Unit-cell parameters determination from a set of independent electron diffraction zonal patterns

Due to the short de Broglie wavelength of electrons compared with X-rays, the curvature of their Ewald sphere is low, and individual electron diffraction patterns are nearly flat in reciprocal space. As a result, a reliable unit-cell determination from a set of randomly oriented electron diffraction patterns, an essential step in serial electron diffraction, becomes a non-trivial task. Here we describe an algorithm for unit-cell determination from a set of independent electron diffraction patterns, as implemented in the program PIEP (Program for Interpreting Electron diffraction Patterns), written in the early 1990s. We evaluate the performance of the algorithm by unit-cell determination of two known structures - copper perchlorophthalocyanine (CuPcCl₁₆) and lysozyme, challenging the algorithm by high-index zone patterns and long crystallographic axes. Finally, we apply the procedure to a new, structurally uncharacterized five amino acid peptide.