Dingle temperature calculated for electrons gyrating in a perfect crystal lattice

2006 ◽  
Vol 371 (2) ◽  
pp. 215-217 ◽  
Author(s):  
S. Olszewski ◽  
T. Roliński
Keyword(s):  
Crystal Lattice ◽  
Perfect Crystal

Observation of multiple Bragg reflections accompanying forbidden Si(002) reflection in bent-perfect Si crystal

2021 ◽  
pp. 1-6
Author(s):  
P. Mikula ◽  
M. Vrána ◽  
J. Šaroun ◽  
V. Ryukhtin
Keyword(s):  
High Resolution ◽  
Crystal Lattice ◽  
Perfect Crystal ◽  
Monochromatic Beam ◽  
Very High

Strong multiple Bragg reflections (MBRs) which can be realized in a bent-perfect-crystal (BPC) slab provide a monochromatic beam of excellent resolution parameters. For identifying MBR effects in the BPC Si crystal, we used the method of azimuthal rotation of the crystal lattice around the scattering vector of the primary forbidden Si(200) reflection for a fixed chosen wavelength. In this paper, several azimuthal scans searching strong MBR effects with the intention of a possible practical exploitation for very high-resolution diffractometry are presented.

Micro Grain Analysis in Plastically Deformed Silicon by 2nd-Order X-Ray Diffraction

MRS Advances ◽  
2018 ◽  
Vol 3 (39) ◽  
pp. 2347-2352 ◽  
Author(s):  
Gabriel Dina ◽  
Ariel Gomez Gonzalez ◽  
Sérgio L. Morelhão ◽  
Stefan Kycia
Keyword(s):  
Crystal Lattice ◽  
Perfect Crystal ◽  
Relative Orientation ◽  
Silicon Single Crystal ◽  
Grain Structure ◽  
X Rays ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
X Ray ◽  
Micro Scale

AbstractSecond-order diffraction (SOD) of x-rays refers to all diffraction processes where the photons reaching the detector have been diffracted twice within a crystal lattice. By measuring the two dimensional intensity profile of SOD, it is possible to distinguishing rescattering processes taking place inside each grain (perfect crystal domain) or in between grains. These two SOD regimes, usually called dynamical and kinematical, respectively, are ruled by size and relative orientation of the grains. In this work, we demonstrate how to explore SOD phenomena to understand the micro scale grain structure in plastically deformed silicon single crystal.

Study on Influence of Silicon Crystal Dislocation on Removal in Atmospheric Pressure Plasma Polishing

2016 ◽  
Vol 878 ◽  
pp. 83-88 ◽  
Author(s):  
Guang Lu Jia ◽  
Bing Li ◽  
Ju Fan Zhang
Keyword(s):  
Dislocation Density ◽  
Crystal Lattice ◽  
Dislocation Structure ◽  
Edge Dislocation ◽  
Atmospheric Pressure ◽  
Silicon Crystal ◽  
Atmospheric Pressure Plasma ◽  
Perfect Crystal ◽  
Pressure Plasma ◽  
Quantum Chemistry Simulation

Compared to perfect crystal lattice, typical edge dislocation structure has been modeled by quantum chemistry simulation in order to analyze the influence of crystal structure defects on removal process in atmospheric pressure plasma polishing (APPP). The Partial density of states (PDOS), number of states, average number of bonding electrons and energy have been calculated and analyzed further for these models. The analysis results reveal that silicon crystal with edge dislocation can be etched more easily than that of perfect crystal lattice. It is also found that the removal rate of sample with higher dislocation density is larger than that of lower dislocation density in the same experiment conditions. Thus, theoretical simulation demonstrates that structure dislocation is helpful for raising the etching rate, which accords well with testifying experiments results. But maybe structure dislocation could deteriorate surface roughness to some extent in initial stage of machining, as the dislocation structure is usually etched unevenly, although this is just a transition period.

Internal Structure of Diamond Nanocrystals by Modeling and PDF Analysis

2013 ◽  
Vol 1554 ◽  
Author(s):  
S. Stelmakh ◽  
W. Palosz ◽  
S. Gierlotka ◽  
K. Skrobas ◽  
B. Palosz
Keyword(s):  
Crystal Lattice ◽  
Inner Core ◽  
Diamond Crystal ◽  
Perfect Crystal ◽  
Density Waves ◽  
Atomistic Models ◽  
Pdf Analysis ◽  
Density Modulation ◽  
Modulated Waves ◽  
Grain Core

ABSTRACTThe structure of nanocrystalline diamond was approximated by spherical nanograins assuming that the grain core with a perfect crystal lattice is surrounded by a sequence of shells with (essentially) identical atomic architecture but with altered density. We call such a model a nanocrystal with density modulated waves. To examine the effect of density modulation present in nanograins, we built atomistic models of nanodiamond grains and compared the average values of inter-atomic distances calculated for the grains with density waves to those calculated for grains with the perfect, diamond crystal lattice. We show that the atomic structure of nanodiamond can be best described by a model where, between the inner core and the surface layer, three density waves with intermittent compressive and tensile strains exist. The sequence of the density waves is preserved in all examined nanodiamond samples without regard to chemical treatment and vacuum annealing (at up to 1200°C).

Experimental studies of dispersive double reflections excited in cylindrically bent perfect-crystal slabs at a constant neutron wavelength

2012 ◽  
Vol 45 (1) ◽  
pp. 98-105 ◽  
Author(s):  
Pavol Mikula ◽  
Miroslav Vrána ◽  
Jan Šaroun ◽  
Vadim Davydov ◽  
Vyacheslav Em ◽  
...  
Keyword(s):  
High Resolution ◽  
Crystal Lattice ◽  
Experimental Studies ◽  
Perfect Crystal ◽  
Monochromatic Beam ◽  
Diffraction Geometry ◽  
Neutron Wavelength ◽  
Selected Effects ◽  
Very High

Multiple Bragg reflections (MBRs), which can be realized in a bent perfect crystal (BPC) slab and are mutually in dispersive diffraction geometry, provide a monochromatic beam of excellent resolution. After identifying many MBR effects in a BPC Si crystal by using the method of θ–2θDscanning, we have turned our attention to the study of selected effects using the method of azimuthal rotation of the crystal lattice around the scattering vector of the primary reflection for a fixed chosen wavelength. In this paper, several azimuthal scans with the intention of possible practical exploitation for very high resolution diffractometry are presented.

Diffraction contrast of electron microscope images of crystal lattice defects - II. The development of a dynamical theory

1961 ◽  
Vol 263 (1313) ◽  
pp. 217-237 ◽  
Keyword(s):  
Electron Microscope ◽  
Electron Diffraction ◽  
Crystal Lattice ◽  
Formal Solution ◽  
Dynamical Theory ◽  
Perfect Crystal ◽  
Lattice Defects ◽  
Microscope Images ◽  
Crystal Lattice Defects ◽  
Kinematical Theory

The dynamical theory of electron diffraction is developed in a form suitable for the computation of images of crystal lattice defects such as dislocations observed by transmission electron microscopy. As shown in a previous kinematical theory, the contrast arises because the waves diffracted by atoms near the defect are changed in phase as a result of the displacements of these atoms from the perfect crystal positions. The two-beam dynamical theory of diffraction in the symmetrical Laue case is derived from simple kinematical principles by methods similar to those used by Darwin in the Bragg case. Simultaneous differential equations describing the changes of incident and diffracted wave amplitudes with depth in a crystal are obtained. In a perfect crystal these equations lead to the well-known Laue solutions of the dynamical equations of electron diffraction and in a deformed crystal they reduce to the kinematical theory when the deviation from the reflecting position is large. The effects of absorption can be included phenomenologically by use of a complex atomic scattering factor (complex lattice potential). Finally it is shown that an equivalent theory may be derived directly from wave mechanics in a way which allows the effects of absorption and several diffracted beams to be included. From the formal solution of this general theory some important symmetry relations for electron microscope images of defects can be deduced.

Bayesian removal of noise for increased sensitivity in vector pattern recognition lattice imaging of interfaces

1993 ◽  
Vol 51 ◽  
pp. 994-995
Author(s):  
L. Fei ◽  
P. Fraundorf
Keyword(s):  
Pattern Recognition ◽  
Perfect Crystal ◽  
Unit Cell ◽  
Ion Milling ◽  
Beam Radiation ◽  
Major Interest ◽  
Unit Cells ◽  
Mapping Process ◽  
Increased Sensitivity ◽  
Electron Microscopes

Interface structure is of major interest in microscopy. With high resolution transmission electron microscopes (TEMs) and scanning probe microscopes, it is possible to reveal structure of interfaces in unit cells, in some cases with atomic resolution. A. Ourmazd et al. proposed quantifying such observations by using vector pattern recognition to map chemical composition changes across the interface in TEM images with unit cell resolution. The sensitivity of the mapping process, however, is limited by the repeatability of unit cell images of perfect crystal, and hence by the amount of delocalized noise, e.g. due to ion milling or beam radiation damage. Bayesian removal of noise, based on statistical inference, can be used to reduce the amount of non-periodic noise in images after acquisition. The basic principle of Bayesian phase-model background subtraction, according to our previous study, is that the optimum (rms error minimizing strategy) Fourier phases of the noise can be obtained provided the amplitudes of the noise is given, while the noise amplitude can often be estimated from the image itself.

Calculation of many-beam dynamic electron diffraction without high-energy approximation

1996 ◽  
Vol 54 ◽  
pp. 128-129
Author(s):  
B. R. Ahn ◽  
N. J. Kim
Keyword(s):  
Electron Diffraction ◽  
Flat Surface ◽  
Dynamic Theory ◽  
High Energy ◽  
Perfect Crystal ◽  
Zone Axis ◽  
Beam Dynamic ◽  
Diffraction Angle ◽  
Energy Approximation ◽  
The Many

High energy approximation in dynamic theory of electron diffraction involves some intrinsic problems. First, the loss of theoretical strictness makes it difficult to comprehend the phenomena of electron diffraction. Secondly, it is difficult to believe that the approximation is reasonable especially in the following cases: 1) when accelerating voltage is not sufficiently high, 2) when the specimen is thick, 3) when the angle between the surface normal of the specimen and zone axis is large, and 4) when diffracted beam with large diffraction angle is included in the calculation. However, until now the method to calculate the many beam dynamic electron diffraction without the high energy approximation has not been proposed. For this reason, the authors propose a method to eliminate the high energy approximation in the calculation of many beam dynamic electron diffraction. In this method, a perfect crystal with flat surface was assumed. The method was applied to the calculation of [111] zone axis CBED patterns of Si.

Simulation and Contrast Analysis of tem Images of Cracks

1990 ◽  
Vol 48 (1) ◽  
pp. 578-579
Author(s):  
D. Goyal ◽  
A. H. King
Keyword(s):  
Displacement Vector ◽  
Crack Tip ◽  
Perfect Crystal ◽  
Operating Conditions ◽  
Displacement Fields ◽  
Fringe Contrast ◽  
Orthogonal Geometry ◽  
Moire Fringe ◽  
Moiré Fringe

TEM images of cracks have been found to give rise to a moiré fringe type of contrast. It is apparent that the moire fringe contrast is observed because of the presence of a fault in a perfect crystal, and is characteristic of the fault geometry and the diffracting conditions in the TEM. Various studies have reported that the moire fringe contrast observed due to the presence of a crack in an otherwise perfect crystal is distinctive of the mode of crack. This paper describes a technique to study the geometry and mode of the cracks by comparing the images they produce in the TEM because of the effect that their displacement fields have on the diffraction of electrons by the crystal (containing a crack) with the corresponding theoretical images. In order to formulate a means of matching experimental images with theoretical ones, displacement fields of dislocations present (if any) in the vicinity of the crack are not considered, only the effect of the displacement field of the crack is considered.The theoretical images are obtained using a computer program based on the two beam approximation of the dynamical theory of diffraction contrast for an imperfect crystal. The procedures for the determination of the various parameters involved in these computations have been well documented. There are three basic modes of crack. Preliminary studies were carried out considering the simplest form of crack geometries, i. e., mode I, II, III and the mixed modes, with orthogonal crack geometries. It was found that the contrast obtained from each mode is very distinct. The effect of variation of operating conditions such as diffracting vector (), the deviation parameter (ω), the electron beam direction () and the displacement vector were studied. It has been found that any small change in the above parameters can result in a drastic change in the contrast. The most important parameter for the matching of the theoretical and the experimental images was found to be the determination of the geometry of the crack under consideration. In order to be able to simulate the crack image shown in Figure 1, the crack geometry was modified from a orthogonal geometry to one with a crack tip inclined to the original crack front. The variation in the crack tip direction resulted in the variation of the displacement vector also. Figure 1 is a cross-sectional micrograph of a silicon wafer with a chromium film on top, showing a crack in the silicon.

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