Determining lattice parameters from two electron diffraction patterns

Abstract

Lattice parameters are the fundamental quantities to describe a crystal structure, but the X-ray or neutron diffraction technique can determine only the averaged structure. Local lattice parameters can be determined from two zone-axis electron diffraction patterns (ZAPs) and the overall tilt angle, but the crystal needs to be oriented at the exact zone axis. This is a time-consuming transmission electron microscopy operation and largely limits structure determination of nanocrystallites. Here, a new method is proposed to reconstruct the 3D reciprocal cell and determine the lattice parameters from two ZAPs, one of which contains a high-order Laue zone (HOLZ) ring. The validity of the method was verified on both a low-symmetry monoclinic structure and a high-symmetry cubic crystal. The advantage of the method is that the accuracy of the lattice parameters measured is largely dependent on the HOLZ ring, which will considerably simplify the transmission electron microscopy operation. In this work, both the HOLZ-based method and the angle-based method were integrated into the DigitalMicrograph plugin UnitCell Tools—Two Patterns. With the help of this program, the lattice parameters of a crystal can be determined from two electron diffraction patterns efficiently and precisely.