Phasing of coherent femtosecond X-ray diffraction from size-varying nanocrystals

The scattering between Bragg reflections from nanocrystals is used to aid solution of the phase problem. We describe a method for reconstructing the charge density of a typical molecule within a single unit cell, if sufficiently finely-sampled "snap-shot" diffraction data (as provided a free-electron X-ray laser) are available from many nanocrystals of different sizes lying in random orientations. By using information on the particle-size distribution within the patterns, this digital method succeeds, using all the data, without knowledge of the distribution of particle size or requiring atomic-resolution data.