scholarly journals Application of shape operator under infinitesimal bending of surface

Filomat ◽  
2019 ◽  
Vol 33 (4) ◽  
pp. 1267-1271
Author(s):  
Milica Cvetkovic ◽  
Ljubica Velimirovic
Keyword(s):  
Explicit Form ◽  
Shape Operator ◽  
Regular Surface ◽  
Infinitesimal Bending ◽  
Surface Normal ◽  
Point To Point

In case of bendable surfaces it is useful to discuss the variation of magnitudes such as the shape operator. The shape operator is a good way to measure how a regular surface S bends in R3 by valuation how the surface normal v changes from point to point. We considered the variation of shape operator under infinitesimal bending of surface given in an explicit form and its application in considering what happened with the elliptic, hyperbolic, parabolic kind of points under the infinitesimal bending of surface.

Variation of shape operator under infinitesimal bending of surface

2013 ◽  
Vol 225 ◽  
pp. 480-486 ◽  
Author(s):  
Ljubica S. Velimirović ◽  
Milica D. Cvetković ◽  
Marija S. Najdanović ◽  
Nikola M. Velimirović
Keyword(s):  
Shape Operator ◽  
Infinitesimal Bending

Finding the Right Problems: Some HREM Applications to Interfaces

1984 ◽  
Vol 42 ◽  
pp. 376-379
Author(s):  
D. Cherns
Keyword(s):  
Grain Boundaries ◽  
High Resolution Electron Microscopy ◽  
Boundary Structure ◽  
Atomic Structures ◽  
Grain Boundary Structure ◽  
Resolution Electron ◽  
Point To Point ◽  
The Right ◽  
New Generation ◽  
Better Than

The use of high resolution electron microscopy (HREM) to determine the atomic structure of grain boundaries and interfaces is a topic of great current interest. Grain boundary structure has been considered for many years as central to an understanding of the mechanical and transport properties of materials. Some more recent attention has focussed on the atomic structures of metalsemiconductor interfaces which are believed to control electrical properties of contacts. The atomic structures of interfaces in semiconductor or metal multilayers is an area of growing interest for understanding the unusual electrical or mechanical properties which these new materials possess. However, although the point-to-point resolutions of currently available HREMs, ∼2-3Å, appear sufficient to solve many of these problems, few atomic models of grain boundaries and interfaces have been derived. Moreover, with a new generation of 300-400kV instruments promising resolutions in the 1.6-2.0 Å range, and resolutions better than 1.5Å expected from specialist instruments, it is an appropriate time to consider the usefulness of HREM for interface studies.

An x-ray microprobe based upon a close-coupled focal-spot / glass capillary arrangement

1992 ◽  
Vol 50 (2) ◽  
pp. 1758-1759
Author(s):  
D. A. Carpenter ◽  
M. A. Taylor
Keyword(s):  
Imaging Techniques ◽  
Fluorescence Analysis ◽  
High Sensitivity ◽  
Specimen Preparation ◽  
X Rays ◽  
Glass Capillary ◽  
Close Coupling ◽  
X Ray ◽  
Point To Point ◽  
Beam Damage

The development of intense sources of x rays has led to renewed interest in the use of microbeams of x rays in x-ray fluorescence analysis. Sparks pointed out that the use of x rays as a probe offered the advantages of high sensitivity, low detection limits, low beam damage, and large penetration depths with minimal specimen preparation or perturbation. In addition, the option of air operation provided special advantages for examination of hydrated systems or for nondestructive microanalysis of large specimens.The disadvantages of synchrotron sources prompted the development of laboratory-based instrumentation with various schemes to maximize the beam flux while maintaining small point-to-point resolution. Nichols and Ryon developed a microprobe using a rotating anode source and a modified microdiffractometer. Cross and Wherry showed that by close-coupling the x-ray source, specimen, and detector, good intensities could be obtained for beam sizes between 30 and 100μm. More importantly, both groups combined specimen scanning with modern imaging techniques for rapid element mapping.

Atomic structure imaging of the Si/SiO2 interface with high-resolution electron microscopy

1986 ◽  
Vol 44 ◽  
pp. 390-391
Author(s):  
J.L. Batstone ◽  
J.M. Gibson ◽  
Alice.E. White ◽  
K.T. Short
Keyword(s):  
Electron Microscopy ◽  
High Resolution ◽  
Atomic Structure ◽  
High Resolution Electron Microscopy ◽  
Medium Voltage ◽  
Voltage Electron ◽  
Resolution Electron ◽  
Structural Image ◽  
Electron Microscopes ◽  
Point To Point

High resolution electron microscopy (HREM) is a powerful tool for the determination of interface atomic structure. With the previous generation of HREM's of point-to-point resolution (rpp) >2.5Å, imaging of semiconductors in only <110> directions was possible. Useful imaging of other important zone axes became available with the advent of high voltage, high resolution microscopes with rpp <1.8Å, leading to a study of the NiSi2 interface. More recently, it was shown that images in <100>, <111> and <112> directions are easily obtainable from Si in the new medium voltage electron microscopes. We report here the examination of the important Si/Si02 interface with the use of a JEOL 4000EX HREM with rpp <1.8Å, in a <100> orientation. This represents a true structural image of this interface.

Profile Imaging of Silicon Surface Reconstructions

1985 ◽  
Vol 43 ◽  
pp. 262-263
Author(s):  
O.L. Krivanek ◽  
G.J. Wood
Keyword(s):  
Electron Microscopy ◽  
Surface Structure ◽  
Structure Determination ◽  
Silicon Surface ◽  
Good Resolution ◽  
Surface Reconstructions ◽  
Bulk Structure ◽  
Point To Point ◽  
The Relationship

Electron microscopy at 0.2nm point-to-point resolution, 10-10 torr specimei region vacuum and facilities for in-situ specimen cleaning presents intere; ing possibilities for surface structure determination. Three methods for examining the surfaces are available: reflection (REM), transmission (TEM) and profile imaging. Profile imaging is particularly useful because it giv good resolution perpendicular as well as parallel to the surface, and can therefore be used to determine the relationship between the surface and the bulk structure.

Characterization of Rh/Si multilayer structure by HREM and HAADF

1992 ◽  
Vol 50 (1) ◽  
pp. 122-123
Author(s):  
Y. Cheng ◽  
J. Liu ◽  
M.B. Stearns ◽  
D.G. Steams
Keyword(s):  
Normal Incidence ◽  
High Resolution Electron Microscopy ◽  
X Rays ◽  
Beam Direction ◽  
Cross Sectional ◽  
Optical Elements ◽  
Resolution Electron ◽  
Point To Point ◽  
Better Than

The Rh/Si multilayer (ML) thin films are promising optical elements for soft x-rays since they have a calculated normal incidence reflectivity of ∼60% at a x-ray wavelength of ∼13 nm. However, a reflectivity of only 28% has been attained to date for ML fabricated by dc magnetron sputtering. In order to determine the cause of this degraded reflectivity the microstructure of this ML was examined on cross-sectional specimens with two high-resolution electron microscopy (HREM and HAADF) techniques.Cross-sectional specimens were made from an as-prepared ML sample and from the same ML annealed at 298 °C for 1 and 100 hours. The specimens were imaged using a JEM-4000EX TEM operating at 400 kV with a point-to-point resolution of better than 0.17 nm. The specimens were viewed along Si [110] projection of the substrate, with the (001) Si surface plane parallel to the beam direction.

A TEM investigation of silicon nitride whiskers

1987 ◽  
Vol 45 ◽  
pp. 160-161
Author(s):  
Tapan Roy
Keyword(s):  
Silicon Nitride ◽  
High Resolution ◽  
Ceramic Matrix Composites ◽  
High Resolution Electron Microscopy ◽  
Molten Silicon ◽  
Matrix Composites ◽  
Ceramic Fibers ◽  
Resolution Electron ◽  
Point To Point ◽  
Technological University

Ceramic fibers are being used to improve the mechanical properties of metal matrix and ceramic matrix composites. This paper reports a study of the structural and other microstructural characteristics of silicon nitride whiskers using both conventional TEM and high resolution electron microscopy.The whiskers were grown by T. E. Scott of Michigan Technological University, by passing nitrogen over molten silicon in the presence of a catalyst. The whiskers were ultrasonically dispersed in chloroform and picked up on holey carbon grids. The diameter of some whiskers (<70nm) was small enough to allow direct observation without thinning. Conventional TEM was performed on a Philips EM400T while high resolution imaging was done on a JEOL 200CX microscope with a point to point resolution of 0.23nm.

Atomic resolution AEM (ARAEM) of oxide superconductors

1992 ◽  
Vol 50 (1) ◽  
pp. 74-75
Author(s):  
Vinayak P. Dravid ◽  
H. Zhang ◽  
L.D. Marks ◽  
J.P. Zhang
Keyword(s):  
Electron Microscope ◽  
Field Emission ◽  
Atomic Resolution ◽  
Oxide Superconductors ◽  
Electron Holography ◽  
Analytical Electron ◽  
Analytical Electron Microscope ◽  
Point To Point ◽  
Single Instrument ◽  
Better Than

A 200 kV cold field emission gun atomic resolution analytical electron microscope (ARAEM, Hitachi HF-2000) has been recently installed at Northwestern. The ARAEM offers an unprecedented combination of atomic structure imaging of better than 0.20 nm nominal point-to-point resolution and about 0.10 nm line resolution, alongwith nanoscale analytical capabilities and electron holography in one single instrument. The ARAEM has been fully functional/operational and this paper presents some illustrative examples of application of ARAEM techniques to oxide superconductors. Additional results will be presented at the meeting.

Flux-pinning-related defect structures in melt-processed YBa2Cu3O7-x

1993 ◽  
Vol 51 ◽  
pp. 936-937
Author(s):  
Z. L. Wang ◽  
R. Kontra ◽  
A. Goyal ◽  
D. M. Kroeger ◽  
L.F. Allard
Keyword(s):  
Volume Fraction ◽  
Local Density ◽  
Stacking Faults ◽  
Image Resolution ◽  
Defect Structures ◽  
Atomic Structures ◽  
Transmission Electron ◽  
Point Image ◽  
Related Defect ◽  
Point To Point

Previous studies of Y2BaCuO5/YBa2Cu3O7-δ(Y211/Y123) interfaces in melt-processed and quench-melt-growth processed YBa2Cu3O7-δ using high resolution transmission electron microscopy (HRTEM) and energy dispersive X-ray spectroscopy (EDS) have revealed a high local density of stacking faults in Y123, near the Y211/Y123 interfaces. Calculations made using simple energy considerations suggested that these stacking faults may act as effective flux-pinners and may explain the observations of increased Jc with increasing volume fraction of Y211. The present paper is intended to determine the atomic structures of the observed defects. HRTEM imaging was performed using a Philips CM30 (300 kV) TEM with a point-to-point image resolution of 2.3 Å. Nano-probe EDS analysis was performed using a Philips EM400 TEM/STEM (100 kV) equipped with a field emission gun (FEG), which generated an electron probe of less than 20 Å in diameter.Stacking faults produced by excess single Cu-O layers: Figure 1 shows a HRTEM image of a Y123 film viewed along [100] (or [010]).

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