Threefold Symmetry Research Articles

Conventional epitaxy of NiO thin films on muscovite mica and c-Al2O3 substrates

Fiber-textured and epitaxial NiO thin films were deposited on Si(100), c-Al2O3, and muscovite mica(001) substrates using reactive magnetron sputtering at substrate temperatures of 300°C and 400°C, to investigate the effect of film thickness and substrate temperature on epitaxial growth of NiO films. The as-deposited films exhibited a face-centered cubic structure with a larger lattice constant, attributed to strain induced during the sputtering process. With an increase in substrate temperature to 400°C, the d-spacing decreased due to strain release, approaching the NiO bulk value for the thickest film. The NiO film grown on Si(100) displayed fiber texture. On c-plane sapphire, NiO thin films exhibited twin domains and three-fold symmetry, consistent with expected crystallographic orientation relationship for NaCl-structured materials on sapphire:(111)NiO∥(0001)Al2O3and[01¯1]NiO∥[1¯010]Al2O3, [011¯]NiO∥[101¯0]Al2O3. On muscovite mica(001) substrates, the observed epitaxial shows that the mechanism is conventional epitaxy, rather than van der Waals epitaxy, consistent with the epitaxial growth of the non-layered non-van-der-Waals compound NiO. The epitaxial relationship was identified as of (111)NiO∥(001)Mica and [01¯1]NiO∥[010]Mica, [011¯]NiO∥[01¯0]Mica.

Mott resistive switching initiated by topological defects

Avalanche resistive switching is the fundamental process that triggers the sudden change of the electrical properties in solid-state devices under the action of intense electric fields. Despite its relevance for information processing, ultrafast electronics, neuromorphic devices, resistive memories and brain-inspired computation, the nature of the local stochastic fluctuations that drive the formation of metallic regions within the insulating state has remained hidden. Here, using operando X-ray nano-imaging, we have captured the origin of resistive switching in a V2O3-based device under working conditions. V2O3 is a paradigmatic Mott material, which undergoes a first-order metal-to-insulator phase transition together with a lattice transformation that breaks the threefold rotational symmetry of the rhombohedral metallic phase. We reveal a new class of volatile electronic switching triggered by nanoscale topological defects appearing in the shear-strain based order parameter that describes the insulating phase. Our results pave the way to the use of strain engineering approaches to manipulate such topological defects and achieve the full dynamical control of the electronic Mott switching. Topology-driven, reversible electronic transitions are relevant across a broad range of quantum materials, comprising transition metal oxides, chalcogenides and kagome metals.

The Pyramidalization of sp2 Centers in 3/2‐Systems Is a “Structural Breathing” Independent of Energy

AbstractIn 3/2‐systems, such as the acetate anion H3CαC′OO−, an sp3 center and an sp2 center are connected by a covalent bond. The interaction of threefold and twofold symmetry results in the pyramidalization of the sp2 center during rotation about bond Esp3−Esp2. Rotation angles ψ=0°, ±60°, ±120°, and ±180° account for conformations with a symmetry plane containing the planar sp2 center CαC′OO. However, in all conformations with rotation angles ψ≠0°, ±60°, ±120°, and ±180° this symmetry plane is lost and pyramidalization must occur with maxima at rotation angles ψ=±30°, ±90°, and ±150°, because the two sides of the sp2 center CαC′OO are different. Inevitably, this leads to a pyramidalization/rotation profile θ/ψ with three maxima, three minima, and six zero‐crossings. Thus, myriads of 3/2‐compounds pyramidalize their sp2 centers each moment to the order of about 2° in a coupled pyramidalization/rotation molecular motion independent of energy.

The Formation Criteria of LPSO Phase in Type I LPSO Mg-Y-X Alloy from the Perspective of Liquid-Solid Correlation.

The formation criteria of the LPSO phase are important for the design of long-period stacking-ordered (LPSO) Mg alloys. This work focuses on Type I LPSO Mg-Y-X alloys and attempts to explore the formation criteria of the LPSO phase from the perspective of liquid-solid correlation. With the aid of ab-initio molecular dynamics simulation, liquid Mg-Y-X alloys are investigated to obtain the common liquid characteristics from the reported Type I LPSO Mg-Y-X alloys. Following the liquid characteristics, a new Type I LPSO alloy, i.e., Mg-Y-Au, is experimentally confirmed. The discovery of a new Type I LPSO alloy supports liquid-solid correlation, and hence, the formation criteria of the LPSO phase in Type I LPSO alloys can be developed based on the common liquid characteristics of Type I LPSO Mg-Y-X alloys as follows: X should result in the reduction in equilibrium volume and cohesive energy; Y should repulse Y and be attracted by both Mg and X, and X should be repulsed by both Mg and X; X should enhance the threefold and fourfold symmetries and weaken the fivefold and sixfold ones so that the local structural symmetries are distributed close to liquid pure Mg.

Structural and Magnetic Properties of Dimeric Capsule Assemblies Formed by Cyclic Trinuclear Complexes.

Cyclic trinuclear homo-metal complexes, [{Fe(L3+2Br)py}3] (1) and [{Mn(L3+2Br)}3(py)2 MeOH] (2), along with a hetero-metal complex, [FeMn2(L3+2H)3(DMF)3] (3), were synthesized using asymmetric ditopic ligands (H3L3+2H: 2-(2-hydroxyphenyl)-6-ol-5-(salicylideneamino)benzoxazole, H3L3+2Br: 2-(2-hydrox-5-bromoyphenyl)-6-ol-5-(5-bromosalicylideneamino)benzoxazole). The molecular structure of 1 is characterized by a tripod structure with three-fold symmetry, where an enantiomer pair forms a dimeric capsule with dimensions of approximately 3 × 1.6 × 1.6 nm3. Complexes 2 and 3, which lack three-fold symmetry, exhibit similar molecular structures to previously reported complexes with these ligands, but do not form a capsule structure. Magnetic measurements of 1-3 reveal the presence of significantly weak antiferromagnetic interactions between the metal ions.

Single-crystal growth, crystal structure, and molecular dynamics of organic–inorganic [NH3(CH2)2NH3]CuBr4

As part of obtaining excellent properties that can be used as lead-free hybrid solar cells, the crystal growth, crystal structure, phase transition temperature, and thermal properties for [NH3(CH2)2NH3]CuBr4 were discussed. The crystal structure at 300 K was determined to be monoclinic by single-crystal X-ray diffraction (XRD) analysis. The phase transition temperatures were determined to be 447 and 473 K, and the results were consistent with the powder XRD patterns. Thermogravimetric analysis revealed thermal stability up to ~ 460 K. The continuous changes in the 1H and 13C chemical shifts and 14N static resonance frequency with increasing temperature are related to variations in the local environment and coordination geometry. The significant differences in activation energies obtained from the 1H and 13C spin–lattice relaxation times (t1ρ) at low and high temperatures were discussed. The activation energy results suggested that the energy barrier at low temperatures was related to the reorientation of the NH3 and CH2 groups around the three-fold symmetry axis, and the energy barrier at high temperatures was related to the reorientation of the [NH3(CH2)2NH3] cation. These physical properties will be provide important insights or potential applications of this crystal.Please check and confirm that the corresponding author and their respective corresponding affiliation have been correctly identified and amend if necessary.OK !

X, Y, and Z Subgroups of the Unitary Group

The subgroups XU(2), YU(2), and ZU(2) of the unitary group U(2) allow to find twenty-four different decompositions of an arbitrary [Formula: see text] unitary matrix. Because the group YU(2) has not been considered before, 20 out of the 24 decompositions are new. Introducing this YU(2) group allows to highlight, within quantum circuit design, a symmetry similar to the threefold symmetry of the Pauli matrices of spin systems. Similar subgroups of the unitary group U([Formula: see text]) lead to various new decompositions of an arbitrary [Formula: see text] unitary matrix. Whereas for [Formula: see text] equal 2, this leads to the synthesis of single-qubit quantum gates, for [Formula: see text] equal a power of 2, this leads to new design methods for multiple-qubit circuits.

Directly visualizing nematic superconductivity driven by the pair density wave in NbSe2

Pair density wave (PDW) is a distinct superconducting state characterized by a periodic modulation of its order parameter in real space. Its intricate interplay with the charge density wave (CDW) state is a continuing topic of interest in condensed matter physics. While PDW states have been discovered in cuprates and other unconventional superconductors, the understanding of diverse PDWs and their interactions with different types of CDWs remains limited. Here, utilizing scanning tunneling microscopy, we unveil the subtle correlations between PDW ground states and two distinct CDW phases — namely, anion-centered-CDW (AC-CDW) and hollow-centered-CDW (HC-CDW) — in 2H-NbSe2. In both CDW regions, we observe coexisting PDWs with a commensurate structure that aligns with the underlying CDW phase. The superconducting gap size, Δ(r), related to the pairing order parameter is in phase with the charge density in both CDW regions. Meanwhile, the coherence peak height, H(r), qualitatively reflecting the electron-pair density, exhibits a phase difference of approximately 2π/3 relative to the CDW. The three-fold rotational symmetry is preserved in the HC-CDW region but is spontaneously broken in the AC-CDW region due to the PDW state, leading to the emergence of nematic superconductivity.

Effect of crystallographic orientation on the deformation and mechanical behavior of CoCrFeNi in Berkovich nanoindentation

The hardness and plastic deformation behavior of single-phase concentrated solid solution alloy CoCrFeNi were studied for selected crystallographic orientations (⟨001⟩, ⟨011⟩ and ⟨111⟩) using Berkovich nanoindentation. The integration of transmission electron microscopy (TEM) and molecular dynamics (MD) simulations was carried out to elucidate comprehensively the distinction in the deformation mechanisms, the evolution of dislocation structures, and the pile-up of differently oriented CoCrFeNi alloys subjected to indentation by a Berkovich indenter. In MDs, a Berkovich indenter, meticulously crafted to replicate its real geometry, was effectively employed in investigating the nanoindentation. The ⟨001⟩-oriented CoCrFeNi exhibited the highest hardness and the lowest magnitude of pop-in events, followed by the ⟨011⟩ and then the ⟨111⟩ orientations. The pile-up behavior was strongly dependent on the crystallographic orientation and occurred by three sequential processes. The deformation twinning was activated only in the ⟨001⟩ orientation and inclined toward the center direction of the indent due to the force inclining toward the radial direction of the indent. The clear manifestation of the evolution of dislocations in the three orientations during indentation was elucidated. More SFTs or Stair-rods were observed in the ⟨001⟩ orientation, attributable to the intensified reaction of Shockley partials stemming from its higher density of Shockley partials, followed by the ⟨011⟩ and then the ⟨111⟩ orientations. The anisotropic nanoindentation-hardness was correlated with the microstructures. The highest hardness and lowest magnitude of pop-in events of the ⟨001⟩ orientation could be ascribed to its intense dislocation interactions, high-density SFTs and the formation of twins. In the ⟨111⟩ orientation, the three-fold symmetry emission of prismatic dislocation loops along the three slip directions not parallel to the surface leaded to a weak interaction between dislocations, and then resulted in the lowest hardness. This research may be helpful to enhance our comprehension of the intricate mechanical behaviors exhibited by different oriented FCC high entropy alloys under Berkovich indentation.

Sedimentation dynamics of triply twisted Möbius bands: Geometry versus topology

We explore the sedimentation dynamics of triply twisted Möbius bands, each characterized by threefold rotational symmetry but distinguished by its construction and intrinsic geometrical properties. Three types of bands are considered: one with vanishing Gaussian curvature, constructed by isometrically deforming flat rectangular strips through bending without stretching; and two with negative Gaussian curvature, one being constructed by isometrically deforming helicoids. Experiment on these three types of bands, with a focus on varying aspect ratios, reveals a singular phenomenon: while the spin directions of bands not derived from helicoids spin in directions consistent with their inherent chirality, bands derived from helicoids exhibit an aspect-ratio-dependent spin, pointing to the existence of a critical aspect ratio at which geometric factors dominate over chiral influences. Supported by numerical simulations and a detailed analysis of the resistance tensors, we propose the unique response of bands derived from helicoids originates from a complex interaction among geometry, topology, and hydrodynamics. Two explanations are offered for the chiral transition observed in bands derived from helicoid. First, this transition may parallel the dynamics of superhelices, for which competing chiralities influence rotational behavior. Second, the unique geometrical properties of bands derived from helicoids, coupled with deviations between the rotation axis and the local symmetry axis, may underlie the observed aspect-ratio-dependent chiral transition. Our study underscores the significant role of geometrical and topological nuances in determining the behavior of chiral objects suspended in fluids. In addition to offering transformative potential across diverse fields, it promises advancements in mixing, separation processes, and innovative passive swimmers. Published by the American Physical Society 2024

Triphenylamine[3]arenes: Streamlining Synthesis of a Versatile Macrocyclic Platform for Supramolecular Architectures and Functionalities.

Triphenylamine[3]arenes (TPA[3]s), featuring [16]paracyclophane backbone with alternating carbon and nitrogen bridging atoms, were synthesized through a BF3 ⋅ Et2O-catalyzed cyclization reaction using triphenylamine derivatized monomers and paraformaldehyde. This molecular design yielded a series of TPA[3] macrocycles with high efficiency, with their facile derivatizations also successfully demonstrated. On account of the strong electron-donating properties of the TPA moieties, these TPA[3]s exhibit remarkable delayed fluorescence, and possess a significant affinity for iodine. Furthermore, their inherent three-fold symmetry rendered TPA[3]s as novel building blocks for the construction of extended frameworks and molecular cages. This advancement expands the versatility of discrete macrocycles into complex architectures, enhancing their applicability across a broad spectrum of applications.

Ising fracton spin liquid on the honeycomb lattice

We study a classical Ising model on the honeycomb lattice with local two-body interactions and present strong evidence that at low temperature it realizes a higher-rank Coulomb liquid with fracton excitations. We show that the excitations are (type-I) fractons, appearing at the corners of membranes of spin flips. Because of the threefold rotational symmetry of the honeycomb lattice, these membranes can be locally combined such that no excitations are created, giving rise to a set of ground states described as a liquid of membranes. We devise a cluster Monte Carlo algorithm purposefully designed for this problem that moves pairs of defects, and use it to study the finite-temperature behavior of the model. We show evidence for a first order transition from a high-temperature paramagnet to a low-temperature phase whose correlations precisely match those predicted for a higher-rank Coulomb phase. Published by the American Physical Society 2024

Effect of cation site occupancy on the structure and magnetic properties of SrCoxTixFe12–2xO19 thin films

Multiferroic materials have potential applications in multifunctional electronic devices, and M-type hexaferrite with conical spin order is a promising candidate. In this paper, a series of SrCoxTixFe12–2xO19 thin films were prepared by a sol-gel method, and x-dependent structure, cation site occupancy and magnetic properties were investigated to explore the origin of conical spin order in M-type hexaferrite. It was found that the introduction of Co2+ and Ti4+ ions decreases the uniaxial magnetocrystalline anisotropy and breaks the threefold symmetry of the lattice, inducing a conical magnetic structure. Moreover, the appearance temperature of the conical spin order (Tcone) increases first and then decreases with the increase of x, and the largest Tcone of about 324 K is obtained in SrCo1.8Ti1.8Fe8.4O19 thin film. The evolution of magnetization is closely related to the site occupancy of Co2+ and Ti4+ ions, and the net effective substitution ratio of spin-down Fe3+ is positive correlation to the Tcone of SrCoxTixFe12–2xO19 and thus considered to be responsible for the introduction of conical spin order. The results reveal the correlation between the structure, magnetic properties and cation site occupancy, pointing out an effective method to induce conical spin order in M-type hexaferrites.

Small Organic Molecules with Anchoring Adsorption Enhance Corrosion Inhibition of Zinc Electrodes in ZnSO4 Medium

AbstractIn this study, trimercapto‐S‐triazine trisodium salt (TMT) with threefold rotational symmetry as a corrosion inhibitor was introduced into 2 mol ⋅ L−1 ZnSO4 medium. By electrochemical measurements, the corrosion inhibition efficiency of the zinc electrodes was 92.52 % when the concentration of TMT corrosion inhibitor was 2 mmol ⋅ L−1. Based on the microstructural characterization and theoretical analysis of Zn electrodes, it was confirmed that S and N atoms of TMT corrosion inhibitor serve as alternately zinc‐philic adsorption sites with sixfold rotational symmetry for the formation of intermolecular complexes. Adsorption energies of TMT on Zn surfaces were calculated and indicated that the bonds of Zn−N and Zn−S promoted anchoring adsorption on sixfold symmetric (002) plane of zinc. Meanwhile, TMT corrosion inhibitor can adsorb Zn2+ from the electrolyte and directionally deposit them on the surface of Zn (002), effectively avoiding the occurrence of dendrites. This study changes the common knowledge that organic corrosion inhibitors must form hydrophobic films to have corrosion inhibition performance, and provides a new approach for using small organic molecules with anchoring adsorption as metal corrosion inhibitors.

Solution structure, dynamics and tetrahedral assembly of Anti-TRAP, a homo-trimeric triskelion-shaped regulator of tryptophan biosynthesis in Bacillus subtilis

Cellular production of tryptophan is metabolically expensive and tightly regulated. The small Bacillus subtilis zinc binding Anti-TRAP protein (AT), which is the product of the yczA/rtpA gene, is upregulated in response to accumulating levels of uncharged tRNATrp through a T-box antitermination mechanism. AT binds to the undecameric axially symmetric ring-shaped protein TRAP (trp RNA Binding Attenuation Protein), thereby preventing it from binding to the trp leader RNA. This reverses the inhibitory effect of TRAP on transcription and translation of the trp operon. AT principally adopts two symmetric oligomeric states, a trimer (AT3) featuring three-fold axial symmetry or a dodecamer (AT12) comprising a tetrahedral assembly of trimers, whereas only the trimeric form binds and inhibits TRAP. We apply native mass spectrometry (nMS) and small-angle x-ray scattering (SAXS), together with analytical ultracentrifugation (AUC) to monitor the pH and concentration-dependent equilibrium between the trimeric and dodecameric structural forms of AT. In addition, we use solution nuclear magnetic resonance (NMR) spectroscopy to determine the solution structure of AT3, while heteronuclear 15N relaxation measurements on both oligomeric forms of AT provide insights into the dynamic properties of binding-active AT3 and binding-inactive AT12, with implications for TRAP binding and inhibition.

Symmetry breaking induced asymmetric dislocation-planar fault interactions in ordered intermetallic alloys

In this study, we present the first comprehensive examination of symmetry breaking in the interactions between dislocation and superlattice planar faults, including anti-phase boundary (APB), complex stacking fault (CSF), superlattice intrinsic stacking fault (SISF), to reveal the underlying asymmetric dislocation reaction mechanisms depending on the sense of applied stress, employing both large-scale atomistic simulations and continuum dislocation theory. Four ordered intermetallic alloy systems including γ−Ni/γ′−Ni3Al and γ−Ni/γ′−Ni3Fe, γ−Al/γ−TiAl, and α−Ti/α2−Ti3Al were selected as the representative model systems, with two primary symmetry breaking effects, i.e., translational and three-fold rotational symmetry breaking considered. Detailed atomic steps of asymmetrical dislocation reactions and the corresponding asymmetrical dislocation bypassing mechanisms of precipitation have been elucidated, shown to be highly dependent on the geometrical configuration of the precipitate and the relative magnitudes of APB, CSF and SISF fault energies. A continuum model framework was then developed, which, for the first time, provides accurate and quantitative predictions of the threshold conditions triggering critical asymmetrical dislocation slips, verified to be in good agreement with the simulation results. Our study also successfully reproduced the experimentally observed dislocation-induced APB-SISF transformation, with a new dislocation reaction mechanism proposed to explain the transformation process. The findings are expected to be a key enabling stepstone for future innovation in intermetallic alloys strengthened through ordered phases for advanced applications in aeronautic and automotive industries.

Highly controlled synthesis of symmetrically branched tripod and pentapod nanocrystals with enhanced photocatalytic performance

Anisotropic nanostructures with tunable optical properties induced by controllable size and symmetry have attracted much attention in many applications. Herein, we report a controlled synthesis of symmetrically branched AuCu alloyed nanocrystals. By varying Au:Cu atom ratio in precursor, Y-shaped tripods with three-fold symmetry and star-shaped pentapods with five-fold symmetry are synthesized, respectively. The growth mechanism of AuCu tripods from icosahedral seeds and AuCu pentapods from decahedral seeds is revealed. Aiming to excellent photocatalytic performance, CdS nanocrystals are controlled grown onto the sharp tips of AuCu tripods and pentapods. In addition, a carrier-selective blocking layer of Ag2S is introduced between AuCu and CdS, for achieving effective charge separation in AuCu-Ag2S-CdS nanohybrids. Through evaluating the photocatalytic performance by hydrogen generation experiments, the AuCu-Ag2S-CdS tripod nanocrystals exhibit an optimized hydrogen evolution rate of 2182 μmol·g−1·h−1. These findings will contribute greatly to the understanding of complex nanoparticle growth mechanism and provide a strategy for the design of anisotropic nanoalloys for widely photocatalytic applications.

The Electrochemical Hydrogen Evolution Reaction Based on Helical Chain Stacked 2D Tellurium Nanoflakes

AbstractA crucial factor in advancing the broad utilization of electrocatalytic hydrogen evolution reaction (HER) is the development of efficient catalysts with sufficient active sites. Herein, a hydrothermal approach is utilized to fabricate helical chain stacked two‐dimensional (2D) tellurium (Te) nanoflakes, whose HER performance hasn't been systematically studied yet. It is found that Te nanoflakes transferred on carbon fiber paper (CFP) exhibit impressive HER properties and show a load dependence. The overpotential required for HER is significantly reduced to 279 mV under a load condition of 0.86 mg cm−2 at a current density of 10 mA cm−2. Density functional theory (DFT) calculations are further systematically carried out on Te catalytic sites along the helical chain at [0001] direction with a threefold screw symmetry. It is found that the Gibbs free energy of adsorbed hydrogen atom (ΔGH*) on Te sites is significantly lower than that of molybdenum disulfide (MoS2). Besides, the active sites based on surface atom density calculation reveal that Te provides more adsorption sites than layered MoS2. The decreased adsorption energy and efficient adsorption sites in Te may highlight the promising application of elemental crystal Te in electrocatalytic hydrogen production and pave the way for developing new types of electrocatalysts.

Field‐Free Memristive Spin–Orbit Torque Switching in A1 CoPt Single Layer for Image Edge Detection

AbstractWhile spin–orbit torque (SOT) devices are extensively investigated due to their potential for use in neural network computation, it remains challenging to explore the hardware for neural networks. In this paper, the field‐free memristive SOT switching of the CoPt single layer is used to propose a neuromorphic hardware circuit for detecting edges in images. Owing to its threefold symmetry of inversion, the polarity of SOT switching can be reversed by rotating the current by 60°. Moreover, the process of current‐induced SOT switching exhibits stable multi‐state magnetic switching behavior, and can be controllably tuned by using the pulse of the current. As the slope of the applied ramp pulse current increased, the wave of the anomalous Hall resistance changed from a curve with normally memristive property to trigonometric, and finally to cosine. The design of the hardware circuit for a single SOT device is subsequently formulated to detect the edges in images. The results of experiments verified the capability of this device to detect the edge lines in images with high accuracy, which confirms its potential for use in the hardware of neuromorphic computing platforms. The work here provides guidance for the application of SOT‐based devices to neuromorphic hardware.

Excitonic instability towards a Potts-nematic quantum paramagnet

Magnetic frustration can lead to peculiar magnetic orderings that break a discrete symmetry of the lattice in addition to the fundamental magnetic symmetries (i.e., spin rotation invariance and time-reversal symmetry). In this work, we focus on frustrated quantum magnets and study the nature of the quantum phase transition between a paramagnet and a magnetically ordered state with broken threefold (Z3) crystal rotation symmetry. We show that the transition can occur in two stages, giving rise to an intermediate nematic phase in which rotation symmetry is broken but the system remains magnetically disordered. Since the nematic transition is described by the three-state Potts model, the intermediate phase is a Z3 Potts-nematic phase. Our prediction of the existence of a Potts-nematic phase is based on an analysis of bound states formed from two-magnon excitations in the paramagnet, which become gapless while single-magnon excitations remain gapped. By considering three different lattice models, we demonstrate a generic instability towards two-magnon bound state formation in the Potts-nematic channel. We present both numerical results and a general analytical perturbative formula for the bound state binding energy similar to BCS theory. We further discuss a number of different materials that realize key features of the model considered, and thus provide promising venues for possible experimental observation. Published by the American Physical Society 2024