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Modulated Structure (modulated + structure)
Selected AbstractsSingle crystal X-ray study of the modulated structure in Ga2XTe3 with the defect zinc-blende structurePHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 5 2009S. Kashida Abstract Ga2Te3 crystallizes into the zinc-blende structure, where one third of the cation sites is vacant. Single crystal X-ray diffraction studies on quenched and annealed Ga2Te3 and CuGaTe2 crystals are reported. The obtained diffraction maps show, other than the zinc-blende type main reflections, satellite reflections at q1,1/17[110]c in quenched Ga2Te3 crystals and q2,1/20[210]c in annealed Ga2Te3 crystals, where the subscript c means the cubic sub-lattice. The analysis of the satellite reflections shows that the modulation is two dimensional, and is ascribed to a coupled mode of the amplitude type modulation caused by Ga vacancies and the displacive modulation of surrounding Te atoms, which has the polarization vector along the <001>c direction. The nature of the atomic modulations is discussed and the origin of the modulation is ascribed to Jahn-Teller type distortions around Ga vacancies. The experiments done on CuGaTe2 crystals indicate that the cation disorder compound sphalerite type CuGaTe2 contain the same modulated structure as Ga2Te3 crystals, but the cation ordered compound chalcopyrite type CuGaTe2 does not show the modulation. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Differential geometry: a natural tool for describing symmetry operationsACTA CRYSTALLOGRAPHICA SECTION A, Issue 5 2009Philippe Kocian Differential geometry provides a useful mathematical framework for describing the fundamental concepts in crystallography. The notions of point and associated vector spaces correspond to those of manifold and tangent space at a given point. A space-group operation is a one-to-one map acting on the manifold, whereas a point-group operation is a linear map acting between two tangent spaces of the manifold. Manifold theory proves particularly powerful as a unified formalism describing symmetry operations of conventional as well as modulated crystals without requiring a higher-dimensional space. We show, in particular, that a modulated structure recovers a three-dimensional periodicity in any tangent space and that its point group consists of linear applications. [source] Ternary fluorides BaMF4 (M = Zn, Mg and Mn) at low temperaturesACTA CRYSTALLOGRAPHICA SECTION B, Issue 5 2009Jose Maria Posse Ternary fluorides BaMF4 (M = Zn, Mg, Mn) have been studied in the temperature range from 300 to 10,K using synchrotron and laboratory powder and single-crystal diffraction. The first two compounds are stable down to 10,K, while the third one undergoes a phase transition to an incommensurately modulated structure at approximately 250,K. The modulated phase is stable down to 10,K. The magnetic anomalies at 45 and 27,K observed previously in BaMnF4 are exclusively reflected in the behavior of the , component of the q vector, which assumes an irrational value of approximately 0.395,Å,1 at the temperature corresponding to the onset of the magnetic ordering and then stays constant down to 10,K. Mn,Mn distances do not indicate any structural response to the magnetic ordering. The formation of the modulated phase can be explained on the basis of simple geometrical criteria. The incorporation of the large Mn cation in the octahedral sheets implies an increase of the cavity in which the Ba ion is incorporated. This leads to the formation of the modulated structure to adapt the coordination sphere around Ba in such a way that the bond-valence sums can be kept close to the ideal value of two. With further lowering of the temperature, the charge balance around the Ba ion requires an increasingly anharmonic character of the modulation function of Ba, until finally at 10,K a crenel-like shape is assumed for the modulation of this atom. [source] Modulated structure and phase transitions of Sr10Ga6O19ACTA CRYSTALLOGRAPHICA SECTION B, Issue 5 2009Hannes Krüger The crystal structure of Sr10Ga6O19 was investigated by in situ single-crystal X-ray diffraction in the temperature range 298,673,K. At ambient conditions the compound shows a (3,+,1)-dimensional modulated structure in the superspace group C2/c(0,0)s0 [a = 34.9145,(13), b = 7.9369,(2), c = 15.9150,(7),Å and , = 103.551,(3)°] with a modulation wavevector of q = 0.4288,(2)b*. Whereas the presented structural model uses first-order harmonic modulation functions only, some features of the modulations are discussed utilizing an electron density derived by the maximum entropy method. Furthermore, two phase transitions were identified: between 453 and 503,K the incommensurate superstructure is replaced by a doubling of the a and b lattice constants, and between 503 and 673,K a phase with the basic cell is formed, identical to ,-Sr10Ga6O19. Under some cooling conditions crystals showing a combined diffraction pattern of both superstructures can be obtained. The relation of these results to ,-Sr10Ga6O19 [Kahlenberg (2001). J. Solid State Chem.160, 421,429] is discussed. [source] Superspace description of the modulated structure of the metal-salt-hybrid Bi7,,,,Ni2Br5,,,2, (, = 1/9)ACTA CRYSTALLOGRAPHICA SECTION B, Issue 5 2009B. Wahl The compound Bi7,,,,Ni2Br5,,,2, = (Bi3Ni)2[Bi1,,,,Br4]Br1,,2, (, = 1/9) is a sub-bromide of the intermetallic phase Bi3Ni. Its crystal structure contains metallic rods, [Bi3Ni], which are embedded in a salt-like matrix of bromido-bismuthate(III) and bromide anions. The non-stoichiometry originates from the variation of the number n of trans edge-sharing octahedra in the [BinBr4n,+,2](n,+,2), oligomers (3 ,n, 5), as well as from vacancies on the sites of the isolated Br atoms. The simplified structure is described in the orthorhombic space group Cmcm with a = 4.0660,(4), b = 23.305,(3), c = 17.130,(2),Å. It shows a statistical distribution of vacancies and orientational disorder of the concatenated octahedra. By choosing the modulation vector q = a*/9 + b*/2, the additional weak reflections of the diffraction pattern can be indexed. In the [3,+,1]-dimensional superspace group Pmnm(,½0)000, an ordered structure model is achieved. The modulated crystal structure bears a strong resemblance to the somewhat higher oxidized sub-bromide Bi7,,,,Ni2Br5 (, = 1/9). [source] The incommensurately modulated crystal structure of ,-Pb2BiVO6: interpretation of the phase transition ,,,,, and conduction properties of related materialsACTA CRYSTALLOGRAPHICA SECTION B, Issue 4 2009Pascal Roussel A new polymorph of Pb2BiVO6 was prepared under ambient conditions and its crystal structure was determined by single-crystal X-ray diffraction. The phase transitions ,,, and ,,, were identified in the mother phase; the high-temperature form ,-Pb2BiVO6 eventually decomposes at 753,K to a mixture of Pb4BiVO8 and the high-temperature form of PbBiVO5 before showing recombination at 923,K. ,-Pb2BiVO6 has an incommensurate monoclinic modulated structure. This crystal structure is twinned and complementary structural investigations of a powder sample of ,-Pb2BiVO6 by TEM diffraction studies confirmed the lattice and incommensurate modulation character. Log , = f(T,1) dependences for Pb2BiVO6 -related materials (6% M -for-V-substituted compositions; M = Cr, Mn, P) are reported, which allow the characterization (Ea and isothermal , values) of the ,- as well as the ,- and ,-Pb2BiVO6 varieties. [source] A non-mathematical introduction to the superspace description of modulated structuresACTA CRYSTALLOGRAPHICA SECTION B, Issue 3 2009Trixie Wagner The X-ray analysis of (6R,7aS)-6-(tert -butyl-dimethylsilanyloxy)-1-hydroxy-2-phenyl-5,6,7,7a-tetrahydropyrrolizin-3-one, C19H27NO3Si, revealed a diffraction pattern which is typical for modulated structures: strong Bragg peaks surrounded by weaker reflections which cannot be indexed with the same three reciprocal lattice vectors that are used to describe the strong peaks. For this class of crystal structures the concept of superspace has been developed which, however, for many crystallographers still constitutes a Gordian Knot. As a possible tool to cut this knot the crystal structure of the above-mentioned tetrahydropyrrolizinone derivative is presented as an illustrative example for handling and describing the modulated structure of a typical pharmaceutical (i.e. molecular) compound. Having established a working knowledge of the concepts and terminology of the superspace approach a concise and detailed description of the complete process of peak indexing, data processing, structure solution and structure interpretation is presented for the incommensurately modulated crystal structure of the above-mentioned compound. The superspace symmetry applied is P21(,0,)0; the (incommensurate) q vector components at 100,K are , = 0.1422,(2) and , = 0.3839,(8). [source] Incommensurate structure of Ca2Al2O5 at high temperatures , structure investigation and Raman spectroscopyACTA CRYSTALLOGRAPHICA SECTION B, Issue 4 2008Biljana Lazic A high-temperature X-ray diffraction study revealed that brownmillerite-type Ca2Al2O5 transforms to an incommensurately modulated structure at elevated temperatures. Single crystals of Ca2Al2O5 were synthesized in an end-loaded piston cylinder press at 2.5,GPa and 1273,K. The diffraction pattern observed at 1090,(10),K by in situ single-crystal diffraction experiments can be indexed by an I -centred orthorhombic cell and a modulation wavevector of q = 0.595,(1)c*. A (3,+,1)-dimensional model in superspace group Imma(00,)s00 was used to refine the modulated structure. The structure is assembled from two building units: (i) layers of corner-sharing [AlO6] octahedra, stacked along b alternate with (ii) layers of zweier single chains of [AlO4] tetrahedra running along a. The modulated structure arises from an aperiodic sequence of two different configurations of the chains within the tetrahedral layers. The modulated high-temperature phase of Ca2Al2O5 is isotypic to the modulated high-temperature modification of Ca2Fe2O5. A large hysteresis was found in the phase-transition temperature. On heating, the transition occurs at ca 1075,(10),K; on cooling, satellite reflections can be observed down to 975,(10),K. The characterization of Ca2Al2O5 is completed by Raman spectroscopy, including a partial interpretation of the spectra. [source] Modulated corrugations in the crystal structure of the superconductor CaAlSiACTA CRYSTALLOGRAPHICA SECTION B, Issue 5 2006Karine M. Sparta We report the crystal structure analyses of CaAlSi from single-crystal and powder X-ray diffraction and the existence of two commensurately modulated phases, a sixfold and a fivefold modulated structure. This polymorphism seems to be correlated to the thermal history of the sample. We describe both modulated structures using a three-dimensional and a (3,+,1)-dimensional formalism. [source] Diffuse scattering and short-range order in uranium iodine phthalocyanine [U1,xPc2]I2,y and the X-ray structure analysis of crystals with diffuse superstructure reflectionsACTA CRYSTALLOGRAPHICA SECTION B, Issue 3 2003J. Krawczyk Crystals of uranium iodine phthalocyanine present an example of a disordered commensurate modulated structure of the intergrowth type. The short-range order of both uranium ions and iodine chains [I]n has been analysed by Reverse Monte Carlo (RMC) simulation of X-ray diffuse scattering. The diffraction pattern of uranium iodine phthalocyanine contains diffuse superstructure reflections. In the routine crystal structure analysis diffuse superstructure reflections may be either omitted or measured and classified along with other Bragg reflections. The crystal structure of uranium iodine phthalocyanine is an example of such ambiguity. The crystal structures of two specimens of [U1,xPc2]I2,y with slightly different composition have been published in the literature with different space groups and unit cells. We have shown that the structure of both specimens differs only in the degree of short-range order and is isostructural with [YbPc2]I2. We have also shown that while the omission of diffuse reflections results in the average crystal structure, the treatment of these reflections as normal Bragg reflections is incorrect and produces the structure averaged over a limited small range. [source] Refinement of modulated structures against X-ray powder diffraction data with JANA2000JOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 3 2001M. Du JANA is a computer program for the refinement and analysis of periodic and aperiodic (incommensurately modulated structures and composite crystals) crystal structures. Here a new module is introduced that allows Rietveld refinements against powder diffraction data. It is shown that JANA2000 provides a state-of-the-art description of the peak profiles. A re-analysis of the low-temperature structure of (CO)xC60 showed that the application of icosahedral symmetry restrictions to the C60 molecule leads to a better description of the electron density and to a corrected position of the CO molecule as compared with a rigid-body refinement. The incommensurately modulated structure of NbTe4 has been successfully refined against X-ray powder diffraction data. The structural parameters are equal to, but less accurate, than the parameters obtained from a single-crystal study. [source] Spin-dependent tunneling in modulated structures of (Ga,Mn)AsPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 2 2007P. Sankowski Abstract The spin-dependent tunneling in layered structures based on (Ga,Mn)As, in particular the dependence of the tunneling current on magnetization direction, is studied theoretically. To capture the complexity of the tunneling effects in these semiconductor devices we combine a multi-orbital tight-binding approach with Landauer-Büttiker formalism. This theory allows us to reproduce the tunneling anisotropic magnetoresistance effects observed in (Ga,Mn)As/GaAs Esaki-Zener diodes. The model is also used to describe the in-plane and out-of-plane anisotropy of tunneling magnetoresistance in (Ga,Mn)As-based trilayers. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] A non-mathematical introduction to the superspace description of modulated structuresACTA CRYSTALLOGRAPHICA SECTION B, Issue 3 2009Trixie Wagner The X-ray analysis of (6R,7aS)-6-(tert -butyl-dimethylsilanyloxy)-1-hydroxy-2-phenyl-5,6,7,7a-tetrahydropyrrolizin-3-one, C19H27NO3Si, revealed a diffraction pattern which is typical for modulated structures: strong Bragg peaks surrounded by weaker reflections which cannot be indexed with the same three reciprocal lattice vectors that are used to describe the strong peaks. For this class of crystal structures the concept of superspace has been developed which, however, for many crystallographers still constitutes a Gordian Knot. As a possible tool to cut this knot the crystal structure of the above-mentioned tetrahydropyrrolizinone derivative is presented as an illustrative example for handling and describing the modulated structure of a typical pharmaceutical (i.e. molecular) compound. Having established a working knowledge of the concepts and terminology of the superspace approach a concise and detailed description of the complete process of peak indexing, data processing, structure solution and structure interpretation is presented for the incommensurately modulated crystal structure of the above-mentioned compound. The superspace symmetry applied is P21(,0,)0; the (incommensurate) q vector components at 100,K are , = 0.1422,(2) and , = 0.3839,(8). [source] Modulated corrugations in the crystal structure of the superconductor CaAlSiACTA CRYSTALLOGRAPHICA SECTION B, Issue 5 2006Karine M. Sparta We report the crystal structure analyses of CaAlSi from single-crystal and powder X-ray diffraction and the existence of two commensurately modulated phases, a sixfold and a fivefold modulated structure. This polymorphism seems to be correlated to the thermal history of the sample. We describe both modulated structures using a three-dimensional and a (3,+,1)-dimensional formalism. [source] Phosphate tungsten bronze series: crystallographic and structural properties of low-dimensional conductorsACTA CRYSTALLOGRAPHICA SECTION B, Issue 5 2001P. Roussel Phosphate tungsten bronzes have been shown to be conductors of low dimensionality. A review of the crystallographic and structural properties of this huge series of compounds is given here, corresponding to the present knowledge of the different X-ray studies and electron microscopy investigations. Three main families are described, monophosphate tungsten bronzes, Ax(PO2)4(WO3)2m, either with pentagonal tunnels (MPTBp) or with hexagonal tunnels (MPTBh), and diphosphate tungsten bronzes, Ax(P2O4)2(WO3)2m, mainly with hexagonal tunnels (DPTBh). The general aspect of these crystal structures may be described as a building of polyhedra sharing oxygen corners made of regular stacking of WO3 -type slabs with a thickness function of m, joined by slices of tetrahedral PO4 phosphate or P2O7 diphosphate groups. The relations of the different slabs with respect to the basic perovskite structure are mentioned. The structural description is focused on the tilt phenomenon of the WO6 octahedra inside a slab of WO3 -type. In this respect, a comparison with the different phases of the WO3 crystal structures is established. The various modes of tilting and the different possible connections between two adjacent WO3 -type slabs involve a great variety of structures with different symmetries, as well as the existence of numerous twins in MPTBp's. Several phase transitions, with the appearance of diffuse scattering and modulation phenomena, were analysed by X-ray scattering measurements and through the temperature dependence of various physical properties for the MPTBp's. The role of the W displacements within the WO3 -type slabs, in two modulated structures (m = 4 and m = 10), already solved, is discussed. Finally, the complexity of the structural aspects of DPTBh's is explained on the basis of the average structures which are the only ones solved. [source] A new stacking motif: complex alloy structures interpreted as modulated structuresACTA CRYSTALLOGRAPHICA SECTION B, Issue 4 2000Masaya Uchida The structures of ,-Al4Mn, manganese aluminide, ,-Al177Cr49Ni, chromium nickel aluminide, and ,-Al4Cr, chromium aluminide, which have been described in terms of the aggregation of clusters until now, are interpreted as modulated structures. They are basically composed of close-packed layers with ordered atomic vacancies. The observed stacking motif of the atoms can be found in many phases related to icosahedral and decagonal quasicrystals. This analysis will be helpful in the study of not only many complex alloys, but also quasicrystals. [source] | ||||||||||