Towards the theoretical limitations of X-ray nanocrystallography at high intensity: the validity of the effective-form-factor description

X-ray free-electron lasers (XFELs) broaden horizons in X-ray crystallography. Facilitated by the unprecedented high intensity and ultrashort duration of the XFEL pulses, they enable us to investigate the structure and dynamics of macromolecules with nano-sized crystals. A limitation is the extent of radiation damage in the nanocrystal target. A large degree of ionization initiated by the incident high-intensity XFEL pulse alters the scattering properties of the atoms leading to perturbed measured patterns. In this article, the effective-form-factor approximation applied to capture this phenomenon is discussed. Additionally, the importance of temporal configurational fluctuations at high intensities, shaping these quantities besides the average electron loss, is shown. An analysis regarding the applicability of the approach to targets consisting of several atomic species is made, both theoretically and via realistic radiation-damage simulations. It is concluded that, up to intensities relevant for XFEL-based nanocrystallography, the effective-form-factor description is sufficiently accurate. This work justifies treating measured scattering patterns using conventional structure-reconstruction algorithms.