An optical method of studying the diffraction from imperfect crystals III. Layer structures with stacking faults

1958 ◽  
Vol 248 (1253) ◽  
pp. 183-198 ◽  
Keyword(s):  
Intensity Distribution ◽  
Optical Method ◽  
Reciprocal Lattice ◽  
Stacking Faults ◽  
Hexagonal Structure ◽  
Optical Diffraction ◽  
Layer Structures ◽  
The Face ◽  
Cubic Structure

The reciprocal lattice intensity distribution has been determined quantitatively using a photomultiplier to measure the optical diffraction intensities. The systems examined included the simple-cubic structure with 'wollastonite-type’ stacking faults, the close-packed-hexagonal structure with growth faults, and the face-centred-cubic structure with de­formation faults on one set and on two sets of {111} planes. It is shown that the Paterson (1952) analysis of the diffraction from deformation faulted f. c. c. crystals can be extended to intersecting faulted {111} planes, provided that the faulting parameter, α , is not greater than about 0·1. The main limitation of the optical method concerns the restriction in the number of layers (10 3 ) which can be conveniently represented in one grating. This restriction gives rise to weak fluctuations in the observed intensity distribution and to an uncertainty of up to 0·03 in the determination of α from this distribution.

An optical method of studying the diffraction from imperfect crystals II. Crystals with dislocations

1957 ◽  
Vol 239 (1217) ◽  
pp. 192-201 ◽  
Keyword(s):  
Intensity Distribution ◽  
Optical Method ◽  
Reciprocal Lattice ◽  
Lattice Points ◽  
Dimensional Problem ◽  
Single Edge ◽  
General Complex ◽  
Diffraction Patterns ◽  
Special Points ◽  
The Ideal

Lipson’s optical diffractometer has been used to determine the diffraction patterns of gratings representing crystals with dislocations. The optical method lends itself readily to the solution of the two-dimensional problem of diffraction by a single edge dislocation. The intensity distribution near the ideal reciprocal lattice points is, in general, complex, but for certain special points it is relatively simple and in agreement with that deduced by a new theory of Suzuki. An earlier theory of Wilson’s fails to explain the observed intensity distribution. Diffuse scattering, not predicted by Suzuki’s theory, occurs in the form of streaks joining the reciprocal lattice points. The diffraction has also been studied from gratings consisting of photographs of dislocated bubble rafts, and from a grating whose diffraction pattern is related to that of a screw dislocation. A brief discussion is given of the expected diffraction patterns from crystals with various arrays of dislocations.

Determination of dispersion and polarization of thermal plane waves in crystals

1971 ◽  
Vol 134 (3-4) ◽  
Author(s):  
P. L. La Fleur
Keyword(s):  
Intensity Distribution ◽  
Phonon Scattering ◽  
Reciprocal Lattice ◽  
Plane Waves ◽  
Lattice Points ◽  
X Ray Diffraction ◽  
Diffraction Intensity ◽  
Reciprocal Lattice Point ◽  
X Ray

AbstractThe dispersion of the thermal plane waves (phonons) in crystals can be determined from the x-ray diffraction intensity distribution around a reciprocal lattice point. In the method presented here no higher-order phonon-scattering corrections are necessary. It is shown furthermore that polarizations and dispersion of the phonons can be determined from the intensity distributions around six properly chosen reciprocal lattice points.

Propagation of an X-ray beam modified by a photonic crystal

2014 ◽  
Vol 21 (4) ◽  
pp. 729-735 ◽  
Author(s):  
V. G. Kohn ◽  
I. Snigireva ◽  
A. Snigirev
Keyword(s):  
Numerical Simulation ◽  
Approximate Solution ◽  
Photonic Crystal ◽  
Photonic Crystals ◽  
Intensity Distribution ◽  
Step Size ◽  
X Ray ◽  
The Face ◽  
Cubic Structure ◽  
First Time

A method of calculating the transmission of hard X-ray radiation through a perfect and well oriented photonic crystal and the propagation of the X-ray beam modified by a photonic crystal in free space is developed. The method is based on the approximate solution of the paraxial equation at short distances, from which the recurrent formula for X-ray propagation at longer distances is derived. A computer program for numerical simulation of images of photonic crystals at distances just beyond the crystal up to several millimetres was created. Calculations were performed for Ni inverted photonic crystals with the [111] axis of the face-centred-cubic structure for distances up to 0.4 mm with a step size of 4 µm. Since the transverse periods of the X-ray wave modulation are of several hundred nanometres, the intensity distribution of such a wave is changed significantly over the distance of several micrometres. This effect is investigated for the first time.

Weak Beam Imaging and Diffraction Studies of Stacking Faults in Silicon

1976 ◽  
Vol 34 ◽  
pp. 590-591
Author(s):  
T. Y. Tan ◽  
W. K. Tice
Keyword(s):  
Fast Neutron ◽  
Rapid Determination ◽  
Stacking Faults ◽  
Imaging Method ◽  
Large Reduction ◽  
Dislocation Loops ◽  
Fringe Spacing ◽  
Weak Beam ◽  
Kinematical Theory

In studying ion implanted semiconductors and fast neutron irradiated metals, the need for characterizing small dislocation loops having diameters of a few hundred angstrom units usually arises. The weak beam imaging method is a powerful technique for analyzing these loops. Because of the large reduction in stacking fault (SF) fringe spacing at large sg, this method allows for a rapid determination of whether the loop is faulted, and, hence, whether it is a perfect or a Frank partial loop. This method was first used by Bicknell to image small faulted loops in boron implanted silicon. He explained the fringe spacing by kinematical theory, i.e., ≃l/(Sg) in the fault fringe in depth oscillation. The fault image contrast formation mechanism is, however, really more complicated.

A new method of complex structure analysis by electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 628-629
Author(s):  
V.V. Rybin ◽  
E.V. Voronina
Keyword(s):  
Complex Structure ◽  
Reciprocal Lattice ◽  
Stacking Faults ◽  
Plastic Strains ◽  
Base Position ◽  
Structural Regularity ◽  
Orientation Matrix ◽  
Computerized Processing ◽  
Fully Automatic ◽  
Diffraction Patterns

Recently, it has become essential to develop a helpful method of the complete crystallographic identification of fine fragmented crystals. This was maainly due to the investigation into structural regularity of large plastic strains. The method should be practicable for determining crystallographic orientation (CO) of elastically stressed micro areas of the order of several micron fractions in size and filled with λ>1010 cm-2 density dislocations or stacking faults. The method must provide the misorientation vectors of the adjacent fragments when the angle ω changes from 0 to 180° with the accuracy of 0,3°. The problem is that the actual electron diffraction patterns obtained from fine fragmented crystals are the superpositions of reflections from various fragments, though more than one or two reflections from a fragment are hardly possible. Finally, the method should afford fully automatic computerized processing of the experimental results.The proposed method meets all the above requirements. It implies the construction for a certain base position of the crystal the orientation matrix (0M) A, which gives a single intercorrelation between the coordinates of the unity vector in the reference coordinate system (RCS) and those of the same vector in the crystal reciprocal lattice base : .

Fast calibration of CBED patterns for quantitative analysis

1993 ◽  
Vol 51 ◽  
pp. 674-675
Author(s):  
M.A. Gribelyuk ◽  
M. Rühle
Keyword(s):  
Reciprocal Lattice ◽  
Accurate Determination ◽  
Incident Beam ◽  
Crystal Thickness ◽  
Structure Model ◽  
Beam Direction ◽  
Transmitted Beam ◽  
Reciprocal Vector ◽  
On Line

A new method is suggested for the accurate determination of the incident beam direction K, crystal thickness t and the coordinates of the basic reciprocal lattice vectors V1 and V2 (Fig. 1) of the ZOLZ plans in pixels of the digitized 2-D CBED pattern. For a given structure model and some estimated values Vest and Kest of some point O in the CBED pattern a set of line scans AkBk is chosen so that all the scans are located within CBED disks.The points on line scans AkBk are conjugate to those on A0B0 since they are shifted by the reciprocal vector gk with respect to each other. As many conjugate scans are considered as CBED disks fall into the energy filtered region of the experimental pattern. Electron intensities of the transmitted beam I0 and diffracted beams Igk for all points on conjugate scans are found as a function of crystal thickness t on the basis of the full dynamical calculation.

scholarly journals Determination of the Vertical Dimension and the Position of the Occlusal Plane in a Removable Prosthesis Using Cephalometric Analysis and Golden Proportion

2021 ◽  
Vol 11 (15) ◽  
pp. 6948
Author(s):  
Gabriele Cervino ◽  
Sergio Sambataro ◽  
Chiara Stumpo ◽  
Salvatore Bocchieri ◽  
Fausto Murabito ◽  
...  
Keyword(s):  
Vertical Dimension ◽  
Occlusal Plane ◽  
X Rays ◽  
Common Procedure ◽  
Lower Incisor ◽  
Golden Proportion ◽  
The Face ◽  
Removable Prosthesis ◽  
Edentulous Patients

The aim of this study is to demonstrate the use and the effectiveness of cephalometry and golden proportions analysis of the face in planning prosthetic treatments in totally edentulous patients. In order to apply this method, latero-lateral and posterior-anterior X-rays must be performed in addition to the common procedure. Two main concerns for totally edentulous patients are the establishment of the vertical dimension and the new position of the occlusal plane. The divine proportion analysis was carried out by the use of a golden divider. The prosthetic protocol was divided into three steps and a case was selected for better understanding. Referring to the golden relations, if the distance from the chin to the wing of the nose is 1.0, the distance from the nose to eye is 0.618. This proportion is useful and effective in determining the correct prosthetic vertical dimension. The incisal margin of the lower incisor must be positioned between Point A (A) and protuberance menti (Pm) according to the gold ratio 0.618 of the total height A-Pm. Posteriorly the occlusal plane must be placed 2 mm below the divine occlusal plane (traced from the incisal margin of lower incisors to Xi point). A prosthesis made in accordance with cephalometric parameters and divine proportions of the face helps to improve the patient’s aesthetics, function and social personality.

scholarly journals On-chip trans-dimensional plasmonic router

Nanophotonics ◽  
2020 ◽  
Vol 9 (10) ◽  
pp. 3357-3365 ◽  
Author(s):  
Shaohua Dong ◽  
Qing Zhang ◽  
Guangtao Cao ◽  
Jincheng Ni ◽  
Ting Shi ◽  
...  
Keyword(s):  
High Speed ◽  
High Efficiency ◽  
Incident Angle ◽  
Reciprocal Lattice ◽  
Plasmonic Waveguide ◽  
Optical Diffraction ◽  
Local Dynamic ◽  
Phase Gradient ◽  
On Chip ◽  
Plasmon Polaritons

AbstractPlasmons, as emerging optical diffraction-unlimited information carriers, promise the high-capacity, high-speed, and integrated photonic chips. The on-chip precise manipulations of plasmon in an arbitrary platform, whether two-dimensional (2D) or one-dimensional (1D), appears demanding but non-trivial. Here, we proposed a meta-wall, consisting of specifically designed meta-atoms, that allows the high-efficiency transformation of propagating plasmon polaritons from 2D platforms to 1D plasmonic waveguides, forming the trans-dimensional plasmonic routers. The mechanism to compensate the momentum transformation in the router can be traced via a local dynamic phase gradient of the meta-atom and reciprocal lattice vector. To demonstrate such a scheme, a directional router based on phase-gradient meta-wall is designed to couple 2D SPP to a 1D plasmonic waveguide, while a unidirectional router based on grating metawall is designed to route 2D SPP to the arbitrarily desired direction along the 1D plasmonic waveguide by changing the incident angle of 2D SPP. The on-chip routers of trans-dimensional SPP demonstrated here provide a flexible tool to manipulate propagation of surface plasmon polaritons (SPPs) and may pave the way for designing integrated plasmonic network and devices.

Topological crystallography of gas hydrates

2015 ◽  
Vol 71 (4) ◽  
pp. 444-450 ◽  
Author(s):  
Sergey V. Gudkovskikh ◽  
Mikhail V. Kirov
Keyword(s):  
Hydrogen Bonding ◽  
Gas Hydrates ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Hexagonal Structure ◽  
New Approach ◽  
Quotient Graphs ◽  
Disordered Structure ◽  
Unit Cells ◽  
Cubic Structure

A new approach to the investigation of the proton-disordered structure of clathrate hydrates is presented. This approach is based on topological crystallography. The quotient graphs were built for the unit cells of the cubic structure I and the hexagonal structure H. This is a very convenient way to represent the topology of a hydrogen-bonding network under periodic boundary conditions. The exact proton configuration statistics for the unit cells of structure I and structure H were obtained using the quotient graphs. In addition, the statistical analysis of the proton transfer along hydrogen-bonded chains was carried out.

Sign in / Sign up

Export Citation Format

Share Document