Phasing coherently illuminated nanocrystals bounded by partial unit cells

With the use of highly coherent femtosecond X-ray pulses from a free-electron laser, it is possible to record protein nanocrystal diffraction patterns with far more information than is present in conventional crystallographic diffraction data. It has been suggested that diffraction phases may be retrieved from such data via iterative algorithms, without the use of a priori information and without restrictions on resolution. Here, we investigate the extension of this approach to nanocrystals with edge terminations that produce partial unit cells, and hence cannot be described by a common repeating unit cell. In this situation, the phase problem described in previous work must be reformulated. We demonstrate an approximate solution to this phase problem for crystals with random edge terminations.