Accurate lattice-parameter determination from electron diffraction tomography data using two-dimensional diffraction vectors

Electron diffraction tomography (EDT) has emerged as a successful tool for ab initio atomic structure determination of nanometre-sized crystals. However, lattice parameters obtained from EDT data are often of lower accuracy than those from powder X-ray data, owing to experimental errors and data-processing methods. This work describes a lattice-parameter refinement method for EDT data using two-dimensional diffraction vectors and shows that the accuracy of lattice-parameter determination can be improved significantly. It is also shown that the method is tolerant to sample displacement during data collection and to geometric distortions in the electron diffraction patterns due to lens imperfections. For the data sets tested, the method reduces the 95% confidence interval of the worst errors in angles from +/- 1.98 to +/- 0.82 degrees and the worst relative errors of the unit-cell lengths from +/- 1.8% to +/- 1.3%, compared with the conventional method using clustering of three-dimensional diffraction vectors. The improvement is attributed to the fact that the new method makes use of the positions of two-dimensional diffraction spots, which can be determined with high accuracy, and disregards the position of the central beam, the orientation of the rotation axis and the angles of the diffraction frames, whose errors all contribute to the errors for lattice-parameter determination using the three-dimensional method.