Diffraction Theory

2005 ◽  
pp. 167-202
Keyword(s):  
Diffraction Theory

Relative Intensities in ED Patterns From Thin Gold Films

1972 ◽  
Vol 30 ◽  
pp. 636-637
Author(s):  
R. H. Morriss ◽  
J. D. C. Peng ◽  
C. D. Melvin
Keyword(s):  
Theoretical Calculations ◽  
Diffraction Theory ◽  
Gold Films ◽  
Reasonable Accuracy ◽  
Experimental Conditions ◽  
Crystal Perfection ◽  
Heavy Atoms ◽  
Fine Focus ◽  
Convergent Beam ◽  
Beam Diffraction

Although dynamical diffraction theory was modified for electrons by Bethe in 1928, relatively few calculations have been carried out because of computational difficulties. Even fewer attempts have been made to correlate experimental data with theoretical calculations. The experimental conditions are indeed stringent - not only is a knowledge of crystal perfection, morphology, and orientation necessary, but other factors such as specimen contamination are important and must be carefully controlled. The experimental method of fine-focus convergent-beam electron diffraction has been successfully applied by Goodman and Lehmpfuhl to single crystals of MgO containing light atoms and more recently by Lynch to single crystalline (111) gold films which contain heavy atoms. In both experiments intensity distributions were calculated using the multislice method of n-beam diffraction theory. In order to obtain reasonable accuracy Lynch found it necessary to include 139 beams in the calculations for gold with all but 43 corresponding to beams out of the [111] zone.

“Preparation of Single Crystalline Gold Films for ED Studies”

1972 ◽  
Vol 30 ◽  
pp. 634-635
Author(s):  
Joseph D. C. Peng
Keyword(s):  
Crystal Morphology ◽  
Diffraction Theory ◽  
Scattering Matrix ◽  
Vacuum Evaporation ◽  
Gold Films ◽  
Matrix Formulation ◽  
Silver Films ◽  
Single Crystalline ◽  
Grating Pattern ◽  
Stacking Disorder

The relative intensities of the ED spots in a cross-grating pattern can be calculated using N-beam electron diffraction theory. The scattering matrix formulation of N-beam ED theory has been previously applied to imperfect microcrystals of gold containing stacking disorder (coherent twinning) in the (111) crystal plane. In the present experiment an effort has been made to grow single-crystalline, defect-free (111) gold films of a uniform and accurately know thickness using vacuum evaporation techniques. These represent stringent conditions to be met experimentally; however, if a meaningful comparison is to be made between theory and experiment, these factors must be carefully controlled. It is well-known that crystal morphology, perfection, and orientation each have pronounced effects on relative intensities in single crystals.The double evaporation method first suggested by Pashley was employed with some modifications. Oriented silver films of a thickness of about 1500Å were first grown by vacuum evaporation on freshly cleaved mica, with the substrate temperature at 285° C during evaporation with the deposition rate at 500-800Å/sec.

The Interpretation of Crystal Lattice Images

1972 ◽  
Vol 30 ◽  
pp. 550-551
Author(s):  
J. M. Cowley ◽  
Sumio Iijima
Keyword(s):  
Crystal Orientation ◽  
Diffraction Theory ◽  
Phase Changes ◽  
Electron Wave ◽  
Crystal Lattices ◽  
Heavy Atoms ◽  
Lattice Images ◽  
The Right ◽  
Intuitive Interpretation ◽  
Suitable Approximation

The imaging of detailed structures of crystal lattices with 3 to 4Å resolution, given the correct conditions of microscope defocus and crystal orientation and thickness, has been used by Iijima (this conference) for the study of new types of crystal structures and the defects in known structures associated with fluctuations of stoichiometry. The image intensities may be computed using n-beam dynamical diffraction theory involving several hundred beams (Fejes, this conference). However it is still important to have a suitable approximation to provide an immediate rough estimate of contrast and an evaluation of the intuitive interpretation in terms of an amplitude object.For crystals 100 to 150Å thick containing moderately heavy atoms the phase changes of the electron wave vary by about 10 radians suggesting that the “optimum defocus” theory of amplitude contrast for thin phase objects due to Scherzer and others can not apply, although it does predict the right defocus for optimum imaging.

X-ray diffraction properties of curved crystal diffractors

1992 ◽  
Vol 50 (2) ◽  
pp. 1734-1735
Author(s):  
W. Z. Chang ◽  
D. B. Wittry
Keyword(s):  
Diffraction Theory ◽  
X Rays ◽  
Diffraction Image ◽  
X Ray Diffraction ◽  
Rocking Curve ◽  
X Ray ◽  
Bent Crystal ◽  
Diffraction Geometry ◽  
Crystal Parameter ◽  
Quantitative Procedure

Since Du Mond and Kirkpatrick first discussed the principle of a bent crystal spectrograph in 1930, curved single crystals have been widely utilized as spectrometric monochromators as well as diffractors for focusing x rays diverging from a point. Curved crystal diffraction theory predicts that the diffraction parameters - the rocking curve width w, and the peak reflection coefficient r of curved crystals will certainly deviate from those of their flat form. Due to a lack of curved crystal parameter data in current literature and the need for optimizing the choice of diffraction geometry and crystal materials for various applications, we have continued the investigation of our technique presented at the last conference. In the present abstract, we describe a more rigorous and quantitative procedure for measuring the parameters of curved crystals.The diffraction image of a singly bent crystal under study can be obtained by using the Johann geometry with an x-ray point source.

Highlights in the history of X-ray topography1

1995 ◽  
Vol 210 (6) ◽  
Author(s):  
A. R. Lang
Keyword(s):  
Magnetic Domain ◽  
Diffraction Theory ◽  
Dislocation Loops ◽  
X Ray Diffraction ◽  
X Ray ◽  
Domain Structures ◽  
Structure Factors ◽  
History Of ◽  
Dislocation Sources ◽  
Non Destructive

AbstractX-ray topography provides a non-destructive method of mapping point-by-point variations in orientation and reflecting power within crystals. The discovery, made by several workers independently, that in nearly perfect crystals it was possible to detect individual dislocations by X-ray diffraction contrast started an epoch of rapid exploitation of X-ray topography as a new, general method for assessing crystal perfection. Another discovery, that of X-ray Pendellösung, led to important theoretical developments in X-ray diffraction theory and to a new and precise method for measuring structure factors on an absolute scale. Other highlights picked out for mention are studies of Frank-Read dislocation sources, the discovery of long dislocation helices and lines of coaxial dislocation loops in aluminium, of internal magnetic domain structures in Fe-3 wt.% Si, and of stacking faults in silicon and natural diamonds.

Diffraction theory of optical scintillations due to turbulent layers

1975 ◽  
Vol 65 (1) ◽  
pp. 78 ◽  
Author(s):  
Leonard S. Taylor ◽  
Charles J. Infosino
Keyword(s):  
Diffraction Theory

scholarly journals “Perfect” Terahertz Vortex Beams Formed Using Diffractive Axicons and Prospects for Excitation of Vortex Surface Plasmon Polaritons

2021 ◽  
Vol 11 (2) ◽  
pp. 717
Author(s):  
Boris Knyazev ◽  
Valery Cherkassky ◽  
Oleg Kameshkov
Keyword(s):  
Surface Plasmon ◽  
Surface Plasmon Polaritons ◽  
Bessel Beam ◽  
Diffraction Theory ◽  
Terahertz Range ◽  
High Resistivity ◽  
Visible Range ◽  
Optical Elements ◽  
Scalar Diffraction ◽  
Plasmon Polaritons

Transformation of a Bessel beam by a lens results in the formation of a “perfect” vortex beam (PVB) in the focal plane of the lens. The PVB has a single-ring cross-section and carries an orbital angular momentum (OAM) equal to the OAM of the “parent” beam. PVBs have numerous applications based on the assumption of their ideal ring-type structure. For instance, we proposed using terahertz PVBs to excite vortex surface plasmon polaritons propagating along cylindrical conductors and the creation of plasmon multiplex communication lines in the future (Comput. Opt. 2019, 43, 992). Recently, we demonstrated the formation of PVBs in the terahertz range using a Bessel beam produced using a spiral binary silicon axicon (Phys. Rev. A 2017, 96, 023846). It was shown that, in that case, the PVB was not annular, but was split into nested spiral segments, which was obviously a consequence of the method of Bessel beam generation. The search for methods of producing perfect beams with characteristics approaching theoretically possible ones is a topical task. Since for the terahertz range, there are no devices like spatial modulators of light in the visible range, the main method for controlling the mode composition of beams is the use of diffractive optical elements. In this work, we investigated the characteristics of perfect beams, the parent beams being quasi-Bessel beams created by three types of diffractive phase axicons made of high-resistivity silicon: binary, kinoform, and “holographic”. The amplitude-phase distributions of the field in real perfect beams were calculated numerically in the approximation of the scalar diffraction theory. An analytical expression was obtained for the case of the binary axicon. It was shown that a distribution closest to an ideal vortex was obtained using a holographic axicon. The resulting distributions were compared with experimental and theoretical distributions of the evanescent field of a plasmon near the gold–zinc sulfide–air surface at different thicknesses of the dielectric layer, and recommendations for experiments were given.

Diffraction Theory Of Double Grating And Its Application

1987 ◽  
Author(s):  
Zhang You-wen ◽  
Tu Jing-hong
Keyword(s):  
Diffraction Theory

On the circle polynomials of Zernike and related orthogonal sets

1954 ◽  
Vol 50 (1) ◽  
pp. 40-48 ◽  
Author(s):  
A. B. Bhatia ◽  
E. Wolf
Keyword(s):  
Unit Circle ◽  
Generating Functions ◽  
Legendre Polynomials ◽  
Phase Contrast ◽  
Diffraction Theory ◽  
Zernike Polynomials ◽  
Optical Aberrations ◽  
Orthogonal Set ◽  
Complete Orthogonal Set ◽  
Explicit Expressions

ABSTRACTThe paper is concerned with the construction of polynomials in two variables, which form a complete orthogonal set for the interior of the unit circle and which are ‘invariant in form’ with respect to rotations of axes about the origin of coordinates. It is found that though there exist an infinity of such sets there is only one set which in addition has certain simple properties strictly analogous to that of Legendre polynomials. This set is found to be identical with the set of the circle polynomials of Zernike which play an important part in the theory of phase contrast and in the Nijboer-Zernike diffraction theory of optical aberrations.The results make it possible to derive explicit expressions for the Zernike polynomials in a simple, systematic manner. The method employed may also be used to derive other orthogonal sets. One new set is investigated, and the generating functions for this set and for the Zernike polynomials are also given.

Sign in / Sign up

Export Citation Format

Share Document