Atomic Imaging of Crystals using Large-Angle Electron Scattering in STEM

1990 ◽  
Vol 48 (1) ◽  
pp. 74-75
Author(s):  
D.E. Jesson ◽  
S. J. Pennycook
Keyword(s):  
Wave Function ◽  
Electron Scattering ◽  
Numerical Solutions ◽  
Large Angle ◽  
Real Space ◽  
High Angle ◽  
Analytical Treatment ◽  
Order Zero ◽  
Experimental Conditions ◽  
Ewald Sphere

It is well known that conventional atomic resolution electron microscopy is a coherent imaging process best interpreted in reciprocal space using contrast transfer function theory. This is because the equivalent real space interpretation involving a convolution between the exit face wave function and the instrumental response is difficult to visualize. Furthermore, the crystal wave function is not simply related to the projected crystal potential, except under a very restrictive set of experimental conditions, making image simulation an essential part of image interpretation. In this paper we present a different conceptual approach to the atomic imaging of crystals based on incoherent imaging theory. Using a real-space analysis of electron scattering to a high-angle annular detector, it is shown how the STEM imaging process can be partitioned into components parallel and perpendicular to the relevant low index zone-axis.It has become customary to describe STEM imaging using the analytical treatment developed by Cowley. However, the convenient assumption of a phase object (which neglects the curvature of the Ewald sphere) fails rapidly for large scattering angles, even in very thin crystals. Thus, to avoid unpredictive numerical solutions, it would seem more appropriate to apply pseudo-kinematic theory to the treatment of the weak high angle signal. Diffraction to medium order zero-layer reflections is most important compared with thermal diffuse scattering in very thin crystals (<5nm). The electron wave function ψ(R,z) at a depth z and transverse coordinate R due to a phase aberrated surface probe function P(R-RO) located at RO is then well described by the channeling approximation;

Compositional mapping using large-angle electron scattering

1991 ◽  
Vol 49 ◽  
pp. 10-11
Author(s):  
S. J. Pennycook ◽  
D. E. Jesson
Keyword(s):  
Electron Scattering ◽  
Diffuse Scattering ◽  
Signal To Noise Ratio ◽  
Core Loss ◽  
Large Angle ◽  
X Rays ◽  
High Angle ◽  
Thermal Diffuse Scattering ◽  
Kikuchi Lines ◽  
Thermal Diffuse

High-angle electron scattering represents a relatively small fraction of the total elastic scattering, typically 10%, but is still orders of magnitude larger than the intensity of secondary excitations such as X rays or core loss inelastically scattered electrons. It is possible, therefore, to form an image from thin samples at high resolution with acceptable signal to noise ratio in a reasonable collection time. The STEM high-angle annular detector introduced by Howie detects only the scattering which occurs very close to the atom sites so that the scattering cross section a approaches the Z2 dependence of unscreened Rutherford scattering. Furthermore, in all but the very thinnest crystals the detected signal is dominated by thermal diffuse scattering, which is generated incoherently by each atom in proportion to the electron intensity close to its site. Due to the large angular range of the detector, dynamical effects in the outgoing thermal diffuse scattering (Kikuchi lines) are averaged out and have no effect on the total intensity detected.

High-angle electron scattering from amorphous silicon

1995 ◽  
Vol 53 ◽  
pp. 162-163
Author(s):  
M. Libera ◽  
J.A. Ott ◽  
K. Siangchaew ◽  
L. Tsung
Keyword(s):  
Electron Scattering ◽  
Amorphous Material ◽  
Structural Defects ◽  
Constant Thickness ◽  
High Angle ◽  
Fast Electrons ◽  
Angle Scattering ◽  
Stem Image ◽  
Amorphous Si ◽  
Thermal Vibrations

Channeling occurs when fast electrons follow atomic strings in a crystal where there is a minimum in the potential energy (1). Channeling has a strong effect on high-angle scattering. Deviations in atomic position along a channel due to structural defects or thermal vibrations increase the probability of scattering (2-5). Since there are no extended channels in an amorphous material the question arises: for a given material with constant thickness, will the high-angle scattering be higher from a crystal or a glass?Figure la shows a HAADF STEM image collected using a Philips CM20 FEG TEM/STEM with inner and outer collection angles of 35mrad and lOOmrad. The specimen (6) was a cross section of singlecrystal Si containing: amorphous Si (region A), defective Si containing many stacking faults (B), two coherent Ge layers (CI; C2), and a contamination layer (D). CBED patterns (fig. lb), PEELS spectra, and HAADF signals (fig. lc) were collected at 106K and 300K along the indicated line.

High-angle Kikuchi patterns

1954 ◽  
Vol 221 (1145) ◽  
pp. 224-242 ◽  
Keyword(s):  
Lithium Fluoride ◽  
High Efficiency ◽  
Cylindrical Specimen ◽  
Angle Of Incidence ◽  
High Angle ◽  
Lead Sulphide ◽  
Marked Contrast ◽  
Experimental Conditions ◽  
Low Intensity ◽  
Glancing Angle

A cylindrical specimen chamber and camera have been used to study the high-angle Kikuchi patterns obtained by reflexion of electrons, of energy 6 to 50 keV, from the cleavage surfaces of crystals with the sodium chloride structure. Angles of scattering ranging from 0 to 164° were covered. The relative intensity of the pattern at different scattering angles was measured using a photographic technique. The intensity distribution was found to become less steep as the energy of the incident electrons decreased. In photographs taken with a large value of the glancing angle of incidence, defect bands were found, starting near the shadow edge of the pattern; these changed to excess bands at higher angles of scattering. The most striking feature of the results is the remarkable intensity and clarity at the highest scattering angles of the pattern produced by crystals such as lead sulphide and potassium iodide, the constituents of which have a relatively high elastic scattering cross-section. In marked contrast, a relatively low intensity and low clarity was found at these angles for lithium fluoride under the same experimental conditions. An investigation of the width of Kikuchi bands, visible over the whole available angular range, showed that the electrons forming these bands had the same energy as that of the incident electrons within the experimental error of 10%. A possible mechanism is discussed by means of which electrons can be diffused through large angles with high efficiency, relative to small angles, and with relatively little loss of energy.

Crystallography and Diffraction

2021 ◽  
pp. 220-276
Author(s):  
Kannan M. Krishnan
Keyword(s):  
Rotational Symmetry ◽  
Reciprocal Lattice ◽  
Real Space ◽  
Crystalline Materials ◽  
Space Groups ◽  
Ewald Sphere ◽  
Point Groups ◽  
Diffraction Patterns ◽  
Point Line ◽  
Periodic Arrangement

Crystalline materials have a periodic arrangement of atoms, exhibit long range order, and are described in terms of 14 Bravais lattices, 7 crystal systems, 32 point groups, and 230 space groups, as tabulated in the International Tables for Crystallography. We introduce the nomenclature to describe various features of crystalline materials, and the practically useful concepts of interplanar spacing and zonal equations for interpreting electron diffraction patterns. A crystal is also described as the sum of a lattice and a basis. Practical materials harbor point, line, and planar defects, and their identification and enumeration are important in characterization, for defects significantly affect materials properties. The reciprocal lattice, with a fixed and well-defined relationship to the real lattice from which it is derived, is the key to understanding diffraction. Diffraction is described by Bragg law in real space, and the equivalent Ewald sphere construction and the Laue condition in reciprocal space. Crystallography and diffraction are closely related, as diffraction provides the best methodology to reveal the structure of crystals. The observations of quasi-crystalline materials with five-fold rotational symmetry, inconsistent with lattice translations, has resulted in redefining a crystalline material as “any solid having an essentially discrete diffraction pattern”

The Effect of Low-Angle and High-Angle Grain Boundaries on Elevated Temperature Strength

1994 ◽  
Vol 362 ◽  
Author(s):  
M. E. Kassner
Keyword(s):  
Elevated Temperature ◽  
Mechanical Behavior ◽  
Large Angle ◽  
High Angle ◽  
Elevated Temperature Strength ◽  
Ambient Temperatures ◽  
The Past ◽  
Creep Regime ◽  
New Evidence ◽  
General Opinion

AbstractThe influence of small (subgrain) misorientation interfaces on the mechanical behavior of metals and alloys deforming within the creep regime has been intensively studied over the past several decades. Controversies have existed, but some new experiments suggest, contrary to the general opinion, that low-angle boundaries are not associated with the rate controlling process for plasticity and do not affect strength. The new evidence will be discussed in terms of other established experimental trends. Large-angle boundaries may have a smaller effect on elevated temperature strength than at ambient temperatures and do not appear to dramatically affect elevated temperature strength. Superplastic effects are not addressed.

Rheology of Lubricants in Real Bearing Contacts

1975 ◽  
Vol 97 (2) ◽  
pp. 228-235 ◽  
Author(s):  
J. W. Kannel ◽  
S. S. Bupara
Keyword(s):  
Experimental Data ◽  
Film Thickness ◽  
Dynamic Pressure ◽  
Analytical Treatment ◽  
Experimental Conditions ◽  
X Ray ◽  
Lubricated Contacts ◽  
Fundamental Understanding ◽  
Machine Elements ◽  
Contact Pressures

Experimental traction-slip and lubricant film-thickness data have been determined for selected lubricants to provide information for use in conjunction with the design of lubricated machine elements. The traction-slip experiments were performed using a rolling-disk rheometer which closely simulates those conditions existent in real lubricated contacts; the film-thickness data were obtained using an X-ray technique. The range of experimental conditions included two rolling speeds (5000 and 10,000 rpm), several contact pressures [(690 – 2400 MN/m2) (100 to 350 ksi)], and three temperatures [(338, 366 and 423 K) (150, 200, and 300 F)]. The slip conditions imposed on the lubricants ranged as high as 6 m/s (1200 fpm) which is equivalent to a shear rate of approximately 0.5 × 108 sec−1. Interpretative analyses have been developed to infer basic lubricant properties from the experimental data. These analyses include time delay parameters and “dynamic” pressure-viscosity parameters. The analytical treatment of the data provides: (1) a generalization of the experimental data to apply over a wider range of conditions than those actually covered, and (2) a basis for comparing lubricants and obtaining a more fundamental understanding of lubricant behavior.

Further Results on Moist Nearly Neutral Flow over a Ridge

2006 ◽  
Vol 63 (11) ◽  
pp. 2881-2897 ◽  
Author(s):  
M. M. Miglietta ◽  
R. Rotunno
Keyword(s):  
Coriolis Force ◽  
Numerical Solutions ◽  
Wrf Model ◽  
Rainfall Rate ◽  
Experimental Conditions ◽  
Available Water Content ◽  
Warm Rain ◽  
Temperature Regimes ◽  
Neutral Flow ◽  
Microphysical Processes

Abstract In a recent study, the authors performed numerical simulations of moist nearly neutral flows over a ridge using the Weather Research and Forecasting (WRF) Model in a regime where the Coriolis force can be neglected and with the simple Kessler (warm rain) microphysical scheme. In the present work, further numerical solutions using more general and realistic experimental conditions are discussed. The upstream-propagating disturbance, which was found in the author’s previous study to desaturate the initially saturated sounding for intermediate mountain heights, is present for all the simulations with taller mountains considered in the present work. The inclusion of the Coriolis force however suppresses the upwind propagation of the dry region and weakens the downstream development of convective cells. The sensitivity to different microphysical schemes has also been investigated. The simple Kessler scheme was compared with a more complete scheme, by Lin et al., which includes ice species. Some differences between the warm-rain-only and ice-microphysics simulations emerge mainly as a consequence of the different distributions of initial cloud water needed to produce a steady-state environmental flow. The effects of the different microphysical schemes on the rainfall rate have also been analyzed, with significant differences between them emerging in the case of narrower mountains. Finally, the sensitivity of the rainfall to the surface temperature has been studied, showing that for higher surface temperatures, the rainfall rate can be smaller although the available water content is larger, as a consequence of the differing microphysical processes activated in the different temperature regimes.

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