Fine Focus

10.33043/ff ◽  
2021 ◽  
Keyword(s):  
Fine Focus

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.

An Experimental Study on Bond between Porcelain and Gold : Observation with Fine Focus X-ray Generator (Part 1)

1978 ◽  
Vol 31 (5) ◽  
pp. 425-431
Author(s):  
Shigeki Murakami ◽  
Yasunari Uchida ◽  
Yoshinori Chikaura
Keyword(s):  
Experimental Study ◽  
X Ray ◽  
Fine Focus

Three-Dimensional Hopf Bifurcation for a Class of Cubic Kolmogorov Model

2014 ◽  
Vol 24 (03) ◽  
pp. 1450036 ◽  
Author(s):  
Chaoxiong Du ◽  
Qinlong Wang ◽  
Wentao Huang
Keyword(s):  
Hopf Bifurcation ◽  
Singular Point ◽  
Three Dimensional ◽  
Singular Values ◽  
Bifurcation Problem ◽  
Disturbed Condition ◽  
Differential Systems ◽  
Kolmogorov Model ◽  
Polynomial Differential Systems ◽  
Fine Focus

We study the Hopf bifurcation for a class of three-dimensional cubic Kolmogorov model by making use of our method (i.e. singular values method). We show that the positive singular point (1, 1, 1) of an investigated model can become a fine focus of 5 order, and moreover, it can bifurcate five small limit cycles under certain coefficients with disturbed condition. In terms of three-dimensional cubic Kolmogorov model, published references can hardly be seen, and our results are new. At the same time, it is worth pointing out that our method is valid to study the Hopf bifurcation problem for other three-dimensional polynomial differential systems.

Fine‐focus ion beams with field ionization

1978 ◽  
Vol 15 (3) ◽  
pp. 845-848 ◽  
Author(s):  
J. Orloff ◽  
L. W. Swanson
Keyword(s):  
Ion Beams ◽  
Field Ionization ◽  
Fine Focus

Twelve Limit Cycles in 3D Quadratic Vector Fields with Z3 Symmetry

2018 ◽  
Vol 28 (11) ◽  
pp. 1850139 ◽  
Author(s):  
Laigang Guo ◽  
Pei Yu ◽  
Yufu Chen
Keyword(s):  
Limit Cycles ◽  
Vector Fields ◽  
Center Manifold ◽  
Three Dimensional ◽  
Center Manifold Theory ◽  
Normal Form Theory ◽  
Quadratic Vector Fields ◽  
Fine Focus ◽  
Form Theory ◽  
Manifold Theory

This paper is concerned with the number of limit cycles bifurcating in three-dimensional quadratic vector fields with [Formula: see text] symmetry. The system under consideration has three fine focus points which are symmetric about the [Formula: see text]-axis. Center manifold theory and normal form theory are applied to prove the existence of 12 limit cycles with [Formula: see text]–[Formula: see text]–[Formula: see text] distribution in the neighborhood of three singular points. This is a new lower bound on the number of limit cycles in three-dimensional quadratic systems.

BIFURCATION OF LIMIT CYCLES AND ISOCHRONOUS CENTERS FOR A QUARTIC SYSTEM

2013 ◽  
Vol 23 (10) ◽  
pp. 1350172 ◽  
Author(s):  
WENTAO HUANG ◽  
AIYONG CHEN ◽  
QIUJIN XU
Keyword(s):  
Limit Cycles ◽  
Necessary Conditions ◽  
Polynomial System ◽  
Isochronous Center ◽  
Eighth Order ◽  
Bifurcation Of Limit Cycles ◽  
Quartic Polynomial ◽  
Fine Focus ◽  
Sufficient And Necessary Conditions ◽  
Isochronous Centers

For a quartic polynomial system we investigate bifurcations of limit cycles and obtain conditions for the origin to be a center. Computing the singular point values we find also the conditions for the origin to be the eighth order fine focus. It is proven that the system can have eight small amplitude limit cycles in a neighborhood of the origin. To the best of our knowledge, this is the first example of a quartic system with eight limit cycles bifurcated from a fine focus. We also give the sufficient and necessary conditions for the origin to be an isochronous center.

The Development of a Fine‐Focus Flash X‐Ray Tube

1953 ◽  
Vol 24 (10) ◽  
pp. 944-948 ◽  
Author(s):  
E. L. Criscuolo ◽  
D. T. O'Connor
Keyword(s):  
X Ray ◽  
Fine Focus

X-ray Intensities from Copper-Target Diffraction Tubes

1976 ◽  
Vol 20 ◽  
pp. 565-574
Author(s):  
M. A. Short
Keyword(s):  
Close Agreement ◽  
Microprobe Analysis ◽  
Electron Microprobe Analysis ◽  
X Ray Diffraction ◽  
Characteristic Radiation ◽  
Tube Voltage ◽  
X Ray ◽  
Copper Target ◽  
Fine Focus ◽  
Constant Potential

The relative intensities of the Kα characteristic radiation obtained from copper-target X-ray diffraction tubes have been calculated for a range of tube accelerating voltages and take-off angles. The calculations employ an over-voltage function, and absorption and atomic number corrections similar to those used in electron microprobe analysis. They apply only to constant potential X-ray generators. Measurements of actual intensities obtained on a Picker diffractometer using a sodium chloride monochromator gave relative intensities in close agreement with those calculated. The calculations and measurements show that there is an optimum tube voltage, with respect to intensity, for each take-off angle. This voltage increases with increasing take-off angle. The application of these results to the consideration of the relative intensities obtainable from broad, standard and fine focus copper-target X-ray diffraction tubes is discussed.

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