, and the effect of overall A-site atoms plays a distinctly greater role than that of the B-site atoms. The mechanical results show that the high-entropy CSBLPT has a lower Young’s modulus and higher fracture toughness than ternary SrTiO3. The Debye temperature also indirectly indicates that the thermal expansion coefficient of the studied high-entropy perovskite is greater than that of SrTiO3. As for thermal conductivity, the obtained result of CSBLPT is also appreciably lower than that of SrTiO3, and the lowest thermal conductivity is along the [100] direction. The Fermi level of high-entropy CSBLPT is transferred to the conduction band, exhibiting a degenerate n-type semiconductor behavior with metallic-like characteristics, and the Bader charge values are also related to the local lattice distortion, which may cause differences in thermomechanical properties between high-entropy CSBLPT and SrTiO3. Above all, high-entropy CSBLPT is a preferable TBC material with excellent performance under working conditions compared to SrTiO3. Full article
(This article belongs to the Section Materials Simulation and Design)
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24 pages, 502 KB  
Article
QML Inference for Spatio-Temporal GARCH Models with Spatial Volatility Interactions
by Khaoula Aouati, Soumia Kharfouchi, Khudhayr A. Rashedi, Tariq S. Alshammari and Abdullah H. Alenezy
Mathematics 2026, 14(9), 1507; https://doi.org/10.3390/math14091507 - 29 Apr 2026
Abstract
We propose a new class of spatio-temporal GARCH models designed to capture volatility dynamics that propagate jointly across time and space. Existing spatio-temporal GARCH formulations typically account for either lagged spatial spillovers or contemporaneous interactions separately, and therefore fail to capture the combined [...] Read more.
We propose a new class of spatio-temporal GARCH models designed to capture volatility dynamics that propagate jointly across time and space. Existing spatio-temporal GARCH formulations typically account for either lagged spatial spillovers or contemporaneous interactions separately, and therefore fail to capture the combined effect of instantaneous spatial volatility feedback and its propagation over time. To address this gap, we introduce a unified framework that incorporates both contemporaneous and lagged spatial volatility interactions within a single coherent model. At each time point, conditional variances evolve according to a temporal GARCH recursion combined with both contemporaneous and lagged spatial volatility interactions defined on a lattice. This structure allows volatility shocks to diffuse instantaneously across neighboring locations and persist over time through spatially structured feedback mechanisms, extending existing spatial and spatio-temporal GARCH formulations. We establish sufficient conditions for the existence of a unique strictly stationary and ergodic solution based on contraction properties of a combined spatial–temporal operator. Statistical inference is conducted via Gaussian quasi-maximum likelihood estimation (QMLE). We derive consistency and asymptotic normality of the QMLE under two asymptotic regimes: (i) increasing temporal domain with fixed spatial size, and (ii) joint asymptotics where both the number of time periods and spatial locations diverge. In both cases, the asymptotic covariance matrix admits a standard sandwich form and can be consistently estimated. An extensive Monte Carlo study confirms the theoretical results. The simulations show that the QMLE performs well even under strong spatial and temporal persistence and remains robust to heavy-tailed innovations. In particular, increasing the spatial domain substantially improves estimation accuracy, highlighting the efficiency gains induced by spatial information. The proposed model provides a flexible and tractable framework for analyzing volatility processes evolving jointly in time and space. Full article
(This article belongs to the Section D1: Probability and Statistics)
11 pages, 1026 KB  
Article
Restoration of the Korringa Relation in Disordered Liquid Systems via Transverse Relaxation (T2)
by Yuan Zeng, Lanlan Yang, Jiejun Yao, Wei Tang and Xiaolong Liu
Materials 2026, 19(9), 1826; https://doi.org/10.3390/ma19091826 - 29 Apr 2026
Abstract
This study resolves the apparent breakdown of the Korringa relation in disordered liquid metals by investigating Ga-based alloys (EGaIn and Galinstan). By integrating temperature-dependent Knight shifts (K) with longitudinal (T1) and transverse (T2) relaxation measurements, we demonstrate that deviations [...] Read more.
This study resolves the apparent breakdown of the Korringa relation in disordered liquid metals by investigating Ga-based alloys (EGaIn and Galinstan). By integrating temperature-dependent Knight shifts (K) with longitudinal (T1) and transverse (T2) relaxation measurements, we demonstrate that deviations from classical behavior arise from neglecting transverse spin dephasing induced by structural and electronic disorder. While solid-state alloys follow the conventional Korringa law, the liquid phase exhibits significant discrepancies between T1 and T2 due to enhanced electron scattering and fluctuating hyperfine fields. By explicitly incorporating T2 into a modified framework, the proportionality between the Knight shift and nuclear relaxation is quantitatively restored. This establishes transverse relaxation as a critical parameter for describing nuclear spin dynamics in complex liquid metals, reinforcing NMR as a powerful local probe for optimizing next-generation liquid metal technologies. Full article
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20 pages, 2207 KB  
Article
Critical Benchmark Validation of the Core Physics Multigroup Cross-Section Library TPEX
by Ying Chen, Haicheng Wu, Lili Wen, Yue Xiao, Jinchao Zhang, Qian Zhang, Xiaofei Wu and Huanyu Zhang
Energies 2026, 19(9), 2143; https://doi.org/10.3390/en19092143 - 29 Apr 2026
Abstract
Core physics multigroup cross-section libraries provide essential cross-section and burnup data for reactor neutron physics calculations, serving as a fundamental prerequisite for reactor physics analysis. The China Nuclear Data Center has developed the TPEX multigroup cross-section library for pressurized water reactors (PWRs) based [...] Read more.
Core physics multigroup cross-section libraries provide essential cross-section and burnup data for reactor neutron physics calculations, serving as a fundamental prerequisite for reactor physics analysis. The China Nuclear Data Center has developed the TPEX multigroup cross-section library for pressurized water reactors (PWRs) based on the Chinese Evaluated Nuclear Data Library CENDL-3.2. A systematic critical benchmark validation of the newly developed TPEX library has been performed. To verify its applicability and accuracy, the validation has been conducted against 131 critical benchmark experiments from the International Criticality Safety Benchmark Evaluation Project (ICSBEP 2006) and the WIMS-D library update project. The calculated effective multiplication factors (keff) are compared with the experimental values, results from equivalent multigroup libraries, and reference solutions from Monte Carlo code. The results indicate that the absolute average deviations between the calculated keff values using the TPEX library and the experimental measurements are 280 pcm for the uranium solution experiments, 410 pcm for the plutonium solution experiments, 10 pcm for the uranium metal lattice experiments, 20 pcm for the uranium dioxide lattice experiments, 22 pcm for the MOX fuel lattice experiments, and 150 pcm for the LCT001 uranium oxide assembly experiments. Accordingly, the TPEX library demonstrates excellent performance in reactivity predictions for PWRs. Full article
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