The effect of diffuse scattering on the dark-field contrast from precipitates

1978 ◽  
Vol 11 (3) ◽  
pp. 190-192 ◽  
Author(s):  
J. Gjønnes ◽  
J. K. Solberg
Keyword(s):  
Diffuse Scattering ◽  
Reciprocal Lattice ◽  
Dark Field ◽  
Reciprocal Lattice Vector ◽  
Lattice Vector ◽  
Fringe Contrast ◽  
Field Technique

Precipitate contrast due to Bragg interactions in the diffuse scattering has been studied. Both ordinary dark-field contrast and moiré contrast were found to be preserved at quite large distances from the Bragg spots, especially along the direction normal to the reciprocal lattice vector. The effects, which are similar to those seen in thickness fringe contrast from perfect crystals, may be disturbing in the search for faint precipitate reflections with the dark-field technique, especially in thicker parts of the crystal.

Observation of faint contrast at planar faults in alloys

1978 ◽  
Vol 36 (1) ◽  
pp. 340-341
Author(s):  
K. Kuroda ◽  
Y. Tomokiyo ◽  
T. Kumano ◽  
T. Eguchi
Keyword(s):  
Reciprocal Lattice ◽  
Beam Theory ◽  
Al Alloys ◽  
Small Displacement ◽  
Electron Microscopic ◽  
Lattice Vector ◽  
Fringe Contrast ◽  
Planar Fault ◽  
Lattice Displacement ◽  
The Many

The contrast in electron microscopic images of planar faults in a crystal is characterized by a phase factor , where is the reciprocal lattice vector of the operating reflection, and the lattice displacement due to the fault under consideration. Within the two-beam theory a planar fault with an integer value of is invisible, but a detectable contrast is expected when the many-beam dynamical effect is not negligibly small. A weak fringe contrast is also expected when differs slightly from an integer owing to an additional small displacement of the lattice across the fault. These faint contrasts are termed as many-beam contrasts in the former case, and as ε fringe contrasts in the latter. In the present work stacking faults in Cu-Al alloys and antiphase boundaries (APB) in CuZn, FeCo and Fe-Al alloys were observed under such conditions as mentioned above, and the results were compared with the image profiles of the faults calculated in the systematic ten-beam approximation.

Kinematical and Dynamical CBED Pattern Models: Increasing the Accuracy of the Unit-Cell Parameter Measurements Based on CBED Patterns

1990 ◽  
Vol 48 (2) ◽  
pp. 540-541
Author(s):  
I.N. Yadhikov ◽  
S.K. Maksimov
Keyword(s):  
Reciprocal Lattice ◽  
Unit Cell ◽  
Reciprocal Lattice Vector ◽  
Unit Cell Parameters ◽  
Lattice Vector ◽  
Cell Parameters ◽  
Accuracy Of Measurements ◽  
The Difference ◽  
Image Position ◽  
Convergent Beam

Convergent beam electron diffraction (CBED) is widely used as a microanalysis tool. By the relative position of HOLZ-lines (Higher Order Laue Zone) in CBED-patterns one can determine the unit cell parameters with a high accuracy up to 0.1%. For this purpose, maps of HOLZ-lines are simulated with the help of a computer so that the best matching of maps with experimental CBED-pattern should be reached. In maps, HOLZ-lines are approximated, as a rule, by straight lines. The actual HOLZ-lines, however, are different from the straights. If we decrease accelerating voltage, the difference is increased and, thus, the accuracy of the unit cell parameters determination by the method becomes lower.To improve the accuracy of measurements it is necessary to give up the HOLZ-lines substitution by the straights. According to the kinematical theory a HOLZ-line is merely a fragment of ellipse arc described by the parametric equationwith arc corresponding to change of β parameter from -90° to +90°, wherevector, h - the distance between Laue zones, g - the value of the reciprocal lattice vector, g‖ - the value of the reciprocal lattice vector projection on zero Laue zone.

Angle calculations for a three-circle goniostat

2006 ◽  
Vol 39 (2) ◽  
pp. 151-157 ◽  
Author(s):  
Gunnar Thorkildsen ◽  
Helge B. Larsen ◽  
Jon Are Beukes
Keyword(s):  
General Procedure ◽  
Reciprocal Lattice ◽  
Reciprocal Lattice Vector ◽  
Laboratory System ◽  
Lattice Vector ◽  
New Approach ◽  
Rotation Matrices ◽  
Rotation Axes ◽  
Vector Description

A general procedure for angle calculations for a three-circle goniostat has been developed. This new approach is based on a vector description of the transformation of a reciprocal-lattice vector under the action of a rotation shaft. It does not invoke the use of rotation matrices and applies equally well to cases where the directions of the rotation axes do not conform with coordinate axes of the laboratory system adopted for the analysis.

On The Visibility of Supported Metallic Particles

1980 ◽  
Vol 38 ◽  
pp. 404-405
Author(s):  
D. Romeu ◽  
A. Gómez ◽  
José M. Yacamán ◽  
J.M. Domínguez
Keyword(s):  
Infinite Number ◽  
Reciprocal Lattice ◽  
Computing Time ◽  
Reciprocal Lattice Vector ◽  
Special Treatment ◽  
Twin Boundaries ◽  
Lattice Vector ◽  
Metallic Particles ◽  
Beam Approximation

Several methods have been presented for the calculation of diffraction intensities in the case of twin boundaries and other two-crystal systems in the N-beam approximation (1,2,3). It has been realized that when two or more beams diffracted by the top crystal differ by a reciprocal lattice vector of the bottom crystal, the beams become coupled and the problem requires special treatment. It has been pointed out (3) that the methods described in references (2) and (3) are formally equivalent for an infinite number of beams but the method described by Gomez et al (3) requires less computing time.

Umklapp collisions and thermal conductivity

2021 ◽  
pp. 309-321
Author(s):  
Geoffrey Brooker
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Heat Flow ◽  
Group Velocity ◽  
Thermodynamic Equilibrium ◽  
Reciprocal Lattice ◽  
Reciprocal Lattice Vector ◽  
Momentum Balance ◽  
Lattice Vector ◽  
Phonon Group Velocity

“Umklapp collisions and thermal conductivity” deals with heat conduction in a dielectric solid. Collisions of phonons are divided into Umklapp and normal according as a reciprocal lattice vector is or is not involved in the phonon momentum balance. A local temperature is defined by appeal to local thermodynamic equilibrium. An equilibrium phonon distribution can be off-centred, yet non-decaying, if the only collisions are “normal”, conserving the total phonon momentum. Then heat flow does not decay, even if a representative collision reverses the phonon group velocity. Conversely, in an Umklapp collision it is the non-conservation of phonon momentum that causes heat flow to decay.

Determination by high-resolution X-ray diffraction of shape, size and lateral separation of buried empty channels in silicon-on-nothing architectures

2007 ◽  
Vol 40 (2) ◽  
pp. 338-343 ◽  
Author(s):  
Marco Servidori
Keyword(s):  
High Resolution ◽  
Lattice Point ◽  
Reciprocal Lattice ◽  
Reciprocal Lattice Vector ◽  
X Ray Diffraction ◽  
Lattice Vector ◽  
Reciprocal Lattice Point ◽  
One Dimensional ◽  
X Ray ◽  
Planar Array

High-resolution multi-crystal X-ray diffraction was employed to characterize silicon-on-nothing samples made by a one-dimensional periodic planar array of buried empty channels. When the channels are normal to the scattering plane, under the constraint of lattice continuity from the perfect substrate to the surface, this periodic array gives rise to a well defined Fraunhofer diffraction in a scan crossing a selected reciprocal lattice point and normal to the reciprocal lattice vector (transverse or ω scan). In a longitudinal scan (ω/2θ scan crossing the reciprocal lattice point and parallel to the reciprocal lattice vector) interference fringes are observed. By analysis of the ω scan and numerical fit of the ω/2θ scan, the period of the buried empty channels and their shape, size and lateral gap were easily determined, thanks to the high-resolution optics used for the measurements.

Angle calculations for a six-circle κ diffractometer

1999 ◽  
Vol 32 (5) ◽  
pp. 943-950 ◽  
Author(s):  
Gunnar Thorkildsen ◽  
Ragnvald H. Mathiesen ◽  
Helge B. Larsen
Keyword(s):  
Reciprocal Lattice ◽  
Reciprocal Lattice Vector ◽  
Lattice Vector ◽  
Rotation Axes

By parametrizing the conic surfaces spanned by the reciprocal-lattice vector under the action of the rotation axes, a new procedure for angle calculations for a κ diffractometer is presented. It is applied to obtain angle settings in various modes for a newly developed six-circle diffractometer.

High Resolution X-ray Diffraction from Epitaxial Gallium Nitride Films

1996 ◽  
Vol 449 ◽  
Author(s):  
T. Lafford ◽  
N. Loxley ◽  
BK Tanner
Keyword(s):  
Gallium Nitride ◽  
High Resolution ◽  
Reciprocal Lattice ◽  
Wide Distribution ◽  
Reciprocal Lattice Vector ◽  
Mosaic Structure ◽  
X Ray Diffraction ◽  
Lattice Vector ◽  
Instrument Function ◽  
X Ray

ABSTRACTThe width of double axis X-ray rocking curves of epitaxial GaN layers is shown to be critically dependent on the width of the detector aperture. We show that triple axis diffraction measurements using a crystal analyser before the detector enables the instrument function to be defined and the tilt and dilation distributions separated. All GaN samples examined showed a mosaic structure of misoriented sub-grains with little dilation within the mosaic blocks. In reciprocal space maps this was revealed as a wide distribution of intensity in a direction perpendicular to the reciprocal lattice vector.

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