An experimental approach to mapping chemical bonds in nanostructured materials

We introduce a number of techniques in quantitative convergent-beam electron diffraction under development by our group and discuss the basis for measuring interatomic electrostatic potentials (and therefore also electron densities), localised at sub-nanometre scales, with sufficient accuracy and precision to map chemical bonds in and around nanostructures in nanostructured materials. This has never been possible as experimental measurements of bonding have always been restricted to homogeneous single-phased crystals. Introduction The electronic structure of chemical bonds is the dominant determinant of almost all materials properties1 and it is in the accurate experimental measurement of chemical bonding as well as its modelling and interpretation by quantum theory, that the modern field of quantum crystallography resides.2 Originally the domain of X-ray diffraction experiments, 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 (called structure factors).24 Transforming crystal potential structure factors into electron density structure factors (measured directly by X-ray diffraction) is trivial via the Mott-Bethe formula2, 4-6 and it is in the measurement of bonding-sensitive 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 By definition, QCBED is the fitting of a calculated CBED pattern to an experimental one while adjusting the parameters to which the intensities in the pattern are most sensitive in order to minimise the pattern mismatch. Fig. 1 schematically illustrates CBED in the context of a specimen and gives an example of the comparison of experimental and calculated CBED intensities within QCBED. A significant benefit of QCBED, besides accuracy and precision, is its spatial selectivity. It is routine to form focussed electron probes with nanometre or smaller dimensions in the process of obtaining convergent-beam electron diffraction (CBED) patterns. This is by virtue of electrons being charged and thus being easily manipulable by magnetic and electrostatic optical elements in electron microscopes. This means that CBED patterns can be acquired from volumes of crystal of order ~109 times smaller than in X-ray diffraction experiments, even at synchrotrons. Furthermore, these tiny electron probes can be positioned with sub-Ångström lateral precision to avoid inhomogeneities such as precipitate phases and crystal defects as shown in Fig. 1. Our new research concerning bonding in and around nanostructures in inhomogeneous materials means that we will be aiming to do the opposite of what is illustrated in Fig. 1: instead of targeting only the perfect regions of the matrix material, we will selectively probe the nanostructures as well. With the aid of computer-controlled scanning of the CBED probe over areas of, in principle, arbitrary user-defined shape, QCBED measurements of localised bonding structure as a function of position in nanostructured materials become a very interesting prospect. Figure 1: A schematic illustration of CBED and pattern matching within QCBED. QCBED involves the collection of an experimental CBED pattern from a real material, often replete with crystal defects, using a probe size of the order of 1 nm or smaller. The experimental intensities are pre-processed to eliminate errors due to instrumental point spread function (PSF) and inelastic scattering.44, 57, 58 QCBED involves the fitting of a calculated CBED pattern to an experimental one while refining the parameters to which the intensities (I) – and therefore also the derivative of the intensities with respect to scattering angle (I’ = dI/dθ) – are most sensitive, in order to minimise the mismatch (shown here in multiples of the standard uncertainty of the experimental data, σ, in every pixel). Nanostructures are, by definition, 3-dimensional of course and whilst sub-Ångström positioning of a nanometre or smaller sized electron probe in the x and y coordinates of a transmission electron microscope (TEM) has become routine, the ability to resolve structural information along the electron beam direction (defined as z) is a complex challenge. This difficulty is one that we are developing new QCBED techniques to overcome. We discuss these in this paper with the view to expanding bonding measurements from the current domain of homogeneous, single-phased crystals, to nanostructured