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EN
A geometric study of twin and grain boundaries in crystals and quasicrystals is achieved via coincidence site lattices and coincidence site modules, respectively. Recently, coincidences of shifted lattices and multilattices (i.e. finite unions of shifted copies of a lattice) have been investigated. Here, we solve the coincidence problem for a shifted hexagonal lattice. This result allows us to analyze the coincidence isometries of the hexagonal packing by viewing the hexagonal packing as a multilattice.
EN
We derive a structure model for icosahedral quasicrystals. The model is based on a statistical approach involving the concept of average unit cell. This approach enables limiting calculations to real space as opposed to higher-dimensional analysis involving to unphysical atomic surface modeling. We start with the three-dimensional Ammann tiling with its two rhombohedral prototiles. For monoatomic decoration of the lattice nodes the perfect agreement with the higher-dimensional description was recently shown. In this paper we discuss the shape of the average unit cell and the first attempts for decoration scheme.
Acta Physica Polonica A
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2010
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vol. 117
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issue 1
215-217
EN
Magnetic symmetry of possible plane domain walls in arbitrary oriented plates of the crystal of hexoctahedral crystallographic class is considered. The symmetry classification is applied for ferro- and ferrimagnets.
EN
The statistical approach based on the average unit cell concept was recently successfully applied to structural modelling of icosahedral quasicrystals. The structure factor for arbitrarily decorated icosahedral structure was derived for model Ammann tiling (3D Penrose tiling). It is a fully physical-space model where no higher-dimensional description is needed. In the present paper we show the application of the model to the so-called simple decoration scheme - atomic decoration in the nodes, at mid-edges and along body-diagonal of structural units of 3D Penrose tiling. By analyzing the obtained calculated diffraction patterns we show the correctness of the model and its applicability to binary and ternary icosahedral phases.
EN
The investigation of the ab initio band structure and the resulting spatial electron density distribution of the In-Se system in the framework of the density functional theory and the elementary energy bands concept is presented. It gives us reliable information about the valence band structure and peculiarities of the chemical bonding in these crystals. Some regularities in the evolution of the elementary energy bands topology is established, together with the choice of the actual Wyckoff position that is responsible for this topology and, at the same time, for the valence band formation in the InSe, In_2Se_3, In_4Se_3, and In_6Se_7 crystals. The calculated Mulliken charges and the degree of ionicity allow to estimate the character of chemical bonding in these crystals.
EN
An important issue in modern solid state chemistry is the development of a general methodology to predict the possible (meta)-stable modifications of a solid. This requires the global exploration of the energy landscape of the chemical system, since each stable phase corresponds to a locally ergodic region of the landscape. The global search in the lead sulfide system has been performed with simulated annealing on the ab initio level, while zinc oxide was studied with an empirical potential using simulated annealing, both at standard and elevated pressure (up to 100 GPa). The local optimization of the modifications found in the PbS system was performed using various density functionals. Next, the energy E(V) and enthalpy H(p) as function of volume and pressure, respectively, were computed for these modifications and their electronic structure was analyzed. The structures found for ZnO were locally optimized on ab initio level (DFT and Hartree-Fock). In both systems the structures found were in good agreement with the experiment. Furthermore, we employed the threshold algorithm to explore the barrier structure of the landscape of ZnO as function of the number of formula units in the simulation cell. Based on the barrier and minima information 2-D models of the energy landscape were constructed.
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Hyperbolic Icosahedral Tilings by Buckyballs

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EN
Hyperbolic icosahedral tilings by Buckyballs with 4 or 8 Buckyballs sharing a vertex are considered as an example of tilings by Archimedean polyhedra. Representation requires Poincaré balls; colour symmetry may be derived by GAP. Colour symmetries preserving both rotation and reflection symmetry as well as only rotation symmetry are discussed.
EN
The values of electronic polarizabilities of La³⁺, Ga³⁺, Si⁴⁺, O²¯ ions are specified using new experimental data about optical activity of La₃Ga₅SiO₁₄ crystals. A calculation technique based on the dipole electron shifting model is applied to estimate linear electrooptic coefficients for the La₃Ga₅SiO₁₄. Wavelength dependences of the both linear electro-optic tensor components r₁₁ and r₄₁ are calculated.
9
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From Colorings to Weavings

80%
EN
We present a methodology for constructing weavings from 2-colorings of the plane. In particular, we consider tilings T of the plane by triangles and their corresponding triangle groups G. We derive 2-colorings of T using the index 2 subgroups of G.
EN
Symmetry relations between the domain states in GdFeO_{3} type crystals have been obtained using group-theoretical analysis for prototype and ferroelastic space groups. Models for possible domain pairs are developed. The ion locations on the domain boundary were estimated as intermediate positions between the sites in crystal structure of neighboring domain states. It is shown that the crystalline structure of the boundary approaches to the prototype phase structure - the ideal ABO_{3} perovskite-type structure, however certain deformations remain. In addition to the shifts of the all ions the tilts of oxygen octahedra of the some type and related displacements of A ions should take place during the switching of orientation states. The tilts of octahedra and displacements of A ions are sufficient to form translation states (antiphase domains). Antiphase domains can have boundaries between themselves basically along the three faces of the orthorhombic cell.
EN
Theoretical analysis of the ferro-elastic domain structure of a La_{0.95}Sr_{0.05}Ga_{0.9}Mg_{0.1}O_{2.925} crystal in three different crystallographic phases is presented. Parameters of these configurations are obtained using group theoretical approach, the method of spontaneous deformation as well as theoretical interpretation of twinning resulting from mechanical deformation (mechanical twinning theory). In the three phases of La_{0.95}Sr_{0.05}Ga_{0.9}Mg_{0.1}O_{2.95} - trigonal, orthorhombic and monoclinic - the parameters of ferro-elastic domain structures are determined; namely the quantity of orientation states, symmetry elements of connection between states, orientations and types of domain walls, tensors of spontaneous deformations of the perovskite-type cells for every orientation state, elements of twin shifts, which are needed for the reorientation of some orientation states to others. By using the found parameters of bidomain configurations a mechanism is proposed, which causes chevron-like domain configurations in compounds with martensitic phase transitions.
EN
This paper deals with the identification of multidomain configuration in ferroelastic phases of La_{0.95}Sr_{0.05}Ga_{0.9}Mg_{0.1}O_{3-x} using polychromatic synchrotron X-ray radiation (Laue method). A nondestructive approach for the determination of domain misorientations, orientation of domain walls and their configuration in the nanosize ferroelastic domain structure was developed. The proposed approach can be used to study the nanosize ferroelastic domain structure in small crystals of submillimeter sizes at different external fields, including temperature. The ferroelastic domain structure in the orthorhombic as well as in the rhombohedral phases of La_{0.95}Sr_{0.05}Ga_{0.9}Mg_{0.1}O_{3-x} crystals has been identified. The intersection of walls leads to the formation of a chevron-like pattern. The observed reversibility of domain patterns during temperature cycles is probably caused by the interaction of domain boundaries with point defects, most likely oxygen vacancies.
EN
We present a description of the symmetry-based method for the construction of the adiabatic potential of a symmetric molecule near the charged semiconductor surface. For this purpose, a transformation of the adiabatic potential of a free high symmetric molecule (D_{3d}) in the presence of uniform electric field is investigated. The obtained adiabatic potential is analyzed with respect to the stability of molecule in the vicinity of charged surface, as a dependence of its orientation in the electric field.
EN
Crystal structures of two single crystals SrₓBa_{1-x}Nb₂O₆ and CaₓBa_{1-x}Nb₂O₆ have been reinvestigated using automated electron diffraction tomography method with beam precession. 3D reciprocal space has been reconstructed based on recorded tilt series. For both samples the crystal structure was refined and the tetragonal symmetry with space group P4bm was confirmed. The three dimensional reciprocal space allowed to observe and to study satellite reflections in both materials.
15
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EN
The main purpose of crystallography is to solve and refine crystal structures based on measured diffraction data. One of important corrections crucial in the refinement process is the Debye-Waller factor correction for phonons in physical, and phasons in perpendicular space. In our paper we show the limitations of the standard approaches to the Debye-Waller correction in case of quasicrystals and propose new approach based on the statistical method. For the model 1D quasicrystal we show that in case of phonons there is no significant objection against classical (exponential) Debye-Waller factor, however using different forms can slightly improve the results of a refinement. In case of phasons the classical formula gives no rise to the efficiency of the refinement and completely new approach is required. We propose a redefinition of the Debye-Waller factor in terms of the statistical approach and show its effectiveness.
EN
Structural properties of ZnTe, MnTe, and Mn_{1-x}Zn_xTe alloy with zinc-blende, NiAs, and wurtzite phases were investigated by ab initio calculations. The calculated structural properties are in good agreement with the available experimental data. Theory predicts that the zinc-blende phase is more stable than wurtzite for all compositions. Mn_{1-x}Zn_xTe samples with 0.01 < x < 0.20 were grown by MBE. X-ray analysis of their crystalline structure revealed the presence of zinc-blende, wurtzite, and NiAs phases. The dominant phase changes from NiAs for the sample with x=0.01 to wurtzite for x=0.20. The observed stabilization of the wurtzite phase is possibly due to the hexagonal structure of the MnTe buffer.
Acta Physica Polonica A
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2015
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vol. 128
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issue 2
185-189
EN
Transition metal chalcogenides of a zinc-blende structure are theoretically predicted to be half metallic and, therefore, they are interesting for spintronic applications. However, the ground state of these compounds is hexagonal, of NiAs type, whereas the cubic phase is a metastable one. Here, we investigate the Cr-Te bondings of both phases of Cr-Te from point of view of symmetry. The hybridization in octahedral and tetrahedral lattice is studied for both structures. The fiber bundle presentation of the hybridization problem is also addressed.
EN
Large-scale molecular dynamics simulations of the high-pressure transformations of the xenon/water system were performed involving special purpose molecular dynamics machines. We investigated several systems of different sizes and geometry at the suitable simulational conditions (density, temperature, etc.), which are similar to the experiments conducted on the xenon hydrates. A binary mixture (ice water + Xe) undergoes at high pressure a long evolution and the Xe-guest atoms, enclosed inside the water molecules, were observed and analyzed. Even for the thin slabs, starting with the capture of the guest atoms by the water molecules, the water clusters around the xenon atoms are formed. The results show that such a hydrate-like formation preserves its structural stability over a long period of the simulation time of order of nanosecond. The molecular dynamics simulations were performed on a basis of the MDGRAPE-2 modifications of the DL_POLY general purposes package, with the efficient treatment of the Ewald real and reciprocal-space components of the Coulombic and Van der Waals forces. The MDGRAPE-2 accelerates the calculations of the Coulomb and Van der Waals forces, without applying a spherical cut of a fixed distance. 31.15.Qg, 61.20.-p, 61.50.Ah, 81.10.Aj, 91.60.Gf
EN
Bulk monocrystals of Pb_{1-x}Cd_{x}Te, with the Cd content x up to 0.11, were grown by physical vapour transport method. The structural, electrical and optical properties of these ternary crystals were studied experimentally and theoretically. All investigated samples exhibit rock-salt structure and high crystal quality, which was confirmed by X-ray rocking curve width parameter of about 100 arcsec. The decrease of the lattice parameter with increasing Cd content x was found experimentally, in agreement with ab initio calculations. The band structures of Pb_{1-x}Cd_{x}Te mixed crystals for x values up to 0.2 were calculated using tight binding approach. The calculated band gap in the L-point increases with the Cd content in qualitative agreement with photoluminescence measurements in the infrared. For all studied Pb_{1-x}Cd_{x}Te samples, the Hall effect and electrical conductivity measurements, performed in the temperature range from 4 to 300 K, revealed p-type conductivity.
EN
An expression for the Green function of anisotropic face centered cubic lattice is evaluated analytically and numerically for a single impurity problem. The density of states, phase shift and scattering cross-section are expressed in terms of complete elliptic integrals of the first kind.
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