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Quantitative interpretation of transmission electron microscopy (TEM) data of crystalline specimens often requires the accurate knowledge of the local crystal orientation. A method is presented which exploits momentum-resolved scanning TEM (STEM) data to determine the local mistilt from a major zone axis. It is based on a geometric analysis of Kikuchi bands within a single diffraction pattern, yielding the centre of the Laue circle. Whereas the approach is not limited to convergent illumination, it is here developed using unit-cell averaged diffraction patterns corresponding to high-resolution STEM settings. In simulation studies, an accuracy of approximately 0.1mrad is found. The method is implemented in automated software and applied to crystallographic tilt and in-plane rotation mapping in two experimental cases. In particular, orientation maps of high-Mn steel and an epitaxially grown La$_{\text{0.7}}$Sr$_{\text{0.3}}$MnO$_{\text{3}}$-SrTiO$_{\text{3}}$ interface are presented. The results confirm the estimates of the simulation study and indicate that tilt mapping can be performed consistently over a wide field of view with diameters well above 100nm at unit cell real space sampling.

We compare the Frequency-Resolved Frozen Phonon Multislice (FRFPMS) method, introduced in Phys. Rev. Lett. 124, 025501 (2020), with other theoretical approaches used to account for the inelastic scattering of high energy electrons, namely the first-order Born approximation and the quantum excitation of phonons model. We show, that these theories lead to similar expressions for the single inelastically scattered intensity as a function of momentum transfer for an anisotropic quantum harmonic oscillator in a weak phase object approximation of the scattered waves, except for a too small smearing of the scattering potential by the effective Debye-Waller factor (DWF) in the FRFPMS method. We propose that this issue can be fixed by including an explicit DWF smearing into the potential and demonstrate numerically, that in any realistic situation, a FRFPMS approach revised in this way, correctly accounts for the single inelastically scattered intensity and the correct elastic scattering intensity. Furthermore our simulations illustrate that the only requirement for such a revised FRFPMS method is the smallness of mean squared displacements for all atomic species in all frequency bins. The analytical considerations for the FRFPMS method also explain the $1/\omega^2$-scaling of FRFPMS spectra observed in Phys. Rev. B 104, 104301 (2021) by the use of classical statistics in the molecular dynamics simulation. Moreover, we find that the FRFPMS method inherently adds the contributions of phonon loss and gain within each frequency bin. Both of these issues related to the frequency-scaling can be fixed by a system-independent post-processing step.

The isotopic mass of constituent elements of materials has a well-known effect on the energy of vibrational modes. By means of monochromated scanning transmission electron microscopy we have experimentally studied the phonon bandstructure of hexagonal BN, where a phonon band gap appears between in-plane optical phonon modes and the lower energy part of the phonon spectrum. The size of the phonon band gap can be manipulated by the isotopic mass of the boron. While in $^{11}$BN the phonon band gap is about 7 meV wide, in $^{10}$BN the gap nearly closes, being an order of magnitude smaller (below 0.5 meV). This opens exciting options for manipulating terahertz wave propagation through isotopically structured devices having otherwise no interfaces between chemically distinct components., Comment: 5 pages, 3 figures

A unified method for three-dimensional reconstruction of objects from transmission images collected at multiple illumination directions is described. The method may be applicable to experimental conditions relevant to absorption-based, phase-contrast or diffraction imaging using X-rays, electrons and other forms of penetrating radiation or matter waves. Both the phase retrieval (also known as contrast transfer function correction) and the effect of Ewald sphere curvature (in the cases with a shallow depth of field and significant in-object diffraction) are incorporated in the proposed algorithm and can be taken into account. Multiple scattering is not treated explicitly, but can be mitigated as a result of angular averaging that constitutes an essential feature of the method. The corresponding numerical algorithm is based on three-dimensional gridding which allows for fast computational implementation, including a straightforward parallelization. The algorithm can be used with any scanning geometry involving plane-wave illumination. A software code implementing the proposed algorithm has been developed, tested on simulated and experimental image data and made publicly available., Comment: 16 pages, 3 figures

Increasing interest in three-dimensional nanostructures adds impetus to electron microscopy techniques capable of imaging at or below the nanoscale in three dimensions. We present a reconstruction algorithm that takes as input a focal series of four-dimensional scanning transmission electron microscopy (4D-STEM) data. We apply the approach to a lead iridate, Pb$_2$Ir$_2$O$_7$, and yttrium-stabilized zirconia,Y$_{0.095}$Zr$_{0.905}$O$_2$ , heterostructure from data acquired with the specimen in a single plan-view orientation, with the epitaxial layers stacked along the beam direction. We demonstrate that Pb-Ir atomic columns are visible in the uppermost layers of the reconstructed volume. We compare this approach to the alternative techniques of depth sectioning using differential phase contrast scanning transmission electron microscopy (DPC-STEM) and multislice ptychographic reconstruction., Comment: 27 pages, 6 figures in main manuscript. 6 pages, 5 figures in supplementary. All computer code for electron microscopy simulation and reconstruction included in directory anc. Submitted to Microscopy & Microanalysis