Quantitative zone-axis convergent-beam electron diffraction (CBED) studies of metals. II. Debye-Waller-factor measurements.

Abstract

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.