Limitations on the s-state approach to the interpretation of sub-angstrom resolution electron microscope images and microanalysis

Anstis, GR; Cai, DQ; Cockayne, DJH

Limitations on the s-state approach to the interpretation of sub-angstrom resolution electron microscope images and microanalysis

Anstis, GR Cai, DQ Cockayne, DJH

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Publication Type:: Journal Article
Citation:: Ultramicroscopy, 2003, 94 (3-4), pp. 309 - 327
Issue Date:: 2003-04-01

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Field	Value	Language
dc.contributor.author	Anstis, GR	en_US
dc.contributor.author	Cai, DQ	en_US
dc.contributor.author	Cockayne, DJH	en_US
dc.date.issued	2003-04-01	en_US
dc.identifier.citation	Ultramicroscopy, 2003, 94 (3-4), pp. 309 - 327	en_US
dc.identifier.issn	0304-3991	en_US
dc.identifier.uri	http://hdl.handle.net/10453/4278
dc.description.abstract	The s-state approach is useful for analysing transmission electron microscope images of a thin crystalline foil consisting of well-separated atomic columns. It assumes that the signal collected (e.g., the annular dark-field image, the EELS spectrum) can be attributed to only the lowest-energy bound eigenstate of the two-dimensional projected potential of a single column. When, however, columns are close, the form of the bound states depends on more than one column, which implies that interpretation of the signal may not be so simple. For closely spaced columns we show that the simple s-state approach fails for the case of a sub-Angstrom probe initially centred on one column of a pair, because two bound states are excited. The energy in the probe is almost completely transferred to the neighbouring column after it has propagated some tens of nanometres through the foil and then is transferred back. Signals which relate directly to the local probe intensity (e.g. annular dark-field formed by thermal diffuse scattering, EELS) must be analysed in terms of the two bound states. Accurate calculations of bound states of pairs of columns are more demanding than for a single column but sufficient accuracy can be achieved from knowledge of the 1s-states of isolated columns. We provide formulae for the bound states of a column pair. These can be used to determine if image analysis requires the extension to the s-state approach described in this paper. © 2002 Elsevier Science B.V. All rights reserved.	en_US
dc.relation.ispartof	Ultramicroscopy	en_US
dc.relation.isbasedon	10.1016/S0304-3991(02)00341-8	en_US
dc.subject.classification	Microscopy	en_US
dc.subject.mesh	Arsenic	en_US
dc.subject.mesh	Gallium	en_US
dc.subject.mesh	Electron Probe Microanalysis	en_US
dc.subject.mesh	Microscopy, Electron, Scanning Transmission	en_US
dc.subject.mesh	Spectrum Analysis	en_US
dc.subject.mesh	Algorithms	en_US
dc.subject.mesh	Fourier Analysis	en_US
dc.subject.mesh	Scattering, Radiation	en_US
dc.title	Limitations on the s-state approach to the interpretation of sub-angstrom resolution electron microscope images and microanalysis	en_US
dc.type	Journal Article
utslib.citation.volume	3-4	en_US
utslib.citation.volume	94	en_US
utslib.for	0205 Optical Physics	en_US
utslib.for	0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics	en_US
utslib.for	0299 Other Physical Sciences	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	closed_access
pubs.issue	3-4	en_US
pubs.publication-status	Published	en_US
pubs.volume	94	en_US

Abstract:

The s-state approach is useful for analysing transmission electron microscope images of a thin crystalline foil consisting of well-separated atomic columns. It assumes that the signal collected (e.g., the annular dark-field image, the EELS spectrum) can be attributed to only the lowest-energy bound eigenstate of the two-dimensional projected potential of a single column. When, however, columns are close, the form of the bound states depends on more than one column, which implies that interpretation of the signal may not be so simple. For closely spaced columns we show that the simple s-state approach fails for the case of a sub-Angstrom probe initially centred on one column of a pair, because two bound states are excited. The energy in the probe is almost completely transferred to the neighbouring column after it has propagated some tens of nanometres through the foil and then is transferred back. Signals which relate directly to the local probe intensity (e.g. annular dark-field formed by thermal diffuse scattering, EELS) must be analysed in terms of the two bound states. Accurate calculations of bound states of pairs of columns are more demanding than for a single column but sufficient accuracy can be achieved from knowledge of the 1s-states of isolated columns. We provide formulae for the bound states of a column pair. These can be used to determine if image analysis requires the extension to the s-state approach described in this paper. © 2002 Elsevier Science B.V. All rights reserved.

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http://hdl.handle.net/10453/4278