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In order to analyze the trap in the multi-quantum well (MQW) consisting of a GaN–InGaN pair, the extraction of the location and energy level of the trap using random-telegraph-noise experiment was presented. Through the simplification of the band diagram of the complex MQW into an approximate structure, the equation for the location and the energy level of the trap was expressed as simply as possible. As a result of the extraction, we found that the traps of each sample are located very close to p-GaN or n-GaN interfaces. [ABSTRACT FROM AUTHOR]

By means of chemical and X-ray phase analysis with the use of a rotating disc electrode, it is found that the dissolution of Mg-Cu and In-Bi intermetallic compounds proceeds via magnesium ionization and subsequent $Mg_2 Cu\xrightarrow[{ - Mg^{2 + } }]{}MgCu_2 $ and $In_2 Bi\xrightarrow[{ - In^{3 + } }]{}InBi$ InBi phase regrouping. It is postulated that the process is accompanied by the formation of a defective crystal lattice and the appearance of reactive clusters, which interact to produce, at first, nuclei of a new phase and, then, the crystal lattice of a new intermetallic compound that is enriched in the electrochemically less active component. [ABSTRACT FROM AUTHOR]

Novel photocatalysts Y2MSbO7 (M = Ga, In, Gd) were synthesized by the solid state reaction method for the first time. A comparative study on the structural and photocatalytic properties of Y2MSbO7 (M = Ga, In, Gd) was reported. The results showed that Y2GaSbO7, Y2InSbO7 and Y2GdSbO7 crystallized with the pyrochlore-type structure, cubic crystal system, and space group Fd3m. The lattice parameter for Y2GaSbO7 was 10.17981 Å. The lattice parameter for Y2InSbO7 was 10.43213 Å. The lattice parameter for Y2GdSbO7 was 10.50704 Å. The band gap of Y2GaSbO7 was estimated to be 2.245 eV. The band gap of Y2InSbO7 was 2.618 eV. The band gap of Y2GdSbO7 was 2.437 eV. For the photocatalytic water-splitting reaction, H2 or O2 evolution was observed from pure water with Y2GaSbO7, Y2InSbO7 or Y2GdSbO7 as catalyst under visible light irradiation. (Wavelength > 420 nm). Furthermore, H2 and O2 were also evolved by using Y2GaSbO7, Y2InSbO7 or Y2GdSbO7 as a catalyst from CH3OH/H2O and AgNO3/H2O solutions, respectively, under visible light irradiation (λ > 420 nm). Y2GaSbO7 showed the highest activity compared with Y2InSbO7 or Y2GdSbO7. At the same time, Y2InSbO7 showed higher activity compared with Y2GdSbO7. The photocatalytic activities were further improved under visible light irradiation with Y2GaSbO7, Y2InSbO7 or Y2GdSbO7 being loaded by Pt, NiO or RuO2. The effect of Pt was better than that of NiO or RuO2 for improving the photocatalytic activity of Y2GaSbO7, Y2InSbO7 or Y2GdSbO7. [ABSTRACT FROM AUTHOR]

A modified algorithm for X-ray dynamical diffraction theory is presented for curved boundary crystals and a detailed description of the numerical procedure is given. The simulated and experimental results both show an anomalous focusing behavior in a curved multi-plate crystal cavity of silicon under the back-diffraction condition at a photon energy of 14.4388 keV. The focusing effects are analyzed, within the framework of the dynamical theory of X-ray diffraction, from the excitation of the dispersion surface and modification of the index of refraction with respect to the non-plane-parallel boundaries of a curved crystal cavity. [ABSTRACT FROM AUTHOR]

All homogeneous sphere packings and all interpenetrating layers of spheres were derived that can be realized in the ten orthorhombic trivariant lattice complexes belonging to the space groups of crystal class mmm without mirror symmetry. Altogether, sphere packings of 186 different types have been found; the maximal inherent symmetry is orthorhombic for 124 of these types. In addition, ten types of interpenetrating sphere packings were detected, and in three lattice complexes interpenetrating 63 nets occur. [ABSTRACT FROM AUTHOR]

Spectral dispersion of the polarization states occurs after passage of linearly polarized light through a thin layer of a chiral nematic crystal along the helical axis. It is clearly pronounced for crystals with a high optical anisotropy and a helical pitch somewhat larger than the light wavelength. The results of numerical analysis of the spectral dependence of polarization states at the output of the liquid crystal layer and the method for compensating for the dispersion are presented for the first time. It is shown that polarization dispersion can be eliminated using phase plates of two types, one of which should have a high anomalous birefringence dispersion. The possibility of developing fast light modulators operating in a wide spectral range is discussed. [ABSTRACT FROM AUTHOR]

Copyright of Symmetry (20738994) is the property of MDPI and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A new trinuclear Cd (II) complex [Cd3(L)6(2,2-bipyridine)3] [L = N-phenylsulfonyl-L-leucinato] has been synthesized and characterized by elemental analysis, IR and X-ray single crystal diffraction analysis. The results show that the complex belongs to the orthorhombic, space group P212121 with a = 16.877(3) Å, b = 22.875(5) Å, c = 29.495(6) Å, α = β = γ = 90°, V = 11387(4) Å3, Z = 4, Dc= 1.416 μg.m-3, μ = 0.737 mm-1, F (000) = 4992, and final R1 = 0.0390, ωR2 = 0.0989. The complex comprises two seven-coordinated Cd (II) atoms, with a N2O5 distorted pengonal bipyramidal coordination environment and a six-coordinated Cd (II) atom, with a N2O4 distorted octahedral coordination environment. The molecules form one dimensional chain structure by the interaction of bridged carboxylato groups, hydrogen bonds and p-p interaction of 2,2-bipyridine. The luminescent properties of the Cd (II) complex and N-Benzenesulphonyl-L-leucine in solid and in CH3OH solution also have been investigated [ABSTRACT FROM AUTHOR]

The results of studying the effect of grain-boundary diffusion acceleration during the annealing of submicrocrystalline (SMC) materials prepared by severe plastic deformation techniques are described. It is shown that the grain-boundary diffusion coefficient during recrystallization of SMC materials depends on the density of lattice dislocations and the pattern and rate of migration of the grain boundaries. It is found that, in SMC metals that undergo anomalous grain growth during annealing, the grain-boundary diffusion coefficient increases and its activation energy decreases. In SMC materials in which the recrystallization process exhibits conventional behavior, the diffusion properties of grain boundaries hardly differ from the equilibrium properties. Expressions describing the dependence of the grain-boundary diffusion coefficient on the migration rate of grain boundaries, as well as the thermodynamic and crystallographic parameters of the material, are derived. The calculation results are compared with the experimental data. [ABSTRACT FROM AUTHOR]

This paper introduces the idea of a maniplex, a common generalization of map and of polytope. The paper then discusses operators, orientability, symmetry and the action of the symmetry group. [ABSTRACT FROM AUTHOR]

For a suitable sequence of Weyl group elements {w(l)}l≥0 we give explicit combinatorial descriptions of the crystals Bw(l)(kΛ0) for the Demazure modules Vw(l)(kΛ0) of the quantum affine Lie algebra $U_q(\widehat{sl}(n))$ in terms of extended Young diagrams. [ABSTRACT FROM AUTHOR]

To evaluate the efficiency of reinforcing layers in pulsed magnets with different reinforcing materials, reinforcement methods, and sizes by the same standard, evaluation indexes of reinforcement, Reinforcement Ratio (RR) and material Utilization Ratio (UR), are introduced. The RR is used to evaluate the reinforcing ability of a reinforcing layer, and the UR is used to indicate the material utilization ratio of a reinforcing layer. The approximate analytical formulas of RR and UR are derived in the approximation of zero axial stress. Both the approximate formulas can reflect the effects of the radius, thickness of reinforcing layer, and the anisotropy of the reinforcing materials. Two examples about optimizing the magnet design using the indexes are discussed. One is about poly-layer reinforcement scheme for pulsed magnets, which can utilize reinforcement material effectively. The indexes are used to determine the thickness of each layer with different reinforcing materials in this scheme. The other is about dividing conductor layer into thinner layers, which is an effective method for reducing the peak stress in the reinforcing layer, the indexes are applied to optimize the number of layer division. [ABSTRACT FROM PUBLISHER]

This article briefly summarizes the ideal structure-factor statistics, which are usually the only ones that are applied at the stage of resolution of space-group ambiguities, and points out their disadvantages. Next, the non-ideal structure-factor statistics, i.e. those taking any atomic composition into account, are summarized and applied to several examples, based on real intensity data. The superiority of the non-ideal statistics, when applied to the problematic space group , is obvious. It is also shown that statistics for some orthorhombic space groups are rather insensitive to atomic heterogeneity. A table of coefficients is presented from which non-ideal statistics can be computed for all the space groups of the triclinic, monoclinic and orthorhombic systems. [ABSTRACT FROM AUTHOR]

The reaction of Tb(NO) · 6HO with 1,3-bis(1,3-dimethyl-1 H-pyrazol-4-yl)-1,3-propanedi-one (HL) and 1,10-phenanthroline (Phen) in the presence of NaOH in a water-alcohol medium afforded the neutral complex [Tb(L)(Phen)] ( I). The unstable adduct [Tb(L)(Phen)] · 0.4 MeCN ( II), whose structure is studied by X-ray diffraction analysis, is obtained from an acetonitrile solution. The crystals of compound II at 100 K are triclinic, a = 11.2508(13), b = 11.4246(14), c = 22.486(3) Å, α = 96.522(2)°, β = 91.578(2)°, γ = 110.073(2)°, V = 2690.3(5) Å, space group P $$\bar 1$$, Z= 2, R = 0.0433. The complex is characterized by the green luminescence (λ = 380 nm, λ = 550 nm). [ABSTRACT FROM AUTHOR]

In 2006 Guo, Labate, Lim, Weiss, and Wilson introduced the theory of MRA composite dilation wavelets. We continue their work by studying the filter properties of such wavelets and present several important examples. [ABSTRACT FROM AUTHOR]

This is an expository article on modern crystallography based on discrete geometric analysis, a hybrid field of several traditional disciplines: graph theory, geometry, theory of discrete groups, and probability, which has been developed in the last decade. The mathematical part relying on algebraic topology is fairly elementary, but may be still worthwhile for crystallographers who want to learn how well-established mathematics is effectively used in the practical science. A brief history of crystallography is also explained. [ABSTRACT FROM AUTHOR]

X-ray diffraction and magnetic measurements of R2Ni2—xIn (R = Ho, Dy, x = 0.3 and R = Gd, Tb, Er, x = 0.22) compounds are reported. The compounds crystallize in the tetragonal Mo2FeB2-type crystal structure (space group P4/mbm). Magnetic measurements reveal antiferromagnetic order with the Néel temperatures TN equal to 26.4 K (Gd), 20.2 K (Tb), 8.3 K (Dy), 7.1 K (Ho), and 6.3 K (Er). For R = Gd, Tb and Er an additional phase transition below TN is observed at 13.5, 13.1, and 5.0 K, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we establish regularity and uniqueness for solutions to density dependent nematic liquid crystals systems. The results presented extend the regularity and uniqueness for constant density liquid crystals systems, obtained by Lin and Liu (1995 Commun. Pure Appl. Math. XLVIII 501-37). [ABSTRACT FROM AUTHOR]

Copyright of Visión Electrónica is the property of Fondo de Universidad Distrital Francisco Jose de Caldas and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A Sudoku grid is a constrained Latin square. In this paper a reduced Sudoku grid is described, the properties of which differ, through necessity, from that of a reduced Latin square. The Sudoku symmetry group is presented and applied to determine a mathematical relationship between the number of reduced Sudoku grids and the total number of Sudoku grids for any size. This relationship simplifies the enumeration of Sudoku grids and an example of the use of this method is given. [ABSTRACT FROM AUTHOR]

The crystal structure of the manganese phosphate mineral gatehouseite, ideally Mn2+5(PO4)2(OH)4, space group P212121, a= 17.9733(18), b= 5.6916(11), c= 9.130(4) Å, V= 933.9(4) Å3, Z= 4, has been solved by direct methods and refined from single-crystal X-ray diffraction data (T= 293 K) to an Rindex of 3.76%. Gatehouseite is isostructural with arsenoclasite and with synthetic Mn2+5(PO4)2(OH)4. The structure contains five octahedrally coordinated Mn sites, occupied by Mn plus very minor Mg with observed distances from 2.163 to 2.239 Å. Two tetrahedrally coordinated P sites, occupied by P, Si and As, have distances of 1.559 and 1.558 Å. The structure comprises two types of building unit. A strip of edge-sharing Mn(O,OH)6octahedra, alternately one and two octahedra wide, extends along [010]. Chains of edge- and corner-shared Mn(O,OH)6octahedra coupled by PO4tetrahedra extend along [010]. By sharing octahedron and tetrahedron corners, these two units form a dense three-dimensional framework, which is further strengthened by weak hydrogen bonding. Chemical analyses by electron microprobe gave a unit formula of (Mn4.99Mg0.02)Σ5.01(P1.76Si0.20As0.07)Σ2.03O8(OH)3.97. [ABSTRACT FROM AUTHOR]

The aim of this article is to propose a mathematical model describing the electronic structure of crystals with local defects in the framework of the Thomas-Fermi-von Weizsäcker (TFW) theory. The approach follows the same lines as that used in Cancès et al. (Commun Math Phys 281:129-177, ) for the reduced Hartree-Fock model, and is based on thermodynamic limit arguments. We prove, in particular, that it is not possible to model charged defects within the TFW theory of crystals. [ABSTRACT FROM AUTHOR]

We give a full description of the finite symmetry groups of the cut-and-project model for three-dimensional quasicrystals under the assumption that the phase space dimension is at most 3. [ABSTRACT FROM AUTHOR]

A new method for pure modes of elastic waves search in crystals is presented. The method is based on the analysis of 3D-surfaces of phase velocities and differs from the known analogous methods by accounting for the piezoeffect. The piezoelectric corrections have an essential effect on the result of the search. The computer code is prepared to construct these surfaces and their sections by the base planes of a crystal. The code also permits to calculate the directions of pure longitudinal and pure transverse elastic wave propagation on these surfaces. [ABSTRACT FROM AUTHOR]

Variation in the density of clay minerals with a crystal lattice that swells during hydration is examined. It is demonstrated that greatest intracrystal swelling is attained at the maximum hygroscopic moisture content, involving a reduction to 49% in the density of the solid component. The concept of intracrystal ultramicroporosity n is introduced. The values of n, which must be considered for solution of practical problems, is analyzed. [ABSTRACT FROM AUTHOR]

The article discusses the study on the various atomic resolution imaging technologies which are used to probe the atomic structure of matter. It highlights several electron microscopy technologies including transmission electron microscopy (TEM), high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM), and scanning confocal electron microscopy (SCEM). It discusses mathematical crystallography, electron scattering, and electron microscopy.

The article discusses the study on the Bayesian algorithms in relation to X-ray free-electron lasers that is used to determine the structure of individual particles in relation to crystallography. It states that these lasers are part of femtosecond lasers which has the potential to take single-shot diffraction snapshots in an intense femtosecond pulse. It discusses mathematical crystallography, iterative algorithm, and diffraction pattern.

The article discusses the study on the radial integrals of the 5d transition metals' magnetic form factor in relation to crystallography. It mentions that radial wavefunctions from the pseudo-relativistic Hartfree-Fock method was used to calculate the radial integrals of several electronic configurations in the 5d electrons of the transition metal atoms and ions. It also discusses mathematical crystallography, diamagnetism, and ferromagnetism.

The article discusses the study on anisotropic extinction in crystallography. It mentions that a direct experiment approach was applied to this study which performed structure-factor measurements from a vanadium and a niobium crystal. It discusses mathematical crystallography, extrapolation, and body-centered cubic metals.

The article discusses the study on the mathematical aspects of crystal structure refinements, particularly its iteratively reweighted least squares. It states that this research aims at depicting the capability of a robust regression in providing accuracy and precision of the least-square estimates in crystal structure refinement. It discusses mathematical crystallography, robust statistics, and probability distribution functions.

The article discusses the study on the joint probability distribution functions which is applied to formulate a probabilistic analysis of the hybrid Fourier synthesis in crystallography. It states that this issue presents Fourier coefficients which are used in calculating any hybrid synthesis while electron-density maps are discussed. It discusses electron densities, atomic scattering factors, and mathematical crystallography.

The article discusses the mathematical aspects of molecular replacement (MR) and algebraic properties of motion spaces in a crystal. It states that MR is a method in X-ray crystallography which is used in phasing X-ray diffraction patterns for crystals with biological macromolecules. It discusses space groups, x-ray crystallography technique, and mathematical crystallography.

The article discusses the study on the shake-and-bake (SnB) direct methods program which is used in solving mathematical problems that are related with crystal structures. It states that the direct methods failure is due to the increasing number of phase trials in an attempt to seek a different starting set of phases which might lead to converge to the correct solution. It discusses convergence, variance analysis, and standard deviation.

The article discusses the study on space groups in symmetry matrices with elements 0 and ±1 and its properties and application to arithmetic symmetry of reduced lattices in crystals. It provides a complete geometric description which is analyzed as the practical framework in dealing with the symmetry of reduced lattices. It discusses matrices, consecutive powers, and mathematical crystallography.

In 2006 Guo, Labate, Lim, Weiss, and Wilson introduced the theory of MRA composite dilation wavelets. We continue their work by studying the filter properties of such wavelets and present several important examples. [ABSTRACT FROM AUTHOR]

We present an explicit difference operator diagonalized by the Macdonald polynomials associated with an (arbitrary) admissible pair of irreducible reduced crystallographic root systems. By the duality symmetry, this gives rise to an explicit Pieri formula for the Macdonald polynomials in question. The simplest examples of our construction recover Macdonald's celebrated difference operators and associated Pieri formulas pertaining to the minuscule and quasi-minuscule weights. As further by-products, explicit expansions, and Littlewood–Richardson type formulas are obtained for the Macdonald polynomials associated with a special class of small weights. [ABSTRACT FROM PUBLISHER]

We apply the group theory to Kadomtsev-Petviashvili-Burgers (KPBII) equation which is a natural model for the propagation of the two-dimensional damped waves. In correspondence with the generators of the symmetry group allowed by the equation, new types of symmetry reductions are performed. Some new exact solutions are obtained, which can be in the form of solitary waves and periodic waves. Specially, our solutions indicate that the equation may have time-dependent nonlinear shears. Such exact explicit solutions and symmetry reductions are important in both applications and the theory of nonlinear science. [ABSTRACT FROM AUTHOR]

Trianguline representations are a certain class of p-adic representations of Gal(Q̄p/Qp), like the crystalline, semistable and de Rham representations of Fontaine. Their definition involves the theory of (ϕ, Γ)-modules. In this survey, we explain the theory of (ϕ, Γ)-modules and the definition and properties of trianguline representations. After that, we give some examples of their occurrence in arithmetic geometry. [ABSTRACT FROM PUBLISHER]

The principle of operation of a crystalline temperature indicator for measuring the maximum temperature is described and examples of its application are given. The operation of the device is based on the expansion of the crystal lattice of diamond or silicon carbide under irradiation in a reactor and a decrease of this expansion depending on the duration and temperature of heating. The results obtained during flights of shuttle models Bor-4 and −5 are presented as examples of practical applications. In the tests, the temperature of the heat-shielding coatings intended for installation on the Buran shuttle was tested. Another example of an application is thermometry of the Siemens (Germany) GTX-800 power-generation turbine. In this case, the temperature of the working and guiding blades of different steps of the motor as well as the gas in direct proximity to the blades was measured. The temperature in the space behind a VVER-1000 vessel was measured with the sensor. [ABSTRACT FROM AUTHOR]

The structure of an orthorhmbic Al72Pd18Mn5Si5 phase was determined by single crystal X-ray diffraction: space group Pnma (No.148), a = 1.4396(3) nm, b = 2.4003(2) nm, c = 0.7603(2) nm, V = 2.6272(9) nm3, atoms/cell = 168, F(000) = 3341, μ = 7.355 mm-1, Dcalc = 4.613 Mgm-3, R(F) = 0.0312 for observed 3919 reflections measured by Mo-Kα radiation (λ = 0.071073 nm). The orthorhombic AlPdMnSi structure is well described by the stacking of a decagonal (0.72 nm) and pentagonal column (0.48 nm) along the b-axis. A new type of decagonal column structures with a periodicity of 1.2 nm (=0.48 + 0.72 nm) is proposed for the decagonal quasicrystals. [ABSTRACT FROM AUTHOR]

The structures of mono, di, and tri- O-methyl derivatives of 2,4,6-trinitrophloroglucinol were determined by single crystal X-ray diffraction. As the number of methoxy groups increased from one to three the unit cell volume increased at a rate greater than the formula weight of the asymmetric unit such that crystal density decreased from 1.823 to 1.619 Mg/m. The structural data reveal that the decreased density is related to increased angles between the plane of the phenyl ring and the planes defined by the nitro and methoxy groups, as well as fewer inter molecular interactions. Graphical Abstract: The structures of mono, di, and tri- O-methyl derivatives of 2,4,6-trinitrophloroglucinol were determined by single crystal X-ray diffraction. As the number of methoxy groups increased from one to three the unit cell volume increased at a rate greater than the formula weight of the asymmetric unit such that crystal density decreased from 1.823 to 1.619 Mg/m.[Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR]

We describe computer algorithms that produce the complete set of isohedral tilings by n-omino or n-iamond tiles in which the tiles are fundamental domains and the tilings have pmm, pmg, pgg or cmm symmetry [1]. These symmetry groups are members of the crystal class D2 among the 17 two-dimensional symmetry groups [2]. We display the algorithms' output and give enumeration tables for small values of n. This work is a continuation of our earlier works for the symmetry groups p3, p31m, p3m1, p4, p4g, p4m, p6, and p6m [3-5]. [ABSTRACT FROM AUTHOR]

The complex [Ni(En)][Ni(CN)] · 3.5HO ( I) (En = ethylenediamine) was synthesized by the reaction of [Ni(En)](ClO) and K[Ni(CN)] in an H-shaped tube. The crystal structure of I has been determined by single-crystal X-ray analysis. The crystal of complex I is orthorhombic, space group Pnna with a = 28.151(3), b = 8.3946(8), c = 14.5441(13)Å, M =404.76, Z = 8, V = 3437.0(5)Å. The structure of complex I reveals infinite zigzag chains shaped structure are formed by cis-Ni(En)-μ-(NC), cis-μ-(NC)Ni(CN), and trans-μ-(CN)Ni(En). [ABSTRACT FROM AUTHOR]

novel trinuclear manganese(II) complex, Mn(CHN)(CHO) ( I), has been hydrothermally synthesized and characterized by single-crystal X-ray diffraction. The crystal belongs to the monoclinic system, space group P2/ n, with cell parameters a = 12.1935(7), b = 19.0249(11), c = 18.0515(10)Å, β = 105.0430(10)°, V = 4044.1(4)Å, Z = 2. Two of the three manganese atoms in the crystal structure are crystallographically equivalent and adopt NO coordination mode, whereas the remaining manganese atom adopts O coordination mode, which forms a nearly regular octahedron. The experimental result of thermal analysis shows that complex I remains stable below 300°C. [ABSTRACT FROM AUTHOR]

Two new cobalt(III) and zinc(II) complexes, [Co(L) (HO)] · ClO ( I) and [Ni(L) (HO)] · 2ClO ( II), where L is the deprotonated form of 5-methoxy-2-[(2-morpholin-4-ylethylimino)methyl]phenol, and L is the zwitterionic form of 2-[(2-isopropylaminoethylimino)methyl]-5-methoxyphenol, were synthesized and structurally characterized by elemental analyses, IR spectra, and single-crystal X-ray diffraction. The crystal of I is monoclinic: space group P2/ c, a = 11.1512(4), b = 28.2424(11), c = 10.9655(4) Å, β = 95.746(2)°, V = 3436.1(2) Å, Z = 4. The crystal of II is triclinic: space group P2/ c, a = 8.1441(2), b = 10.4531(3), c = 10.8849(3) Å, α = 84.0240(10)°, β = 76.9800(10)°, γ = 74.2280(10)°, V = 867.92(4) Å, Z = 1. Complex I consists of a mononuclear cobalt(III) complex cation and a perchlorate anion. Complex II consists of a crystallographic centrosymmetric mononuclear nickel(II) complex cation and two perchlorate anions. Each metal atom in the complexes is in an octahedral coordination. [ABSTRACT FROM AUTHOR]

The article presents a study which aimed to show an exact geometric notation for conditions of asymmetric units. A cut notation was introduced to manage a concise representation of the definitions of direct-space asymmetric units (DAUs). The study was able to present a notation that serves as the basis for a reference table of accurate DAU explanations for the crystallographic space groups which totaled 230.

The article focuses on the creation of symmetric tessellations with the concept of orbifolds as artifacts. It mentions that symmetric tessellations could be examined through algebraic and geometric languages wherein in geometric language orbifolds could be viewed as artifacts that stamp the corresponding symmetric design. It adds that tessellation was a design consisting of one or more types of tiles with 17 crystallographic groups in determining the possible tessellations of Eclidean plane.

Atom probe tomography (APT) represents a significant step toward atomic resolution microscopy, analytically imaging individual atoms with highly accurate, though imperfect, chemical identity and three-dimensional (3D) positional information. Here, a technique to retrieve crystallographic information from raw APT data and restore the lattice-specific atomic configuration of the original specimen is presented. This lattice rectification technique has been applied to a pure metal, W, and then to the analysis of a multicomponent Al alloy. Significantly, the atoms are located to their true lattice sites not by an averaging, but by triangulation of each particular atom detected in the 3D atom-by-atom reconstruction. Lattice rectification of raw APT reconstruction provides unprecedented detail as to the fundamental solute hierarchy of the solid solution. Atomic clustering has been recognized as important in affecting alloy behavior, such as for the Al-1.1Cu-1.7Mg (at. %) investigated here, which exhibits a remarkable rapid hardening reaction during the early stages of aging, linked to clustering of solutes. The technique has enabled lattice-site and species-specific radial distribution functions, nearest-neighbor analyses, and short-range order parameters, and we demonstrate a characterization of solute-clustering with unmatched sensitivity and precision. [ABSTRACT FROM AUTHOR]

The article proposes a cross-validation-based method to address estimation bias which applies a bias-correction parameter Β to maximum-likelihood phase-combination functions. It notes that an electron-density map can be improved by density modification (DM) by incorporating features that are expected to appear in the map. A likelihood function can be constructed in order to combine the experimental and modified phases optimally. Particular focus is also given to techniques that have been developed to reduce the bias.

The article discusses the algorithms which have led to the substantial improvements and performance of CRANK on more than 100 real data sets. CRANK is a software package aimed at providing a user-friendly and automated system with computational developments in stages of structure solution. SHELXC, SHELXE and DM are some of the externally developed program that CRANK can interface with. Developments in substructure determination, substructure phasing and density modification are also mentioned.