Center Of Symmetry Research Articles

Chiral Metal Self‐Assemblies of Zirconium‐Tetrahedra and Their Second Harmonic Generation Activity

AbstractThe chirality of metal‐organic cages holds enormous potential for novel applications in diverse fields, while it is relatively rare to employ such asymmetric units for the construction of noncentrosymmetric materials. Herein, by self‐assembling the 4,4′,4′′‐nitrilotribenzoic acid (H3NBA) with bis(cyclopentadienyl)‐zirconium dichloride (Cp2ZrCl2, Cp=η5‐C5H5) in different solvent conditions, we have obtained three hierarchical packing modes of metallo‐tetrahedra with distinct spatial symmetry groups (designated as Zr‐α, Zr‐β, and Zr‐γ). Among them, Zr‐α employs a simple cubic arrangement and is a common centrosymmetric superstructure, which consists of a pair of equimolar metallo‐tetrahedra enantiomers in its unit cell. While Zr‐β results in conglomerates with spontaneous resolution without using any resolving agents, giving rise to two enantiopure entities separately (Zr‐β‐P, Zr‐β‐M). More importantly, Zr‐γ breaks the inversion center of symmetry and crystallizes into a racemic yet non‐centrosymmetric superstructure with face‐centered cubic packing mode. Based on the non‐centrosymmetric nature, the hierarchical superstructure Zr‐γ displayed good second harmonic generation activities. This work presents a successful instance wherein the reaction solvent induces the modulation of intermolecular packing mode to afford non‐centrosymmetric solid materials, which can greatly promote the development of noncentrosymmetric solid (NCS) materials.

Chiral Metal Self-Assemblies of Zirconium-Tetrahedra and Their Second Harmonic Generation Activity.

The chirality of metal-organic cages holds enormous potential for novel applications in diverse fields, while it is relatively rare to employ such asymmetric units for the construction of noncentrosymmetric materials. Herein, by self-assembling the 4,4',4''-nitrilotribenzoic acid (H3NBA) with bis(cyclopentadienyl)-zirconium dichloride (Cp2ZrCl2, Cp=η5-C5H5) in different solvent conditions, we have obtained three hierarchical packing modes of metallo-tetrahedra with distinct spatial symmetry groups (designated as Zr-α, Zr-β, and Zr-γ). Among them, Zr-α employs a simple cubic arrangement and is a common centrosymmetric superstructure, which consists of a pair of equimolar metallo-tetrahedra enantiomers in its unit cell. While Zr-β results in conglomerates with spontaneous resolution without using any resolving agents, giving rise to two enantiopure entities separately (Zr-β-P, Zr-β-M). More importantly, Zr-γ breaks the inversion center of symmetry and crystallizes into a racemic yet non-centrosymmetric superstructure with face-centered cubic packing mode. Based on the non-centrosymmetric nature, the hierarchical superstructure Zr-γ displayed good second harmonic generation activities. This work presents a successful instance wherein the reaction solvent induces the modulation of intermolecular packing mode to afford non-centrosymmetric solid materials, which can greatly promote the development of noncentrosymmetric solid (NCS) materials.

Synthesis and structure of trans-2,5-dimethylpiperazine-1,4-diium dihydrogen diphosphate

In the title salt, C6H16N2 2+ ·H2P2O7 2−, the complete dication is generated by a crystallographic centre of symmetry with the methyl groups in equatorial orientations. The complete dianion is generated by a crystallographic twofold axis with the central O atom lying on the axis: the P—O—P bond angle is 135.50 (12)°. In the crystal, the dihydrogen diphosphate anions are linked by O—H...O hydrogen bonds, generating (001) layers. The organic cations bond to the inorganic layers by way of N—H...O and C—H...O hydrogen bonds. A Hirshfeld surface analysis shows that the most important contributions for the crystal packing are from O...H/H...O (60.5%) and H...H (39.4%) contacts.

Unveiling the recently synthesis noncentrosymmetric layered ASb3X2O12 (A = K, Rb, Cs, Tl; X = Se, Te) via first principles calculations

This study explores the structural, optical, and thermoelectric properties of non-centrosymmetric layered selenite and tellurite compounds KSb3Se2O12, RbSb3Se2O12, CsSb3Se2O12, TlSb3Se2O12, KSb3Te2O12, RbSb3Te2O12, CsSb3Te2O12, TlSb3Te2O12 to assess their potential for sustainable and renewable energy technologies. The selenite and tellurite compounds feature distinct non-centrosymmetric layered crystal structures, which are key to their unique optical and electronic properties. The materials display a layered structure without a center of symmetry, characterized by distinct atomic arrangements, and their band gaps vary depending on the constituent elements. For selenites, band gaps range from 2.97 eV to 3.19 eV, while for tellurites, they range from 2.75 eV to 3.02 eV, indicate their suitability for indirect semiconducting applications. The investigated materials exhibit high absorbance in the ultraviolet region, suggesting they are promising for solar cell applications. The energy loss function peaks at 14 eV, indicating minimal optical loss in the infrared and visible spectra. The static dielectric constants ε1(0) were calculated, showing variations based on the elemental composition. The response of ε2(ω) demonstrates strong interactions in the ultraviolet region, corresponding to electronic transitions from the valence to the conduction bands. Thermoelectric properties, evaluated with the BoltzTrap code using transport theory. The Seebeck coefficient of p-type semiconductors typically increases with temperature, but TlSb3Se2O12 shows an even greater increase, suggesting enhanced thermoelectric properties. Both selenites and tellurites have rising electrical conductivities, with ASb3Se2O12 peaking at 800 K. The Power Factor improves with temperature, reaching a peak for TlSb3Se2O12. These compounds exhibit favorable electrical conductivity and power factor, suggesting potential applications in thermoelectric systems. The figure of merit (ZT) values spanning from 0.90 to 1.51, with a maximum ZT value of 1.41 at 800 K, TlSb3Se2O12 shows great potential for high-temperature thermoelectric applications. These findings advance the understanding of non-centrosymmetric oxide materials and provide valuable insights for developing advanced materials for energy technologies.

Black flowers and real forms of higher spin symmetries

Using Chern-Simons formulation, we investigate higher spin (HS) black holes in AdS3 with soft Heisenberg hair and establish linkage with the real forms of the underlying complexified gauge symmetries taken here as SL(N, ℂ)L × SL(N, ℂ)R. We study the various conserved currents characterizing the HS black flowers (HS-BF) and show that they can be formed of layers indexed by the elements of the centre of the gauge symmetry. This feature follows from requiring the holonomy of the asymptotic gauge connection around the thermal cycle to sit in the centre ℤN of the symmetry group. With regard to the compact subgroups of the real forms of the complexified gauge symmetry, we calculate the entropies of the HS-BF and verify that, unless we are considering trivial holonomies, there are no continuous paths joining the HS-BF to the core spin 2 black holes. As explicit illustrations, we give quantum field realisations of the soft Heisenberg hair in terms of bosonic and fermionic primary conformal fields and compute the HS-BF entropy as a function of the number of fermions occupying the ground state of the Heisenberg soft hair.

The role of coherent nano precipitates on stacking fault and deformation twin formation during tensile deformation of wire arc additive manufactured nickel-aluminum-bronze

The strain hardening mechanisms and dislocation interactions of a wire arc additively manufactured (WAAM) nickel-aluminum-bronze (NAB) alloy was investigated using multi-scale characterization approach cross-correlating scanning electron microscopy (SEM), SEM-based electron back-scatter diffraction (EBSD), site- and crystallographic orientation-specific focused ion beam (FIB) nanofabrication, scanning transmission electron microscopy (STEM) and STEM-based energy dispersive X-ray spectroscopy (EDS). Flat, rectangular dog bone specimens were strained under uniaxial tension conditions. To understand the micro- and nanometer scale deformation mechanisms throughout the microstructure, tensile test specimens were interrupted near the yield strength and ultimate tensile strength. STEM microstructural characterization revealed that tensile deformation occurs by planar slip and multiple slip bands interacting on different {111} planes as well as the nucleation of dislocations from the interfaces associated with grains and secondary phase particles. To the authors knowledge for the first time the Center of symmetry (COS) analysis revealed that in both samples the shearing of nanoscale precipitates led to the formation of extended stacking faults including a combination of intrinsic stacking faults and 2-layer extrinsic stacking faults. At high strain levels more dislocations and stacking faults were nucleated, as well as intersecting slip bands further facilitating the activation of the stair-rod cross-slip mechanism and thickening of an ESF to create a 3-layer nano-twin. Activated mechanisms of plastic deformation and associated role of the precipitates are discussed with respect to the microscopic strength-plasticity characteristics as well as macroscopic mechanical properties of WAAM NAB alloy.

Global solution of spherically symmetric compressible Navier–Stokes equations with bounded density and density‐dependent viscosity

We consider the compressible Navier–Stokes equations with viscosities in bounded domains when the initial data are spherically symmetric, which covers the Saint‐Venant model for the motion of shallow water. First, based on the exploitation of the one‐dimensional feature of symmetric solutions, we prove the global existence of weak solutions with initial vacuum, where the upper bound of the density is obtained. Then, with more conditions imposed on the nonvacuum initial data, we obtain the global weak solution which is a strong one away from the symmetry center. The analysis allows for the possibility that a vacuum state emerges at the symmetry center; in particular, we give the uniform bound of the radius of the vacuum domain.

Crystal structures, electron spin resonance, and thermogravimetric analysis of three mixed-valence copper cyanide polymers.

The crystal structures of three mixed-valence copper cyanide alkanolamine polymers are presented, together with thermogravimetric analysis (TGA) and electron spin resonance (ESR) data. In all three structures, a CuII moiety on a crystallographic center of symmetry is coordinated by two alkanolamines and links two CuICN chains via cyanide bridging groups to form diperiodic sheets. The sheets are linked together by cuprophilic CuI-CuI interactions to form a three-dimensional network. In poly[bis(μ-3-aminopropanolato)tetra-μ-cyanido-dicopper(I)dicopper(II)], [Cu4(CN)4(C3H8NO)2]n, 1, propanolamine bases have lost their hydroxyl H atoms and coordinate as chelates to two CuII atoms to form a dimeric CuII moiety bridged by the O atoms of the bases with CuII atoms in square-planar coordination. The ESR spectrum is very broad, indicating exchange between the two CuII centers. In poly[bis(2-aminopropanol)tetra-μ-cyanido-dicopper(I)copper(II)], [Cu3(CN)4(C3H9NO)2]n, 2, and poly[bis(2-aminoethanol)tetra-μ-cyanido-dicopper(I)copper(II)], [Cu3(CN)4(CH7NO)2]n, 3, a single CuII atom links the CuICN chains together via CN bridges. The chelating alkanolamines are not ionized, and the OH groups form rather long bonds in the axial positions of the octahedrally coordinated CuII atoms. The coordination geometries of CuII in 2 and 3 are almost identical, except that the Cu-O distances are longer in 2 than in 3, which may explain their somewhat different ESR spectra. Thermal decomposition in 2 and 3, but not in 1, begins with the loss of HCN(g), and this can be correlated with the presence of OH protons on the ligands in 2 and 3, which are not present in 1.

From Cd(SCN)2(CH4N2S)2 to Cd(SCN)2(C4H6N2)2: Controlling Sulfur Content in Thiocyanate Systems Significantly Improves the Overall Performance of UV Nonlinear Optical Materials.

Combining a strong second-order nonlinear optical (NLO) effect (>1×KH2PO4 (KDP)), a large band gap (>4.2 eV), and a moderate birefringence in ultraviolet (UV) NLO crystals remains a formidable challenge. Herein, Cd(SCN)2(C4H6N2)2, the first example of a thiocyanate capable of realizing a phase-matched UV NLO crystal material, is obtained by reducing the sulfur (S) content in the centrosymmetric (CS) structure of Cd(SCN)2(CH4N2S)2. Compared to the "shoulder-to-shoulder" one-dimensional (1D) chain of Cd(SCN)2(CH4N2S)2, Cd(SCN)2(C4H6N2)2 has a different sawtooth 1D chain structure. Cd(SCN)2(CH4N2S)2 has second harmonic generation (SHG) inertia with a band gap of 3.90 eV and a UV cutoff edge of 342 nm, however, it possesses a large birefringence (0.35@546 nm). In contrast, the symmetry center breaking of Cd(SCN)2(C4H6N2)2 leads to remarkably strong SHG intensity (10 times that of KDP). Furthermore, it has a wide band gap (4.74 eV), short UV cutoff edge (234 nm), and moderate birefringence capable of phase matching (0.17@546 nm). This research indicates that thiocyanates are a promising class of UV NLO crystal materials, and that modulation of the sulfur content of CS thiocyanates is an effective strategy for the development of UV NLO crystals with excellent overall performances.

Self-similar solutions to a multidimensional singular heat equation with power nonlinearity

The paper deals with the construction of exact solutions to a singular heat equation with power nonlinearity in the case of numerous independent variables with spatial (e.g. axial or central) symmetry. A new class of self-similar solutions is proposed, which reduce to solving the Cauchy problem for a second-order nonlinear ordinary differential equation having singularities at the higher derivative with respect to the required function and/or the independent variable. The ordinary differential equation is studied in two ways: analytically and numerically. The analytical study uses a truncated Taylor series with recurrently computed coefficients, for which explicit formulas are obtained. The numerical solution to the problem uses an iteration algorithm based on the collocation method and radial basis functions. The numerical analysis shows the convergence of the proposed numerical algorithm and its sufficient accuracy enabling one to use the found self-similar solutions to verify approximate solutions to the original heat equation. Besides, the numerical analysis has allowed the radius of convergence of the constructed Taylor series to be evaluated. The form of the constructed self-similar solutions, namely their unboundedness near the symmetry center (axis), enables us to study the behavior and exactness of the numerical solutions to the nonlinear singular parabolic-type equation that have been obtained by the stepwise solution method proposed by us earlier and possess the same property.

Novel Trinuclear Copper(II) Complex: Crystal Structure at 100 K and Magnetic Properties of (R, S)-di[(6,7-dimethoxy-isoquinolin-1-yl)-(3,4-dimethoxy-phenyl)-methanolato]-tetra(2-hydroxybenzoato)-diaqua-tricopper dihydrate, [Cu3(C7H5O3)4(C20H20NO5)2(H2O)2]·2(H2O)

The crystal structure of [Cu3(C7H5O3)4(C20H20NO5)2(H2O)2]·2(H2O) (1) and analysis of temperature and field dependence of magnetic susceptibility is reported in this work. The structure of 1 is composed of trinuclear complex units and water molecules. The middle copper atom occupies the center of symmetry. N, O-bonded (6,7-dimethoxy-isoquinolin-1-yl)-(3,4-di­methoxy-phenyl)-methanolato ligands, 2-hydroxybenzoates with bridging carboxylic groups, and oxo-bridged water molecules connect the middle Cu(II) atom with the terminal copper atoms. Two 2-hydroxybenzoates coordinate the terminal copper atoms via one carboxylic oxygen and an O atom of the hydroxyl group. The analysis of copper coordination by bond-valence sum approach and relevant structural correlation is consistent with hexacoordinated Cu(II) centers. Cu···Cu separation is 3.0269(3) Å. The magnetism of 1 shows a strong ferromagnetic interaction between the neighboring metallic centers accompanied by very weak antiferromagnetic intermolecular interactions. The complex units are mutually held by π···π stack interactions of 2-hydroxybenzoates and hydrogen bonds.Graphical A new N,O bonded ligands, (R, S)-[(6,7-dimethoxy-isoquinolin-1-yl)-(3,4-dimethoxy-phenyl)-methanolate] coordinate the terminal atoms of the trinuclear copper(II) complex.

Variable Photoluminescence Intensity Ratio with the Excitation Wavelength in Eu3+-Doped Perovskite-Type Alkaline Earth Zirconates─Possibility of a Unique Visualization of Ultraviolet Light.

Photoluminescence (PL) spectra arising from 4f-4f dipole transitions of Eu3+ doped at both the A and B sites of perovskite-type alkaline earth zirconates obtained at various excitation wavelengths were evaluated. Changes in the excitation wavelength caused obvious differences in the PL intensity ratio of the induced electric dipole (ED) 5D0 → 7F2 transition to the magnetic dipole (MD) 5D0 → 7F1 transition for Eu3+-doped SrZrO3 and CaZrO3, in which only the B site had a center of symmetry. Two charge transfer (CT) bands associated with the excitation of Eu3+ were observed in the spectra of these oxide samples, which arose from the difference in the electronic structure of the Eu-O coordination at the A and B sites. We conclude that simultaneous Eu3+ substitution at sites with and without a center of symmetry, which have different charge transfer energies, induced the observed novel PL changes with a changing excitation wavelength. Our results may enable the development of a new type of ultraviolet light detector.

Spherically symmetric evolution of self-gravitating massive fields

We are interested in the global dynamics of a massive scalar field evolving under its own gravitational field and, in this paper, we study spherically symmetric solutions to Einstein's field equations coupled with a Klein-Gordon equation with quadratic potential. For the initial value problem we establish a global existence theory when initial data are prescribed on a future light cone with vertex at the center of symmetry. A suitably generalized solution in Bondi coordinates is sought which has low regularity and possibly large but finite Bondi mass. A similar result was established first by Christodoulou for massless fields. In order to deal with massive fields, we must overcome several challenges and significantly modify Christodoulou's original method. First of all, we formulate the Einstein-Klein-Gordon system in spherical symmetry as a non-local and nonlinear hyperbolic equation and, by carefully investigating the global dynamical behavior of the massive field, we establish various estimates concerning the Einstein operator, the Hawking mass, and the Bondi mass, including novel positivity and monotonicity properties. Importantly, in addition to a regularization at the center of symmetry we find it necessary to also introduce a regularization at null infinity. We also establish new energy and decay estimates for, both, regularized and generalized solutions.

An X-Ray Synchrotron Shell and a Pulsar: The Peculiar Supernova Remnant G32.4+0.1

We present a deep Chandra observation of the shell supernova remnant (SNR) G32.4+0.1, whose featureless X-ray spectrum has led to its classification as an X-ray synchrotron-dominated SNR. We find a partial shell morphology whose outline is quite circular, with a radius of about 11 pc at an assumed distance of 11 kpc. Thermal and power-law spectral models for three relatively bright regions provided equally good fits, but the absence of spectral lines required ionization timescales from thermal fits that are inconsistent with the mean densities derived from emission measures. We thus confirm the nonthermal, i.e., synchrotron, origin of X-rays from G32.4+0.1. Shock velocities needed to accelerate electrons to the required TeV energies are ≳1000 km s−1, giving a remnant age ≲ 5000–9000 yr. There is no obvious X-ray counterpart to the radio pulsar PSR J1850−0026, but its position adjoins a region of X-ray emission whose spectrum is somewhat harder than that of other regions of the shell, and which may be a pulsar-wind nebula (PWN), though its spectrum is steeper than almost all known X-ray PWNe. The distance of the pulsar from the center of symmetry of the shell disfavors a birth in a supernova event at that location only a few thousand years before; either the pulsar (and putative PWN) are not associated with the shell SNR, requiring a coincidence of both position and (roughly) absorbing column density, or the SNR is much older, making the origin of nonthermal emission problematic.

Enhanced chiroptical activity for narrow deep-blue emission in axial chiral frameworks via three-dimensional interlocking.

The advancement of desirable circularly polarized luminescence (CPL) emitters is predominantly constrained by the effective regulation of magnetic and electric transition vectors, particularly within the deep-blue spectral domain. Herein, we present four pairs of novel chiral emitters with systematically varied molecular rigidity, symmetry, and chiral centers to elucidate the intrinsic coupling of key molecular parameters influencing their chiroptical properties. Notably, the incorporation of appropriate intramolecular 3D-interlocking within a natural binaphthyl chirality skeleton offers an effective approach to achieving both significantly narrowed full width at half maximum (FWHM, as low as 18 nm) and substantially enhanced chiroptical activity (luminous dissymmetry factor, g PL, up to 3.0 × 10-3). Additionally, introducing a secondary chiral center closely parallel to the primary chiral plane facilitates strong chiral-chiral interactions, further affording a 50% improvement in their g PL values. As a demonstration, vacuum-deposited circularly polarized organic light-emitting diodes incorporating these pure fluorescent emitters exhibit outstanding electroluminescent performance, with maximum external quantum efficiency exceeding 5.35%, favorable FWHM of approximately 25 nm, and extreme CIE y values below 0.03.

Magnetic structure and properties of the honeycomb antiferromagnet [Na(OH2)3]Mn(NCS)3.

We report the magnetic structure and properties of a thiocyanate-based honeycomb magnet [Na(OH2)3]Mn(NCS)3 which crystallises in the unusual low-symmetry trigonal space group P3̄. Magnetic measurements on powder samples show this material is an antiferromagnet (ordering temperature TN,mag = 18.1(6) K) and can be described by nearest neighbour antiferromagnetic interactions J = -11.07(4) K. A method for growing neutron-diffraction sized single crystals (>10 mm3) is demonstrated. Low temperature neutron single crystal diffraction shows that the compound adopts the collinear antiferromagnetic structure with TN,neut = 18.94(7) K, magnetic space group P3̄'. Low temperature second-harmonic generation (SHG) measurements provide no evidence of breaking of the centre of symmetry.

Conformal Mapping of a Z-Shaped Domain

For the problem of conformal mapping of a half-plane onto a Z-shaped domain with arbitrary geometry, an efficient method is developed for finding parameters of the Schwarz–Christoffel integral, i.e., the preimages of the vertices (prevertices) and the pre-integral multiplier. Special attention is given to the situation of crowding prevertices, in which case conventional integration methods face significant difficulties. For this purpose, the concept of a cluster is introduced, its center is determined, and all integrand binomials with prevertices from this cluster are expanded into a fast-convergent series by applying a unified scheme. Next, the arising integrals are reduced to single or double series in terms of Gauss hypergeometric functions F(a, b, c, q). The fast convergence of the resulting expansions is ensured by applying formulas for analytic continuation of F(a, b, c, q) to a neighborhood of the point q = 1 and using numerically stable recurrence relations. The constructed expansions are also fairly efficient for choosing initial approximations for prevertices in Newton’s iteration method. By using the leading terms of these expansions, the approximations for the prevertices are expressed in explicit form in terms of elementary functions, and the subsequent iterations ensure the fast convergence of the algorithm. After finding the parameters in the integral, the desired mapping is constructed as a combination of power series expansions at prevertices, regular expansions at the preimage of the center of symmetry, a Laurent series in a semi-annulus, and special series near the preimages of the vertical segments. Numerical results demonstrate the high efficiency of the developed method, especially in the case of strong crowding of prevertices.

Stability Analysis of Trench Wall for Diaphragm Wall in Ultra-Deep Circular Foundation Pit: A Comprehensive Investigation

Circular diaphragm walls are increasingly being used in ultra-deep foundation pits due to their arch-shaped bearing system, which provides reasonable structural support. The trench walls that form the circular ground connection wall are typically double-angled in shape, and their stability analysis remains a challenge. In this paper, an instability model for double-angled trench walls based on 3D sliding body analysis is proposed. The objective of this paper is to determine the minimum amount of slurry needed to maintain the integrity of the trench wall. The results show that the center of symmetry on the inside of the wall is the most vulnerable to damage, followed by the inside corner, and then the center and corner on the outside. The consideration of sliding bodies in overall and local stability calculations for double-angled trench wall shapes can provide a reasonable stability assessment.

Spectral optimization for weighted anisotropic problems with Robin conditions

We study a weighted eigenvalue problem with anisotropic diffusion in bounded Lipschitz domains Ω⊂RN, N≥1, under Robin boundary conditions, proving the existence of two positive principal eigenvalues λ± respectively associated with a positive and a negative eigenfunction. Next, we analyze the minimization of λ± with respect to the sign-changing weight, showing that the optimal eigenvalues Λ± are equal if the domain has a center of symmetry and the optimal weights are of bang-bang type, namely piece-wise constant functions, each one taking only two values. As a consequence, the problem is equivalent to the minimization with respect to the subsets of Ω satisfying a volume constraint. Then, we completely solve the optimization problem in one dimension, in the case of homogeneous Dirichlet or Neumann conditions, showing new phenomena induced by the presence of the anisotropic diffusion. The optimization problem for λ+ naturally arises in the study of the optimal spatial arrangement of resources for a species to survive in an heterogeneous habitat.

Self-Similar Flows with a Shock Wave Advancing toward the Center or Axis of Symmetry

We study one-dimensional flows of an ideal (inviscid and non-heat-conducting) perfect gas with an adiabatic exponent γ behind a shock wave moving toward the center (ν = 3) or axis (ν = 2) of symmetry in a cold gas at rest. Flows with a reflected shock wave and flows terminating with simultaneous arrival of a shock wave and a piston, which has compressed the gas into a point or line, to the center of symmetry are admitted.