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We consider the relation between the simultaneous approximation of two functions and the uniform approximation to one of these functions. In particular, F1 and F2 are continuous functions on a closed interval [a,b], S is an n-dimensional Chebyshev subspace of C [a,b] and s1* & s2* are the best uniform approximations to F1 and F2 from S respectively. The characterization of the best approximation solution is used to show that, under some restrictions on the point set of alternations of F1−s1* and F2−s2*, s1* or s2* is also a best A(1) simultaneous approximation to F1 and F2 from S with F1≥F2 and n=2.

The processes of restructuring of the deep toroidal magnetic field, which is excited by radial differential rotation in a stable radiant zone filled with the primary (relic) poloidal magnetic field, are analyzed. According to the data of helioseismological experiments on the internal rotation of the Sun, the radial angular velocity gradient covers layers of the ray zone deeper than the solar convective zone (SCZ). We believe that this radial angular velocity gradient acts on the primary diploid type poloidal field and thus excites a toroidal field (Ω-effect) of a time-constant direction, which will be pushed out of the generation zone due to magnetic buoyancy. From the steady state condition, when the Ω-effect compensates for the field losses caused by magnetic buoyancy, we derived a formula for estimating the maximum value of a stationary toroidal field, which can be maintained in the radiating zone for a long time. Taking into account the intensity of the relict radial field in the radiant zone B_r≈ 0,1...10 G, the radial angular velocity gradient (∂Ω/∂r ≈ 7⋅10^-18 rad/s⋅cm) determined from helioseismological measurements is capable of generating a sufficiently strong deep toroidal magnetic field B_T≈10^6...10^8 G. Toroidal fields, the magnitude of which outweighs these steady-state values, are gradually removed from the radiant zone due to magnetic buoyancy into the higher layers of the SCZ where the αΩ-dynamo mechanism operates. In view of this, the total toroidal field in the SCZ will consist of two components: variable and stationary. The first magnetic component is excited by the dynamo process and so it changes its direction (polarity) with a period of 11 years. At the same time, the second component of permanent orientation, which penetrates into the SCZ from below (from the radiant zone), cannot be the cause of cyclicity. However, it will be affect the amplitude of neighboring cycles of solar activity. In one cycle, the total toroidal field, when the directions of the two components of the field coincide, will have a greater intensity than in the neighboring cycle, when the directions of these components are opposite. Since the intensity of the sunspots formation is determined by the floating up to the solar surface of the total toroidal field, this should ultimately lead to the observed alternation of the amplitude of the neighboring 11-year cycles of solar activity.

The development of technologies for nuclear reactors based on molten salts has seen a big resurgence. The success of thermodynamic models for these hinges in part on our ability to predict at the a...

The heterobifunctional organic ligand, 3-(1,2,4-triazol-4-yl)adamantane-1-carboxylate (tr-ad-COO− ), was employed for the synthesis of the title silver(I) coordination polymer, {[Ag(C13H16N3O2)]·2H2O} n , crystallizing in the rare orthorhombic C2221 space group. Alternation of the double μ2-1,2,4-triazole and μ2-η2:η1-COO− (chelating, bridging mode) bridges between AgI cations supports the formation of sinusoidal coordination chains. The AgI centers possess a distorted {N2O3} square-pyramidal arrangement with τ5 = 0.30. The angular organic linkers connect the chains into a tetragonal framework with small channels along the c-axis direction occupied by water molecules of crystallization, which are interlinked via O—H...O hydrogen bonds with carboxylate groups, leading to right- and left-handed helical dispositions.

"Secondary doping" in poly(3,4-ethylenedioxy-thiophene):poly(styrenesulfonate) (PEDOT:PSS) is quite effective and a frequently used method for the conductivity enhancement. This simple approach, the addition of co-solvents to the PEDOT:PSS solution before film fabrication, is an essential way to derive the high electrical performance of PEDOT:PSS, but the mechanism still remains unclear. In this study, nanoscale structural changes synchronized with the conductivity enhancement via secondary doping in PEDOT:PSS films were investigated. During secondary doping with ethylene glycol near the critical dopant concentration, non-crystalized PEDOT molecules uncoupled from PSS chains and then underwent nano-crystallization. These structural changes might be the key driving force for conductivity enhancement via secondary doping., 9 pages, 7 figures, accepted for publication in J. Phys. Chem. C

For a given knot, we study the minimal number of positive eigenvalues of the double branched cover over spanning surfaces for the knot. The value gives a lower bound for various genera, the dealternating number and the alternation number of knots, and we prove that Batson's bound for the non-orientable 4-genus gives an estimate of the value. In addition, we use the value to give a necessary condition for being quasi-alternating., Comment: 13 pages, 15 figures

Cyclo[18]carbon (C18, a molecular carbon allotrope) can be synthesized by dehalogenation of a bromocyclocarbon precursor, C18Br6, in 64% yield, by atomic manipulation on a sodium chloride bilayer on Cu(111) at 5 K, and imaged by high-resolution atomic force microscopy. This method of generating C18gives a higher yield than that reported previously from the cyclocarbon oxide C24O6. The experimental images of C18were compared with simulated images for four theoretical model geometries, including possible bond-angle alternation:D18hcumulene,D9hpolyyne,D9hcumulene, andC9hpolyyne. Cumulenic structures, with (D9h) and without (D18h) bond-angle alternation, can be excluded. Polyynic structures, with (C9h) and without (D9h) bond-angle alternation, both show a good agreement with the experiment and are challenging to differentiate.

We consider the triangular lattice ice model (20-Vertex model) with four types of domain-wall type boundary conditions. In types 1 and 2, the configurations are shown to be equinumerous to the quarter-turn symmetric domino tilings of an Aztec-like holey square, with a central cross-shaped hole. The proof of this statement makes extensive use of integrability and of a connection to the 6-Vertex model. The type 3 configurations are conjectured to be in same number as domino tilings of a particular triangle. The four enumeration problems are reformulated in terms of four types of Alternating Phase Matrices with entries 0 and sixth roots of unity, subject to suitable alternation conditions. Our result is a generalization of the ASM-DPP correspondence. Several refined versions of the above correspondences are also discussed., Comment: 63 pages, 22+16 figures

The goal of this work is to investigate the optimality of the $d$-dimensional rock-salt structure, i.e., the cubic lattice $V^{1/d}\mathbb{Z}^d$ of volume $V$ with an alternation of charges $\pm 1$ at lattice points, among periodic distribution of charges and lattice structures. We assume that the charges are interacting through two types of radially symmetric interaction potentials, according to their signs. We first restrict our study to the class of orthorhombic lattices. We prove that, for our energy model, the $d$-dimensional rock-salt structure is always a critical point among periodic structures of fixed density. This holds for a large class of potentials. We then investigate the minimization problem among orthorhombic lattices with an alternation of charges for inverse power laws and Gaussian interaction potentials. High density minimality results and low-density non-optimality results are derived for both types of potentials. Numerically, we investigate several particular cases in dimensions $2$, $3$ and $8$. The numerics support the conjecture that the rock-salt structure is the global optimum among all lattices and periodic charges, satisfying some natural constraints. For $d=2$, we observe a phase transition of the type 'triangular-rhombic-square-rectangular' for the minimizer's shape as the density decreases., 29 pages, 17 Figures. To appear in Mathematical Models and Methods in Applied Sciences

Despite many reviews and original articles, the actual crystal structure of tubular halloysites remains unclear. Analysis of the structural features of defect-free kaolinite, refined by Bish & von Dreele (1989), shows that the ordered 1Tc kaolinite structure can be described equally well by the orthogonal layer cell {a0, b0, γ0} (γ0 = 90°) or by two enantiomorphic oblique layer cells {a1, b1, γ1} and {a2, b2, γ2}, related to each other by a mirror plane. To simulate diffraction effects for tubular halloysite, the parameters and atomic coordinates of the orthogonal layer unit cell and the layer-displacement vectors t1 and t2 responsible for formation of the kaolinite enantiomorphs were deduced by transformation of the parameters of the defect-free kaolinite refined by Bish & von Dreele (1989). Modelling X-ray diffraction patterns show that the samples consist of either single, two or three phases, with the number and their structural features depending on the morphology of the particles. Samples formed of prismatic particles consist of halloysite-like structure (HLS), kaolinite-like structure (KLS) and halloysite cylindrical structure (HCS) phases occurring in various proportions. Samples of proper cylindrical tubes consist of a single HCS phase, whilst samples formed by particles having morphologies intermediate between proper cylindrical and well-developed prismatic forms consist of the KLS and HCS phases. The KLS phase is comparable to low-ordered platy kaolinite with identical unit-cell parameters, layer-displacement vectors and arbitrary stacking faults, except that the layer displacements are not random as in kaolinite, but are distributed at R = 1 such that t1 and t2 displacements have a strong tendency to be segregated. Structural parameters describing the HLS and KLS phases are identical, but in the HLS phase there is a strong tendency to the regular alternation of the t1 and t2 displacements, and the HLS phases do not contain arbitrary stacking faults. A characteristic feature of the three-phase prismatic samples is that the stacking of the layers along the c* axis is periodic and the layer thicknesses are similar to those of platy kaolinite. In contrast, in the KLS phase formed in samples with particles of intermediate morphologies, the hydrated 10 and 7.25 Å layers are interstratified. The relationship between the structural and morphological features of the coexisting phases suggests a sequence of phase formation from the centre to the surface of halloysite tubes that progresses from the HCS to the HLS via the KLS phase. The results of this study demonstrate that all kaolinite and halloysite (7 Å) varieties are built by the same fundamental structural units.

Given m + 1 strictly decreasing numbers h 0 , h 1 , … , h m , we give an algorithm to construct a corresponding finite sequence of orthogonal polynomials p 0 , p 1 , … , p m such that p 0 = 1 , p j has degree j and p m − j ( h n ) = ( − 1 ) n p j ( h n ) for all j , n = 0 , 1 , … , m . Using these polynomials, we construct bivariate Lagrange polynomials and cubature formulas for nodes that are points in R 2 where the coordinates are taken from given finite decreasing sequences of the same length and where the indices have the same (or opposite) parity.

A new superstructure of the mineral camerolaite, Cu6Al3(OH)18(H2O)2[Sb(OH)6](SO4), has been refined in space group P\bar 1 with unit-cell parameters aP = 7.7660 (16), bP = 8.759 (4), cP = 11.306 (2) Å, α P = 108.67 (4), β P = 83.41 (3), γ P = 126.64 (2)°, V = 581.6 (3) Å3 and Z = 1, with R 1 = 0.0951 (all data). This is the first refined example of a cyanotrichite-group mineral in which long-range order of interlayer anions produces a superstructure along b, although diffuse scattering has previously been reported that corresponds to short-range order. Though the structure shares with other members of the cyanotrichite group a structural unit in which ribbons of edge-sharing Cu and Al octahedra form layers || (001), the superstructure arises from regular alternation of [SO4] and [Sb(OH)6] polyhedra along rods that lie between the layers, and phase coupling between rods that maximizes the distance between [SO4] groups of adjacent rods along a and c directions. This arrangement suggests an alternative nearly orthogonal choice of unit cell in F\bar 1 with parameters aF = 12.473 (26), bF = 8.759 (4), cF = 21.476 (7) Å, α F = 85.94 (4), β F = 95.91 (5), γ F = 92.34 (9)°, which is recommended for comparing this structural variety of camerolaite with other members of the group.

Single-phase concentrated solid-solution alloys (SP-CSAs) have recently gained unprecedented attention due to their promising properties. To understand effects of alloying elements on irradiation-induced defect production, recombination and evolution, an integrated study of ion irradiation, ion beam analysis and atomistic simulations are carried out on a unique set of model crystals with increasing chemical complexity, from pure Ni to Ni80Fe20, Ni50Fe50, and Ni80Cr20 binaries, and to a more complex Ni40Fe40Cr20 alloy. Both experimental and simulation results suggest that the binary and ternary alloys exhibit higher radiation resistance than elemental Ni. The modeling work predicts that Ni40Fe40Cr20 has the best radiation tolerance, with the number of surviving Frenkel pairs being factors of 2.0 and 1.4 lower than pure Ni and the 80:20 binary alloys, respectively. While the reduced defect mobility in SP-CSAs is identified as a general mechanism leading to slower growth of large defect clusters, the effect of specific alloying elements on suppression of damage accumulation is clearly demonstrated. This work suggests that concentrated solid-solution provides an effective way to enhance radiation tolerance by creating elemental alternation at the atomic level. The demonstrated chemical effects on defect dynamics may inspire new design principles of radiation-tolerant structural alloys for advanced energy systems.

The crystal structure of balkanite from the San Giovanni mine, Sardinia, Italy, has been solved by X-ray single-crystal diffraction on the basis of 883 reflections with F o > 4σ F o , with a final R 1 = 0.055. Balkanite is monoclinic, space group P 2/ m , with unit-cell parameters a = 9.5539(11), b = 3.9150(4), c = 10.6424(12) A, β = 90.047(9)°, V = 398.06(8) A 3 . Its formula derived through the single-crystal structure refinement is Cu 9.00 Ag 4.73 Hg 1.00 S 8 , with Z = 1. Electron-microprobe analysis gave the formula (Cu 8.69 Fe 0.12 Zn 0.08 Ni 0.07 ) Σ8.96 Ag 4.63 Hg 0.93 S 8 , close to the ideal formula (Cu 8.70 Me 2+ 0.30 )Ag 4.70 HgS 8 , or (Cu 9− x Me 2+ x )Ag 5− x HgS 8 , with x = 0.3. Although balkanite is not a layered compound, its crystal structure can be described as formed by the alternation, along a, of Cu-pure and Ag-rich layers. Additionally, it can also be described as based on two different alternating atomic (010) layers with all atoms on special positions (at y / b = 0 and ½), having chemical composition [Cu 4 Ag 3 HgS 4 ] + and [Cu 5 Ag 2 S 4 ] − , or as formed by the alternation of two ( 10 1 ¯ − ) polyhedral layers, having composition [Cu 7 Ag 3 S 4 ] 2+ and [Cu 2 Ag 2 HgS 4 ] 2− . Hg is linearly coordinated, Ag assumes a tetrahedral or a distorted octahedral coordination, whereas Cu displays a linear or planar triangular coordination. A critical comparison with the related mineral danielsite, ideally (Cu,Ag) 14 HgS 8 , is also presented.

Alstonite, BaCa(CO3)2, is a mineral described almost two centuries ago. It is widespread in Nature and forms magnificent cm-sized crystals. Notwithstanding, its crystal structure was still unknown. Here, we report the crystal-structure determination of the mineral and discuss it in relationship to other polymorphs of BaCa(CO3)2. Alstonite is trigonal, space groupP31m, with unit-cell parametersa= 17.4360(6),c= 6.1295(2) Å,V= 1613.80(9) Å3andZ= 12. The crystal structure was solved and refined toR1= 0.0727 on the basis of 4515 reflections withFo> 4σ(Fo) and 195 refined parameters. Alstonite is formed by the alternation, alongc, of Ba-dominant and Ca-dominant layers, separated by CO3groups parallel to {0001}. The main take-home message is to show that not all structure determinations of minerals/compounds can be solved routinely. Some crystals, even large ones displaying excellent diffraction quality, can be twinned in complex ways, thus making their study a crystallographic challenge.

A general series solution to the problem of interacting circular inclusions in plane elastostatics is presented in this paper. The analysis is based on the use of the complex stress potentials of Muskhelishvili and the theorem of analytical continuation. The general forms of the complex potentials are derived explicitly for the circular inhomogeneities under arbitrary plane loading. Using the alternation technique, these general expressions were subsequently employed to treat the problem of an infinitely extended matrix containing two arbitrarily located inhomogeneities. The major contribution of the present proposed method is shown to be capable of yielding approximate closed-form solutions for multiple inclusions, thus providing the explicit dependence of the solution on the pertinent parameters. The result shows that the dislocation has a stable equilibrium position at a certain combination of material constants. The case of an inhomogeneity interacting with a circular hole under a remote uniform load is also investigated.

AIMS: We studied unique data of a nova-like system MV Lyr during transition from the high to low state and vice versa taken by the Kepler space telescope. We were interested in evolution of frequency components found previously by Scaringi et al. in different data also obtained by Kepler. METHODS: We divided the light curve into 10 day segments and investigated the corresponding power density spectra. We searched for individual frequency components by fitting with Lorentzian functions. Additionally, we investigated the variability using averaged shot profiles calculated from the light curve divided into 10 equally spaces subsamples. RESULTS: We found very complex changes of the power density spectra. We focused our study onto three frequency components. Strong activity increase is seen at low frequencies. Contrariwise, the high frequency part of the spectrum strongly decreases in power with specific rise in characteristic frequencies of the individual components. We discuss various scenarios of this phenomenology as reprocessing of X-rays in a receding accretion disc or a radiation from a more active region at the outer disc. Finally, we show that various cataclysmic variables show similar characteristic frequencies in their power density spectra. These are dependent on activity stage, making the situation similar to X-ray binaries., Comment: accepted for publication to A&A

Complex sulfides of thallium with As, Sb, or Bi and with other cations (‘thallium sulfosalts’) are a large group of crystal structures with extreme variability. Incorporation of the large Tl+ cation in them is solved in several different ways: housing of Tl in columns of capped trigonal coordination prisms, which form separate walls in the structure (in different combinations with Pb and/or Sb), regular alternation of large Tl with small cations (As), presence of structural arrays of Tl coordination polyhedra paralleled by arrays of As coordination pyramids with a frequency ratio 1:2, omission derivatives with cavities for Tl accommodation and formation of layer structures with thallium concentrated into separate (inter)layers of different types. The first principle leads to a large family of sartorite homologues and rare lillianite homologues, as well as to the chabournéite group. The second one to the hutchinsonite family, omission derivatives form the routhierite and galkhaite groups, and the 1:2 periodicity ratio principle results in several outstanding structures from different groups. Layer structures consist of two-component and three-component layer combinations. Close cation-cation interactions are present but rare.

International audience; Three mononuclear Dy complexes with the same auxiliary ligand Lz (2,4-diamino-6-pyridyl-1,3,5-triazine), [Dy(TTA)Lz] (1Dy) (TTA = 4,4,4-trifluoro-1-(2-thienyl)-1,3-butanedionate), [Dy(acac)Lz]·CHOH·0.5HO (2Dy) (acac = acetylacetonate), and [Dy(MQ)Lz]Br·CHOH (3Dy) (HMQ = 2-methyl-8-quinolinol), have been synthesized through alteration of the ligands containing O donors. In all three complexes, the Dy ions are eight-coordinate and submitted to pseudo- D symmetry in the first coordination sphere. It is noteworthy that the TTA ligands in 1Dy are easily substituted by other bidentate capping ligands with O donors, leading to distinct magnetic properties, which were studied experimentally and via ab initio calculations. All three complexes were found to exhibit single-molecule magnet behavior with U of 22 cm (1Dy), 112 cm (2Dy), and 56 cm (3Dy) under zero applied dc field. Complex 1Dy demonstrates inferior SIM properties compared with 2Dy and 3Dy, which can be attributed to the strong electron-withdrawing effects of TTA ligands, as confirmed by theoretical calculations. However, butterfly-shaped magnetic hysteresis in 1Dy and 3Dy was observed at 1.9 K, while not in 2Dy.

Halogen substitution, that is, bromine for iodine, in the series of topological BinTeI (n = 1, 2, 3) materials was conducted in order to explore the impact of anion exchange on topological electronic structure. In this proof-of-concept study, we demonstrate the applicability of the modular view on crystal and electronic structures of new Bi2TeBr and Bi3TeBr compounds. Along with the isostructural telluroiodides, they constitute a family of layered structures that are stacked from two basic building modules, ∞2[Bi2] and ∞2[BiTeX] (X = I, Br). We present solid-state synthesis, thermochemical studies, crystal growth, and crystal-structure elucidation of Bi2TeBr [space group R3̅m (no. 166), a = 433.04(2) pm, c = 5081.6(3) pm] and Bi3TeBr [space group R3m (no. 160), a = 437.68(3) pm, c = 3122.9(3) pm]. First-principles calculations establish the topological nature of Bi2TeBr and Bi3TeBr. General aspects of chemical bonding appear to be similar for BinTeX (X = I, Br) with the same n, so that alternation of the global gap size upon substitution is insignificant. The complex topological inversion proceeds between the states of two distinct modules, ∞2[Bi2] and ∞2[BiTeBr]; thus, the title compounds can be seen as heterostructures built via a modular principle. Furthermore, highly disordered as well as incommensurately modulated ternary phase(s) are documented near the Bi2TeBr composition. Single-crystal X-ray diffraction experiments on BiTeBr and Bi2TeI resolve some discrepancies in prior published work., This work was supported by the German Research Foundation (DFG) in the framework of the Special Priority Program (SPP 1666) Topological Insulators and by the ERANET-Chemistry Program. We acknowledge support by Academic D. I. Mendeleev Fund Program of Tomsk State University (Project 8.1.01.2018), by St. Petersburg State University (Project 15.61.202.2015), by Ministry of Education and Science of the Russian Federation within the framework of the governmental program Megagrants (State Task 3.8716.2017/P220 or 3.8716.2017/9.10), by Russian Science Foundation 18-12-00169 (for surface electronic structure within tight-binding method), by Spanish Ministry of Science and Innovation (Grants FIS 2013-48286-C02-02-P, FIS 2013-48286-C02-440-01-P, and FIS 2016-75862-P).

[6.8]3Cyclacene is an interesting belt-like structure displaying aromatic-non-aromatic alternation, which is useful to gain an understanding of the intramolecular and intermolecular interactions between the anisotropic cones in the magnetic behavior of such rings. From the analysis of certain components in an induced magnetic field and (13)C-NMR shielding under its own principal axis system (PAS), the individual and overall magnetic behavior of each respective aromatic and non-aromatic fragments can be clearly described. Interestingly, the magnetic response of [6.8]3cyclacene suggests a characteristic behavior given by its confinement into a belt-like structure.

Alternation Current (AC) electrical field is introduced into Electrohydrodynamic Direct-Write (EDW) to control the deposition of micro/nano structure on insulated substrate. Under the AC electrical field, the charge repulsive force was decreased and the stability of EDW jet was improved. The swing amplitude of charged jet decreased with the increasing of voltage frequency. The influence of the applied voltage frequency on printed structure was discussed. When the voltage frequency increased from 0Hz to 750Hz, the average line width increased from 18μm to 33μm. Then the stable straight jet was used to direct-write orderly pattern on insulated PET substrate. This work provides a novel way to break through the obstacle of inkjet printing technology in the fields of micro/nano manufacturing.

We investigate the ground and low energy states of a one dimensional non local free energy functional describing at a mean field level a spin system with both ferromagnetic and antiferromagnetic interactions. In particular, the antiferromagnetic interaction is assumed to have a range much larger than the ferromagnetic one. The competition between these two effects is expected to lead to the spontaneous emergence of a regular alternation of long intervals on which the spin profile is magnetized either up or down, with an oscillation scale intermediate between the range of the ferromagnetic and that of the antiferromagnetic interaction. In this sense, the optimal or quasi-optimal profiles are "froth-like": if seen on the scale of the antiferromagnetic potential they look neutral, but if seen at the microscope they actually consist of big bubbles of two different phases alternating among each other. In this paper we prove the validity of this picture, we compute the oscillation scale of the quasi-optimal profiles and we quantify their distance in norm from a reference periodic profile. The proof consists of two main steps: we first coarse grain the system on a scale intermediate between the range of the ferromagnetic potential and the expected optimal oscillation scale; in this way we reduce the original functional to an effective "sharp interface" one. Next, we study the latter by reflection positivity methods, which require as a key ingredient the exact locality of the short range term. Our proof has the conceptual interest of combining coarse graining with reflection positivity methods, an idea that is presumably useful in much more general contexts than the one studied here., 38 pages, 2 figures

The crystal structure of ramdohrite, Pb5.9Fe0.1Mn0.1In0.1Cd0.2Ag2.8Sb10.8S24, from the Chocaya mine, Potosi, Bolivia, determined by Makovicky and Mumme from film data in 1983, was refined from single-crystal diffractometer data to the R value 0.060, based on 5230 reflections [ I > 2σ( I )] from a twinned crystal. Lattice parameters are a = 8.7348(3), b = 13.0543(4), c = 19.3117(6) A, and β = 90.179(2)°, space group P 21/ n . Two bicapped trigonal prismatic sites of lead bridge and unite adjacent (311)PbS slabs. These slabs contain five distinct coordination pyramids of Sb with trapezoidal cross sections, a mixed and disordered Sb-Ag-Cd-(Pb) site, refined as 0.39 Sb + 0.61 Ag, a pure Ag site with a very open, irregular tetrahedral coordination, and an octahedral site occupied by Pb. The (311)PbS slabs contain large lone electron pair micelles formed by four distinct antimony sites in alternation with small such micelles formed by a single Sb site. The geometric arrangement of these slabs is not based on crankshaft chains of short, strong Me-S bonds but on a chess-board arrangement of (predominantly) Sb pairs that share two common S atoms via short bonds. Relationships to, and differenced from, fizelyite and uchucchacuaite are described and discussed.

A bottom-up design rationale was adopted to devise β/γ-peptide foldamer manifolds which would adopt preferred 13-helix conformations, relying on minimal steric imposition brought by the constituent amino acid residues. In this way, a well-defined 13-helix conformer was revealed for short oligomers of trans-2-aminocyclobutanecarboxylic acid and γ(4)-amino acids in alternation, which gave good topological superposition upon an α-helix motif.

Droplets can bounce indefinitely on a liquid bath vertically vibrated in a sinusoidal fashion. We here present experimental results that extend this observation to forcing signals composed of a combination of two commensurable frequencies. The Faraday and Goodridge thresholds are characterized. Then a number of vertical bouncing modes are reported, including walkers. The vertical motion can become chaotic, in which case the horizontal motion is an alternation of walk and stop.

Although never emphasized and increasingly used in organic electronics, PEDOT-PSS (poly(3,4-ethylenedioxythiophene)-poly(styrene sulfonate)) layer-by-layer (lbl) film construction violates the alternation of polyanion and polycation rule stated as a prerequisit for a step-by-step film buildup. To demonstrate that this alternation is not always necessary, we studied the step-by-step construction of films using a single solution containing polycation/polyanion complexes. We investigated four different systems: PEDOT-PSS, bPEI-PSS (branched poly(ethylene imine)-poly(sodium 4-styrene sulfonate)), PDADMA-PSS (poly(diallyl dimethyl ammonium)-PSS), and PAH-PSS (poly(allylamine hydrochloride)-PSS). The film buildup obtained by spin-coating or dipping-and-drying process was monitored by ellipsometry, UV-vis-NIR spectrophotometry, and quartz-crystal microbalance. The surface morphology of the films was characterized by atomic force microscopy in tapping mode. After an initial transient regime, the different films have a linear buildup with the number of deposition steps. It appears that, when the particles composed of polyanion-polycation complex and complex aggregates in solution are more or less liquid (case of PEDOT-PSS and bPEI-PSS), our method leads to smooth films (roughness on the order of 1-2 nm). On the other hand, when these complexes are more or less solid particles (case of PDADMA-PSS and PAH-PSS), the resulting films are much rougher (typically 10 nm). Polycation/polyanion molar ratios in monomer unit of the liquid, rinsing, and drying steps are key parameters governing the film buildup process with an optimal polycation/polyanion molar ratio leading to the fastest film growth. This new and general lbl method, designated as 2-in-1 method, allows obtaining regular and controlled film buildup with a single liquid containing polyelectrolyte complexes and opens a new route for surface functionalization with polyelectrolytes. journal article research support, non-u.s. gov't 2012 Jun 12 2012 05 31 imported

The structure of O-AlFePd has been analyzed by single-crystal X-ray diffraction, yielding space group Cmca (No. 64), a = 0.8130(1) nm, b = 1.5474(2) nm, c = 2.3868(4) nm, atoms/cell = 204, F(000) = 3339, Dcalc = 5.621Mgm13 and R = 0.0294 for the 2117 observed reflections with Fobs > 4.0·(Fobs). The structure consists of four Fe sites, one Fe/Pd mixed site, and fifteen Al sites, and the corresponding structural formula is Al13(Fe,Pd)4 (Z = 8). The O-AlFePd phase is a new type of approximant of decagonal quasicrystals with a periodicity of 0.8 nm, and the alternation of flat and puckered layers at an interval of about 0.2 nm is the fundamental structural feature. The structure could be also described by a linkage of pentagonal atom columns similar to that found in monoclinic Al13Fe4. Nevertheless, the columnar linkage for the O-AlFePd phase is unique, and this allows us to advance an idea explaining the fine (001) glide twins frequently found in the Al13Fe4 phase. [doi:10.2320/matertrans.M2012130]

The present paper deals with the stress state of a piecewise homogeneous plane formed by alternation junction of two distinct strips of equal height manufactured of different materials. There is a doubly periodic system of cracks on the plane. The governing system of singular integral equations of the first kind for the density of the crack dislocation is derived. The solution of the problem in the case where only one of the repeated strips contains one doubly-periodic crack is obtained by the method of mechanical quadratures.

Enormous effort has been devoted to the elucidation of possible effects of bond-length alternation on the benzene pi-system. Benzene tends to stay highly aromatic and highly diatropic even if strong bond-length alternation is introduced artificially into the pi-system. Such peculiar aromatic and magnetic characters of benzene were justified consistently and unambiguously within a single theoretical framework. From all physically sound points of view, bond-alternate benzene is highly aromatic with a large aromatic stabilization energy. We confirmed that in the annulene family benzene is least sensitive in aromaticity to bond-length alternation.

Anandite, a trioctahedral mica, has an ideal chemical formula of Ba(FeMg)3(SiFe3+)O10(OH)S and a microprobe-derived formula of (Ba0.96K0.03Na0.01)∑=1.00(Fe2.012+Mg0.46Fe0.283+Al0.10Mn0.043+Mn0.042+Ti0.01)∑=2.93(Si2.60Fe1.403+)∑=4.00O10[(OH)0.96S0.84Cl0.16F0.04]∑=2.00, where S2− primarily substitutes for (OH)−. A single-crystal, X-ray structure determination of anandite-2 M was refined to R 1 = 0.0443 and w R 2 = 0.1232 on F 2 in space group Am . Cell parameters are: a = 5.4431(3), b = 9.4719(6), c = 20.042(1) A, and β = 95.046(1)°. Layer stacking is analogous to a 1 M stacking pattern (parallel unidirectional a /3 shifts within layers and octahedral set I only occupied), however cation order and (S,OH) positional disorder produce a two-layer repeat with β equaling ~95°. Subgroup symmetry of Am results from tetrahedral sheets within layers that are non-centrosymmetric with unequal compositions (Si0.61Fe0.393+ vs. Si0.79Fe0.213+) and thicknesses (difference of 0.209 A), and there is positional and site-occupancy disorder (four sites with S of 0, 30, 52, and 58%) of (S,OH). Characteristics of anandite-2 M , which are similar to those of anandite-2 O , include (1) alternation of smaller tetrahedral rings containing four Si-rich tetrahedra (T1a: 1.643 A, T2b: 1.657 A) and two Fe3+-rich tetrahedra (T2a: 1.733 A, T1b: 1.760 A) and larger rings containing four Fe3+-rich tetrahedra and two Si-rich tetrahedra within each layer; (2) nearly in-phase wave forms of basal O atoms across the interlayer (Δ z = −0.110 and 0.011 A and across the interlayer Δ z = −0.121 and 0.007 A); and (3) attraction that results in Ba being shifted toward S (0.070 A) and S being shifted toward Ba (0.117 A average) along the c axis, relative to the ideal. Bond-valence calculations show that Ba is shifted toward the undersaturated, bridging-basal O atoms of the Fe3+-rich tetrahedra and toward S-rich sites to achieve charge balance. Comparison of anandite-2 M and anandite-2 O shows that they possess unit cells (2 M setting) that have nearly equal a axes, unequal b and c axes, and β (anandite-2 M is smaller by 0.0371 A, larger by 0.08 A, and smaller by 0.089°, respectively). Moreover, anandite-2 O exhibits larger Fe3+-rich tetrahedral rings than anandite-2 M , which allow for a greater shift in Ba (difference of 0.03 A). The ordering and consequent absence of a twofold axis in anandite-2 M allows the in-phase wave structure of basal O atoms, which was previously thought only possible in the orthorhombic P cell.

We report vibrational predissociation spectra of the O n − , n = 3–10, 12 cluster ions in the 700–2400 cm−1 range. The odd numbered clusters are consistent with their identification as O 3 − ⋅ ( O 2 ) n . The even numbered clusters are based on the O 4 − core ion, where the first two O2 molecules add to O 4 − in locations that individually break the symmetry of the core ion, but together restore this symmetry. Beyond O 4 − ⋅ ( O 2 ) 2 , subsequent O2 attachment yields bands close to that of neutral O2, indicating that the special character of the O 4 − ⋅ ( O 2 ) 2 cluster is retained.

The thermochemistry of the carbon clusters C$_n$ (n=2--10) has been revisited by means of W4 theory and W3.2lite theory. Particularly the larger clusters exhibit very pronounced post-CCSD(T) correlation effects. Despite this, our best calculated total atomization energies agree surprisingly well with 1991 estimates obtained from scaled CCD(ST)/6-31G* data. Accurately reproducing the small singlet-triplet splitting in C$_2$ requires inclusion of connected quintuple and sextuple excitations. Post-CCSD(T) correlation effects in C$_4$ stabilize the linear form. Linear/cyclic equilibria in C$_6$, C$_8$, and C$_{10}$ are not strongly affected by connected quadruples, but they are affected by higher-order triples, which favor polyacetylenic rings but disfavor cumulenic ones. Near the CCSD(T) basis set limit, C$_{10}$ does undergo bond angle alternation in the bottom-of-the-well structure, although it is expected to be absent in the vibrationally averaged structure. The thermochemistry of these systems, and particularly the longer linear chains, is a particularly difficult test for density functional methods. Particularly for the smaller chains and the rings, double-hybrid functionals clearly outperform convential DFT functionals for these systems. Among compound thermochemistry schemes, G4 clearly outperforms the other members of the G$n$ family. Our best estimates for total atomization energies at 0 K should be reliable to 1 kJ/mol up to C$_5$ inclusive, and to better than 1 kcal/mol up to C$_9$ inclusive., Comment: [Mol. Phys., in press (Henry F. Schaefer III Festschrift)]

New uranyl vanadates A3(UO2)7(VO4)5O (M=Li (1), Na (2), Ag (3)) have been synthesized by solid-state reaction and their structures determined from single-crystal X-ray diffraction data for 1 and 3. The tetragonal structure results of an alternation of two types of sheets denoted S for ∞2[UO2(VO4)2]4− and D for ∞2[(UO2)2(VO4)3]5− built from UO6 square bipyramids and connected through VO4 tetrahedra to ∞1[U(3)O5-U(4)O5]8− infinite chains of edge-shared U(3)O7 and U(4)O7 pentagonal bipyramids alternatively parallel to a- and b-axis to construct a three-dimensional uranyl vanadate arrangement. It is noticeable that similar ∞[UO5]4− chains are connected only by S-type sheets in A2(UO2)3(VO4)2O and by D-type sheets in A(UO2)4(VO4)3, thus A3(UO2)7(VO4)5O appears as an intergrowth structure between the two previously reported series. The mobility of the monovalent ion in the mutually perpendicular channels created in the three-dimensional arrangement is correlated to the occupation rate of the sites and by the geometry of the different sites occupied by either Na, Ag or Li. Crystallographic data: 293 K, Bruker X8-APEX2 X-ray diffractometer equipped with a 4 K CCD detector, MoKα, λ=0.71073 A, tetragonal symmetry, space group P4¯m2, Z=1, full-matrix least-squares refinement on the basis of F2; 1, a=7.2794(9) A, c=14.514(4) A, R1=0.021 and wR2=0.048 for 62 parameters with 782 independent reflections with I⩾2σ(I); 3, a=7.2373(3) A, c=14.7973(15) A, R1=0.041 and wR2=0.085 for 60 parameters with 1066 independent reflections with I⩾2σ(I).

Recently, it has been shown that for any higher order pushdown system $\mathcal{H}$ and for any regular set $\mathcal{C}$ of configurations, the set $pre^{\ast}_\mathcal{H}(\mathcal{C})$, is regular. In this paper, we give an alternative proof of this result for second order automata. Our construction of automaton for recognizing $pre^{\ast}_\mathcal{H}(\mathcal{C})$ is explicit. The termination of saturation procedure used is obvious. It gives EXPTIME bound on size of the automaton recognizing $pre^{\ast}_\mathcal{H}(\mathcal{C})$ if there is no alternation present in $\mathcal{H}$ and in the automaton recognizing $\mathcal{C}$.

The structure and properties of the different linear, fan and cyclic isomers of CoC n + and CoC n − ( n = 1–8) clusters have been calculated using the B3LYP method with the 6–311+G(d) basis set. The stability of clusters as a function of the size has been discussed in terms of the incremental binding energies. Linear, fan and cyclic structures of CoC n + clusters show a clear even–odd alternation in stability, n -odd members being more stable than the corresponding n -even ones. An opposite parity effect is found for linear and fan CoC n − clusters, whereas the relative stability of cyclic isomers decrease with n . Linear structures are the most stable CoC n + and CoC n − clusters, with the only exception of CoC 2 +/− and CoC 7 − where the fan and cyclic arrangements are slightly lower in energy. The computed ionization potentials for the three structures show a clear even–odd alternation, with higher values for n -even clusters than for n -odd ones. Electron affinities for CoC n clusters increase along the series.

The monosignate character of resonance Raman optical activity (RROA) spectra has been often taken as granted in experimental and computational approaches, on the basis of basic theoretical approximations only considering resonance with a single electronic state of the molecule and the scattering process to be governed by the Franck-Condon mechanism. We show in this letter for the first time that, by resorting to a fully quantum mechanical (QM) methodology able to take into account all terms entering the general definition of RROA, and which considers excited state interference and Herzberg-Teller effects, sign alternation and at the same time intensity enhancement in RROA spectra is obtained. Such features constitute an important milestone toward the exploration of RROA of a wide range of chiral biological molecules.

International audience; Open shell singlet di- and multiradicals are of great importance in the framework of developing organic materials with enhanced nonlinear optical properties. We present here Hartree-Fock and DFT calculations of the structure and static second hyperpolarizabilty (γ) of the infinite periodic polymer containing stacked planar phenalenyl radicals. At the equilibrium geometry the oligomer structures are closed shell singlets with a significant alternation of the monomer-monomer distances in the stacking direction, thereby forming dimer units. However, the open shell singlet with reduced alternation becomes more favorable at chain lengths greater than about 40 dimer units. In the infinite polymer limit the alternation of stacking distance is essentially zero and the open shell singlet has intermediate diradical character, which is conducive to producing a high value of γ. DFT functionals, such as B3LYP and PBE0, largely overestimate the value of this property. However, a good estimate for the polymer γ = (1.0 ± 0.3) × 106 au per dimer is obtained by a hybrid approach wherein CCSD calculations for the dimer are combined with HF and LC-BLYP results for the polymer/dimer ratio. This value of γ is comparable to that found for the -(CH=CH)- unit of polyacetylene. An infinite polymer of stacked coronene molecules was also investigated, showing a considerably smaller enhancement of γ with respect to the corresponding dimer. (Figure Presented). © 2016 American Chemical Society.

The structures and stabilities of TiCn+/− (n = 1–8) clusters have been studied by density functional theory (DFT) using the hybrid B3LYP functional. Molecular properties for three different isomers, linear, cyclic and fan species have been computed. The fan isomers, where the titanium atom interacts with the whole carbon chain, are predicted generally, to be more stable than both linear and cyclic structures. For linear and fan TiCn+/− isomers an even-odd alternation in stability is found, isomers with n-even being in general more stable than the adjacent n-odd numbered. The ionization potentials and electron affinities of linear and fan TiCn clusters also show an even–odd parity effect. Generally n-odd clusters have higher ionization potentials than the n-even ones whereas the electron affinities show an opposite alternation trend, n-even systems having higher values than the adjacent n-odd ones.

金沢大学総合メディア基盤センター, We study the effect of step permeability on step instabilities on a growing vicinal face. When alternation of kinetic coefficients is taken into account, pairing of steps occurs on the vicinal face. Irrespective of the step permeability, the step pairs are stable for a wandering instability. The bunching of step pairs occurs if the steps are impermeable. The bunch size increases with time as tβ with β=1/2, which does not depend on the form of the repulsive interaction potential between steps. The repulsion influences the relation between the step distance in a bunch and the bunch size. When the repulsive potential ζ with the step distance l is given by ζ l-ν, the average step distance l in a bunch decreases as l ∼ N-α with α=1/(ν+1). The exponents, β and α are the same as those in the bunching induced by the Ehrlich-Schowebel effect in growth. © 2007 EDP Sciences/Società Italiana di Fisica/Springer-Verlag.

The cancrinite–sodalite group includes about 30 minerals, which are being studied in depth owing to their adsorption and ion-exchange properties. The minerals consist of a framework of Si and Al tetrahedra combined into six-membered rings. The rings of the same level along z are linked not to each other but to rings of neighbor levels shifted by 1/3 along x and y . The succession of alternation of rings is designated by letters A , B , and C , where A designates the rings around the axis [2/3 1/3 z ] ; B , around [1/3 2/3 z ]; and C , around [0 0 z ]. Minerals with 2 to 28 layers, which correspond to parameters with c ~ 5–74 A, are known in this group. The channels and cages within the framework are occupied by large cations and anions (monoand/or multiatom), while some minerals also include the water molecules. As is accepted for zeolites, the cages and chanCrystal Structure of Alloriite R. K. Rastsvetaeva a , A. G. Ivanova a, N. V. Chukanov b , and I. A. Verin a

The crystal structure of the A -site deficient perovskite Ln 1/3 NbO 3 ( Ln =Nd, Pr) at room temperature has been determined, for the first time, as orthorhombic in space group Cmmm using high-resolution neutron powder diffraction. Pertinent features are the alternation of unoccupied layers of A -sites and layers partly occupied by Ln cations, as well as out-of-phase tilting of the NbO 6 octahedra around an axis perpendicular to the direction of the cation/vacancy ordering. The phase transition behaviour of Nd 1/3 NbO 3 has also been studied in situ. This compound undergoes a continuous phase transition at around 650 °C to a tetragonal structure in space group P 4/ mmm due to the disappearance of the octahedral tilting. The analysis of spontaneous strains shows that this phase transition is tricritical in nature.

Let an $(r, s)$-formation be a concatenation of $s$ permutations of $r$ distinct letters, and let a block of a sequence be a subsequence of consecutive distinct letters. A $k$-chain on $[1, m]$ is a sequence of $k$ consecutive, disjoint, nonempty intervals of the form $[a_{0}, a_{1}] [a_{1}+1, a_{2}] \ldots [a_{k-1}+1, a_{k}]$ for integers $1 \leq a_{0} \leq a_{1} < \ldots < a_{k} \leq m$, and an $s$-tuple is a set of $s$ distinct integers. An $s$-tuple stabs an interval chain if each element of the $s$-tuple is in a different interval of the chain. Alon et al. (2008) observed similarities between bounds for interval chains and Davenport-Schinzel sequences, but did not identify the cause.We show for all $r \geq 1$ and $1 \leq s \leq k \leq m$ that the maximum number of distinct letters in any sequence $S$ on $m+1$ blocks avoiding every $(r, s+1)$-formation such that every letter in $S$ occurs at least $k+1$ times is the same as the maximum size of a collection $X$ of (not necessarily distinct) $k$-chains on $[1, m]$ so that there do not exist $r$ elements of $X$ all stabbed by the same $s$-tuple.Let $D_{s,k}(m)$ be the maximum number of distinct letters in any sequence which can be partitioned into $m$ blocks, has at least $k$ occurrences of every letter, and has no subsequence forming an alternation of length $s$. Nivasch (2010) proved that $D_{5, 2d+1}(m) = \Theta( m \alpha_{d}(m))$ for all fixed $d \geq 2$. We show that $D_{s+1, s}(m) = \binom{m- \lceil \frac{s}{2} \rceil}{\lfloor \frac{s}{2} \rfloor}$ for all $s \geq 2$. We also prove new lower bounds which imply that $D_{5, 6}(m) = \Theta(m \log \log m)$ and $D_{5, 2d+2}(m) = \Theta(m \alpha_{d}(m))$ for all fixed $d \geq 3$.

The crystal structure of a specimen of `Pb-rich' chabournéite from Jas Roux, Hautes-Alpes, France, with the chemical formula obtained by electron microprobe analysis of Ag0.04 (1)Tl2.15 (2)Pb0.64 (1)Sb5.12 (1)As5.05 (1)S17.32 (5), has been solved by X-ray single-crystal diffraction on the basis of 36 550 observed reflections (withFo> 4σFo) with a finalR1= 0.074. Pb-rich chabournéite is triclinicP1, with unit-cell parametersa= 8.5197 (4),b= 42.461 (2),c= 16.293 (8) Å, α = 83.351 (2), β = 90.958 (2), γ = 84.275 (2)°,V= 5823 (3) Å3. Its structural formula is close to [Tl2(Pb0.8Tl0.1Sb1.1)](Sb4.1As4.9)S17, withZ= 8. Its crystal structure is formed by the alternation of two pairs of slabs along thebaxis, deriving from the SnS and PbS archetypes, respectively. 104 independent cation sites and 136 S sites occur in the unit cell. Slab interfaces show the alternation, alongc, of Tl sites, ninefold coordinated, with Pb, Sb or mixed/split (Pb,Sb) and (Pb,Tl) sites. Within the slabs, 72 independentM3+sites (M3+= As, Sb) occur. ConsideringM3+—S bond distances shorter than 2.70 Å,MS3triangular pyramidal groups are condensed according to variousMmSnchain fragments (`polymers'). The solution of the crystal structure of chabournéite allows its comparison with the closely related homeotypes protochabournéite and dalnegroite.

The ground-state structures of neutral, cationic, and anionic phosphorus clusters P(n), P(n)(+), and P(n)(-) (n = 3-15) have been calculated using the B3LYP/6-311+G* density functional method. The P(n)(+) and P(n)(-) (n = 3-15) clusters with odd n were found to be more stable than those with even n, and we provide a satisfactory explanation for such trends based on concepts of energy difference, ionization potential, electron affinity, and incremental binding energy. The result of odd/even alternations is in good accord with the relative intensities of cationic and anionic phosphorus clusters observed in mass spectrometric studies.