Quantitative convergent-beam electron diffraction and quantum crystallography—the metallic bond in aluminium

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.…”

Towards Mapping Chemical Bonds in Nanostructured Materials

“…The purpose of showing these diffraction patterns is twofold, namely: (i) to evidence that for nanostructures with crystallographically coherent interfaces throughout the probed volume and perpendicular to the electron beam direction, the CBED patterns have sharply defined reflection discs because the 2-dimensional projection of the reciprocal lattice along the beam direction is invariant as a function of depth within the specimen; and (ii) to show that there are many turning points in the intensity distributions within these patterns that will constrain the refinement of structural parameters, including the structure factors to which the pattern intensities are most sensitiveparticularly those with short scattering vectors at or near their Bragg conditions (such as those that are shown in the present examples). These also contain the most bonding information [9,37,53,54].…”

“…Originally the domain of X-ray diffraction experiments [3], quantum crystallography now also embraces quantitative convergent-beam electron diffraction (QCBED) measurements of quantum mechanical observables in crystals, namely the Fourier coefficients of the crystal potential (structure factors) [2,4]. Transforming crystal potential structure factors into electron density structure factors (measured directly by X-ray diffraction) is trivial via the Mott-Bethe formula [2, 4 -6] and it is in the measurement of bondingsensitive structure factors that QCBED has made a name for itself in the last few decades, in terms of both precision and accuracy [2, 4, 7 -56].…”

“…Figure 2 also presents two CBED patterns. The first, Fig.2f, was collected with the CBED probe aligned along the [001] direction in a (ZnO)kIn2O3 thermoelectric superlattice material, an example of which is imaged in the[1][2][3][4][5][6][7][8][9][10] direction in Fig.2b. The second pattern was obtained with the probe incident in a near-[001] orientation on an Al-Cu-Sn alloy containing voids coated with single atomic layers of tin[65] like the one shown in Fig.2c and d. The CBED probe was positioned to pass through the void, resulting in the pattern shown in Fig.2g.…”

Three-beam convergent-beam electron diffraction for measuring crystallographic phases

“…The current three-beam CBED method is an ab initio approach where no structural model is assumed. This is in contrast to quantitative CBED for refining structure factors and three-phase invariants within a given structural model (Goodman & Lehmpfuhl, 1967;Spence, 1993;Nakashima, 2017). A quantitative analysis of experimental three-beam CBED patterns has been used to refine three-phase invariants to an accuracy of within one degree (for example, Høier et al, 1999).…”