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## Tensor Components (tensor + component)
## Selected Abstracts## Phase transition of L -Ser monohydrate crystal studied by 13C solid-state NMR, MAGNETIC RESONANCE IN CHEMISTRY, Issue 3 2006Tsunenori KamedaAbstract We used gravimetric analysis (GA) and 13C solid-state nuclear magnetic resonance (NMR) to study solid-phase transition from the transparent single crystal of L -serine (L -Ser) monohydrate to a turbid powder. We found that L -Ser monohydrate loses water molecules and transforms into an anhydrate, thus experimentally demonstrating Frey's assumption (Acta Cryst., B29, 876, 1973). Application of a handmade cross-polarization (CP) NMR probe with a saddle-type coil to the oriented crystal of the L -Ser monohydrate revealed the dehydration mechanism. Furthermore, the chemical shift tensor components of the carboxyl carbon in L -Ser monohydrate were determined. The difference in the tensor component of ,22 between the monohydrate and anhydrate forms was more than 7 ppm, probably owing to differences in the hydrogen-bonding structure of each form. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Identification of van Hove singularities in the GaN dielectric function: a comparison of the cubic and hexagonal phase PHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 7 2009C. CobetAbstract We present a detailed analysis of interband transition structures in the dielectric function of GaN. The dielectric function of the stable wurtzite and the metastable zinc blende phase were determined by means of synchrotron spectroscopic ellipsometry in the spectral range between 3 eV and 20 eV where the most significant structures of the dielectric function are located. In the hexagonal case, both the ordinary and extraordinary dielectric tensor component was measured on GaN films with M -plane/[1 00] orientation. In a comparative discussion of the two hexagonal tensor components and the zinc blende dielectric function, all prominent absorption structures were assigned to specific interband transitions at high symmetry points in the Brillouin zone. The assignment considers the individual dipole transition probabilities depending on the crystal symmetry and the geometry of the measurement. Furthermore, a detailed theoretical band-to-band analysis of dielectric function features, published by Lambrecht et al. [1], was considered. In conclusion, we suggest a new labeling of absorption structures as used in classical III,V materials like GaAs, which reflects the origin of transition structures from specific points in the respective Brillouin zones. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Influence of YAB:Cr3+ nanocrystallite sizes on two-photon absorption of YAB:Cr3+ PHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 13 2004A. MajchrowskiAbstract An influence of nanocrystalline sizes of YAB:Cr particles incorporated within olygoetheracrylate polymer matrix on the two-photon absorption was investigated. Maximal values of the two-photon absorption diagonal tensor component was observed at low temperatures (about 4.2 K) and corresponded to concentration of the YAB:Cr NC about the 3% by weight and about 22 nm in sizes. The Cr3+ ions inside investigated NC play the crucial role in the observed nonlinear optical phenomena. The observed temperature dependence is explained within a model of anharmonic electron,phonon contribution in the nanocrystallites. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Magnetoelectric Memories,a Disruptive Techology? CHEMPHYSCHEM, Issue 11 2009FRS Prof., James F. ScottFlip-flop: Recently, a diode whose diode effect can switch direction under the influence of an external voltage was reported. The polarization data of this BiFeO3 indicate that the largest photovoltaic tensor component is diagonal (see picture). This exciting development is Highlighted herein. [source] ## Metric spaces in NMR crystallography CONCEPTS IN MAGNETIC RESONANCE, Issue 4 2009David M. GrantAbstract The anisotropic character of the chemical shift can be measured by experiments that provide shift tensor values and comparing these experimental components, obtained from microcrystalline powders, with 3D nuclear shielding tensor components, calculated with quantum chemistry, yields structural models of the analyzed molecules. The use of a metric tensor for evaluating the mean squared deviations, d2, between two or more tensors provides a statistical way to verify the molecular structure governing the theoretical shielding components. The sensitivity of the method is comparable with diffraction methods for the heavier organic atoms (i.e., C, O, N, etc.) but considerably better for the positions of H atoms. Thus, the method is especially powerful for H-bond structure, the position of water molecules in biomolecular species, and other proton important structural features, etc. Unfortunately, the traditional Cartesian tensor components appear as reducible metric representations and lack the orthogonality of irreducible icosahedral and irreducible spherical tensors, both of which are also easy to normalize. Metrics give weighting factors that carry important statistical significance in a structure determination. Details of the mathematical analysis are presented and examples given to illustrate the reason nuclear magnetic resonance are rapidly assuming an important synergistic relationship with diffraction methods (X-ray, neutron scattering, and high energy synchrotron irradiation). © 2009 Wiley Periodicals, Inc.Concepts Magn Reson Part A 34A: 217,237, 2009. [source] ## Dielectric Characteristics for Radio Frequency Waves in a Laboratory Dipole Plasma CONTRIBUTIONS TO PLASMA PHYSICS, Issue 4 2006N. I. GrishanovAbstract Transverse and parallel dielectric permittivity elements have been derived for radio frequency waves in a laboratory dipole magnetic field plasma. Vlasov equation is resolved for both the trapped and untrapped particles as a boundary value problem to define their separate contributions to the dielectric tensor components. To estimate the wave power absorbed in the plasma volume the perturbed electric field and current density components are decomposed in a Fourier series over the poloidal angle. In this case, the dielectric characteristics can be analyzed independently of the solution of the Maxwell's equations. As usual, imaginary part of the parallel permittivity elements is necessary to estimate the electron Landau damping of radio frequency waves, whereas imaginary part of the transverse permittivity elements is important to estimate the wave dissipation by the cyclotron resonances. Computations of the imaginary part of the parallel permittivity elements are carried out in a wide range of the wave frequencies. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Three-dimensional thermoelastic stresses in off-axis oriented single crystals with hexagonal symmetry CRYSTAL RESEARCH AND TECHNOLOGY, Issue 3 2007K. BöttcherAbstract A three-dimensional (3D) thermoelastic stress analysis is carried out on a single crystal with axisymmetric geometry but with a hexagonal crystallographic symmetry. The crystallographic orientation is off-axis with respect to the cylindrical coordinate system. By applying a Fourier series expansion with respect to the rotational angle , of the cylindrical coordinates, the 3D boundary value problem is reduced to a sequence of 2D ones on the meridian plane, which are solved by the finite-element method. In our example, the off-axis orientation is towards a direction of high symmetry, and therefore only four of the six stress tensor components are non-zero. In the end, the stress tensor is projected onto the slip system of the crystal. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Vertically fractured transversely isotropic media: dimensionality and deconstruction GEOPHYSICAL PROSPECTING, Issue 2 2009Michael A. SchoenbergABSTRACT A vertically fractured transversely isotropic (VFTI) elastic medium is one in which any number of sets of vertical aligned fractures (each set has its normal lying in the horizontal x1, x2 -plane) pervade the medium and the sets of aligned fractures are the only features of the medium disturbing the axi-symmetry about the x3 -axis implying that in the absence of fractures, the background medium is transversely isotropic (TI). Under the assumptions of long wavelength equivalent medium theory, the compliance matrix of a fractured medium is the sum of the background medium's compliance matrix and a fracture compliance matrix. For sets of parallel rotationally symmetric fractures (on average), the fracture compliance matrix is dependent on 3 parameters , its normal and tangential compliance and its strike direction. When one fracture set is present, the medium is orthorhombic and the analysis is straightforward. When two (non-orthogonal) or more sets are present, the overall medium is in general elastically monoclinic; its compliance tensor components are subject to two equalities yielding an 11 parameter monoclinic medium. Constructing a monoclinic VFTI medium with n embedded vertical fracture sets, requires 5 TI parameters plus 3×n fracture set parameters. A deconstruction of such an 11 parameter monoclinic medium involves using its compliance tensor to find a background transversely isotropic medium and several sets of vertical fractures which, in the long wavelength limit, will behave exactly as the original 11 parameter monoclinic medium. A minimal deconstruction, would be to determine, from the 11 independent components, the transversely isotropic background (5 parameters) and two fracture sets (specified by 2 × 3 = 6 parameters). Two of the background TI medium's compliance matrix components are known immediately by inspection, leaving nine monoclinic components to be used in the minimal deconstruction of the VFTI medium. The use of the properties of a TI medium, which are linear relations on its compliance components, allows the deconstruction to be reduced to solving a pair of non-linear equations on the orientations of two fracture sets. A single root yielding a physically meaningful minimum deconstruction yields a unique minimal representation of the monoclinic medium as a VFTI medium. When no such root exists, deconstruction requires an additional fracture set and uniqueness is lost. The boundary between those monoclinic media that have a unique minimal representation and those that do not is yet to be determined. [source] ## Phase transition of L -Ser monohydrate crystal studied by 13C solid-state NMR, MAGNETIC RESONANCE IN CHEMISTRY, Issue 3 2006Tsunenori KamedaAbstract We used gravimetric analysis (GA) and 13C solid-state nuclear magnetic resonance (NMR) to study solid-phase transition from the transparent single crystal of L -serine (L -Ser) monohydrate to a turbid powder. We found that L -Ser monohydrate loses water molecules and transforms into an anhydrate, thus experimentally demonstrating Frey's assumption (Acta Cryst., B29, 876, 1973). Application of a handmade cross-polarization (CP) NMR probe with a saddle-type coil to the oriented crystal of the L -Ser monohydrate revealed the dehydration mechanism. Furthermore, the chemical shift tensor components of the carboxyl carbon in L -Ser monohydrate were determined. The difference in the tensor component of ,22 between the monohydrate and anhydrate forms was more than 7 ppm, probably owing to differences in the hydrogen-bonding structure of each form. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Identification of van Hove singularities in the GaN dielectric function: a comparison of the cubic and hexagonal phase PHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 7 2009C. CobetAbstract We present a detailed analysis of interband transition structures in the dielectric function of GaN. The dielectric function of the stable wurtzite and the metastable zinc blende phase were determined by means of synchrotron spectroscopic ellipsometry in the spectral range between 3 eV and 20 eV where the most significant structures of the dielectric function are located. In the hexagonal case, both the ordinary and extraordinary dielectric tensor component was measured on GaN films with M -plane/[1 00] orientation. In a comparative discussion of the two hexagonal tensor components and the zinc blende dielectric function, all prominent absorption structures were assigned to specific interband transitions at high symmetry points in the Brillouin zone. The assignment considers the individual dipole transition probabilities depending on the crystal symmetry and the geometry of the measurement. Furthermore, a detailed theoretical band-to-band analysis of dielectric function features, published by Lambrecht et al. [1], was considered. In conclusion, we suggest a new labeling of absorption structures as used in classical III,V materials like GaAs, which reflects the origin of transition structures from specific points in the respective Brillouin zones. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Giant reflectance anisotropy of polar cubic semiconductors in the far infrared PHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 8 2003Yu. A. KosevichAbstract We present our measurements and model for the reflectancre anisotropy of the (001) surface of polar cubic zinc-blende semiconductor in the far infrared. We observe that the relative reflectance difference of GaAs(001) in the far infrared can reach the value of twenty percents which is two orders of magnitude higher than the reflectance difference of the GaAs(001) in the near-ultraviolet - visible range. The most strong reflectance anisotropy was observed in the optical phonon Reststrahlbande and its vicinity. We relate the observed reflectance anisotropy with the anisotropy of the optical-phonon and plasma damping constants. Such anisotropy can be caused by anisotropic inhomogeneous broadening of the frequencies of the optical-phonon and plasma oscillations polarized respectively along the [110] and directions. This effect can be understood in terms of the lattice-deformation-induced changes of the optical-phonon force constants and electron-effective-mass tensor components. Anisotropic inhomogeneous strain of the lattice can in turn be induced by anisotropic microscopic short-range ordering of point defects (dopants) and dislocations in near-surface regions of noncentrosymmentric zinc-blende semiconductors. The observed giant reflectance anisotropy can be used as a sensitive tool for the far infrared characterization of zinc-blende semiconductors. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Phenomenology of magnetic second harmonic generation from low symmetry surfaces and interfaces PHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 8 2003L. CarrollAbstract Low dimensional magnetic structures show interesting and novel phenomena such as oscillatory magnetic coupling and giant magnetoresistance. Magnetic second harmonic generation (MSHG) can provide unique information on magnetic surfaces and interfaces because, within the dipole approximation, broken space-inversion symmetry at the surface or interface of centrosymmetric media, and broken time-reversal symmetry arising from the magnetization, are both required in order to observe a magnetic-field-dependent second harmonic response. However, the additional reduction in symmetry arising from the magetization produces many non-zero susceptibility tensor components, particularly in the case of vicinal, stepped surfaces of 1m symmetry, and care is needed in designing experiments that will produce readily interpretable results. Phenomenological expressions for the MSHG response from systems of 1m symmetry are presented, where combinations of input and output polarizations and magnetic field orientations allow the essential physics of these systems to be explored, particularly in relation to distinguishing terrace and step contributions to the magnetization from vicinal surfaces and interfaces. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Application of modern tensor calculus to engineered domain structures. ACTA CRYSTALLOGRAPHICA SECTION A, Issue 2 2006The theory of domain states is reviewed as a prerequisite for consideration of tensorial distinction of domain states. It is then shown that the parameters of the first domain in a ferroic phase transition from a set of isomorphic groups of the same oriented Laue class can be systematically and suitably represented in terms of typical variables. On replacing these variables by actual tensor components according to the previous paper [Kopský (2006), Acta Cryst. A62, 4764], we can reveal the tensorial parameters associated with each particular symmetry descent. Parameters are distinguished by the ireps to which they belong and this can be used to determine which of them are the principal parameters that distinguish all domain states, in contrast to secondary parameters which are common to several domain states. In general, the parameters are expressed as the covariant components of the tensors. A general procedure is described which is designed to transform the results to Cartesian components. It consists of two parts: the first, called the labelling of covariants, and its inverse, called the conversion equations. Transformation of parameters from the first domain state to other states is now reduced to irreducible subspaces whose maximal dimension is three in contrast with higher dimensions of tensor spaces. With this method, we can explicitly calculate tensor parameters for all domain states. To find the distinction of pairs of domain states, it is suitable to use the concept of the twinning group which is briefly described. [source] |