Observation of the two-dimensional reciprocal lattice by use of lattice grating sheets and a laser pointer

2014 ◽  
Vol 35 (5) ◽  
pp. 055021
Author(s):  
Takanori Tsutaoka ◽  
Tomohito Tokunaga ◽  
Takashi Umeda ◽  
Toshinobu Maehara
Keyword(s):  
Reciprocal Lattice ◽  
Two Dimensional ◽  
Laser Pointer

An Instructional Two-Dimensional Diffraction Laboratory Using Patterns Created with Electron-Beam Lithography

2002 ◽  
Vol 760 ◽  
Author(s):  
Colin Inglefield ◽  
Royce Anthon
Keyword(s):  
Electron Beam ◽  
Undergraduate Students ◽  
Electron Beam Lithography ◽  
Materials Science ◽  
Reciprocal Lattice ◽  
Real Space ◽  
Two Dimensional ◽  
Solid State Physics ◽  
Modern Physics ◽  
Order Of Magnitude

ABSTRACTAn instructional laboratory in two-dimensional diffraction is discussed. The experiment is appropriate for undergraduate students in materials science, solid-state physics (as was the case with our group), modern physics, or optics. The experiment is performed using visible light from a laser incident on a 2D lattice of gold dots deposited with electron beam lithography on a glass substrate. The pattern is microscopic with a lattice constant on the same order of magnitude as the wavelength of light used. Students observe the diffraction pattern, and then quantitatively determine the positions of maxima. These data are used by the students to reconstruct the (real space) microscopic lattice. The students can simulate the experiment with software that computes reciprocal lattice and diffraction patterns for an arbitrary 2D lattice.

scholarly journals Applications of dynamical theory of X-ray diffraction by perfect crystals to reciprocal space mapping

2017 ◽  
Vol 50 (5) ◽  
pp. 1256-1266 ◽  
Author(s):  
Vasily I. Punegov ◽  
Konstantin M. Pavlov ◽  
Andrey V. Karpov ◽  
Nikolai N. Faleev
Keyword(s):  
Reciprocal Lattice ◽  
Dynamical Theory ◽  
Two Dimensional ◽  
Instrumental Function ◽  
X Ray Diffraction ◽  
Reciprocal Space Mapping ◽  
Lattice Vector ◽  
Reflected Waves ◽  
X Ray ◽  
Special Case

The classical dynamical theory of X-ray diffraction is expanded to the special case of transversely restricted wavefronts of the incident and reflected waves. This approach allows one to simulate the two-dimensional coherently scattered intensity distribution centred around a particular reciprocal lattice vector in the so-called triple-crystal diffraction scheme. The effect of the diffractometer's instrumental function on X-ray diffraction data was studied.

scholarly journals Development of Four Kinds of Mobile Robot with Preliminary-Announcement and Indication Function of Upcoming Operation

2007 ◽  
Vol 19 (2) ◽  
pp. 148-159 ◽  
Author(s):  
Takafumi Matsumaru ◽  
Keyword(s):  
Mobile Robot ◽  
Mobile Robots ◽  
Two Dimensional ◽  
Flat Panel Display ◽  
Laser Pointer ◽  
Flat Panel ◽  
Future Time ◽  
Evaluation Score ◽  
Gender And Age ◽  
Direction Of Movement

We propose approaches and equipment for preliminarily announcing and indicating to people the speed and direction of movement of mobile robots moving on a two-dimensional plane. We introduce the four approaches categorized into (1) announcing the state just after the present and (2) indicating operations from the present to some future time continuously. To realize the approaches, we use omni-directional display (PMR-2), flat-panel display (PMR-6), laser pointer (PMR-1), and projection equipment (PMR-5) for the announcement unit of protobots. The four protobots were exhibited at the 2005 International Robot Exhibition (iREX05). We had visitors answer questionnaires in a 5-stage evaluation. The projector robot PMR-5 received the highest evaluation score among the four. An examination of differences by gender and age suggested that some people prefer simple information, friendly expressions, and a minimum of information to be presented at one time.

Bloch waves and higher order Laue zone effects in high energy electron diffraction

1976 ◽  
Vol 350 (1662) ◽  
pp. 335-361 ◽  
Keyword(s):  
Reciprocal Lattice ◽  
Wave Dispersion ◽  
High Energy ◽  
Zone Axis ◽  
Lattice Points ◽  
Two Dimensional ◽  
Perturbation Expansions ◽  
Bloch Waves ◽  
Bloch Functions ◽  
Dispersion Surface

The theory of the scattering of fast electrons by a thin crystalline slab is formulated in terms of the Bloch waves of an infinite perfect crystal. In the symmetric Laue case, effects due to the variation of the crystal potential U(r) along the zone axis parallel to the surface normal, are investigated by expanding these Bloch waves in terms of the Bloch functions of a two dimensional potential obtained by averaging U(r) along the zone axis. A high energy and forward scattering approximation is introduced which allows the scattering to be treated as an initial value problem. Perturbation expansions are used to analyse the changes in the dispersion surface and the Bloch waves when the variation of the potential along the zone axis is included. It is found that the most important perturbations are due to interactions associated with reciprocal lattice points in the Laue zones. These lead to hybridization of the Bloch functions of the two dimensional projected potential. A [111] zone axis of silicon at 293 K is studied as an example. In this case, the first order Laue zone leads to the strongest effects which can appear as fine bright lines in reflections in this zone, and also as fine lines in the strong reflexions in the zero Laue zone.The latter are usually dark, but can sometimes be bright. It is shown how it is often possible to separate the effects into the geometry of the intersection of free wave dispersion spheres centred on points in the non-zero Laue zones with the dispersion surface of the projected potential, and the strength of the matrix elements of the deviation of the potential U(r) from the projected potential.

scholarly journals BINoculars: data reduction and analysis software for two-dimensional detectors in surface X-ray diffraction

2015 ◽  
Vol 48 (4) ◽  
pp. 1324-1329 ◽  
Author(s):  
Sander Roobol ◽  
Willem Onderwaater ◽  
Jakub Drnec ◽  
Roberto Felici ◽  
Joost Frenken
Keyword(s):  
Data Reduction ◽  
Modular Design ◽  
Reciprocal Lattice ◽  
Measurement Techniques ◽  
Three Dimensional ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
Data Set ◽  
High Resolution Data ◽  
X Ray

BINocularsis a tool for data reduction and analysis of large sets of surface diffraction data that have been acquired with a two-dimensional X-ray detector. The intensity of each pixel of a two-dimensional detector is projected onto a three-dimensional grid in reciprocal-lattice coordinates using a binning algorithm. This allows for fast acquisition and processing of high-resolution data sets and results in a significant reduction of the size of the data set. The subsequent analysis then proceeds in reciprocal space. It has evolved from the specific needs of the ID03 beamline at the ESRF, but it has a modular design and can be easily adjusted and extended to work with data from other beamlines or from other measurement techniques. This paper covers the design and the underlying methods employed in this software package and explains howBINocularscan be used to improve the workflow of surface X-ray diffraction measurements and analysis.

A Laser Projection Device for Locating Points on the Plane Object

2012 ◽  
Vol 190-191 ◽  
pp. 1094-1098
Author(s):  
He Ding ◽  
Jian Fei Ouyang ◽  
Xiang Ma ◽  
Yong Gang Yan
Keyword(s):  
Mathematical Model ◽  
Image Processing ◽  
Digital Image Processing ◽  
Rotation Angle ◽  
Control Unit ◽  
Stepper Motor ◽  
Two Dimensional ◽  
Laser Pointer ◽  
Projection Device ◽  
The Mathematical Model

Digital image processing technology can extract the main feature of an image. In order to achieve the interaction between virtual points and plane objects, we propose the equipment for indicating points on the plane object using laser projection. We designed the equipment with a bracket, stepper motor, two-dimensional turntable, PC control unit, and a laser pointer. Next, we analyzed the mathematical model of the equipment and developed an algorithm for solving the motor rotation angle. Finally, we verified our design with an image. Here, we develop a system that can control a laser projection to a specified location by adjusting coordinates of virtual points on a computer.

Two-dimensional incommensurately modulated structure of (Sr0.13Ca0.87)2CoSi2O7 crystals

2000 ◽  
Vol 56 (5) ◽  
pp. 811-821 ◽  
Author(s):  
B. Bagautdinov ◽  
K. Hagiya ◽  
K. Kusaka ◽  
M. Ohmasa ◽  
K. Iishi
Keyword(s):  
Reciprocal Lattice ◽  
Basic Structure ◽  
Partial Ordering ◽  
Partial Substitution ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
Modulated Structure ◽  
X Ray ◽  
Oxygen Coordination ◽  
Incommensurate Structure

The incommensurate structure of (Sr0.13Ca0.87)2CoSi2O7 at room temperature has been determined from single-crystal X-ray diffraction data. The compound has a non-centrosymmetric tetragonal basic cell of a = 7.8743 (4) and c = 5.0417 (2) Å with the space group P4¯21 m. The refinements of the basic structure converged to R = 0.038 for 757 main reflections. The two-dimensional incommensurate structure is characterized by the wavevectors q 1 = 0.286 (3)(a* + b*) and q 2 = 0.286 (3)(−a* + b*), where a*, b* are the reciprocal lattice vectors of the basic structure. With the (3 + 2)-dimensional superspace group P p4mg P4¯21 m , the refinements converged to R = 0.071 for 1697 observed reflections (757 main and 940 satellite reflections). The structure is described in terms of displacement of the atoms, rotation, distortion of CoO4 and SiO4 tetrahedra, and the partial ordering of the Sr and Ca atoms accompanied with the modulation. Correlated evolution of these features throughout the crystal gives rise to various oxygen coordination around Ca/Sr. Comparison of the derived modulated structure to that of Ca2CoSi2O7 clarified that the partial substitution of Ca by large alkaline-earth atoms such as Sr should decrease the distortion of the polyhedra around the cations.

Phase Microidentification from Selected Area Electron Diffraction (SAED) and Energy Dispersive Spectroscopy (EDS) Data

1991 ◽  
Vol 35 (A) ◽  
pp. 687-691 ◽  
Author(s):  
Josef Macicek
Keyword(s):  
Electron Diffraction ◽  
Energy Dispersive Spectroscopy ◽  
Reciprocal Lattice ◽  
Energy Dispersive ◽  
Phase Identification ◽  
Two Dimensional ◽  
Selected Area Electron Diffraction ◽  
Elemental Data

AbstractTwo-dimensional geometry information contained in SAED spot patterns augmented with EDS elemental data is employed in a computerized phase identification of microcrystalline particles. The initial chemistry screening of a laboratory managed database using the 'bitmap' concept is followed by a geometry search/match treating of the spot patterns as planar sections through the reciprocal lattice of a candidate phase. The identification is selective, fast, and yields to a complete automatization,

Spectrophotometric measurements of objective-prism spectra

1966 ◽  
Vol 24 ◽  
pp. 118-119
Author(s):  
Th. Schmidt-Kaler
Keyword(s):  
Progress Report ◽  
Two Dimensional ◽  
Objective Prism ◽  
Made In

I should like to give you a very condensed progress report on some spectrophotometric measurements of objective-prism spectra made in collaboration with H. Leicher at Bonn. The procedure used is almost completely automatic. The measurements are made with the help of a semi-automatic fully digitized registering microphotometer constructed by Hög-Hamburg. The reductions are carried out with the aid of a number of interconnected programmes written for the computer IBM 7090, beginning with the output of the photometer in the form of punched cards and ending with the printing-out of the final two-dimensional classifications.

Introductory paper

1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan
Keyword(s):  
Line Intensity ◽  
Classification Scheme ◽  
Two Dimensional ◽  
Spectral Classification ◽  
Dimensional Array ◽  
Rr Lyrae ◽  
Metallic Line ◽  
Introductory Paper ◽  
Parameter Varying ◽  
Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

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