Friedel'S law breakdown and interpretation of stacking fault images in tetrahedral semiconductors

1987 ◽  
Vol 45 ◽  
pp. 318-319
Author(s):  
Rob. W. Glaisher ◽  
A.E.C. Spargo
Keyword(s):  
Relative Phase ◽  
Point Group ◽  
Binary Compound ◽  
Stacking Fault ◽  
Fold Axis ◽  
Atom Pair ◽  
Tetrahedral Semiconductors ◽  
Group Symmetries ◽  
Thin Crystal ◽  
Phase Differences

Images of <11> oriented crystals with diamond structure (i.e. C,Si,Ge) are dominated by white spot contrast which, depending on thickness and defocus, can correspond to either atom-pair columns or tunnel sites. Olsen and Spence have demonstrated a method for identifying the correspondence which involves the assumed structure of a stacking fault and the preservation of point-group symmetries by correctly aligned and stigmated images. For an intrinsic stacking fault, a two-fold axis lies on a row of atoms (not tunnels) and the contrast (black/white) of the atoms is that of the {111} fringe containing the two-fold axis. The breakdown of Friedel's law renders this technique unsuitable for the related, but non-centrosymmetric binary compound sphalerite materials (e.g. GaAs, InP, CdTe). Under dynamical scattering conditions, Bijvoet related reflections (e.g. (111)/(111)) rapidly acquire relative phase differences deviating markedly from thin-crystal (kinematic) values, which alter the apparent location of the symmetry elements needed to identify the defect.

scholarly journals Combined Reduced Phase Dual-Directional Illumination Digital Holography and Speckle Displacements for Shape Measurement

2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Davood Khodadad
Keyword(s):  
Phase Difference ◽  
Digital Holography ◽  
Relative Phase ◽  
Groove Depth ◽  
Phase Unwrapping ◽  
Shape Measurement ◽  
Phase Ambiguity ◽  
Holographic Method ◽  
Height Range ◽  
Phase Differences

We present a digital holographic method to increase height range measurement with a reduced phase ambiguity using a dual-directional illumination. Small changes in the angle of incident illumination introduce phase differences between the recorded complex fields. We decrease relative phase difference between the recorded complex fields 279 and 139 times by changing the angle of incident 0.5° and 1°, respectively. A two cent Euro coin edge groove is used to measure the shape. The groove depth is measured as ≈300  μm. Further, numerical refocusing and analysis of speckle displacements in two different planes are used to measure the depth without a use of phase unwrapping process.

scholarly journals Random k-Body Ensembles for Chaos and Thermalization in Isolated Systems

Entropy ◽  
2018 ◽  
Vol 20 (7) ◽  
pp. 541 ◽  
Author(s):  
Venkata Kota ◽  
Narendra Chavda
Keyword(s):  
Hermite Polynomials ◽  
Point Group ◽  
Majorana Fermions ◽  
Many Body ◽  
Boson Systems ◽  
Random Matrix Ensembles ◽  
Isolated Systems ◽  
Group Symmetries ◽  
Statistical Relaxation

Embedded ensembles or random matrix ensembles generated by k-body interactions acting in many-particle spaces are now well established to be paradigmatic models for many-body chaos and thermalization in isolated finite quantum (fermion or boson) systems. In this article, briefly discussed are (i) various embedded ensembles with Lie algebraic symmetries for fermion and boson systems and their extensions (for Majorana fermions, with point group symmetries etc.); (ii) results generated by these ensembles for various aspects of chaos, thermalization and statistical relaxation, including the role of q-hermite polynomials in k-body ensembles; and (iii) analyses of numerical and experimental data for level fluctuations for trapped boson systems and results for statistical relaxation and decoherence in these systems with close relations to results from embedded ensembles.

scholarly journals Sc0.43(2)Rb2Mo15S19, a partially Sc-filled variant of Rb2Mo15S19

2012 ◽  
Vol 68 (5) ◽  
pp. i25-i28 ◽  
Author(s):  
Patrick Gougeon ◽  
Rabih Al Rahal Al Orabi ◽  
Régis Gautier ◽  
Michel Potel
Keyword(s):  
Charge Transfer ◽  
Solid State ◽  
Unique Feature ◽  
Point Group ◽  
Tight Binding ◽  
Median Plane ◽  
Structural Motif ◽  
Space Group ◽  
Group Symmetries ◽  
Cluster Unit

The structure of scandium dirubidium pentadecamolybdenum nonadecasulfide, Sc0.43 (2)Rb2Mo15S19, constitutes a partially Sc-filled variant of Rb2Mo15S19[Picard, Saillard, Gougeon, Noel & Potel (2000),J. Solid State Chem.155, 417–426]. In the two compounds, which both crystallize in theR\overline{3}cspace group, the structural motif is characterized by a mixture of Mo6Si8Sa6and Mo9Si11Sa6cluster units (`i' is inner and `a' is apical) in a 1:1 ratio. The two components are interconnected through interunit Mo—S bonds. The cluster units are centred at Wyckoff positions 6band 6a(point-group symmetries \overline{3}. and 32, respectively). The Rb+cations occupy large voids between the different cluster units. The Rb and the two inner S atoms lie on sites with 3. symmetry (Wyckoff site 12c), and the Mo and S atoms of the median plane of the Mo9S11S6cluster unit lie on sites with .2 symmetry (Wyckoff site 18e). A unique feature of the structure is a partially filled octahedral Sc site with \overline{1} symmetry. Extended Hückel tight-binding calculations provide an understanding of the variation in the Mo—Mo distances within the Mo clusters induced by the increase in the cationic charge transfer due to the insertion of Sc.

scholarly journals β-K3Fe(MoO4)2Mo2O7

2014 ◽  
Vol 70 (7) ◽  
pp. i38-i38 ◽  
Author(s):  
Amira Souilem ◽  
Mohamed Faouzi Zid ◽  
Ahmed Driss
Keyword(s):  
Solid State ◽  
Solid State Reaction ◽  
Title Compound ◽  
Point Group ◽  
Coordination Numbers ◽  
Group Symmetries

The title compound, tripotassium iron(III) bis(orthomolybdate) dimolybdate, was obtained by a solid-state reaction. The main structural building units are one FeO6octahedron, two MoO4tetrahedra and one Mo2O7dimolybdate group, all with point group symmetriesm. These units are linkedviacorner-sharing to form ribbons parallel to [010]. The three K+cations are located between the ribbons on mirror planes and have coordination numbers of 10 and 12. Two O atoms of one of the MoO4tetrahedra of the dimolybdate group are disordered over two positions in a 0.524 (11):0.476 (11) ratio. The structure of the title compound is compared briefly with that of Rb3FeMo4O15.

NUCLEAR POINT-GROUP SYMMETRIES AND NEW IDEAS ABOUT NUCLEAR STABILITY: AN OVERVIEW

2009 ◽  
Vol 18 (10) ◽  
pp. 2155-2159
Author(s):  
J. DUDEK ◽  
D. CURIEN ◽  
A. GÓŹDŹ ◽  
K. MAZUREK
Keyword(s):  
Mean Field Theory ◽  
Point Group ◽  
Mean Field ◽  
Shell Effects ◽  
Nuclear Stability ◽  
Particle Spectra ◽  
New Ideas ◽  
Group Symmetries ◽  
Nuclear Shell ◽  
Nuclear Shell Effects

The nuclear mean-field theory and the group representation theory can be used to optimise the search for strong nuclear shell effects. The two theories allow to correlate the symmetry aspects with the presence of large gaps in the single-particle spectra, facilitate in this way the conditions of search for strong nucleonic- and nuclear-binding and thus for an increased nuclear stability. In this article we give a short overview of the related on-going research, focussing on the results of the TetraNuc Collaboration.

Magnetic Point Group Symmetries of Spontaneously Polarized and/or Magnetized Domain Walls

2002 ◽  
Vol 269 (1) ◽  
pp. 39-44 ◽  
Author(s):  
J. Přívratská ◽  
B. Shaparenko ◽  
V. Janovec ◽  
D. B. Litvin
Keyword(s):  
Domain Walls ◽  
Point Group ◽  
Group Symmetries
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