Spectral functions of half-filled one-dimensional Hubbard rings with varying boundary conditions

We study the effect of varying the boundary condition on: the spectral function of a finite one-dimensional Hubbard chain, which we compute using direct (Lanczos) diagonalization of the Hamiltonian. By direct comparison with the two-body response functions and with the exact solution of the Bethe ansatz equations, we can identify both spinon and holon features in the spectra. At half-filling the spectra have the well-known structure of a low-energy holon band and its shadow-which spans the whole Brillouin zone-and a spinon band present for momenta less than the Fermi momentum. Features related to the twisted boundary condition are cusps in the spinon band. We show that the spectral building principle, adapted to account for both the finite system size and the twisted boundary condition, describes the spectra well in terms of single spinon and holon excitations. We argue that these finite-size effects are a signature of spin-charge separation and that their study should help establish the existence and nature of spin-charge separation in finite-size systems.

One-dimensional zinc phosphates with linear chain structure

Three one-dimensional zinc phosphates, [C5N2H14][Zn(HPO4)2], I, [C10N4H26][Zn(HPO4)2].2H2O II, and [C4N2H6]2[Zn(HPO4)], III, have been prepared employing hydro/solvothermal methods in the presence of organic amines. While I and II consist of linear chains of corner-shared four-membered rings, III is a polymeric wire where the amine molecule is directly bonded to the metal center. The wire, as well as the chain in these structures, are held together by hydrogen bond interactions involving the amine and the framework oxygens. The polymeric zinc phosphate with wire-like architecture, III, is only the second example of such architecture. Crystal data: I, monoclinic, P21/c (no. 14), a=8.603(2), b=13.529(2), c=10.880(1) Å, β=94.9(1)°, V=1261.6(1) Å3, Z=4, ρcalc.=1.893 gcm−3, μ(MoKα)=2.234 mm−1, R1=0.032, wR2=0.086, [1532 observed reflections with I>2σ(I)], II, orthorhombic, Pbca (no. 61), a=8.393(1), b=15.286(1), c=22.659(1) Å, V=2906.9(2) Å3, Z=8, ρcalc.=1.794 gcm−3, μ(MoKα)=1.957 mm−1, R1=0.055, wR2=0.11, [1565 observed reflections with I>2σ(I) and III, monoclinic, P21/c (no. 14), a=8.241(1), b=13.750(2), c=10.572(1) Å, β=90.9(1)°, V=1197.7(2) Å3, Z=4, ρcalc.=1.805 gcm−3, μ(MoKα)=2.197 mm−1, R1=0.036, wR2=0.10, [1423 observed reflections with I>2σ(I)].

Catena-Poly[bis(ethane-1,2-diammonium) [manganese(II)-di-mu-phosphato-kappa O-4 : O ']]: a one-dimensional manganese phosphate

The title compound,{(C2H10N2)(2)[Mn(PO4)(2)]}(n), contains anionic square-twisted chains of formula [Mn(PO4)(2)](4-) constructed from corner-sharing four-membered rings of alternating MnO4 and PO4 units. The Mn and P atoms have distorted tetrahedral coordination and the Mn atom lies on a twofold axis. The linear manganese-phosphate chains are held together by hydrogen-bonding interactions involving the framework O atoms and the H atoms of the ethane-1,2-diammonium cations, which lie in the interchain spaces.

Solvothermal synthesis of one-dimensional chalcogenides containing group 13 elements

The solvothermal synthesis and characterisation of [C6H16N2][GaS2]2 (1), [C6H16N2][Ga2Se3(Se2)] (2), and mixed-metal phases with composition [C6H16N2][Ga2–xInxSe3(Se2)] (0 < x < 2)(3–5), is described. These materials have been characterised by single-crystal and powder X-ray diffraction, thermogravimetric analysis and UV/Vis diffuse reflectance spectroscopy. The materials contain one-dimensional anionic chains. In 1, these chains consist of edge-linked GaS4 tetrahedra, whilst in 2–5, the chains contain perselenide (Se2)2– units and comprise alternating four-membered [M2Se2] and five-membered [M2Se3] rings (where M = Ga, In). Compounds 3–5 represent the first examples of ternary mixed-metal [M2Se3(Se2)]2– chains.

Hydrothermal synthesis of [C6H16N2][In2Se3(Se2)]: a new one-dimensional indium selenide

A new organically templated indium selenide, [C6H16N2][In2Se3(Se2)], has been prepared hydrothermally from the reaction of indium, selenium and trans-1,4-diaminocyclohexane in water at 170 °C. This material was characterised by single-crystal and powder X-ray diffraction, thermogravimetric analysis, UV–vis diffuse reflectance spectroscopy, FT-IR and elemental analysis. The compound crystallises in the monoclinic space group C2/c (a=12.0221(16) Å, b=11.2498(15) Å, c=12.8470(17) Å, β=110.514(6)°). The crystal structure of [C6H16N2][In2Se3(Se2)] contains anionic chains of stoichiometry [In2Se3(Se2)]2−, which are aligned parallel to the [1 0 1] direction, and separated by diprotonated trans-1,4-diaminocyclohexane cations. The [In2Se3(Se2)]2− chains, which consist of alternating four-membered [In2Se2] and five-membered [In2Se3] rings, contain perselenide (Se2)2− units. UV–vis diffuse reflectance spectroscopy indicates that [C6H16N2][In2Se3(Se2)] has a band gap of 2.23(1) eV

The benefits of one-dimensional detectors for high-pressure powder X-ray diffraction

High-pressure powder X-ray diffraction is a fundamental technique for investigating structural responses to externally applied force. Synchrotron sources and two-dimensional detectors are required. In contrast to this conventional setup, high-resolution beamlines equipped with one-dimensional detectors could offer much better resolved peaks but cannot deliver accurate structure factors because they only sample a small portion of the Debye rings, which are usually inhomogeneous and spotty because of the small amount of sample. In this study, a simple method to overcome this problem is presented and successfully applied to solving the structure of an L-serine polymorph from powder data. A comparison of the obtained high-resolution high-pressure data with conventional data shows that this technique, providing up to ten times better angular resolution, can be of advantage for indexing, for lattice parameter refinement, and even for structure refinement and solution in special cases.

Sodium 2-nitrocinnamate dihydrate: a one-dimensional hydrogen-bonded coordination polymer

The title compound catena-poly[aqua-mu3-2-nitrocinnamato], [Na(C9H6NO4)(H2O)2]n, the sodium salt of trans-2-nitrocinnamic acid, is a one-dimensional coordination polymer based on six-coordinate octahedral NaO6 centres comprising three facially-related monodentate carboxylate O-atom donors from separate ligands (all bridging)[Na-O, 2.4370(13)-2.5046(13)A] and three water molecules (two bridging, one monodentate) [Na-O, 2.3782(13)-2.4404(17)A]. The structure is also stabilized by intra-chain water-O-H...O(carboxylate) and O-H...O(nitro) hydrogen bonds.

One-dimensional hydrogen-bonded structures in the 1:1 proton-transfer salts of 4,5-dichlorophthalic acid with the aliphatic Lewis bases diisopropylamine and hexamethylenetetramine

The crystal structures of the 1:1 proton-transfer compounds of 4,5-dichlorophthalic acid with the aliphatic Lewis bases diisopropylamine and hexamethylenetetramine, viz. diisopropylaminium 2-carboxy-4,5-dichlorobenzoate (1) and hexamethylenetetraminium 2-carboxy-4,5-dichlorobenzoate hemihydrate (2), have been determined. Crystals of both 1 and 2 are triclinic, space group P-1, with Z = 2 in cells with a = 7.0299(5), b = 9.4712(7), c = 12.790(1)Å, α = 99.476(6), β = 100.843(6), γ = 97.578(6)o (1) and a = 7.5624(8), b = 9.8918(8), c = 11.5881(16)Å, α = 65.660(6), β = 86.583(4), γ = 86.987(8)o (2). In each, one-dimensional hydrogen-bonded chain structures are found: in 1 formed through aminium N+-H...Ocarboxyl cation-anion interactions. In 2, the chains are formed through anion carboxyl O...H-Obridging water interactions with the cations peripherally bound. In both structures, the hydrogen phthalate anions are essentially planar with short intra-species carboxylic acid O-H...Ocarboxyl hydrogen bonds [O…O, 2.381(3) Å (1) and 2.381(8) Å (2)].

Formation of one-dimensional capped ZnO nanoparticle assemblies at the air/water interface

The self-assembling behavior and microscopic structure of zinc oxide nanoparticle Langmuir-Blodgett monolayer films were investigated for the case of zinc oxide nanoparticles coated with a hydrophobic layer of dodecanethiol. Evolution of nanoparticle film structure as a function of surface pressure (π) at the air-water interface was monitored in situ using Brewster’s angle microscopy, where it was determined that π=16 mN/m produced near-defect-free monolayer films. Transmission electron micrographs of drop-cast and Langmuir-Schaefer deposited films of the dodecanethiol-coated zinc oxide nanoparticles revealed that the nanoparticle preparation method yielded a microscopic structure that consisted of one-dimensional rodlike assemblies of nanoparticles with typical dimensions of 25 x 400 nm, encased in the organic dodecanethiol layer. These nanoparticle-containing rodlike micelles were aligned into ordered arrangements of parallel rods using the Langmuir-Blodgett technique.

Pattern recognition using invariants defined from higher order spectra - one-dimensional inputs

A new approach to pattern recognition using invariant parameters based on higher order spectra is presented. In particular, invariant parameters derived from the bispectrum are used to classify one-dimensional shapes. The bispectrum, which is translation invariant, is integrated along straight lines passing through the origin in bifrequency space. The phase of the integrated bispectrum is shown to be scale and amplification invariant, as well. A minimal set of these invariants is selected as the feature vector for pattern classification, and a minimum distance classifier using a statistical distance measure is used to classify test patterns. The classification technique is shown to distinguish two similar, but different bolts given their one-dimensional profiles. Pattern recognition using higher order spectral invariants is fast, suited for parallel implementation, and has high immunity to additive Gaussian noise. Simulation results show very high classification accuracy, even for low signal-to-noise ratios.

Synthesis of one-dimensional nanocomposites based on alumina nanofibres and their catalytic applications

Materials with one-dimensional (1D) nanostructure are important for catalysis. They are the preferred building blocks for catalytic nanoarchitecture, and can be used to fabricate designer catalysts. In this thesis, one such material, alumina nanofibre, was used as a precursor to prepare a range of nanocomposite catalysts. Utilising the specific properties of alumina nanofibres, a novel approach was developed to prepare macro-mesoporous nanocomposites, which consist of a stacked, fibrous nanocomposite with a core-shell structure. Two kinds of fibrous ZrO2/Al2O3 and TiO2/Al2O3 nanocomposites were successfully synthesised using boehmite nanofibers as a hard temperate and followed by a simple calcination. The alumina nanofibres provide the resultant nanocomposites with good thermal stability and mechanical stability. A series of one-dimensional (1D) zirconia/alumina nanocomposites were prepared by the deposition of zirconium species onto the 3D framework of boehmite nanofibres formed by dispersing boehmite nanofibres into a butanol solution, followed by calcination at 773 K. The materials were characterised by X-ray diffraction (XRD), Scanning electron microscopy (SEM), Transmission electron microscope (TEM), N2 adsorption/desorption, Infrared Emission Spectroscopy (IES), and Fourier Transform Infrared spectroscopy (FT-IR). The results demonstrated that when the molar percentage, X, X=100*Zr/(Al+Zr), was > 30%, extremely long ZrO2/Al2O3 composite nanorods with evenly distributed ZrO2 nanocrystals formed on their surface. The stacking of such nanorods gave rise to a new kind of macroporous material without the use of any organic space filler\template or other specific drying techniques. The mechanism for the formation of these long ZrO2/Al2O3 composite nanorods is proposed in this work. A series of solid-superacid catalysts were synthesised from fibrous ZrO2/Al2O3 core and shell nanocomposites. In this series, the zirconium molar percentage was varied from 2 % to 50 %. The ZrO2/Al2O3 nanocomposites and their solid superacid counterparts were characterised by a variety of techniques including 27Al MAS-NMR, SEM, TEM, XPS, Nitrogen adsorption and Infrared Emission Spectroscopy. NMR results show that the interaction between zirconia species and alumina strongly correlates with pentacoordinated aluminium sites. This can also be detected by the change in binding energy of the 3d electrons of the zirconium. The acidity of the obtained superacids was tested by using them as catalysts for the benzolyation of toluene. It was found that a sample with a 50 % zirconium molar percentage possessed the highest surface acidity equalling that of pristine sulfated zirconia despite the reduced mass of zirconia. Preparation of hierarchically macro-mesoporous catalyst by loading nanocrystallites on the framework of alumina bundles can provide an alternative system to design advanced nanocomposite catalyst with enhanced performance. A series of macro-mesoporous TiO2/Al2O3 nanocomposites with different morphologies were synthesised. The materials were calcined at 723 K and were characterised by X-ray diffraction (XRD), Scanning electron microscopy (SEM), Transmission electron microscope (TEM), N2 adsorption/desorption, Infrared Emission Spectroscopy (IES), and UV-visible spectroscopy (UV-visible). A modified approach was proposed for the synthesis of 1D (fibrous) nanocomposite with higher Ti/Al molar ratio (2:1) at lower temperature (<100oC), which makes it possible to synthesize such materials on industrial scale. The performances of a series of resultant TiO2/Al2O3 nanocomposites with different morphologies were evaluated as a photocatalyst for the phenol degradation under UV irradiation. The photocatalyst (Ti/Al =2) with fibrous morphology exhibits higher activity than that of the photocatalyst with microspherical morphology which indeed has the highest Ti to Al molar ratio (Ti/Al =3) in the series of as-synthesised hierarchical TiO2/Al2O3 nanocomposites. Furthermore, the photocatalytic performances, for the fibrous nanocomposites with Ti/Al=2, were optimized by calcination at elevated temperatures. The nanocomposite prepared by calcination at 750oC exhibits the highest catalytic activity, and its performance per TiO2 unit is very close to that of the gold standard, Degussa P 25. This work also emphasizes two advantages of the nanocomposites with fibrous morphology: (1) the resistance to sintering, and (2) good catalyst recovery.