Energies of π*- and π-states of the conduction band and valence band of chiral carbon nanotubes

Nanotubes (NTs) are mainly represented by (n,p) chiral NTs with chirality indices 0 < p < n delimited by (n,0) and (n,n) for achiral NTs. In (n,p) chiral NTs, the unit cell hexagons have a helical arrangement on the cylindrical surface of an NT and common angular and axial translations. An analytical formula was derived for calculation of the band structure of both chiral and achiral NTs with chirality indices 0 ≤ p ≤ n and band diagrams of some chiral NTs. Chiral NTs significantly extend the range of semiconducting NTs. An equation for the band gap width ΔЕ of semiconducting chiral and achiral NTs was derived: \(\frac{{\vartriangle E}}{{{\gamma _0}}} = \frac{{2\pi }}{{\sqrt {3{n^2} + 3np + 3{p^2}} }}\). Tables of the band structure parameters of metallic and semiconducting chiral NTs are presented.     

High-temperature properties of new perovskite-like oxides

New complex oxides of composition Pr_1–y Ca _y Fe_{0.5 + x} (Mg_0.25Mo_0.25)_0.5–x O₃, 0.0 ≤ x ≤ 0.1, 0.42 ≤ y ≤ 0.8 having an orthorhombically distorted perovskite structure have been prepared. The thermal expansion and electric conductivity of the new phases have been studied in the temperature range between 100–900°C. The results of our study imply that thin films of the oxides studied can be treated as electrode materials for symmetric solid-oxide fuel cells.     

Synthesis of Block Copolymers of Styrene with <Emphasis Type="Italic">D</Emphasis>,<Emphasis Type="Italic">L</Emphasis>-Lactide by the Sequential Controlled Cationic Polymerization and Ring-Opening Anionic Polymerization

The cationic polymerization of styrene initiated by the system 2-chloro-2-phenylpropane–TiCl₄–pyridine is studied in a mixture CH₂Cl₂–n-hexane at a temperature of –80°С. It is shown that under these conditions polymerization occurs via the living mechanism at [monomer]: [initiator] ≤ 100. The method of preparing polystyrenes with terminal primary hydroxyl groups (M_n = 4000–10000 g/mol) by the sequential controlled cationic polymerization of styrene and the in situ alkylation of 4-phenoxy-1-butanol by polystyrene macrocations is proposed. The resulting functionalized polystyrenes are used as macroinitiators of anionic-coordination ring-opening polymerization of D,L-lactide in the presence of tin bis(2-ethyl hexanoate) [Sn(Oct)₂] in toluene at 80°С. Copolymers polystyrene-block-poly(D,L-lactide) with the controlled length of the poly(D,L-lactide) block (M_n = 10000–17000 g/mol) and a relatively low molecular-weight distribution (M_w/M_n = 1.6–1.8) are synthesized. Formation of the block copolymers is confirmed by ¹Н NMR spectroscopy, gel-permeation chromatography, and atomic force microscopy.     

New Phosphate-Sulfates with NZP Structure

NaZr_2–xB_x(PO₄)_3–2x(SO₄)_2x (0 ≤ x ≤ 1.25, B = Mg, Co, Ni, Cu, Zn), and NaZr_2–xR_x(PO₄)_3–x(SO₄)_x (0 ≤ x ≤ 1.25, R = Al, Fe) phosphate-sulfates series have been prepared by a sol–gel process. These compounds belong to the NaZr₂(PO₄)₃ (NZP) structure family and crystallize in hexagonal crystal system, space group R\(\bar 3\)c. Limited solid solution series were found to exist; their formation temperatures and thermal stability limits were determined. Particle sizes as determined by microstructure observation were 50–200 nm, and for Cu- and Zn-containing samples, 200–500 nm. The thermal expansion of phosphate-sulfate NaZr_1.25Cu_0.75(PO₄)_1.5(SO₄)_1.5 was studied in the range 25–700°C. Thermal expansion coefficients and thermal expansion anisotropy were found to be α_a =–5.40 × 10^–6 °C^–1, α_с = 18.88 × 10^–6 °C^–1, α_avg = 2.69 × 10^–6 °C^–1, and Δα = 24.28 × 10^–6 °C^–1.     

Compositions and structures of nanoparticles of pentagonal axial symmetry <Emphasis Type="Italic">D</Emphasis><Subscript>5<Emphasis Type="Italic">d</Emphasis></Subscript>: Nanotubes

The method of determination of the structure and the number of atoms in the shells of nanoparticles as a function of the arrangement of atoms at the symmetry elements of a symmetry group has been developed. The formulas for the calculation of the number of particles with symmetry group D _5d are reported. The number of particles in these shells is determined by three structurally invariant numbers and the “quantum number” of the group order n. The classification of all possible nanostructures with symmetry group D _5d is given: C _θ+10z , z = 0, 1, 2, …, where the basic shells are C _θ = C ₂, C ₁₀, C ₁₂. The sum rule has been obtained for the coordination numbers of shell sites located at symmetry axes. Pentagonal axial nanoparticles are shown to be the initial shells for obtaining (5,5) and (10,10) armchair nanotubes or (5,0) and (10,0) zigzag nanotubes. The general formula of these nanotubes closed with icosahedral and dodecahedral caps is N _20+10p , N _60+10p (p = 1, 2, …). The graphical constructions of all classes of nanoparticles and nanotubes of the pentagonal axial type are reported.     

Ion mobility,phase transitions,and ion transport in potassium-ammonium hexafluorozirconates

The mobility of fluoride and ammonium ions (180–480 K) in compounds K_{2? n} (NH4)_nZrF₆ (0.2 ≤ n ≤ 1.70) was investigated by ¹⁹F and ¹H NMR. Correlations have been found between the composition of the cation sublattice, the character of ion motions, and phase transition temperature in these compounds. The hightemperature modifications with n ≥ 0.85 of the compounds are characterized by translational diffusion of fluoride and ammonium ions and by uniaxial anisotropy of the ¹⁹F magnetic shielding tensor. The electrophysical characteristics of these compounds were studied in the temperature range 300–480 K.     

Systems Li<Subscript>2</Subscript>O(Na<Subscript>2</Subscript>O)-CdO-V<Subscript>2</Subscript>O<Subscript>5</Subscript>: Phase composition and phase diagrams

The subsolidus phase composition of the M₂O-CdO-V₂O₅ systems with M = Li or Na is studied. Double orthovanadates MCdVO₄ and MCd₄(VO₄)₃ form solid solutions of composition Li_{1 ? 2x/3}Cd _x/3CdVO₄ (0 ≤ x ≤ 1, orthorhombic space group Cmcm, modulation at x = 0.6) and Na_{3 ? 2x} Cd_{3 + x} (VO₄)₃ (0 ≤ x ≤ 0.10 and 0.30 ≤ x ≤ 1, orthorhombic space group Cmcm and Pn2₁ a or Pnma, respectively). In the range 0.10 < x < 0.30, the end-members of the solid solutions coexist. Isothermal sections of the systems are mapped.     

Geometries,stabilities, electronic and magnetic properties of small aluminum cluster anions doped with cobalt: A density functional theory study

The geometrical structures, relative electronic and magnetic properties of small Al_nCo^– (1 ≤ n ≤ 9) clusters are systematically investigated within the framework of density functional theory at the BPW91 level. The single Co doping can dramatically affect the ground state geometries of the 1 Al_n+1^- clusters. At the same time, the resulting geometries show that the lowest energy Al_nCo^– clusters prefer to be three dimensional structures. Here, the relative stabilities are investigated in terms of the calculated average binding energies, fragmentation energies, and second-order energy differences. Moreover, the result of the highest occupiedlowest unoccupied molecular orbital energy gaps indicates that Al₆Co^– clusters have the highest chemical stability for Al_nCo^– (1 ≤ n ≤ 9) clusters. Furthermore, the natural population analysis reveals that the charges in Al_nCo^– clusters transfer from the Al frames to the Co atom. Additionally, the analyses of the local and total magnetic moments of the Al_nCo^– clusters show that the magnetic effect mainly comes from the Co atom.     

Compositions and structures of nanoparticles of trigonal symmetry <Emphasis Type="Italic">D</Emphasis><Subscript>3<Emphasis Type="Italic">d</Emphasis></Subscript>: Nanotubes

A method has been developed for the determination of the structure and number of atoms in the shells of nanoparticles as a function of the arrangement of atoms at the symmetry elements of a symmetry group. The formulas for calculation of the number of particles of symmetry D _3d have been reported. It has been shown that the number of atoms in trigonal shells is determined by three structurally invariant numbers and the quantum number of the group order n. All possible nanostructures of symmetry D _3d have been classified: C_{θ + 6z} , z = 0, 1, 2, ..., where the basic shells are C_θ = C₆, C₈, and C₁₄. A sum rule has been obtained for the coordination numbers of the shell sites located on symmetry axes. Trigonal nanoparticles are parent ones for obtaining (3,0), (6,0), and (9,0) nanotubes of trigonal type. The general formulas of these nanotubes with icosahedral, dodecahedral, and cubic caps are N_{8 + 12p} , N_{20 + 24p} , and N_{60 + 36p} (p = 1, 2, ...), respectively. The graphical constructions of all classes of trigonal nanoparticles and nanotubes are reported.     

Solubility of B-Nb<Subscript>2</Subscript>O<Subscript>5</Subscript> and the Hydrolysis of Niobium(V) in Aqueous Solution as a Function of Temperature and Ionic Strength

B-Nb₂O₅ was recrystallized from commercially available oxide, and XRD analyses indicated that it is stable in contact with solutions over the pH range 0 to 9, whereas solid polyniobates such as Na₈Nb₆O₁₉?13H₂O(s) appear to predominate at pH>9. Solubilities of the crystalline B-Nb₂O₅ were determined in five NaClO₄ solutions (0.1≤I _m /mol?kg^?1≤1.0) over a wide pH range at (25.0±0.1)?°C and at 0.1 MPa. A limited number of measurements were also made at I _m =6.0 mol?kg^?1, whereas at I _m =1.0 mol?kg^?1 the full range of pH was also covered at (10, 50 and 70)?°C. The pH of these solutions was fixed using either HClO₄ (pH≤4) or NaOH (pH≥10) and determined by mass balance, whereas the pH on the molality scale was measured in buffer mixtures of acetic acid?+?acetate (4≤pH≤6), Bis-Tris (pH≈7), Tris (pH≈8) and boric acid?+?borate (pH≈9). Treatment of the solubility results indicated the presence of four species, \(\mathrm{Nb(OH)}_{n}^{5-n}\) (where n=4–7), so that the molal solubility quotients were determined according to:

$0\mathrm{.5Nb}_{2}\mathrm{O}_{5}\mathrm{(cr)+0}\mathrm{.5(2}n-5\mathrm{)H}_{2}\mathrm{O(l)}_{\leftarrow}^{\to}\mathrm{Nb(OH)}_{n}^{5-n}+(n-5)\mathrm{H}^{+}\quad (n=4\mbox{--}7)$

and were fitted empirically as a function of ionic strength and temperature, including the appropriate Debye-Hückel term. A Specific Interaction Theory (SIT) approach was also attempted. The former approach yielded the following values of log?₁₀ K _sn (infinite dilution) at 25?°C: ?(7.4±0.2) for n=4; ?(9.1±0.1) for n=5; ?(14.1±0.3) for n=6; and ?(23.9±0.6) for n=7. Given the experimental uncertainties (2σ), it is interesting to note that the effect of ionic strength only exceeded the combined uncertainties significantly in the case of log?₁₀ K _s6 to I _m =1.0 mol?kg^?1, such that these values may be of use by defining their magnitudes in other media. Values of Δ _f G ^o, Δ _f H ^o, S ^o and \(C_{p}^{\mathrm{o}}\) (298.15 K, 0.1 MPa) for each hydrolysis product were calculated and tabulated.

     

Crystal Structure of <Emphasis Type="Italic">DL</Emphasis>-Valinium Tetrafluoroantimonate(III) Monohydrate

The crystal structure of an antimony(III) fluoride complex of the composition (C₅H₁₂NO₂)SbF₄·H₂O (I) involving a cation of α-amino isovaleric acid (DL-valine, Val) is determined. Crystals are monoclinic: a = 12.2024(2) Å, b = 6.1636(1) Å, c = 15.5167(3) Å, Z = 4, space group P2₁/c. The structure is formed of DL-valinium (C₅H₁₂NO₂)⁺ cations, complex [SbF₄]_n^n? anions having a polymeric chain structure, and crystallization water molecules. The [SbF₄]_n^n? complex anions consist of trigonal SbF4E bipyramids joined together by asymmetric bridging Sb–F(3)···Sb bonds. The structural units are organized into a threedimensional framework via N–H···F, N–H···O, and O–H···F hydrogen bonds.     

Computational Studies on the Mo-Doped Gold Nanoclusters Au<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>Mo(<Emphasis Type="Italic">n</Emphasis> = 1–10): Structures,Stabilities and Magnetic Properties

The geometric structures, relative stabilities, magnetic properties of Mo-doped gold clusters Au _n Mo(n = 1–10) have been investigated at the PBE1PBE/def2TZVP level of theory. The results show that molybdenum doping has a significant effect on the geometric structures and electronic properties of Au _n Mo(n = 1–10) clusters. For the lowest energy structures of Au _n Mo(n = 1–10), the two dimensional to three dimensional transition occurs at cluster size n ≥ 8, and their relative stabilities exhibit odd–even oscillation with the change of Au atom number. It is found that charge in corresponding Au _n Mo clusters transfers from Mo atom to Au _n host in the size range n = 1–7, whereas the charge in opposition direction in the size range n = 8–10. In addition, the magnetic properties of Au _n Mo clusters are enhanced after doping single Mo atom into the corresponding gold clusters. Our results are valuable for the design of magnetic material.     

Electronic Structure and Relative Stabilities of 10- and 12-Vertex. <Emphasis Type="Italic">Closo</Emphasis>and <Emphasis Type="Italic">Nido</Emphasis>-Heteroborane Clusters of Ga,Ge, and As Elements

A DFT method with the B3LYP functional and the 6-311++G(d,p) diffuse basis set is used to predict geometries, relative stabilities, electronic structures, and the bonding of closo- and nido-Ga_mB_n–mH _n ^2? , Ge_mB_n–mH _n ^m?2 , and As_mB_n–mH _n ^{2 m?2} (n = 10, 12 and m = 1, 2) Clusters are obtained by replacing BH with isolobal GaH, GeH⁺, and AsH²⁺ fragments, keeping the same skeleton electron pairs (SEP). Based on the polyhedral skeletal electron pairs theory (PSEPT), closo and nido structures are predicted and can be of significant interest for experimentalists working in the field of heteroboranes. Different cluster stabilities are studied according to Gimarc′s and Williams′ rules, where our calculations show that the monosubstituted clusters deviate from these rules, giving rise to open structures. As₂B₈H _n ²⁺ as 10-vertex structures lead to nido-type clusters, however, Ge_mB_n–mH _n ^m?2 (n = 10, 12 and m = 1, 2) give rise to closo isomers with close energies. All optimized structures exhibit large HOMO–LUMO gaps suggesting a good kinetic stability, thus predicting their isolation and characterization.     

Structure of A Coordination Polymer [Cu(En)<Subscript>2</Subscript>CrO<Subscript>4</Subscript>]<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

The crystal structure of [Cu(En)₂CrO₄]_n (En is ethylenediamine) is determined: a = 14.7359(4) Å, b = 9.8083(3) Å, c = 14.2664(4) Å, V = 2061.98(10) ų, space group Cmce, Z = 8, d_x = 1.931 g/cm³. It is demonstrated that the studied phase is isostructural with [Сu(Еn)₂SO₄]_n. A pseudotetragonal copper atom coordination (Cu–N 2.0204 Å and 2.0244 Å, ∠N–Cu–N 84.73°) is completed to distorted octahedral by two oxygen atoms of chromate anions (Cu–O 2.433 Å and 2.380 Å).     

Alkali (alkaline-earth) metal,aluminum, and titanium complex orthophosphates: Synthesis and characterization

Phase formation in the A_{1 + x} Al _x Ti_{2 ? x} P₃O₁₂ (A = Li, Na, K, Rb, or Cs; 0 ≤ x ≤ 2.0) and B_{0.5(l + x)}Al _x Ti_{2 ? x} P₃O₁₂ (B = Mg, Ca, Sr, or Ba; 0 ≤ x ≤ 2.0) systems was studied using X-ray powder diffraction, electron probe microanalysis, and IR spectroscopy. The following double and triple orthophosphates were found to exist: A_{1 + x} Al _x Ti_{2 ? x} (PO₄)₃ with A = Li (0 ≤ x ≤ 0.3), Na (0 ≤ x ≤ 1.0), K (x = 0, 1.0, or 2.0), Rb (x = 0, 1.0, or 2.0), or Cs (0 ≤ x ≤ 1.0) and B_{0.5(l + x)}Al _x Ti_{2 ? x} (PO₄)₃ with B = Mg and Ba (x = 0), Ca and Sr (0 ≤ x ≤ 0.2). These orthophosphates crystallize in the structure types of kosnarite, langbeinite, cesium titanium arsenate, potassium aluminum phosphate, or rubidium aluminum phosphate. Their crystal parameters were calculated. For CsTi₂(PO₄)₃ (x = 0), Rietveld refinement was carried out: space group Ia \(\bar 3\) d, Z = 32, a = 19.909(5) Å, V = 7892(1) ų. This compound has a framework structure. The framework is built of TiO₆ octahedra and PO₄ tetrahedra; eight- and 12-coordinated Cs⁺ cations populate interstices.     

Formation of Nd<Subscript>1–<Emphasis Type="Italic">x</Emphasis></Subscript>Bi<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>FeO<Subscript>3</Subscript> Nanocrystals under Conditions of Glycine-Nitrate Synthesis

Nd_1–xBi_xFeO₃ nanocrystals with crystallite size 30?60 nm have been prepared under conditions of glycine–nitrate burning. Single-phase Nd_1–xBi_xFeO₃ nanocrystals are formed over the entire studied concentrations range if the glycine–nitrate synthesis is performed in excess of the oxidizer. Under these conditions, a continuous range of the Nd_1–xBi_xFeO₃ solid solutions (0 ≤ х ≤ 0.75) crystallized in the rhombic system (space group Pbnm) are formed without crystallization of the burning intermediates. The Nd_1–xBi_xFeO₃ solid solutions (х = 0.775, 0.8) crystallize in the rhombic system (space group Pbаm).     

Synthesis,structure, and properties of Schiff base iodobismuthate and its alteration in DMSO solution

New hybrid iodobismuthates (C₁₂H₁₈N₂)(BiI₄)₂ (1, C₁₂H₁₈N₂ is N,N´-bis(1- methylethylidene)-1,4-benzоdiammonium dication) and (C₆H₄(NH₃)₂) [Bi₂I₈?2DMSO]?4DMSO (2, C₆H₄(NH₃)₂ is p-phenylenediammonium dication) were synthesized and their crystal structures were established. Compound 1 crystallizes in the space group P2₁/n, a = 7.632(4), b = 13.471(6), c = 14.556(5) Å, β = 93.57(4)°; compound 2 crystallizes in the space group P\(\overline 1 \), a = 9.208(4), b = 12.203(5), c = 13.600(5) Å, α = 110.20(3)°, β = 97.28(4)°, γ = 110.04(4)°. In the crystal structure of compound 1, one-dimensional infinite BiI ₄ ^– polyanions are linked into a three-dimensional structure by N,N'-bis(1-methylethylidene)- 1,4-benzоdiammonium dications through N–H…I and C–H…I hydrogen bonds. Compound 1 is stable up to 200 °С, optical studies showed that it has a band gap of 2.15 eV. The recrystallization of compound 1 from DMSO is accompanied by the transformation of chain BiI ₄ ^– anions to binuclear [Bi₂I₈?2DMSO]^2– anions, while the azomethine cation decomposes to form a p-phenylenediammonium dication.     

A Systematic Search for Structures and Stabilities of Asymmetric Clusters (HfInN<Subscript>3</Subscript>)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 1-6)

In order to find single source precursors (SSP), the structures, relative stabilities, and IR spectra of small asymmetric clusters (HFInN₃) _n (n = 1–6) are systematically investigated by means of the density functional theory at the B3LYP level. The obtained geometries show that the frameworks of clusters (HFInN₃) _n (n = 2–6) prefer to be 2n-membered ring with alternating indium and α-nitrogen atoms. The averaged binding energies reveal that all of asymmetric clusters (HFInN₃) _n (n = 1–6) can continue to gain energy as the cluster size n increasing. The second-order difference of energy (Δ₂E) and the HOMO-LUMO energy gap (E_gap) as a function of the cluster size n both exhibit a pronounced even-odd alternation phenomenon. The influences of cluster size n and temperature T on the thermodynamic properties of clusters are discussed. Judged by enthalpies and Gibbs free energies, the formations of the most stable clusters (HFInN₃) _n (n = 2–6) from the monomer are thermodynamically favorable in the range of 200–800 K.     

Isomorphic substitution of neodymium and gadolinium for calcium in synthetic hydroxovanadate

Isomorphic substitution of neodymium and gadolinium for calcium in synthetic hydroxovanadate Ca_{5 ? x} M _x (VO₄)₃(OH)_{1 ? x} O _x (M = Nd, Gd) is studied in the range 700–1000°C using X-ray powder diffraction, single-crystal X-ray diffraction (Rietveld technique), and IR spectroscopy. Single-phase solid solutions at 800°C are formed with x ≤ 0.35 for M(III) = Nd and x ≤ 0.3 for M(III) = Gd. With high x, the apatite solid solution coexists with Ca₃(VO₄)₂, Nd₂O₃, and X phases. With increasing x in the homogeneous region, the intensity of the bands of stretching vibrations and librations of OH groups decrease. Single-crystal X-ray diffraction shows that neodymium and gadolinium substitute for calcium in solid solutions mostly in Ca(2) positions.