4. Diffraction

2016 ◽  
pp. 64-93
Author(s):  
A. M. Glazer
Keyword(s):  
Powder Diffraction ◽  
Fourier Transformation ◽  
Reciprocal Lattice ◽  
Academic Research ◽  
Three Dimensional ◽  
Metal Alloys ◽  
Convolution Theorem ◽  
Diffraction Reflection ◽  
New Type ◽  
Dimensional Crystal

In order to understand diffraction from a three-dimensional crystal, a new type of lattice, constructed from the real lattice used so far, is defined. It is the reciprocal lattice proposed by Paul Ewald around 1911. ‘Diffraction’ considers how this lattice is constructed and investigates its uses in understanding diffraction. Reflection intensities and amplitudes are also explained along with Friedel’s Law; the convolution theorem; Fourier Transformation; powder diffraction, which has many uses in industry and in academic research; incommensurate or modulated crystals; and quasicrystals, often seen in metal alloys, which cannot be explained by conventional crystal symmetry ideas. Finally, disorder in crystals is discussed.

Cd4 Tetrahedra and Condensed RE6Rh Trigonal Prisms as Building Units in the Rare Earth-rich Compounds RE15Rh5Cd2 (RE = La, Ce, Pr, Nd)

2011 ◽  
Vol 66 (6) ◽  
pp. 559-564 ◽  
Author(s):  
Frank Tappe ◽  
Ute Ch. Rodewald ◽  
Rolf-Dieter Hoffmann ◽  
Rainer Pöttgen
Keyword(s):  
Rare Earth ◽  
Single Crystal ◽  
Powder Diffraction ◽  
Three Dimensional ◽  
Induction Melting ◽  
X Ray ◽  
Dimensional Network ◽  
New Type ◽  
The Rare Earth ◽  
Trigonal Prisms

The rare earth-rich compounds RE15Rh5Cd2 (RE = La, Ce, Pr, Nd) were synthesized by induction melting of the elements in sealed tantalum tubes and characterized by X-ray powder diffraction. The structure of La15Rh5Cd2 was refined from single-crystal diffractometer data: new type, R3m, a = 1016.4(2), c = 4418.7(9) pm, wR2 = 0.0417, 2258 F2, 95 variables. Striking structural motifs in the RE15Rh5Cd2 intermetallics are rhodium-centered trigonal prisms RE6Rh which are condensed via common corners and edges to a complex three-dimensional network which leaves cavities for Cd4 tetrahedra and RE6 octahedra. The structural relationship with the recently discovered structure types Gd4RhIn and Pr23Ir7Mg4 is discussed.

convergent-beam diffraction from surfaces

1987 ◽  
Vol 45 ◽  
pp. 30-33
Author(s):  
J. A. Eades ◽  
A. E. Smith ◽  
D. F. Lynch
Keyword(s):  
Reciprocal Lattice ◽  
Three Dimensional ◽  
Grazing Incidence ◽  
Three Dimensions ◽  
Plane Figure ◽  
Transmission Electron ◽  
Convergent Beam ◽  
Beam Patterns ◽  
Beam Diffraction

It is quite simple (in the transmission electron microscope) to obtain convergent-beam patterns from the surface of a bulk crystal. The beam is focussed onto the surface at near grazing incidence (figure 1) and if the surface is flat the appropriate pattern is obtained in the diffraction plane (figure 2). Such patterns are potentially valuable for the characterization of surfaces just as normal convergent-beam patterns are valuable for the characterization of crystals.There are, however, several important ways in which reflection diffraction from surfaces differs from the more familiar electron diffraction in transmission.GeometryIn reflection diffraction, because of the surface, it is not possible to describe the specimen as periodic in three dimensions, nor is it possible to associate diffraction with a conventional three-dimensional reciprocal lattice.

Simulation of small-angle scattering curves by numerical Fourier transformation

2007 ◽  
Vol 40 (1) ◽  
pp. 16-25 ◽  
Author(s):  
Klaus Schmidt-Rohr
Keyword(s):  
Form Factor ◽  
Small Angle ◽  
Fourier Transformation ◽  
Three Dimensional ◽  
Power Laws ◽  
Numerical Approach ◽  
Peak Position ◽  
Two Dimensions ◽  
Correlation Peak ◽  
Scattering Intensity

A simple numerical approach for calculating theq-dependence of the scattering intensity in small-angle X-ray or neutron scattering (SAXS/SANS) is discussed. For a user-defined scattering density on a lattice, the scattering intensityI(q) (qis the modulus of the scattering vector) is calculated by three-dimensional (or two-dimensional) numerical Fourier transformation and spherical summation inqspace, with a simple smoothing algorithm. An exact and simple correction for continuous rather than discrete (lattice-point) scattering density is described. Applications to relatively densely packed particles in solids (e.g.nanocomposites) are shown, where correlation effects make single-particle (pure form-factor) calculations invalid. The algorithm can be applied to particles of any shape that can be defined on the chosen cubic lattice and with any size distribution, while those features pose difficulties to a traditional treatment in terms of form and structure factors. For particles of identical but potentially complex shapes, numerical calculation of the form factor is described. Long parallel rods and platelets of various cross-section shapes are particularly convenient to treat, since the calculation is reduced to two dimensions. The method is used to demonstrate that the scattering intensity from `randomly' parallel-packed long cylinders is not described by simple 1/qand 1/q4power laws, but at cylinder volume fractions of more than ∼25% includes a correlation peak. The simulations highlight that the traditional evaluation of the peak position overestimates the cylinder thickness by a factor of ∼1.5. It is also shown that a mix of various relatively densely packed long boards can produceI(q) ≃ 1/q, usually observed for rod-shaped particles, without a correlation peak.

scholarly journals Effect of the Reynolds Number and Clearance Flow on the Aerodynamic Characteristics of a New Variable Inlet Guide Vane

Aerospace ◽  
2021 ◽  
Vol 8 (7) ◽  
pp. 172
Author(s):  
Hengtao Shi
Keyword(s):  
Reynolds Number ◽  
Guide Vane ◽  
Three Dimensional ◽  
High Growth ◽  
Aerodynamic Characteristics ◽  
Inlet Guide Vane ◽  
Separation Region ◽  
Clearance Flow ◽  
New Type ◽  
Variable Inlet Guide Vane

Recently, a new type of low-loss variable inlet guide vane (VIGV) was proposed for improving a compressor’s performance under off-design conditions. To provide more information for applications, this work investigated the effect of the Reynolds number and clearance flow on the aerodynamic characteristics of this new type of VIGV. The performance and flow field of two representative airfoils with different chord Reynolds numbers were studied with the widely used commercial software ANSYS CFX after validation was completed. Calculations indicate that, with the decrease in the Reynolds number Rec, the airfoil loss coefficient ω and deviation δ first increase slightly and then entered a high growth rate in a low range of Rec. Afterwards, a detailed boundary-layer analysis was conducted to reveal the flow mechanism for the airfoil performance degradation with a low Reynolds number. For the design point, it is the appearance and extension of the separation region on the rear portion; for the maximum incidence point, it is the increase in the length and height of the separation region on the former portion. The three-dimensional VIGV research confirms the Reynolds number effect on airfoils. Furthermore, the clearance leakage flow forms a strong stream-wise vortex by injection into the mainflow, resulting in a high total-pressure loss and under-turning in the endwall region, which shows the potential benefits of seal treatment.

New Type ofd-Band-Metal Alloys: The Valence-Band Structure of the Metallic Glasses Pd-Zr and Cu-Zr

1979 ◽  
Vol 43 (15) ◽  
pp. 1134-1137 ◽  
Author(s):  
P. Oelhafen ◽  
E. Hauser ◽  
H. -J. Güntherodt ◽  
K. H. Bennemann
Keyword(s):  
Band Structure ◽  
Valence Band ◽  
Metallic Glasses ◽  
Metal Alloys ◽  
Valence Band Structure ◽  
New Type

New Type of Two Degree of Freedom Motor Three-Dimensional Tooth Layer Field Application and Solution

2013 ◽  
Vol 391 ◽  
pp. 232-236
Author(s):  
Wen Huan Yang ◽  
Hai Xu Chen ◽  
Shuang Xie ◽  
Chun Ren Fang
Keyword(s):  
Linear Equations ◽  
Three Dimensional ◽  
Field Application ◽  
Degree Of Freedom ◽  
Refined Method ◽  
New Type ◽  
Type Motor ◽  
Quasi Newton ◽  
Two Degree Of Freedom ◽  
Non Linear Equations

A new Multi-degree of freedom motor and its establishing of teeth layer parameters have been introduced in the paper, also including application method of database, namely using Quasi-Newton methods to solve the non-linear equations of the new motors magnetic circuit net, formed a refined method for designing and analyzing of motor. The establishment of 3d tooth layer parameters database, is provided for the calculation in the design of the new type motor conveniently.

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