Determination of the Projected Atomic Potential by Deconvolution of the Auto-Correlation Function of TEM Electron Nano-Diffraction Patterns

Abstract

Abstract:We present a novel method to determine the projected atomic potential of a specimen directly from transmission electron microscopy coherent electron nano-diffraction patterns, overcoming common limitations encountered so far due to the dynamical nature of electron-matter interaction. The projected potential is obtained by deconvolution of the inverse Fourier transform of experimental diffraction patterns rescaled in intensity by using theoretical values of the kinematical atomic scattering factors. This novelty enables the compensation of dynamical effects typical of transmission electron microscopy (TEM) experiments on standard specimens with thicknesses up to a few tens of nm. The projected atomic potentials so obtained are averaged on sample regions illuminated by nano-sized electron probes and are in good quantitative agreement with theoretical expectations. Contrary to lens-based microscopy, here the spatial resolution in the retrieved projected atomic potential profiles is related to the finer lattice spacing measured in the electron diffraction pattern. The method has been successfully applied to experimental nano-diffraction data of crystalline centrosymmetric and non-centrosymmetric specimens achieving a resolution of 65 pm.

Effective Pattern Intensity Artifacts Treatment for Electron Diffractive Imaging

“…We believe that the methods used here to treat the spurious diffracted intensities are helpful for all the methods based on electron diffraction. For example, it could open new opportunities to apply many approaches already developed in X-ray crystallography to electron diffraction experiments, in analogy with what was demonstrated by De Caro et al [31]. As a result, new fields of application for quantitative electron diffraction could be opened.…”

“…The need for extremely thin specimens for EDI is a reason that limits the application of this methodology despite its capability to image the structure of the matter at atomic resolution. Indeed in a recent paper [31] it has been demonstrated that, if the electron diffraction patterns are free of spurious intensities, it is possible to compensate the dynamical effects by proper constraints based on further information on the specimen chemistry, which can be obtained by energy dispersive X-ray spectroscopy during the same experimental TEM session. In fact, after the treatment of the dynamical effects, the projected potential of the specimen can be quantitatively measured at the atomic resolution by the deconvolution of the autocorrelation function of the experimental diffraction pattern [31].…”

“…Indeed in a recent paper [31] it has been demonstrated that, if the electron diffraction patterns are free of spurious intensities, it is possible to compensate the dynamical effects by proper constraints based on further information on the specimen chemistry, which can be obtained by energy dispersive X-ray spectroscopy during the same experimental TEM session. In fact, after the treatment of the dynamical effects, the projected potential of the specimen can be quantitatively measured at the atomic resolution by the deconvolution of the autocorrelation function of the experimental diffraction pattern [31]. The determination of the specimen atomic projected-potential enables us to distinguish between crystal atomic columns with different compositions and, for example in the case of the SrTiO 3 specimen oriented with the (001) plane perpendicular to the direction of the primary electron beam, enables us to distinguish the atomic column containing Sr, or Ti+O, or only O, gathering fundamental information regarding the properties of the specimen.…”

“…The diffraction data free from spurious intensity, even if acquired on a relatively thick standard TEM specimen, are indeed the effective starting point to apply further methods for the quantification of the properties of the specimen at atomic resolution. This enabled us to develop and demonstrate [31] new methods to manage the dynamical effects, always present in TEM experiments on standard specimen thicknesses, and to quantitatively derive the atomic projected potentials even in the case of atoms of light elements in the crystal matrix of heavy elements [31]. The diffraction data of a KEDI experiment, free from spurious intensities, were also used to image, for the first time and by using new phasing algorithms, the structure of a specimen starting from random phases [32].…”

“…The need for extremely thin specimens for EDI is a reason that limits the application of this methodology despite its capability to image the structure of the matter at atomic resolution. Indeed in a recent paper [31] it has been demonstrated that, if the electron diffraction …”