Electrons in a Periodic Crystal

2012 ◽  
pp. 167-248
Author(s):  
Claus F. Klingshirn
Keyword(s):  
Periodic Crystal

Relation Between Surface Crystallography and Surface Electron Structure of the Superlattice

2003 ◽  
Vol 10 (02n03) ◽  
pp. 195-199 ◽  
Author(s):  
I. Bartoš ◽  
T. Strasser ◽  
W. Schattke
Keyword(s):  
Energy Distribution ◽  
Surface State ◽  
Electron Structure ◽  
Surface Electron ◽  
One Dimensional ◽  
One Step ◽  
Surface Brillouin Zone ◽  
Topmost Layer ◽  
The One ◽  
Periodic Crystal

Profound gradual changes of surface state energies were predicted for varying surface terminations of the periodic crystal potential in one-dimensional models.1 This situation can be realized in superlattices with different thicknesses of topmost layers. For the ideally terminated (100) surface of a very thin superlattice (GaAs)2(AlAs)2, the shift of the energy of the surface state over the whole minigap in the lower part of the valence band has been found for different terminations of the topmost layer. In the center of the surface Brillouin zone the surface state shift follows model trends. The changes of the energy distribution of photoemitted electrons as determined from the one-step photoemission calculation2 indicate that experimental observation by the surface-sensitive technique of angle-resolved photoemission should be feasible, and preliminary data indicate this. The results show a straigthforward tuning of surface electron structure by geometrical means.

NON-PERIODIC TRANSLATIONAL ORDER IN QUASICRYSTALS WITH STABLE ATOMIC DENSITY ON SEVERAL CELLS

1987 ◽  
Vol 01 (01) ◽  
pp. 145-166 ◽  
Author(s):  
PETER KRAMER
Keyword(s):  
Fourier Transform ◽  
Single Cell ◽  
Atomic Density ◽  
Cubic Lattice ◽  
Crystal Model ◽  
The Fourier Transform ◽  
Periodic Crystal ◽  
Translational Order

The projection of the cubic lattice in IE 3 to an intersecting plane IE 2 serves as a paradigm for non-periodic translational order. The quasicrystal model proposed has stable atomic density supported on three parallelogram cells. The Fourier transform is reduced to integrals over the three cells. In case of a periodic projection, the model reduces to the periodic crystal model in the plane with a single cell.

Periodic crystal lattice rotation in microband groups in a bcc metal

2007 ◽  
Vol 57 (8) ◽  
pp. 775-778 ◽  
Author(s):  
Dorothée Dorner ◽  
Yoshitaka Adachi ◽  
Kaneaki Tsuzaki
Keyword(s):  
Crystal Lattice ◽  
Lattice Rotation ◽  
Bcc Metal ◽  
Periodic Crystal

Dressed Atoms in Flight through a Periodic Crystal Field: X-VUV Double Resonance

2008 ◽  
Vol 101 (11) ◽  
Author(s):  
Y. Nakai ◽  
Y. Nakano ◽  
T. Azuma ◽  
A. Hatakeyama ◽  
C. Kondo ◽  
...  
Keyword(s):  
Crystal Field ◽  
Double Resonance ◽  
Periodic Crystal

scholarly journals How to assign a (3 + 1)-dimensional superspace group to an incommensurately modulated biological macromolecular crystal

2017 ◽  
Vol 50 (4) ◽  
pp. 1200-1207 ◽  
Author(s):  
Jason Porta ◽  
Jeff Lovelace ◽  
Gloria E. O. Borgstahl
Keyword(s):  
Crystal Structure ◽  
Three Dimensional ◽  
Real Life ◽  
Group Symmetry ◽  
Protein Crystal ◽  
3D Space ◽  
Structure Solution ◽  
Crystallographic Symmetry ◽  
Aperiodic Crystals ◽  
Periodic Crystal

Periodic crystal diffraction is described using a three-dimensional (3D) unit cell and 3D space-group symmetry. Incommensurately modulated crystals are a subset of aperiodic crystals that need four to six dimensions to describe the observed diffraction pattern, and they have characteristic satellite reflections that are offset from the main reflections. These satellites have a non-integral relationship to the primary lattice and requireqvectors for processing. Incommensurately modulated biological macromolecular crystals have been frequently observed but so far have not been solved. The authors of this article have been spearheading an initiative to determine this type of crystal structure. The first step toward structure solution is to collect the diffraction data making sure that the satellite reflections are well separated from the main reflections. Once collected they can be integrated and then scaled with appropriate software. Then the assignment of the superspace group is needed. The most common form of modulation is in only one extra direction and can be described with a (3 + 1)D superspace group. The (3 + 1)D superspace groups for chemical crystallographers are fully described in Volume C ofInternational Tables for Crystallography. This text includes all types of crystallographic symmetry elements found in small-molecule crystals and can be difficult for structural biologists to understand and apply to their crystals. This article provides an explanation for structural biologists that includes only the subset of biological symmetry elements and demonstrates the application to a real-life example of an incommensurately modulated protein crystal.

THE THUE-MORSE APERIODIC CRYSTAL, A LINK BETWEEN THE FIBONACCI QUASICRYSTAL AND THE PERIODIC CRYSTAL

1987 ◽  
Vol 01 (01) ◽  
pp. 121-132 ◽  
Author(s):  
ROLF RIKLUND ◽  
MATTIAS SEVERIN ◽  
YOUYAN LIU
Keyword(s):  
Tight Binding ◽  
Model System ◽  
Periodic Systems ◽  
Unified Theory ◽  
Tight Binding Model ◽  
Binding Model ◽  
One Dimensional ◽  
Aperiodic Crystals ◽  
Hierarchical Splitting ◽  
Periodic Crystal

The electronic spectrum and eigenstates of a one-dimensional aperiodic Thue-Morse crystal isstudied with an on-site tight-binding model. The relation between the constructing elements andthe hierarchical splitting of the bands into subbands is analysed. The eigenstates are shown to be much more similar to those of a periodic crystal than those of a Fibonacci quasicrystal. We thus claim that the Thue-Morse aperiodic crystal is a link between the Fibonacci quasicrystal and theperiodic crystal, and that the study of non-Fibonaccian aperiodic crystals is a promising steptowards the desired unified theory of disordered, aperiodic and periodic systems. Since the experimentally studied MBE-grown aperiodic crystals typically has 5% fluctuation in layer thickness, we also investigate the density of states and eigenstates for a model system withfluctuating site-energies.

scholarly journals Metallic-mean quasicrystals as aperiodic approximants of periodic crystals

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Joichiro Nakakura ◽  
Primož Ziherl ◽  
Junichi Matsuzawa ◽  
Tomonari Dotera
Keyword(s):  
Rotational Symmetry ◽  
Oxide Films ◽  
Theoretical Framework ◽  
Complex Structures ◽  
Intermetallic Alloys ◽  
Large Unit ◽  
Unit Cells ◽  
Periodic Domains ◽  
Binary Nanoparticles ◽  
Periodic Crystal

Abstract Ever since the discovery of quasicrystals, periodic approximants of these aperiodic structures constitute a very useful experimental and theoretical device. Characterized by packing motifs typical for quasicrystals arranged in large unit cells, these approximants bridge the gap between periodic and aperiodic positional order. Here we propose a class of sequences of 2-D quasicrystals that consist of increasingly larger periodic domains and are marked by an ever more pronounced periodicity, thereby representing aperiodic approximants of a periodic crystal. Consisting of small and large triangles and rectangles, these tilings are based on the metallic means of multiples of 3, have a 6-fold rotational symmetry, and can be viewed as a projection of a non-cubic 4-D superspace lattice. Together with the non-metallic-mean three-tile hexagonal tilings, they provide a comprehensive theoretical framework for the complex structures seen, e.g., in some binary nanoparticles, oxide films, and intermetallic alloys.

scholarly journals Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs

2010 ◽  
Vol 18 (13) ◽  
pp. 14301 ◽  
Author(s):  
Y. Pennec ◽  
B. Djafari Rouhani ◽  
E. H. El Boudouti ◽  
C. Li ◽  
Y. El Hassouani ◽  
...  
Keyword(s):  
Band Gaps ◽  
Photonic Band Gaps ◽  
Simultaneous Existence ◽  
Photonic Band ◽  
Periodic Crystal
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