Three-dimensional rotation electron diffraction: software RED for automated data collection and data processing

Abstract

Implementation of a computer program package for automated collection and processing of rotation electron diffraction (RED) data is described. The software package contains two computer programs: RED data collection and RED data processing. The RED data collection program controls the transmission electron microscope and the camera. Electron beam tilts at a fine step (0.05-0.20°) are combined with goniometer tilts at a coarse step (2.0-3.0°) around a common tilt axis, which allows a fine relative tilt to be achieved between the electron beam and the crystal in a large tilt range. An electron diffraction (ED) frame is collected at each combination of beam tilt and goniometer tilt. The RED data processing program processes three-dimensional ED data generated by the RED data collection program or by other approaches. It includes shift correction of the ED frames, peak hunting for diffraction spots in individual ED frames and identification of these diffraction spots as reflections in three dimensions. Unit-cell parameters are determined from the positions of reflections in three-dimensional reciprocal space. All reflections are indexed, and finally a list with hkl indices and intensities is output. The data processing program also includes a visualizer to view and analyse three-dimensional reciprocal lattices reconstructed from the ED frames. Details of the implementation are described. Data collection and data processing with the software RED are demonstrated using a calcined zeolite sample, silicalite-1. The structure of the calcined silicalite-1, with 72 unique atoms, could be solved from the RED data by routine direct methods.

Keywords: computer programs; electron diffraction; electron diffraction tomography; rotation electron diffraction; structure analysis; three-dimensional electron diffraction.

Figure 1

Schematic representation of the concept of the rotation electron diffraction (RED) method. RED data (individual ED frames) are collected by combining beam tilt and goniometer tilt. After three-dimensional reconstruction, the intensities and positions of the reflections in reciprocal space are obtained and can be visualized. After further data processing the unit cell is determined and the reflections are indexed. A resultant hkl list is then used to determine the atomic structure of the crystals. The example used here is the zeolite silicalite-1.

Figure 2

A flowchart showing the steps of a complete RED data collection procedure using the SAED mode and controlled by the RED data collection program.

Figure 3

Graphical user interface of the RED data collection program.

Figure 4

Graphical user interface of the RED data processing program. It shows the reconstructed three-dimensional reciprocal lattice for calcined silicalite-1, obtained from 1472 individual ED frames. The hk0, hk1 and hk layers are marked in green, red and blue, respectively.

Figure 5

A flowchart showing the steps of data processing using the RED data processing program.

Figure 6

Shift correction window of the RED data processing program. An area of 256 × 256 pixels covering the direct beam is selected for cross-correlation calculation.

Figure 7

Peak hunting settings in the RED data processing program (a) and an example of peak hunting results (c) from an ED frame in the silicalite-1 data set (b). All visible peaks in (b) are detected by RED and marked with crosses in (c). The peak and background radii (i.e. standard deviations of Gaussian functions) as well as the peak–background threshold can be defined by the user.

Figure 8

Back projection of a diffraction spot R in a diffraction pattern onto the Ewald sphere at R′. O is the centre of the diffraction pattern and O′ the centre of the Ewald sphere.

Figure 9

Reconstructed three-dimensional reciprocal lattice of silicalite-1 with (a) incorrectly specified tilt axis orientation (42.5°) and (b) correct tilt axis orientation (48.5°). Notice that the reflection rows are bent when the tilt axis orientation is wrong, as shown in (a). This can be used to refine the tilt axis orientation.

Figure 10

Low-magnification TEM image of the calcined silicalite-1 crystal used here for demonstrating the RED data collection and processing software.

Figure 11

(a) The three-dimensional reciprocal lattice of calcined silicalite-1 reconstructed from the RED data and (b)–(d) two-dimensional slices cut from the reconstructed three-dimensional reciprocal lattice showing the (b) 0kl, (c) h0l and (c) hk0 planes.