KSpaceNavigator as a tool for computer-assisted sample tilting in high-resolution imaging, tomography and defect analysis

Abstract

This article describes a novel software tool, the KSpaceNavigator, which combines sample stage and crystallographic coordinates in a control sphere. It also provides simulated kinematic diffraction spot patterns, Kikuchi line patterns and a unit cell view in real time, thus allowing intuitive and transparent navigation in reciprocal space. By the overlay of experimental data with the simulations and some interactive alignment algorithms, zone axis orientations of the sample can be accessed quickly and with great ease. The software can be configured to work with any double-tilt or tilt–rotation stage and overcomes nonlinearities in existing goniometers by lookup tables. A subroutine for matching the polyhedral shape of a nanoparticle assists with 3D analysis and modeling. The new possibilities are demonstrated with the case of a faceted BaTiO₃ nanoparticle, which is tilted into three low-index zone axes using the piezo-controlled TEAM stage, and with a multiply twinned tetrahedral Ge precipitate in Al, which is tilted into four equivalent zone axes using a conventional double-tilt stage. Applications to other experimental scenarios are also outlined.

Introduction

High-resolution TEM images provide detailed information about the atomic arrangement of nanoparticles when viewed along rational crystallographic directions [1], [2]. A necessary prerequisite is the ability to properly tilt a crystalline sample into a precise zone axis orientation. However, the alignment of small crystallites along a specific zone axis is usually approached by trial and error, and depends critically on the skill and experience of the operator.

There is a growing need for controlled tilting to different zone axis orientations in order to understand the 3D structure of nanoparticles, both in terms of their atomic arrangement and in terms of their external shape, which cannot be determined from a single projection. For example, if the projected shape is square, this could imply that the particle is a cube bounded by {100} planes, or it could be a truncated octahedron bounded by {11} and {100} planes (see Fig. 1). Such ambiguities make it important to observe individual nanoparticles in different orientations along specific zone axes in order to understand their shape in 3D [3]. To achieve such tilts with the precision needed for high-resolution imaging, and with sufficient range to access widely separated zone axes is a major unsolved task for electron microscopy and a requirement for discrete tomography [4], [5], [6]. In addition, the radiation sensitivity of most materials [7] makes it important to minimize the exposure to the electron beam. Thus, tilting a sample to multiple specific orientations with minimal electron dose presents an important challenge.

Usually, sample tilting is done iteratively, by switching between the image and diffraction modes. The sample position is visible in the image mode while the sample orientation is seen in the diffraction mode. For sufficiently thick samples, a zone axis orientation is reached by following a Kikuchi band to a crossover. During tilting, the area of interest is kept in the field of view by following the sample in the image mode. The navigation from one orientation to another requires experience and patience, even when working with large crystals. If the sample is very small, such as a colloidal particle or a nanocrystalline grain, the method usually fails due to the lack of Kikuchi lines and the imprecision of the stage movements.

Another frequent cause of failure in complex tilt series is the limited range of the stage. The accessibility of a target pole within the tilt limits of the stage is usually assessed by trial and error. This often leads to incomplete experimental series when critical sample orientations turn out to be inaccessible in the course of an experiment.

To overcome these difficulties requires a software tool that correlates the orientation of the sample with the orientation of the stage. The present work describes such a software tool and illustrates how it is possible to tilt a sample to several precise zone axis orientations, even if the sample is an individual nanocrystal on a carbon support or a nanoscale precipitate in a polycrystalline matrix.