Large-angle convergent-beam electron diffraction; a simple technique for the study of modulated structures with application to V₂D

Abstract

With a highly convergent electron beam entering a small crystal area, the Bragg condition may be fulfilled simultaneously for many diffraction orders along a reciprocal-lattice direction, and reflections with (sin 0)/2 > 2 A-t are accessible. Considerations based on the dynamical theory of electron diffraction suggest that for Bragg reflections with (sin 0)/2>l/k -x, 100 keV electrons can be treated quasi-kinematically when the crystal thickness is less than 1000 ,~,, and this is supported by experiments. This simple approach has been used to determine the D-induced static displacement modulation 6 of V along the a axis (monochlinic indexing) in the/~ phase of VzD. From visual inspection of the Bragg intensities for large diffraction orders, up to (sin 0)/2=2.35/k -x, it is concluded that 6 = 0-070 (5)/k.

Structure refinement of Al3Zr using single-crystal X-ray diffraction, powder neutron diffraction and CBED

“…The present CBED technique used for structure refinement was first developed by Tafto & Metzger (1985), who showed that a wide cone of incident rays for a converged electron beam in an electron microscope could be used to obtain intensity data from many high-order reflections of a systematic row.…”

“…However, crystal structure determinations of these materials are mostly quite old (Brauer, 1939;Black, 1955). During a study of an A1-Zr alloy containing I~m-size precipitates of A13Zr using convergent-beam electron diffraction (CBED), large discrepancies in the refined z coordinates of the Zr(e) and Al(e) atoms were found between previous powder X-ray diffraction (Brauer, 1939) and a recently proposed electron diffraction method, CBED, with large Bragg and convergent angles (Tafto & Metzger, 1985;Tomokiyo & Kuroiwa, 1991). Since the technique has only recently been developed, it was therefore decided to carry out a coordinate refinement of A13Zr using established quantitative methods of single-crystal X-ray diffraction and powder neutron diffraction.…”

Anharmonic thermal motion of atoms in thermoelectric Mg2Si studied via convergent-beam electron diffraction

“…We use a large convergent-beam angle. 7,8 Thus, many reflections along a reciprocal lattice row may be simultaneously at the Bragg position (Fig. 1).…”

Locating Atoms in Small Crystals by Combining Convergent Beam Electron Diffraction and Electron Channeling

“…However, when the reflections with short g-vectors are far from the Bragg position, while several reflections well out in reciprocal space satisfy the Bragg condition, we come a long way with simple kinematical considerations. A CBED experiment that fulfills these constraints can be realized by tilting the specimen of the order one degree away from symmetrical incidence relative to a reciprocal lattice row [4].…”