Quantitative zone-axis convergent-beam electron diffraction (CBED) studies of metals. II. Debye-Waller-factor measurements.
Quantitative CBED techniques, such as the ZAPMATCH zone-axis pattern-matching method [Bird & Saunders (1992). Ultramicroscopy, 45, 241-251], have been applied with great success to the accurate refinement of low-order structure factors. The major limitation on the accuracy of the structure-factor measurements is uncertainty in the Debye-Waller factors describing the temperature-dependent atomic vibrations. While X-ray and neutron diffraction tech-niques are both capable of accurate measurements of Debye-Waller factors, the frequent use of liquid-nitrogen-cooled samples in CBED experiments means that previous measurements are rarely available at the temperatures required. This has prompted attempts to determine Debye-Waller factors from electron diffraction data obtained under experimental conditions that match those used for the quantitative CBED work. In this paper, the possibility of extracting accurate Debye-Waller factors from the low-order reflections of a zone-axis CBED pattern is investigated. In this way, the Debye-Waller factors and structure factors could be obtained from the same data set. With this new approach, it is shown that errors lower than +/-0.02 Å(2) can be obtained for the measurement of Debye-Waller factors from room- and liquid-nitrogen-temperature nickel and copper <110> zone-axis data. The results obtained are compared with previous measurements and theoretical predictions.
Center for Materials Science and Engineering, Department of Mechanical Engineering, Naval Postgraduate School, Monterey, CA 93943, USA. martin.saunders@angstrom.uu.se
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Saunders
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Fox
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Midgley