Structure Information From Electron Diffraction Intensities

1990 ◽  
Vol 48 (2) ◽  
pp. 516-517
Author(s):  
J. Gjønnes ◽  
N. Bøe ◽  
K. Gjønnes
Keyword(s):  
Computational Effort ◽  
Unit Cell ◽  
Small Unit ◽  
Structure Information ◽  
Dispersion Surface ◽  
Integrated Intensity ◽  
The One ◽  
Image Position ◽  
Convergent Beam ◽  
Beam Patterns

Structure information of high precision can be extracted from intentsity details in convergent beam patterns like the one reproduced in Fig 1. From low order reflections for small unit cell crystals,bonding charges, ionicities and atomic parameters can be derived, (Zuo, Spence and O’Keefe, 1988; Zuo, Spence and Høier 1989; Gjønnes, Matsuhata and Taftø, 1989) , but extension to larger unit cell ma seem difficult. The disks must then be reduced in order to avoid overlap calculations will become more complex and intensity features often less distinct Several avenues may be then explored: increased computational effort in order to handle the necessary many-parameter dynamical calculations; use of zone axis intensities at symmetry positions within the CBED disks, as in Figure 2 measurement of integrated intensity across K-line segments. In the last case measurable quantities which are well defined also from a theoretical viewpoint can be related to a two-beam like expression for the intensity profile:With as an effective Fourier potential equated to a gap at the dispersion surface, this intensity can be integrated across the line, with kinematical and dynamical limits proportional to and at low and high thickness respctively (Blackman, 1939).

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.

Extracting Structure Information from Cbed Patterns

1997 ◽  
Vol 3 (S2) ◽  
pp. 1151-1152
Author(s):  
J.M. Zuo
Keyword(s):  
Practical Method ◽  
High Order ◽  
Unit Cell ◽  
Ray Method ◽  
Structure Information ◽  
Cell Parameters ◽  
Energy Filtering ◽  
Convergent Beam ◽  
Low Order

The advance of digital recording and energy filtering now makes it possible to extract quantitative crystal structure information in an accuracy close to or better than the x-ray method. The extraction of structure information employs the refinement technique by comparing theory and experiment using chisquare criteria ofFor the unit cell or crystal orientation determination, the experiment yx is the line equation of Kikuchi or HOLZ lines, and/or positions of convergent beam disks or diffraction spots. Lines, or disks, can be measured directly from the digitally recorded two-dimensional patterns using techniques of image processing and transformation such as Hough. A practical method for measuring unit cell parameters was described by [1]. For the determination of atomic positions, the experiment yx is the diffracted intensities of medium and high order reflections. For the measurement of charge density, the yx is the energy-filtered diffracted intensities of low order reflections or high order reflections coupled with a low order reflections.

Structure factor refinement by least-squares inversion of 2D convergent-beam patterns

1993 ◽  
Vol 51 ◽  
pp. 682-683
Author(s):  
K. Marthinsen ◽  
R. Holmestad ◽  
R. Høier
Keyword(s):  
Least Squares ◽  
Structure Factor ◽  
Convergent Beam Electron Diffraction ◽  
Alternative Methods ◽  
Automatic Method ◽  
Beam Electron ◽  
Structure Information ◽  
Increasing Trend ◽  
Convergent Beam ◽  
Beam Patterns

While electron microscopy and diffraction for decades mainly have been a qualitative tool, there has been an increasing trend over the last years for more quantitative work. This trend applies in particular to convergent beam electron diffraction (CBED) where different methods for the retrieval of quantitative structure information from CBED intensities have been proposed. In our group we have aimed at developing a general and automatic method based on the strong parameter dependencies that govern the complicated two-dimensional (2-D) intensity variations in the CBED-disks particularly in the nonsystematic many-beam case. The method is based on least squares fitting between digitized experimental and computed patterns. The advantage of this method as compared with alternative methods is many turning points in the intensity variations, which should give a high parameter sensitivity, and the fact that non-systematic many-beam effects are particularly sensitive to structure factor phases, which should make the method especially suitable to non-centric crystals.

Performance and applications of a field-emission gun TEM/STEM

1992 ◽  
Vol 50 (2) ◽  
pp. 942-943
Author(s):  
Judith M. Brock ◽  
Max T. Otten ◽  
Marc. J.C. de Jong
Keyword(s):  
Field Emission ◽  
High Resolution Imaging ◽  
High Quality ◽  
Small Energy ◽  
High Brightness ◽  
Small Probe ◽  
Resolution Imaging ◽  
Convergent Beam ◽  
Beam Patterns ◽  
Beam Diffraction

A Field Emission Gun (FEG) on a TEM/STEM instrument provides a major improvement in performance relative to one equipped with a LaB6 emitter. The improvement is particularly notable for small-probe techniques: EDX and EELS microanalysis, convergent beam diffraction and scanning. The high brightness of the FEG (108 to 109 A/cm2srad), compared with that of LaB6 (∼106), makes it possible to achieve high probe currents (∼1 nA) in probes of about 1 nm, whilst the currents for similar probes with LaB6 are about 100 to 500x lower. Accordingly the small, high-intensity FEG probes make it possible, e.g., to analyse precipitates and monolayer amounts of segregation on grain boundaries in metals or ceramics (Fig. 1); obtain high-quality convergent beam patterns from heavily dislocated materials; reliably detect 1 nm immuno-gold labels in biological specimens; and perform EDX mapping at nm-scale resolution even in difficult specimens like biological tissue.The high brightness and small energy spread of the FEG also bring an advantage in high-resolution imaging by significantly improving both spatial and temporal coherence.

Thickness Measurement in the AEM by Macintosh-Based Analysis of Two-Beam Convergent Beam Patterns

1990 ◽  
Vol 48 (2) ◽  
pp. 504-505
Author(s):  
John F. Mansfield ◽  
Douglas C. Crawford
Keyword(s):  
Electron Microscope ◽  
Video Camera ◽  
Thickness Measurement ◽  
Specimen Thickness ◽  
Crystalline Materials ◽  
Beam Dynamic ◽  
Line Measurement ◽  
On Line ◽  
Image Position ◽  
Convergent Beam

A method has been developed that allows on-line measurement of the thickness of crystalline materials in the analytical electron microscope. Two-beam convergent beam electron diffraction (CBED) patterns are digitized from a JEOL 2000FX electron microscope into an Apple Macintosh II microcomputer via a Gatan #673 CCD Video Camera and an Imaging Systems Technology Video 1000 frame-capture board. It is necessary to know the lattice parameters of the sample since measurements are made of the spacing of the diffraction discs in order to calibrate the pattern. The sample thickness is calculated from measurements of the spacings of the fringes that are seen in the diffraction discs. This technique was pioneered by Kelly et al, who used the two-beam dynamic theory of MacGillavry relate the deviation parameter (Si) of the ith fringe from the exact Bragg condition to the specimen thickness (t) with the equation:Where ξg, is the extinction distance for that reflection and ni is an integer.

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.

Toward quantitative defect analysis using HREM

1994 ◽  
Vol 52 ◽  
pp. 714-715
Author(s):  
David J. Smith
Keyword(s):  
Electron Microscope ◽  
Unit Cell ◽  
Defect Analysis ◽  
Significant Progress ◽  
Detailed Characterization ◽  
Small Unit ◽  
Resolution Electron ◽  
High Resolution Electron Microscope ◽  
Large Unit Cell ◽  
Made In

The electron microscope has evolved to the level where it is now straightforward to record highresolution images from thin samples (t∼10 to 20nm) that are directly interpretable in terms of atomic arrangements. Whilst recorded images necessarily represent two-dimensional projections of the structure, many defects such as dislocations and interfaces may be linear or planar in nature and thus might be expected to be amenable to detailed characterization. In this review, we briefly consider the recent significant progress that has been made in quantitative defect analysis using the high-resolution electron microscope and then discuss some drawbacks to the technique as well as potential scope for further improvements. Surveys of defect modelling for some small-unit-cell materials and interfaces have recently been published, and reference should be made to other papers in this symposium for further examples.The technique of structure imaging originated in the early '70s with observations of large-unit-cell block oxides.

Shelah's work on non-semi-proper iterations, II

2001 ◽  
Vol 66 (4) ◽  
pp. 1865-1883 ◽  
Author(s):  
Chaz Schlindwein
Keyword(s):  
Closed Subset ◽  
Stationary Subset ◽  
Finite Support ◽  
Countable Support ◽  
Final Model ◽  
Axiom A ◽  
Mahlo Cardinal ◽  
The One ◽  
Image Position ◽  
Special Case

One of the main goals in the theory of forcing iteration is to formulate preservation theorems for not collapsing ω1 which are as general as possible. This line leads from c.c.c. forcings using finite support iterations to Axiom A forcings and proper forcings using countable support iterations to semi-proper forcings using revised countable support iterations, and more recently, in work of Shelah, to yet more general classes of posets. In this paper we concentrate on a special case of the very general iteration theorem of Shelah from [5, chapter XV]. The class of posets handled by this theorem includes all semi-proper posets and also includes, among others, Namba forcing.In [5, chapter XV] Shelah shows that, roughly, revised countable support forcing iterations in which the constituent posets are either semi-proper or Namba forcing or P[W] (the forcing for collapsing a stationary co-stationary subset ofwith countable conditions) do not collapse ℵ1. The iteration must contain sufficiently many cardinal collapses, for example, Levy collapses. The most easily quotable combinatorial application is the consistency (relative to a Mahlo cardinal) of ZFC + CH fails + whenever A ∪ B = ω2 then one of A or B contains an uncountable sequentially closed subset. The iteration Shelah uses to construct this model is built using P[W] to “attack” potential counterexamples, Levy collapses to ensure that the cardinals collapsed by the various P[W]'s are sufficiently well separated, and Cohen forcings to ensure the failure of CH in the final model.In this paper we give details of the iteration theorem, but we do not address the combinatorial applications such as the one quoted above.These theorems from [5, chapter XV] are closely related to earlier work of Shelah [5, chapter XI], which dealt with iterated Namba and P[W] without allowing arbitrary semi-proper forcings to be included in the iteration. By allowing the inclusion of semi-proper forcings, [5, chapter XV] generalizes the conjunction of [5, Theorem XI.3.6] with [5, Conclusion XI.6.7].

On functional Nörlund methods

1970 ◽  
Vol 67 (1) ◽  
pp. 47-60 ◽  
Author(s):  
B. Choudhary
Keyword(s):  
The Other ◽  
Integral Transformations ◽  
Other Hand ◽  
Nörlund Means ◽  
The One ◽  
Image Position

Integral transformations analogous to the Nörlund means have been introduced and investigated by Kuttner, Knopp and Vanderburg(6), (5), (4). It is known that with any regular Nörlund mean (N, p) there is associated a functionregular for |z| < 1, and if we have two Nörlund means (N, p) and (N, r), where (N, pr is regular, while the function is regular for |z| ≤ 1 and different) from zero at z = 1, then q(z) = r(z)p(z) belongs to a regular Nörlund mean (N, q). Concerning Nörlund means Peyerimhoff(7) and Miesner (3) have recently obtained the relation between the convergence fields of the Nörlund means (N, p) and (N, r) on the one hand and the convergence field of the Nörlund mean (N, q) on the other hand.

scholarly journals Tensile Strength of NaCl Ice

1962 ◽  
Vol 4 (31) ◽  
pp. 25-52 ◽  
Author(s):  
W. F. Weeks
Keyword(s):  
Tensile Strength ◽  
Sea Ice ◽  
Fresh Water ◽  
Eutectic Point ◽  
Water Ice ◽  
Average Value ◽  
Freshwater Ice ◽  
The One ◽  
Image Position ◽  
Bodies Of Water

AbstractTo resolve some of the factors causing strength variation in natural sea ice, fresh water and five different NaCl–H2O solutions were frozen in a tank designed to simulate the one-dimensional cooling of natural bodies of water. The resulting ice was structurally similar to lake and sea ice. The salinity of the salt ice varied from 1‰ to 22‰. Tables of brine volumes and densities were computed for these salinities in the temperature range 0° to −35° C. The ring-tensile strength σ of fresh-water ice was found to be essentially temperature independent from −10° to −30°C., with an average value of 29.6±8.5 kg./cm.2at −10° C. The strength of salt ice at temperatures above the eutectic point (–21.2° C.) significantly decreases with brine volumev;. The σ–axis intercept of this line is comparable to the a values determined for fresh ice indicating that there is little, if any, difference in stress concentration between sea and lake ice as a result of the presence of brine pockets. The strength of ice containing NaCl.2H2O is slightly less than the strength of freshwater ice and is independent of the volume of solid salt and the ice temperature. No evidence was found for the existence of either phase or geometric hysteresis in NaCl ice. The strength of ice at sub-eutectic temperatures, however, is decreased appreciably if the ice has been subjected to temperatures above the eutectic point; this is the result of the redistribution of brine during the warm-temperature period. Short-term cooling produces an appreciable (20 per cent) decrease in strength, in fresh-water and NaCl.2H2O ice. The present results are compared with tests on natural sea ice and it is suggested that the strength of freshwater ice is a limit which is approached but not exceeded by cold sea ice and that the reinforcement of brine pockets by Na2SO4.10H2O is either lacking or much less than previously assumed.

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