Reflection splitting-induced microstrain broadening

Crystal structure determination on the basis of powder diffraction data frequently involves the question how the given diffraction data with some appreciably hkl-dependent line broadening should be interpreted. In many cases, such line broadening may either: (i) reasonably well be reconciled with a certain high-symmetry structure model or (ii) with a variant of the former with lower symmetry crystal family, which frequently will give a somewhat better fit in Rietveld refinement. In this work, it is shown mathematically that symmetry reduction induced reflection spitting masked by other line broadening contributions, thus leading to some reflection splitting-induced line broadening, shows a similar hkl dependence as typically adopted for anisotropic microstrain broadening with respect to the high-symmetry structure. This implies that Rietveld refinement on the basis of the low-symmetry model (including typically isotropic line broadening) and on the basis of the high-symmetry model with anisotropic microstrain broadening can both lead to similar qualities of the fit. Hence, the refinement results for both possibilities should be carefully considered in combination with possibly available additional information (e.g. results of first-principles calculations) to arrive at adequate conclusions concerning the true symmetry of the material under investigation.

Isotropic Analysis of Line Vector Forces and its Application in the Type Synthesis of Redundantly Actuated 3-DOF Translational Parallel Mechanisms

The load-carrying capacity of a mechanism is closely related to its line vector force. This article presents a thorough isotropic analysis of line vector forces. The results show that the isotropic condition can be satisfied when the line vector forces are evenly distributed on a conical surface with a cone-top angle of 109.472 degrees. By combining the isotropic line vector forces, a method for the type synthesis of 3-DOF, redundantly actuated translational parallel mechanisms (PMs) is proposed, in which the arrangement of the active joints is taken into account in advance. Using this method, a kinematic chain with a twist system reciprocal to both the constraint and actuation wrenches is constructed firstly, and then the active joint reciprocal to the constraint wrenches but not to the actuation wrench is constructed. Thus, a series of typical redundantly actuated PMs with isotropic actuation forces are obtained. Finally, the 4-PRRR PM is analyzed as an example, and the results show that the isotropy of the load-carrying capacity can always be satisfied during its movement.

Foci of Algebraic Curves

Curves have always been part geometry. Initially, there were lines and circle, then it was added to a conic section and later, with the advent of analytic geometry, they added more complex curves. Particularly in a number of lines are algebraic curves that are described by algebraic equations. Curves found application mostly in mechanics. Today algebraic curves used in engineering and in mathematics, in number theory, knot theory, computer science, criminology, etc. With the bringing to account of complex numbers became possible to consider curves in the complex plane. It has expanded the horizons of geometry and enriched their knowledge on curves, particularly on algebraic curves. Our goal is to give a geometric picture of the foci of algebraic curves clearly show the position of the foci in the plane, show how the number of foci associated with a class curve. The solution of this problem we see in the application we have developed ways to visualize imaginary images to the study of foci and focal centers of algebraic curves. This article explains the concept of the foci of algebraic curves shows the basic principle of the curve-theory and offers a method for the identification of the foci. The geometric picture of the foci is shown in a diagram, which is putted together from two tables. One table shows the real curve with her foci, the other table shows an imaginary cut of the curve, on which the isotropic line contacts the cut and under them intersects in a real point. The point is a focal point of the real curve. This project shows 16 diagrams for conic, cubes and quadrics.

Line-Shape Analyses of Solid-state 17O NMR Spectra for Hexagonal Ice

We present the results of experimental and theoretical investigations of line shapes in solid-state 17O NMR spectra of hexagonal ice, Ih. Stationary 17O NMR spectra of Ih at temperatures from 143 to 280 K were obtained at 11.7 and 16.4 T. Line shapes changed drastically as the temperature was increased from 143 to 243 K; at 253 K and above, pseudo-isotropic line shapes appear, indicating the presence of reorientational motions. We find that Ratcliffe’s model, which involves twelve orientations and four-step jumps for water reorientational motions, is effective for analyzing the NMR spectra at temperatures below 243 K. The present analysis demonstrates that the isotropic line shapes arise from proton disorder with respect to the solid-state 17O NMR time scale, producing pseudoicosahedral motional averaging that can completely average out second-order quadrupole interactions.

Une formule intégrale reliée à la conjecture locale de Gross–Prasad

Let V be a vector space over a p-adic field F, of finite dimension, let q be a non-degenerate quadratic form over V and let D be a non-isotropic line in V. Denote by W the hyperplane orthogonal to D, and by G and H the special orthogonal groups of V and W. Let π, respectively σ, be an irreducible admissible representation of G(F) , respectively H(F) . The representation σ appears as a quotient of the restriction of π to H(F) with a certain multiplicity m(π,σ) . We know that m(π,σ)≤1 . We assume that π is supercuspidal. Then we prove a formula that computes m(π,σ) as an integral of functions deduced from the characters of π and σ. Let Π, respectively Σ, be an L-packet of tempered irreducible representations of G(F) , respectively H(F) . Here we use the sophisticated notion of L-packet due to Vogan and we assume some usual conjectural properties of those packets. A weak form of the local Gross–Prasad conjecture says that there exists a unique pair (π,σ)∈Π×Σ such that m(π,σ)=1 . Assuming that the elements of Π are supercuspidal, we prove this assertion.

NMR chemical shift of single-wall carbon nanotubes

We report calculation of the NMR chemical shift anisotropy (CSA) tensor →μ of single-wall carbon nanotubes, within the London approximation (ring currents contribution). Our results indicate that the isotropic line as measured by high resoultion experiments is splited about 11ppm between metallic and semiconductor nanotubes. We carefully check that this result remains vaild and observable when the bundle packing is taken into account. The resulting broadening is aroune 20ppm, but reduces onto a sharp lorentzian (<1ppm) when averaging by high resoultion NMR measurements.

Paramagnetic defects in GaN

In this work, paramagnetic defects in wurtzite GaN crystals were systematically studied using the Electron Spin Resonance (ESR) technique and using electrical measurements. Three different resonance signals were found. The first had g|| = 1.9514 ± 0.0005 and g⊥ = 1.9486 ± 0.0005, a commonly observed defect in n-type crystals ascribed to the shallow donor of GaN [1]. The second ESR signal, an anisotropic line of g|| = 2.0728 ± 0.0015 and g⊥ = 1.9886 ± 0.0015, was observed only in Mg-doped p-type GaN layers, and was assigned to the Mg acceptor. The last ESR resonance signal, an isotropic line with g = 2.0026 ± 0.0005 was observed only in AMMONO GaN crystals after thermal annealing, as well as in Mg-doped GaN epitaxial layers. It was tentatively identified as due to a deep acceptor.

Aluminiumphosphate mit nichtzentrosymmetrischen Schicht-und Raumnetzstrukturen aus topologisch verwandten Motiven: 1. KAl2(PO4)2(OH)·4H2O/Aluminum Phosphates with Non-Centrosym metric Layer-and Framework-Structures of Topologically Related Motifs 1. KAl2(PO4)2(OH)·4H2O

KAl2(PO4)2(OH)·4H2O could be obtained by the reaction of gibbsite with a potassium-phosphate solution of pH = 5.5 at 333 K. A single crystal X-ray structure analysis showed that KAl2(PO4)2(OH)·4H2O is isotypic with the mineral minyulite. Crystal data: orthorhombic space group Pba2, a = 934.7(1), b = 982, 1 (1), c = 551,0(1) pm, Z = 2. It possesses dimeric units of Al-octahedra which are bridged by an OH-and two bidentate phosphate groups. The dimers are linked by phosphate to plane polar layers. Cavities in the layers are occupied by K ions. One corner of each phosphate tetrahedron is not connected to Al but accepts four hydrogen bonds from water molecules bound to Al of the adjacent layer. A powder neutron scattering experiment with KAl2(PO4)2(OD)·4D2O showed that four D atoms and P coordinate the hydrogen bond accepting O in KAl2(PO4)2(OD)·4D2O like a square pyramid. Analogous dimeric building units are found in the Al phosphate minerals minyulite and morinite; similar dimers of Fe octahedra occur in the mineral copiapite, a number of Fe containing enzymes and numerous synthetic iron complexes.High-resolution 31P solid-state NMR spectra show only one isotropic line at δiso = -9.6 ppm and confirm the presence of one symmetry independent phosphorus site in the unit cell. In the 1H-MAS-NMR spectra the water molecules and the bridging OH groups show signals at 5.4 and 1.4 ppm, respectively