Planar Squares Research Articles

Charge order of bismuth ions and nature of chemical bonds in double perovskite-type oxide BaBiO3 visualized by synchrotron radiation X-ray diffraction

Synchrotron radiation X-ray powder diffraction has visualized the charge order of Bi3+ and Bi5+ ions and the nature of chemical bonds in BaBiO3 in electron charge density distribution maps. The Bi3+–O bond is considerably more ionic than the Bi5+–O bond in all four phases. BaBiO3 can be regarded as an ionic crystal in the prototype structure comprising isolated Ba2+ and Bi3+ ions as well as [Bi5+O6]7− octahedra in the Fmm symmetry; a three-dimensional covalent bonding network is formed in the R and I2/m symmetries, and a two-dimensional layered structure comprising Bi3+O4 planar squares and Bi5+O6 octahedra is established in the P21/n symmetry at low temperatures. Our study provides a comprehensive understanding of the structural characteristics, electron charge density distribution, and chemical bonds of BaBiO3, which may be useful for developing BaBiO3-based functional materials such as superconductors.

Sulfur-free synthesis of size tunable rickardite (Cu3-x Te2) spheroids and planar squares.

We report a novel synthesis of monodisperse samples of copper telluride with crystallinity and stoichiometry corresponding to forms of rickardite, Cu3−xTe2 (x < 1). This synthesis makes use of a ligand balanced reaction to allow control over shape and size by varying the relative and absolute concentration of oleylamine to stearic acid. The rickardite samples presented here display size dependent plasmon peaks in the near infrared and direct energy band gaps between 1.7 and 2.3 eV. As such they may find utility in photovoltaic, thermoelectric or as novel optical materials for study of surface plasmons.

Assembly of a New 2D Heterometallic 3d–4f Coordination Polymer Bearing Planar Tetranuclear Square Building Blocks

A new two-dimensional (2D) 3d–4f heterometallic coordination polymer, which is {[Tb2Zn4(µ3-TFMIDC)4(µ4-HTFMIDC)(H2O)8]·2H2O}n, has been successfully synthesized by the solvothermal reaction of 2-(trifluoromethyl)-1H-4,5-imidazole dicarboxylic acid (H3TFMIDC) with Zn(II) and Tb(III) ions. The title compound was structurally characterized by diverse characterization techniques including single-crystal X-ray diffraction, Fourier transform infrared spectroscopy, and thermogravimetric analysis. Single-crystal structure analysis reveals that the as-preprared compound is a 2D heterometallic 3d–4f coordination network based on interesting planar tetranuclear squares [Zn4(TFMIDC)4] as building blocks, representing the first example of novel heterometallic coordination polymer based on the H3TFMIDC ligand. In addition, the title compound exhibits very intense green luminescence and characteristic transitions of the Tb(III) ion when excited at 291 nm. Lattice parameters for the title compound: a = 11.1449(12) A, b = 12.8498(13) A, c = 37.553(4) A, α = β = γ = 90°, V = 5378.0(10) A3, Z = 4. A unique 2D 3d–4f heterometallic coordination polymer containing interesting planar tetranuclear square building blocks has been constructed by the solvothermal reaction of 2-(trifluoromethyl)-1H-4,5-imidazole dicarboxylic acid (H3TFMIDC) with Zn(II) and Tb(III) ions.

Kinetics of deposition in the diffusion-controlled limit.

The adsorption of particles diffusing in a half space bounded by the substrate and irreversibly sticking to the substrate upon contacts is investigated. We show that when absorbing particles are planar disks diffusing in the three-dimensional half space, the coverage approaches its saturated "jamming" value as t^{-1} in the large time limit (generally as t^{-1/(d-1)} when the substrate is d dimensional and d>1, and as e^{-t/ln(t)} when d=1). We also analyze the asymptotic behavior when particles are spherical and when particles are planar aligned squares.

Synthesis, structure and magnetic behaviors of a new spin-1/2 chain compound Na4CuTeO6

A new tellurate compound Na4CuTeO6 was synthesized by a conventional high-temperature solid state reaction. The titled compound crystallizes in the monoclinic system of a space group C2/c and exhibits a unique spin-chain structure built by planar CuO4 squares and TeO6 octahedra along the [101] direction. Magnetic measurements confirm that Na4CuTeO6 possesses an antiferromagnetic ordering at TN = ∼2.5 K. The intrachain and interchain interactions are estimated by a spin-chain model, showing a less pronounced 1D character in the system.

Phase Equilibria in the System CuO‐NiO‐P4O10 and Synthesis, Crystal Structure, and Characterization of the New Copper Nickel Oxide Phosphate Cu3NiO(PO4)2

The system CuO‐NiO‐P4O10 was investigated using a solid state reaction between CuO, NiO, and (NH4)2HPO4 in quartz crucibles at 900 °C. The powder samples were characterized by X‐ray diffraction, TG/DTA, electrochemical measurements, IR, and UV/Vis spectroscopy. Single crystals of a new quaternary phase Cu3NiO(PO4)2 were achieved by cooling the melted compound in a sealed, evacuated quartz ampoule. Cu3NiO(PO4)2 crystallizes in the monoclinic space group P21/n (no 14) with a = 8.2288(2) Å, b = 9.8773(2) Å, c = 8.2777(3) Å, β = 107.82(2)°, Z = 4. The three‐dimensional framework consists of distorted tetragonal pyramides [Cu1O5], distorted planar squares [Cu2O4], octahedra [Cu3O6], and [NiO6] and [PO4] tetrahedra. The TG‐DTA of the new phase showed an incongruent melting at 1055 °C. The open circuit voltage of this material was measured to determine the electrochemical properties. The measurement revealed an initial capacity of 236 Ah·g–1 and a voltage plateau at 2.05 V. Furthermore, it was possible to identify the phase equilibria and to obtain the phase diagram at 900 °C.

Two new three-dimensional metal–organic frameworks with 4-connected diamondoid and unusual (6,16)-connected net topologies based on planar tetranuclear squares as secondary building units

Solvothermal reactions of Co2+ and Mn2+ salts with 2-(trifluoromethyl)-1H-4,5-imidazole dicarboxylic acid (H3TFMIDC) lead to two novel three-dimensional (3D) metal–organic frameworks (MOFs), namely, [Co6(μ3-TFMIDC)4(H2O)12]·15H2O (1) and [(Me2NH2)3][MnII6 MnIII(μ3-TFMIDC)6(H2O)6]·18H2O (2). Single-crystal X-ray diffraction analysis reveals that both of them are based on interesting planar tetranuclear squares [M4(TFMIDC)4] as secondary building units (SBUs). Compound 1 exhibits a unique 3D two-fold interpenetrated network with the diamondoid topology consisting of the tetranuclear square SBUs as 4-connected nodes, while compound 2 features an unusual (6,16)-connected 3D framework based on the novel tetranuclear square SBUs as 16-connected nodes and trivalent manganese ions as 6-connected nodes, representing the first 16-connected MOF utilizing planar tetranuclear square SBUs as building blocks. Our results open up new perspectives to design novel 3D extended MOFs, especially the unique highly connected 3D MOFs by employing planar tetranuclear square SBUs. Moreover, IR spectroscopy, powder X-ray diffraction, thermogravimetric analyses, and a study on the magnetic properties of both compounds, have been also performed.

Syntheses, Structure, and Magnetic Properties of New 3d–4f Heterometallic Hydroxysulfates Ln2Cu(SO4)2(OH)4 (Ln = Sm, Eu, Tb, or Dy) with a Two-Dimensional Triangle Network

A series of 3d–4f hydroxysulfates Ln2Cu(SO4)2(OH)4 (Ln = Sm, Eu, Tb, or Dy) have been successfully obtained by the conventional hydrothermal method. These compounds crystallize in the monoclinic system in space group P21/c, showing a layered structure. The layers are built by the LnO9 polyhedra and CuO4 planar squares, which are separated by SO42– tetrahedra. The topological structure of Sm3+ ions shows a distorted honeycomb lattice, while Cu2+ ions are located at the center of a honeycomb framework forming a triangle lattice. Magnetic measurements reveal that the isostructural Ln2Cu(SO4)2(OH)4 exhibits different magnetic behaviors at low temperatures, which may be attributed to the different contribution of 3d–4f couplings.

Synthesis, structures and surface photovoltage properties of four novel metal phosphonates with a 3D supramolecular structure

By introduction of oxalate as a second organic ligand, four novel metal phosphonates with a 3D supramolecular structure, namely, M1.5(H2O)[(H2L)(C2O4)0.5] (M = Fe (1), Co (2), Zn (3)) and Cu1.5[(H2L)(C2O4)0.5] (4) (H4L = C5H4NCH2CH(OH)(PO3H2)2), have been synthesized under hydrothermal conditions. Compounds 1–3 are isostructural and adopt a three-dimensional supramolecular structure. Every two {M(1)O5} polyhedra are interconnected by {CPO3} tetrahedra to form a unit and these units are linked by {M(2)O6} octahedra to form a 1D chain by corner-sharing down the c-axis. Such 1D infinite chains are cross-linked via oxalate anions into a 2D layer, which are further connected through hydrogen bonding interactions to give rise to a 3D supramolecular structure. The overall structure of compound 4 is similar to that of compounds 1–3 except that the {M(2)O6} octahedra are replaced by {Cu(2)O4} planar squares. Surface photovoltage properties of the four compounds have also been studied.

High-pressure phase transitions of solid HF, HCl, and HBr: Anab initioevolutionary study

Using ab initio evolutionary methodology for structure predictions, we investigated the high-pressure phase diagram for solid-state HF, HCl, and HBr at zero temperature. The ambient-pressure chain-type $Cmc{2}_{1}$ structure and sequent high-pressure symmetric hydrogen-bonded $Cmcm$ structure were successfully reproduced by structural simulations with the only known information of chemical compositions. We have also presented insight into the underlying mechanism of hydrogen-bond symmetrization at the $Cmc{2}_{1}\ensuremath{\rightarrow}Cmcm$ transformation, by analysis of electron localization functions, potential wells, and zone-center phonons with pressure. At higher pressures, it was predicted that HF transforms from the $Cmcm$ phase to another chain-type $Pnma$ structure at $\ensuremath{\sim}143\text{ }\text{GPa}$ while the post-$Cmcm$ phase of HCl and HBr adopts an intriguing triclinic $P\overline{1}$ structure at above 108 GPa and 59 GPa, respectively, which consists of nearly planar squares resembling the ambient phase of HI. The newly predicted high-pressure phases of these halides all contain symmetric hydrogen bonds and satisfy lattice dynamical stability. As for the earlier proposed dissociation of HBr, we found that this can only occur at rather high pressures (above 120 GPa) with the formation of monatomic Br and solid ${\text{H}}_{2}$.

Synthesis and characterizations of a novel 2-D organic–inorganic hybrid constructed from mixed ligands and mixed-valence copper(I/II)

Abstract A new 2-D inorganic–organic hybrid constructed from mixed-valence Cu(I/II) ions and mixed ligands, [ Cu 4 I Cu II ( sip ) 2 ( bipy ) 4 ( H 2 O ) 2 ] n (H3sip = 5-sulfoisophthalic acid, bipy = 4,4′-bipyridine), has been synthesized and characterized by IR, TGA, XPS, EPR and single-crystal X-ray diffraction. Two different kinds of chains in the compound constructed from [CuO4] planar squares and [CuN2O] triangulars, respectively, further interconnect together to give rise to an interesting 2-D layer framework. The compound exhibits strong yellow emission at 445 nm excited by 378 nm in the solid state at room temperature.

A discrete square global grid system based on the parallels plane projection

We developed a direct partitioning method to construct a seamless discrete global grid system (DGGS) with any resolution based on a two‐dimensional projected plane and the earth ellipsoid. This DGGS is composed of congruent square grids over the projected plane and irregular ellipsoidal quadrilaterals on the ellipsoidal surface. A new equal area projection named the parallels plane (PP) projection derived from the expansion of the central meridian and parallels has been employed to perform the transformation between the planar squares and the corresponding ellipsoidal grids. The horizontal sides of the grids are parts of the parallel circles and the vertical sides are complex ellipsoidal curves, which can be obtained by the inverse expression of the PP projection. The partition strategies, transformation equations, geometric characteristics and distortions for this DGGS have been discussed. Our analysis proves that the DGGS is area‐preserving while length distortions only occur on the vertical sides off the central meridian. Angular and length distortions positively correlate to the increase in latitudes and the spanning of longitudes away from a chosen central meridian. This direct partition only generates a small number of broken grids that can be treated individually.

Stabilization of 2D NSHP Recursive Digital Filters with Guaranteed Stability Using PLSI Polynomials

Two-dimensional digital filters have gained wide acceptance in recent years. For recursive filters, nonsymmetric half-plane versions (also known as semicausal) are more general than quarter-plane versions (also known as causal) in approximating arbitrary magnitude characteristics. The major problem in designing two-dimensional recursive filters is to guarantee their stability with the expected magnitude response. In general, it is very difficult to take stability constraints into account during the stage of approximation. This is the reason why it is useful to develop techniques, by which stability problem can be separated from the approximation problem. In this way, at the end of approximation process, if the filter becomes unstable, there is a need for stabilization procedures that produce a stable filter with similar magnitude response as that of the unstable filter. This paper, demonstrates a stabilization procedure for a two-dimensional nonsymmetric half-plane recursive filters based on planar least squares inverse (PLSI) polynomials. The paper's findings prove that, a new way of form-preserving transformation can be used to obtain stable PLSI polynomials. Therefore obtaining PLSI polynomial is computationally less involved with the proposed form-preserving transformation as compared to existing methods, and the stability of the resulting filters is guaranteed.

Stabilization of 2D nonsymmetric half-plane digital filters using the concept of reciprocity

In this paper, the concept of reciprocity for two-dimensional (2D) quarter plane (QP) filters are extended to stabilize 2D nonsymmetric half-plane (NSHP) filters. In general the stabilization of NSHP filters is done by transforming NSHP arrays into QP arrays using mapping theorems. The concept of reciprocity is applied directly without any mapping to stabilize a class of 2D NSHP filters which are otherwise unstable when all singularities lie within the unit bicircle. It is shown that the magnitude spectrum of the stabilized 2D NSHP filter is identical to the magnitude spectrum of the original unstable filter. The proposed stabilization method is simple as compared to two other popular stabilization techniques in the literature, the double planar least squares inverse (DPLSI) and 2D discrete Hilbert transform (2D DHT).

An Overview of Modified Shanks’ Conjecture and Comments on its Validity

This study reports the validity of the modified Shanks’ conjecture on the planar least squares inverse (PLSI) method of stabilizing two-dimensional (2-D) recursive digital filters. A theoretical procedure proposed based on the Lagrange multiplier method of mathematical optimization. The results indicate that the modified Shanks’ conjecture reported by Jury was valid for special classes of 2-D polynomials.

Reinvestigation of CuSe2O5

The crystal structure of the title compound, copper(II) diselenium(IV) pentoxide [Meunier, Svensson & Carpy, (1976). Acta Cryst. B32, 2664–2667], has been reinvestigated and confirmed to much higher precision, and anisotropic displacement parameters has been refined. The structure consists of CuO4 planar squares and Se2O5E2 (E = lone pair) dimers. The Cu atom has site symmetry \overline{1} and one O atom has site symmetry 2.

Magnetic susceptibility, specific heat and magnetic structure of CuNi 2(PO 4) 2

The CuNi 2(PO 4) 2 phosphate has been synthesized by the ceramic method at 800 °C in air. The crystal structure consists of a three-dimensional skeleton constructed from MO 4 (M II Cu and Ni) planar squares and M 2O 8 dimers with square pyramidal geometry, which are interconnected by (PO 4) 3− oxoanions with tetrahedral geometry. The magnetic behavior has been studied on powdered sample by using susceptibility, specific heat and neutron diffraction data. The bimetallic copper(II)–nickel(II) orthophosphate exhibits a three-dimensional magnetic ordering at, approximately, 29.8 K. However, its complex crystal structure hampers any parametrization of the J-exchange parameter. The specific heat measurements exhibit a three-dimensional magnetic ordering ( λ-type) peak at 29.5 K. The magnetic structure of this phosphate shows ferromagnetic interactions inside the Ni 2O 8 dimers, whereas the sublattice of Cu(II) ions presents antiferromagnetic couplings along the y-axis. The change of the sign in the magnetic unit-cell, due to the [1/2, 0, 1/2] propagation vector determines a purely antiferromagnetic structure.

Transformation from a Low-Dimensional Framework to a High-Dimensional Architecture Based on Different Metal Ions: Syntheses, Structures, and Photoluminescences

Five novel metal pamidronates (3-ammonium-1-hydroxypropylidene-1,1-bisphosphonate, APD) formulated as Ni2(C3NH10P2O7)4.4H2O (1), M(C3NH9P2O7).H2O (M = Co (2), Mn (3), Zn (4)) and Cu3(C3NH8P2O7)2.2H2O (5) have been hydrothermally synthesized under similar conditions. Compound 1 is a molecular binuclear nickel cluster. Compounds 2 and 3 exhibit similar one-dimensional ladderlike structures. Compound 4 possesses a novel two-dimensional gridlike framework. Compound 5 shows an unusual three-dimensional architecture, in which two-dimensional layers with a parquet motif are pillared by {CuO4} planar squares. Different dinuclear secondary building units (SBUs) are observed in compounds 1-5, depending on the different coordination modes of APD. They also exhibit different photoluminescence properties.

Investigation of the cation distribution in perovskite-like oxides with Mössbauer spectroscopy

Complex perovskite-like oxides, such as LnFe2/3Mo1/3O3 orthoferrites, Ln 8−y SryCu8−x FexO20 (8-8-20), Pr4BaCu4FeO13-δ(4-1-5), YBa2-y La y Cu3-x Fe x O7-δ and Y1-y Ca y Ba y La y Cu3-x Fe x O7-δ (1-2-3), are studied by means of Mossbauer spectroscopy. At room temperature, the spectra of the orthoferrites contain only magnetic components. The spectra of the 1-2-3 compounds contain only magnetically disordered components: iron atoms substitute for copper at Cu(1) sites, taking various configurations: planar squares, quadratic pyramids, and octahedra. Cuprates 8-8-20 and 4-1-5 have a wide diversity of spectra. In the 8-8-20 oxides, a phase related to the pyramidal environment of the iron cations is present at any iron concentration. In all the perovskites, iron cations become magnetically ordered only at octahedral sites of the structure.

The PLSI Method of Stabilizing Two-Dimensional Nonsymmetric Half-Plane Recursive Digital Filters

Two-dimensional (2D) recursive digital filters find applications in image processing as in medical X-ray processing. Nonsymmetric half-plane (NSHP) filters have definitely positive magnitude characteristics as opposed to quarter-plane (QP) filters. In this paper, we provide methods for stabilizing the given 2D NSHP polynomial by the planar least squares inverse (PLSI) method. We have proved in this paper that if the given 2D unstable NSHP polynomial and its PLSI are of the same degree, the PLSI polynomial is always stable, irrespective of whether the coefficients of the given polynomial have relationship among its coefficients or not. Examples are given for 2D first-order and second-order cases to prove our results. The generalization is done for theth order polynomial.