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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 construction of sophisticated, high-nuclearity polyhedral cages is an attractive yet challenging task in supramolecular chemistry. Herein we report the anion-coordination-driven assembly (ACDA) of a series of A2nL3n architectures ("A" denotes anion, L is ligand, n = 1, 2, 4) with a biphenylene-spaced bis-bis(urea) ligand including triple helicate A2L3 (H), tetrahedron A4L6 (T), and the octanuclear, bicapped trigonal antiprism (or parallelepiped) A8L12 (P). Among them, P is held by 96 hydrogen bonds, the largest number ever reported in a discrete polyhedron, and encapsulates multiple guests (three tetramethylammonium cations) in three compartments. Remarkably, multiple reversible transformations of these dynamic assemblies have been realized by alternation of the template guest, solvent, and concentration. Furthermore, a chiral ligand (L2S) with carbon stereocenters at both termini of the bis-bis(urea) backbone was designed and assembled with phosphate to form the enantio-pure triple helicate or tetrahedron. The chiral amplification effect in the tetrahedral complex is significantly larger than that in the triple helicate as a function of the point chirality.

The computer simulation methods have been applied to calculate structure and energy of symmetric tilt grain boundaries with the misorientation axis [100]. The calculations have been carried out with the use of the structural-vacancy model previously developed by the authors. The misorientation angles of grain boundaries of common type have varied from 0° up to 90° while the increment has amounted 1°. The the reciprocal density of the coincidence sites in special grain boundaries has amounted Σ ≤ 53. The calculations have been carried out with the use of the Morse pair potential and the Cleri–Rosato many-body potential. It is shown that the dependence of the energy of grain boundaries on the misorientation angle when calculated with different potentials has a similar form, and their structure does not depend on the choice of potential and is in good agreement with high-resolution electron microscopic images. Only one special grain boundary is distinguished on the energy curve which is Σ5(013). It has been found that the structure grain boundaries may be represented by a limited number of atomic groups that have been named basic structural units. The structure of low-angle grain boundaries with the misorientation angle less than 8° is described by alternation of basic structural units of D types and ideal crystal, while the structure of low-angle grain boundaries with the misorientation angle ranging from 8° up to 13° is described by alternation of structural units of C and D types, from 14° up to 23° – B and C types. High-angle grain boundaries in the range of misorientation angles from 24° up to 37° contain only of basic structural units of B types, from 38° to 50° – A and B, more than 50° – only A.

The crystal structure of arsenopalladinite, Pd8As2.5Sb0.5, from the Kaarreoja River, Inari commune, Finnish Lapland, Finland, was solved to R1 = 0.0451 on the basis of single-crystal X-ray diffraction data. The mineral is triclinic, space group P$\bar{1}$. The unit-cell parameters are: a = 7.3344(7), b = 7.3870(8), c = 7.5255(7) Å, α = 98.869(8), β = 102.566(8), γ = 119.096(11)°, V = 331.19(7) Å3 and Z = 2. The crystal structure of arsenopalladinite consists of an alternation of layers made by pnictogen (As, Sb) and layers made by palladium atoms stacked along the c axis. Arsenic and (As, Sb) nets exhibit a triangular topology (A and D nets), whereas palladium layers show triangular or pentagon–triangular nets (B and C nets). The unit-cell contains 6 layers, with the ABCDCBA stacking sequence. Although arsenopalladinite shows characteristics very similar (nets of the same topology) to the closely-related mineral mertieite-II, Pd8Sb2.5As0.5, it has a different stacking sequence.

The structural evolution of medium-sized anionic and neutral Au2Sin (n = 8–20) clusters is investigated by using density functional theory (DFT) calculations and CCSD(T) methods in combination with the particle swarm optimization (CALYPSO) global search algorithm. The geometries of anionic and neutral Au2Sin clusters change from exohedral to endohedral ones with the increasing cluster sizes, and the critical size of forming Au2-endohedral structures for both anionic and neutral clusters is confirmed to be n = 20, in which a C2h symmetric Au2-endohedral cage-like structure is observed. Anionic and neutral Au2Sin clusters are primarily dominated by prism-based geometries with most of them adopting different structural features. It is found that the two Au atoms prefer to occupy low coordination sites and interact with fewer Si atoms. The Au atoms carry negative charges because of the electron-transfer from Sin frameworks. Meanwhile, the two Au atoms have very weak interactions. The second-order energy differences and incremental binding energies of anionic and neutral Au2Sin clusters exhibit an odd–even alternation and Au2Si20−/0 clusters are proven to have the highest chemical stability among these Au–Si clusters. Interestingly, Au2Si8−, Au2Si9−, Au2Si13−, Au2Si15−, and Au2Si17− anions, along with Au2Si13, Au2Si14, and Au2Si17 neutrals, have multiplicity of structural forms and their low-lying isomers show dynamical fluxionality due to the low barrier energies.

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...

Alkyl chains of varied length and steric bulk are generally appended to π-conjugated chromophores to increase solubility. These alkyl chains also regulate many aspects of the solid-state packing an...

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

We propose a J-coupling alternation (JCA) value that is demonstrated to be a suitable parameter to evaluate the nuclear magnetic resonance (NMR) indirect spin–spin coupling constants (SSCCs) as a function of molecular properties of chains by increasing their length. As an application, we report a theoretical study of the SSCCs for the interactions between neighbor nuclei in increasingly patterned carbon chains within density functional theory. First, we examine the J-coupling constants between 1H and 13C nuclei (nJHC) considering the separation distance, as well as between two adjacent 13C nuclei (1JCC) considering their relative positions in polyynes and cumulenes. Further, we define and determine JCA in terms of the differences of 1JCC, which is investigated as a function of several molecular properties, e.g., cohesive energy, characteristic vibrational frequency, average polarizability, and energy gap of the systems. We also determine JCA for other types of carbon chains, such as diphenyl-capped polyyn...

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 growth patterns of anionic and neutral B4Sin (n = 4–15) clusters are investigated by using density functional theory (DFT) calculations combined with particle swarm optimization (CALYPSO) software. The geometries of anionic and neutral B4Sin clusters transform from exohedral to endohedral structures with the increasing cluster sizes. The B4Si14− anion size is critical for forming B4-endohedral structures for anionic clusters, while the B4Si15 neutral size is the threshold size for forming B4-endohedral structures for neutral clusters. Both anionic and neutral B4Sin (n = 4–15) clusters are primarily dominated by prism-based or bipyramid-based geometries. The global minima of anionic and neutral B4Sin clusters adopt different geometrical structures, except for anionic and neutral B4Si10. The binding energies, second-order energy differences, and incremental binding energies of B4Sin− clusters show an odd–even alternation with the growing number of Si atoms. The B atoms in B4Sin−/0 exhibit B–B single bonding and BB double bonding properties. The B atoms are found to carry more negative charges due to charge transfer from Sin frameworks to B atoms. Interestingly, the B4Si4− anion adopts a C2h symmetric bicapped tetragonal bipyramid with σ plus π double bonding characters and has the highest relative stability among the anionic clusters. The bonding interactions in B4Si4− are in the order of B–B > B–Si > Si–Si.

This study outlines the synthesis of four cocrystals of aliphatic dicarboxylic acids {pimelic acid to sebacic acid (HOOC–(CH2)n–COOH, n = 5, 6, 7 and 8)} and isonicotinamide in a ratio of 1 : 2. Further, the importance of stoichiometry of chemical components and complementary hydrogen bonds is emphasized by CSD analysis of 14 different cocrystals. Subsequently, the odd–even alternation in melting points of dicarboxylic acid and isonicotinamide cocrystals is studied. Cocrystals containing even dicarboxylic acids (diacids) show higher melting points than odd diacids.

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.

We study uniform approximation of real-valued functions f, f(∞) = 0, on ℝ+ and ℝ by real-valued simple partial fractions (the logarithmic derivatives of polynomials). We obtain a criterion for the best approximation on ℝ+ and ℝ in terms of the Chebyshev alternance. This criterion is similar to the known criterion on finite segments. For the problem of approximating odd functions on ℝ we construct an alternance criterion with a weakened condition on the poles of fractions. We present a criterion for the best approximation by simple partial fractions on ℝ+ and ℝ in terms of Kolmogorov. We prove analogs of the de la Vallee-Poussin alternation theorem.

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.

Single-molecule conductance generally decays exponentially with the length of the molecule when the transport mechanism is a coherent tunneling process. However, it was recently found that this length dependence can be reversed in linear conjugated molecules if the bond-length alternation is reversed. In this work we show that even-carbon cumulenes show this behavior as the bond lengths are reversed for the dominant π-system compared to the equivalent polyenes and polyynes. We explore the electronic origins of the reversed bond-length alternation in cumulenes and its relation to the length dependence of the electronic transmission. Through density functional theory and nonequilibrium Greens function calculations we predict that cumulenic wires have reverse decay of transmission with length; that is, the decay constant β is found to be negative. As a direct consequence of the reversed bond-length alternation, the electronic transmission increases with length as the highest occupied molecular orbital–lowest...

Reversible alternation between bipolar and unipolar resistive switching (RS) modes was observed by controlling voltage-polarity in Ag/MoS2/Au memory on polyethylene terephthalate (PET) substrate. The temperature-dependent low-resistance-state and Raman measurement indicated that Ag and sulphur vacancy (Vs)-based conductive filaments (CFs) were responsible for these two RS modes. The two kinds of CFs had different responses under positive read voltages. Thus, a new operation scheme of multilevel memory was demonstrated in which multiple states were distinguished by CF composition rather than resistance values. The memory capacity of the cell could be further extended by adjustments in CFs’ size in each mode. The RS performance of the device did not degrade under bending conditions even over 104 bending cycles, which indicated good mechanical flexibility. The present Ag/MoS2/Au memory has promise for future high-density flexible information storage.

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.

Three dimensional (3D) and two dimensional (2D) alternation growth was used to grow AlN epitaxial layers on sapphire substrates. AlN samples grown using this technique have higher crystalline quality and lower dislocation density than samples grown using only 3D or 2D growth modes as witnessed by the high-resolution X-ray diffraction. Smooth atomic terraces with root mean square roughness of 0.107 nm were observed using atomic force microscopy (AFM) when the 3D and 2D AlN were 75 nm and 425 nm, respectively. This sample possesses single crystallographic orientation along the c-axis identified by Raman spectroscopy. Furthermore, the 3D/2D alternating growth mode modulates internal stress in AlN epitaxial layer by adjusting 2D AlN thickness, and the mechanism was studied in detail.

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.

We design a one-dimensional chain of two different alternating three-dimensional elastic chiral unit cells. The chain’s topological band gap, a result of the alternation of unit cells combined with their chirality and an effective mirror symmetry, guarantees a protected edge state, corresponding to a localized twist mode with an eigenfrequency inside the one-dimensional band gap. A small axial modulation at the one end of the beam can excite this resonant twist mode at the other end of the beam, via evanescent modes in the gap. The topological robustness of the edge state allows us to add a micromirror to the other end of the beam, turning the arrangement into a resonant mechanical laser-beam scanner. Its scalable operation frequency makes it attractive for applications.

Amine-linked (C−NH) porous organic cages (POCs) are preferred over the imine-linked (C=N) POCs owing to their enhanced chemical stability. In general, amine-linked cages, obtained by the reduction of corresponding imines, are not shape-persistent in the crystalline form. Moreover, they require multistep synthesis. Herein, a one-pot synthesis of four new amine-linked organic cages by the reaction of 1,3,5-triformylphloroglucinol (Tp) with different analogues of alkanediamine is reported. The POCs resulting from the odd diamine (having an odd number of −CH2 groups) is conformationally eclipsed, while the POCs constructed from even diamines adopt a gauche conformation. This odd–even alternation in the conformation of POCs has been supported by computational calculations. The synthetic strategy hinges on the concept of Schiff base condensation reaction followed by keto–enol tautomerization. This mechanism is the key for the exceptional chemical stability of cages and facilitates their resistance towards acids and bases.

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

For simulating the performance of stainless steel reinforcement under temperature change in the tropical environment, passive behavior of 304 stainless steels was studied in the pore solutions under alternating-temperature condition. The results suggested that the passive films were more severely degraded under the higher frequency or the larger amplitude of temperature alternation. Local breakdown of passive film and cracks occurred in the films as the samples experienced the low amplitude and the high amplitude of temperature alternation, respectively. Furthermore, the rupture initially started in the inner Cr2O3 layer and then propagated into the outer iron oxides layer.

Neurodegenerative disorders (NDs) are characterized by dysfunction and loss of neurons associated with altered proteins that accumulate in the human brain and peripheral organs. Mitochondrial and Golgi apparatus (GA) dysfunctions are supposed to be responsible for various NDs. Damaged mitochondria do not produce sufficient adenosine triphosphate (ATP) and produce reactive oxygen species (ROS) and pro-apoptotic factors. Mitochondrial dysfunctions may be caused by various factors such as environmental causes, mutations in both nuclear or mitochondrial deoxyribonucleic acid (DNA), that code many mitochondrial components. Three factors that are mainly responsible for the morphological changes in GA are certain pathological conditions, drugs, and over expression of Golgi associated proteins. In this chapter, common aspects of mitochondrial and GA dysfunction concerned about NDs are summarized and described for Alzheimer's disease (AD), Parkinson's disease (PD), amyotrophic lateral sclerosis (ALS), and Huntington's disease (HD).

Multilayers of sulphur-based anchoring group linkers and CdSe nanocrystals (NCs) were realized on ITO substrate via layer-by-layer alternation. The materials were investigated by UV-vis and FTIR spectroscopy, photoluminescence and photoconductivity. We found that the change of NCs packing during the multilayers build-up produces a progressive increase of exciton delocalization. In fact during multilayer deposition the NCs first excitonic peak shifts progressively towards longer wavelengths. We found a linear relation between the optical bang gap shift ("?" E_gn) and the inverse of number of CdSe-NCs layers ( n ) for n > 2, in particular the decrease of its value for the infinite multilayer from the one of the solution (2.10 eV) goes from 18 meV for the 1,2-ethylene-bis(dithiocarbamate) (EDTC) linker to 66 meV for sulphide dianions, corresponding to an apparent increase of the exciton radius of 0.20 nm and 0.85nm respectively.

A new series of four D–A–D configured conjugated oligomers with H–type structure, possessing two thiophene–imidazo [2,1-b][1,3,4]thiadiazole branches and thiophene (TIT), thiophene–1,3,4-oxadiazole–thiophene (TITO), thiazolo [5,4-d]thiazole (TITz), phenyl–thiazolo [5,4-d]thiazole–phenyl (TIPTz) units as central core moieties were efficiently synthesized. These core moieties were specifically selected to increase the planarity, rigidity, stability, extend the π–conjugation and to understand the influence of central core on nonlinear absorption coefficient (βeff) and optical limiting behavior of the synthesized oligomers. The structure-property relationships of these oligomers were established by the optical absorption (UV–Vis), electrochemical (CV) and theoretical (DFT) studies. The “effective two–photon absorption” of oligomers was confirmed by single–beam Z–scan analysis. The exceptional increase in nonlinear response was achieved with the oligomers TITO and TIPTz with nonlinear absorption coefficient (βeff) of 1.62 and 2.71 × 10−10 m W−1, and limiting thresholds of 6.02 and 3.14 J cm−2, respectively, which suggest that these oligomers could be potent materials for practical applications in laser photonics.

Well-defined structure–property relationships offer a conceptual basis to afford a priori design principles to develop novel π-conjugated molecular and polymer materials for nonlinear optical (NLO) applications. Here, we introduce the bond ellipticity alternation (BEA) as a robust parameter to assess the NLO characteristics of organic chromophores and illustrate its effectiveness in the case of streptocyanines. BEA is based on the symmetry of the electron density, a physical observable that can be determined from experimental X-ray electron densities or from quantum-chemical calculations. Through comparisons to the well-established bond-length alternation and π-bond order alternation parameters, we demonstrate the generality of BEA to foreshadow NLO characteristics and underline that, in the case of large electric fields, BEA is a more reliable descriptor. Hence, this study introduces BEA as a prominent descriptor of organic chromophores of interest for NLO applications.

Owyheeite, Ag1.5Pb4.43Sb6.07S14, monoclinic and pseudo-orthorhombic, is invariably intimately twinned, and its structure displays an alternation of two types of unit order-disorder (OD) layers, with layer symmetries P (2/ n ) 2(1)/ m 2(1)/ m for the thicker OD layer, and P (1) 1 2(1)/ m for the three-times thinner OD layer. These layers occur in two orientations, indexed as (021) and (021) of the owyheeite lattice. Ambiguity in the orientation of the thinner OD layer after the thicker one leads to intimate twinning (stacking disorder). Pseudohexagonality of the lattice ( b × √3/2 ≈ c ) with two alternative sets of OD layers further complicates the twinning situation, which also can be described using a rod representation of the structure.

The variation of hardness as a function of the number of carbon atoms in α,ω-alkanedicarboxylic acids, C(N)H(2N-2)O4 (4≤N≤9), was examined by recourse to nanoindentation on the major faces of single crystals. Hardness exhibits odd-even alternation, with the odd acids being softer and the even ones harder; the differences decrease with increasing chain length. These variations are similar to those seen for other mechanical, physical, and thermal properties of these diacids. The softness of odd acids is rationalized due to strained molecular conformations in them, which facilitate easier plastic deformation. Relationships between structural features, such as interplanar spacing, interlayer separation distance, molecular chain length, and signatures of the nanoindentation responses, namely, discrete displacement bursts, were also examined. Shear sliding of molecular layers past each other during indentation is key to the mechanism for plastic deformation in these organic crystals.

Understanding the relationships between the molecular nonlinear optical (NLO) properties and the bond-length alternation (BLA) or π-bond-order alternation (BOA) along the molecular backbone of linear π-conjugated systems has proven widely useful in the development of NLO organic chromophores and materials. Here, we examine model polymethines to elucidate the reliability of these relationships. While BLA is solely a measure of molecular geometric structure, BOA includes information pertaining to the electronic structure. As a result, BLA is found to be a good predictor of NLO properties only when optimized geometries are considered, whereas BOA is more broadly applicable. Proper understanding of the distinction between BLA and BOA is critical when designing computational studies of NLO properties, especially for molecules in complex environments or in nonequilibrium geometries.

New layered structures corresponding to the general formula [PbBiO2]A(n+1)B(n)O(3n-1)Cl(2) Were prepared. Pb5BiFe3O10Cl2 (n = 3) and Pb5Bi2Fe4O13Cl2 (n = 4) are built as a stacking of truncated A(n+1)B(n)O(3n-1) perovskite blocks and alpha-PbO-type [A(2)O(2)](2+) (A = Pb, Bi) blocks combined with chlorine sheets. The alternation of these structural blocks can be represented as an intergrowth between the hematophanite and Sullen-type structural blocks. The crystal and-Magnetic structures of Pb5BiFe3O10Cl2 and Pb5Bi2Fe4O13Cl2 were investigated in the temperature range of 1.5-700 K using X-ray and neutron powder diffraction, transmission electron microscopy and Fe-57 Mossbauer spectroscopy. Both compounds crystallize in the I4/mmm space group with the unit cell parameters a approximate to a(p) approximate to 3.92 angstrom (a unit-cell parameter of the perovskite-structure), c approximate to 43.0 angstrom for the n = 3 member and c approximate to 53.5 angstrom for the n = 4 member. Despite the large separation between the slabs containing the Fe3+ ions (nearly 14 angstrom), long-range antiferromagnetic order sets in below similar to 600 K with the G-type arrangement of the Fe magnetic moments aligned along the c-axis. The possibility of mixing d(0) and d(n) cations at the B sublattice of these structures was also demonstrated by preparing the Ti-substituted n = 4 member Pb6BiFe3TiO13Cl2.

The new organic inorganic compound [C8H10NO]2CdCl4 crystallizes at room temperature in the orthorhombic system (CmCa space group) with the following unit cell parameters: a = 19.9803(5) A, b = 15.3829(3) A, c = 13.8168(3) A and Z = 8. The atomic arrangement can be described as an alternation of organic/inorganic layers along the a direction. The organic layer is built up by one type of [C8H10NO]+ cation and the inorganic layer is built up by isolated and distorted tetrahedral CdCl42− anions. The TGA–DTA curves revealed two endothermic peaks. The first peak may be due to a phase transition, while the second peak corresponds to the decomposition point. Additionally analysis of the dielectric constants e′ and e″ versus temperature at several frequencies shows a relaxation process which could be due to disorder in the lattice.

Pyrolytic graphite films prepared by means of microsplitting are studied. In the samples, the alternation of pentagonal and hexagonal symmetry planes is revealed. These graphite crystal states can be classified as mesoscopic fullerene-like structures.

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.