Differential convergent beam electron diffraction: Experiment and theory

Abstract

The derivative of intensity with respect to scattering angle in an electron diffraction pattern is shown to be almost completely independent of whether the pattern has been energy filtered or not. This is attributed to the diffuse nature of inelastic scattering. A simple approach to quantitative convergent beam electron diffraction ͑QCBED͒, developed on this basis and tested on a corresponding pair of energy-filtered and unfiltered diffraction patterns from ␣-Al 2 O 3 , produces a fit between experimental and theoretical differential CBED patterns that is well within experimental uncertainty. Structure factors measured from the unfiltered data are indistinguishable from those from the filtered data. Furthermore, those measurements made by angular-difference QCBED appear to be less influenced by parameter correlation and the inelastic components of CBED patterns than those made by conventional QCBED. The outcome is a new avenue for accurate charge density studies that does not depend on energy-filtering optics or acquisition of multiple patterns requiring translation of the specimen.

Quantum Crystallography: Current Developments and Future Perspectives

“…This information can be condensed in matrixf ormat knowna st he Localization-Delocalization Matrix (LDM). [185,188] Selected reflections are pattern matchedw ith full dynamical electrons cattering calculations using either the multislice [189] or Bloch-wave [190,191] formalisms.The structurefactorsofreflections at or nearthe Bragg condition, V hkl or V g ,and the crystal thickness, H,are refined to minimizethe mismatch (following the loop of the grey arrow). The first step is CBED data collection from ar egion of perfect crystal ( % 10 À25 m 3 in volume).V ery high spatials electivity makesi teasytoavoid crystal imperfections and surface blemishes.…”

Differential quantitative analysis of background structure in energy-filtered convergent-beam electron diffraction patterns

“…The most important of these is that a differential approach to QCBED with respect to displacement in reciprocal space, jgj, or equivalently, scattering angle, , is likely to be more canonical than conventional QCBED. It was previously shown that a differential approach to QCBED based on specimen thickness, resulted in improvements in precision even when unfiltered CBED patterns were used (Nakashima, 2007). That approach required the acquisition of more than one pattern whilst the present work suggests that an angular difference approach would depend on only one pattern.…”

“…In addition, differential quantitative analysis of CBED data is not adversely affected by surface imperfections of the specimen, given that they lack structural periodicity. Whilst the thickness difference QCBED approach presented by Nakashima (2007) is one example of differential QCBED, the present work suggests a potentially new technique that involves a differential approach with respect to jgj, or equivalently, scattering angle, , to be developed in a separate paper (Nakashima & Muddle, 2010).…”

“…The high accuracy and precision of electronic structure measurements in inorganic solids with a high degree of crystal perfection by quantitative convergent-beam electron diffraction (QCBED) is now well established (Zuo et al, 1988;Bird & Saunders, 1992;Zuo, 1993;Deininger et al, 1994;Holmestad et al, 1995;Peng & Zuo, 1995;Saunders et al, 1995Saunders et al, , 1996Saunders et al, , 1999Zuo et al, 1997Zuo et al, , 1999Tsuda & Tanaka, 1999;Streltsov et al, 2001Streltsov et al, , 2003Tsuda et al, 2002;Jiang et al, 2003;Ogata et al, 2004;Friis, Madsen et al, 2003;Friis et al, 2004Friis et al, , 2005Nakashima, 2005Nakashima, , 2007. Such measurements are precise enough to allow meaningful comparisons of experimentally measured electronic structure with different ab initio theoretical models (Zuo et al, 1997(Zuo et al, , 1999Saunders et al, 1999;Friis, Madsen et al, 2003;Friis et al, 2004Friis et al, , 2005Nakashima, 2005), including those derived from density functional theory and periodic Hartree-Fock, Dirac-Fock and linear combination of atomic orbitals calculations.…”

Identification of the impurity phase in high-purity CeB6 by convergent-beam electron diffraction

“…Angular difference QCBED (ADQCBED) was applied in this work to reduce the deleterious effects of the inelastic signal in the CBED pattern (Nakashima & Muddle, 2010). The as-captured [111] near-zone-axis CBED pattern shown in Fig.…”