Retrieving atomic structure from dynamical rocking curve measurements in both real and reciprocal space

Abstract

Transmission electron microscopy (TEM) data, in particular high‐resolution TEM and conventional electron diffraction has the reputation of being not easily interpretable in a quantitative manner in terms of the object being probed by the fast electrons. The reason for this lies in the fact that multiple scattering makes the detected signal a non‐linear function of the scattering potential. In cases where the structure is approximately known, refinement of structure factors from convergent beam electron diffraction (CBED) data [1] or atom positions from HRTEM images [2] is possible. But the ab‐initio inversion of multiple scattering to recover the structure of an unknown object has not yet been shown to work in a routine manner for experimental data. Structure determination approaches thus typically revert to techniques which collect tilt‐averaged data, such as precession electron diffraction (PED) and scanning transmission electron microscopy (STEM) with a convergent probe. Integrating the signal over a range of different relative orientations between object and electron beam wave vector averages over different multiple scattering conditions – however, a large amount of structural information encoded in the multiple scattering signal gets lost, including valuable information about the object's 3D structure [3]. Fig. 1 demonstrates that in the case of experimental large‐angle rocking‐beam electron diffraction (LARBED) data [4], i.e. diffraction data for a large range of beam tilts (about 20 times larger than possible in conventional CBED of silicon), the projected potential can be recovered by straight forward gradient optimization from a starting guess in which all structure factors were initialized to the same value, i.e. initially, all Ug = (0.01 + 0.01i) Å −2 [5]. Although rocking curves of only 121 diffraction spots were measured, 456 structure factors could be determined from this data, since, all possible difference vectors between reflections extracted from the diffraction pattern were also included in the dynamical diffraction calculation. Although CBED and HRTEM are very different modes of operation of the microscope, the multiple scattering contribution to the signal in tilt series of HRTEM images allows us to retrieve the 3D scattering potential [6], where the position and height of peaks allows direct interpretation as atom species and positions (see Fig. 2). This inversion of multiple scattering is based on an interpretation of the multislice algorithm as an artificial neural network that is taught by feeding it TEM data recorded under different experimental conditions. This can be HRTEM tilt series, ptychography data sets, or scanning confocal electron microscopy (SCEM) data [7].[8]