Direct atomic structure determination by the inspection of structural phase

A century has passed since Bragg solved the first atomic structure using diffraction. As with this first structure, all atomic structures to date have been deduced from the measurement of many diffracted intensities using iterative and statistical methods. We show that centrosymmetric atomic structures can be determined without the need to measure or even record a diffracted intensity. Instead, atomic structures can be determined directly and quickly from the observation of crystallographic phases in electron diffraction patterns. Furthermore, only a few phases are required to achieve high resolution. This represents a paradigm shift in structure determination methods, which we demonstrate with the moderately complex α-Al2O3. We show that the observation of just nine phases enables the location of all atoms with a resolution of better than 0.1 Å. This level of certainty previously required the measurement of thousands of diffracted intensities.