X-ray Telescopes and Elasticity Theory of Shells

2009 ◽  
pp. 491-523
Author(s):  
Gérard René Lemaitre
Keyword(s):  
Elasticity Theory ◽  
X Ray ◽  
Theory Of Shells

In-situ X-ray Measurements of the Initial Epitaxy of Fe(001) Films on MgO(001)

1992 ◽  
Vol 280 ◽  
Author(s):  
Bruce M. Lairson ◽  
A. P. Payne ◽  
S. Brennan ◽  
N. M. Rensing ◽  
B. J. Daniels ◽  
...  
Keyword(s):  
Elasticity Theory ◽  
Grazing Incidence ◽  
Lattice Parameter ◽  
X Ray ◽  
X Ray Scattering ◽  
Monolayer Coverage ◽  
Continuum Elasticity ◽  
Ray Scattering

ABSTRACTWe have studied die evolution of the lattice parameter of epitaxial Fe(001) on MgO(001) vs. thickness between 1 and 200 monolayers using Grazing Incidence X-ray Scattering. We show that an interaction exists between the islanded film and the substrate, which allows the film to be incommensurate, even when the islands are too small to allow full dislocations to exist. For the conditions studied, the Fe lattice parameter increases toward the MgO lattice parameter with increasing thickness in the 1–10 monolayer coverage regime, and then relaxes back toward the bulk Fe lattice parameter at greater thicknesses. We employ a model for the interaction between film islands and the substrate which explains large changes in the lattice parameter of the Fe in the 1–10 monolayer thickness range. Relaxation at larger thicknesses is described by continuum elasticity theory.

Asymptotic behavior of the solution of an axisymmetric problem of elasticity theory for a sphere with variable elasticity modules

2020 ◽  
Vol 25 (12) ◽  
pp. 2231-2251 ◽  
Author(s):  
Natiq K Akhmedov ◽  
Natavan S Gasanova
Keyword(s):  
Elasticity Theory ◽  
Edge Effect ◽  
Characteristic Equation ◽  
Axisymmetric Problem ◽  
Applied Theory ◽  
Lagrange Principle ◽  
Homogeneous Solutions ◽  
Inhomogeneous Sphere ◽  
Radially Inhomogeneous ◽  
Theory Of Shells

In the paper the axisymmetric problem of elasticity theory is studied for the radially inhomogeneous sphere of small thickness that does not contain any of the poles 0 and [Formula: see text]. Here the case is considered when the elasticity modules vary linearly with respect to the radius. It is assumed that the lateral surface of the sphere is free of stresses, and at the ends of the sphere (at the conical sections) the stresses are set, leaving it in equilibrium. A characteristic equation is obtained and, based on its asymptotic analysis, the existence of three groups of roots is established with respect to the small parameter characterizing the thickness of the sphere. The corresponding homogeneous solutions are constructed, depending on the roots of the characteristic equation. It is shown that the penetrating solution corresponds to the first group of roots. The second group of roots corresponds to the solution of the edge effect type, similar to the edge effect in the applied theory of shells. The third group of roots corresponds to the boundary layer type solution localized in the conical sections. The solution corresponding to the first and second groups of roots determines the internal stress–strain state of the sphere. In the first term of the asymptotic, they can be considered as a solution in the applied theory of shells. The question of satisfying the boundary conditions at the ends (on the conical sections) of the sphere is considered using the variational Lagrange principle.

An Investigation of the Structural Strains and the Breakdown of Poisson'S Effect in Lattice-Mismatched BCC(110)/FCC(111) Metallic Superlattices

1992 ◽  
Vol 280 ◽  
Author(s):  
A. Fartash ◽  
Ivan K. Schuller ◽  
M. Grimsditch
Keyword(s):  
Structural Feature ◽  
Elasticity Theory ◽  
Plane Strain ◽  
Lattice Spacing ◽  
X Ray Diffraction ◽  
X Ray ◽  
Out Of Plane ◽  
Anisotropic Lattice

ABSTRACTThe strain profiles of individual layers of a selected group of stable bcc(110)/fcc(111) metallic superlattices which have been determined by x-ray diffraction methods are compared, and discussed in terms of a number of mechanisms proposed for explaining their anomalous properties. The superlattices in this group are distinguished in terms of a highly anisotropic lattice spacing mismatch of their adjoining bcc and fcc layers (∼20% vs. 3%). The most prominent structural feature of the bcc layers consists of a highly anisotropic in-plane contraction accompanied with a small out-of-plane strain. The fee layers are found to show large out-of-plane expansions which based on their small in-plane expansions cannot be explained within framework of standard elasticity theory.

X-ray Analysis of Si/Ge/Si(001) Heterolayer Structures Grown by Surfactant Mediated Epitaxy.

2001 ◽  
Vol 696 ◽  
Author(s):  
Brad P. Tinkham ◽  
Duane M. Goodner ◽  
Donald A. Walko ◽  
Michael J. Bedzyk
Keyword(s):  
Elasticity Theory ◽  
Linear Elasticity ◽  
Standing Waves ◽  
Grazing Incidence ◽  
X Ray Diffraction ◽  
Linear Elasticity Theory ◽  
X Ray ◽  
Grazing Incidence Diffraction

AbstractX-ray diffraction and x-ray standing waves (XSW) have been used to investigate the quality of epitaxial ultra-thin Ge films grown on Si(001) with and without Te as a surfactant. The efficacy of Te as a surfactant in this application has been debated. We measured samples between 1 and 10 ML in thickness and our results clearly indicate that Ge films grown with Te are superior to those grown without Te. The coherent positions and coherent fract ons determined from XSW analysis agree well with those predicted by linear elasticity theory for Ge/Si(001). Furthermore, grazing incidence diffraction measurements (GIXD) suggests that 9 ML Ge grown on Si(001) with Te is strained in-plane while the same film grown without Te is relaxed.

Strain investigation of low strained buried gratings by grazing incidence X-ray diffraction and elasticity theory

1999 ◽  
Vol 46 (4) ◽  
pp. 479-485 ◽  
Author(s):  
D Lübbert ◽  
T Baumbach ◽  
S Ponti ◽  
U Pietsch ◽  
L. Leprince J Schneck ◽  
...  
Keyword(s):  
Elasticity Theory ◽  
Grazing Incidence ◽  
X Ray Diffraction ◽  
X Ray

Space and Time Distribution of Hard X-Ray Emission in a Loop at the Beginning of a Flare

1994 ◽  
Vol 144 ◽  
pp. 275-277
Author(s):  
M. Karlický ◽  
J. C. Hénoux
Keyword(s):  
Time Distribution ◽  
Electron Bombardment ◽  
Spatial Evolution ◽  
Superthermal Electrons ◽  
Flare Loop ◽  
X Ray ◽  
Superthermal Electron ◽  
Flare Loops ◽  
Chromospheric Evaporation ◽  
Temporal And Spatial

AbstractUsing a new ID hybrid model of the electron bombardment in flare loops, we study not only the evolution of densities, plasma velocities and temperatures in the loop, but also the temporal and spatial evolution of hard X-ray emission. In the present paper a continuous bombardment by electrons isotropically accelerated at the top of flare loop with a power-law injection distribution function is considered. The computations include the effects of the return-current that reduces significantly the depth of the chromospheric layer which is evaporated. The present modelling is made with superthermal electron parameters corresponding to the classical resistivity regime for an input energy flux of superthermal electrons of 109erg cm−2s−1. It was found that due to the electron bombardment the two chromospheric evaporation waves are generated at both feet of the loop and they propagate up to the top, where they collide and cause temporary density and hard X-ray enhancements.

Some Problems in Understanding the Solar Corona

1994 ◽  
Vol 144 ◽  
pp. 1-9
Author(s):  
A. H. Gabriel
Keyword(s):  
Solar Corona ◽  
Solar Atmosphere ◽  
Theoretical Modelling ◽  
Total System ◽  
Major Advance ◽  
X Ray ◽  
Proper Perspective ◽  
Space Observations

The development of the physics of the solar atmosphere during the last 50 years has been greatly influenced by the increasing capability of observations made from space. Access to images and spectra of the hotter plasma in the UV, XUV and X-ray regions provided a major advance over the few coronal forbidden lines seen in the visible and enabled the cooler chromospheric and photospheric plasma to be seen in its proper perspective, as part of a total system. In this way space observations have stimulated new and important advances, not only in space but also in ground-based observations and theoretical modelling, so that today we find a well-balanced harmony between the three techniques.

White-Light Coronal Structures: Streamers and CMEs

1994 ◽  
Vol 144 ◽  
pp. 82
Author(s):  
E. Hildner
Keyword(s):  
Emission Line ◽  
Electron Density ◽  
White Light ◽  
Coronal Mass Ejections ◽  
X Rays ◽  
Solar Cycles ◽  
Temperature Function ◽  
X Ray ◽  
Eclipse Observations ◽  
Coronal Structures

AbstractOver the last twenty years, orbiting coronagraphs have vastly increased the amount of observational material for the whitelight corona. Spanning almost two solar cycles, and augmented by ground-based K-coronameter, emission-line, and eclipse observations, these data allow us to assess,inter alia: the typical and atypical behavior of the corona; how the corona evolves on time scales from minutes to a decade; and (in some respects) the relation between photospheric, coronal, and interplanetary features. This talk will review recent results on these three topics. A remark or two will attempt to relate the whitelight corona between 1.5 and 6 R⊙to the corona seen at lower altitudes in soft X-rays (e.g., with Yohkoh). The whitelight emission depends only on integrated electron density independent of temperature, whereas the soft X-ray emission depends upon the integral of electron density squared times a temperature function. The properties of coronal mass ejections (CMEs) will be reviewed briefly and their relationships to other solar and interplanetary phenomena will be noted.

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