Powder diffraction patterns of very small single crystals, or crystallites, are subject to size-dependent peak broadening, which, below a certain size, renders powder diffraction fingerprinting useless. In this case, peak resolution is only possible in 3D reciprocal space,
i.e. by applying single-crystal electron diffraction techniques.
High-Resolution Transmission Electron Microscopy (HRTEM) provides images and diffraction patterns of nanometer sized crystallites. Fourier transforms of HRTEM images and electron diffraction patterns both supply information about the projected reciprocal lattice geometry
for a certain crystal orientation, where the projection axis coincides with the optical axis of the microscope.
Projected lattice geometries can be represented by so-called ‘lattice-fringe fingerprint plots’ (LFFPs), also called angular covariance plots. The horizontal axis of such a plot is given in reciprocal lattice length and is limited by the point resolution of the microscope. The vertical axis is defined as acute angle between Fourier transformed lattice fringes or electron diffraction spots. A 2D data point is defined by the length of a reciprocal lattice vector and its (acute) angle with another reciprocal lattice vector. Sets of 2D data points that obey Weiss's zone law are subsets of the entirety of data points in an LFFP. A suitable search-match algorithm using LFFPs, therefore, tries to find matching zone axis subsets in the database. It is, essentially, a variant of a lattice matching algorithm.
In the case of electron diffraction patterns, structure factor amplitudes can be used, in a later step, to further discern among a selection of candidate structures (so-called structure factor fingerprinting). Structure factor amplitudes from electron diffraction data are far less reliable than their counterparts from X-ray single-crystal and powder diffraction data. Existing precession electron diffraction techniques greatly improve the quality of structure factor amplitudes, increase their number and, thus, make structure factor amplitude information much more useful for the fingerprinting process.
Fourier transforms of HRTEM images, on the other hand, supply information not only about the projected reciprocal lattice geometry and structure factor amplitudes, but also structure factor phase angles. After crystallographic image processing, structure factor phase angles are far more reliable than structure factor amplitudes. Further discernment of candidate structures is then mainly based on structure factor phase angles and, to a lesser extent, structure factor amplitudes (so-called structure factor fingerprinting).