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Probability of Seeing (001) Cross-Fringes in a Random Cubic Nanocrystal Image

Published online by Cambridge University Press:  02 July 2020

W. Qin  and
P. Fraundorf
W. Qin
Affiliation:
Physics & Astronomy Department and CME, University of Missouri-StL, St. Louis, MO63121
P. Fraundorf
Affiliation:
Physics & Astronomy Department and CME, University of Missouri-StL, St. Louis, MO63121
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Extract

As a crystal gets smaller, diffraction spots stay visible for larger deviations from the Bragg condition. The upper limit of such deviations is connected to the threshold for getting lattice fringes in TEM images. This in turn allows one to quantify the probability of seeing cross lattice fringes along a certain zone axis. In this abstract we examine a simple semi-empirical model for the probability of detecting (001) zone cross-fringes of a spherical crystal of cubic lattice.

The upper limit for the deviation of crystal orientation from the exact Bragg condition, without losing cross fringes down a given zone, is expressed as the maximum half-angle θ1 between the zone and the electron beam. The solid angle σ subtended by a cone with this half-angle is proportional to the probability px that a randomly-oriented crystal will show the cross-fringes associated with that zone. A schematic, illustrating the principle used to calculate the probability of seeing cross-fringes, is given in Figure 1.

Type
High Resolution Electron Microscopy
Information
Microscopy and Microanalysis , Volume 6 , Issue S2: Proceedings: Microscopy & Microanalysis 2000, Microscopy Society of America 58th Annual Meeting, Microbeam Analysis Society 34th Annual Meeting, Microscopical Society of Canada/Societe de Microscopie de Canada 27th Annual Meeting, Philadelphia, Pennsylvania August 13-17, 2000 , August 2000 , pp. 1038 - 1039
Copyright
Copyright © Microscopy Society of America

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References

References:

1.Qin, W. and Fraundorf, P., Lattice fringe visibility after tilt (this conference).Google Scholar
2.Qin, W. and Fraundorf, P., Los Alamos’ arXiv:cond-mat/0001139 (http://arXiv.org).Google Scholar
3.Malm, J.-O. and O'Keefe, M. A., Ultramicroscopy 68 (1997) 13–23.CrossRefGoogle Scholar
4. Acknowledgements: Dr. James and Dr. Shih at U. Missouri-Rolla for the WC filmGoogle Scholar