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Indexing of Kikuchi and Kossel lines is a crucial step in K‐line pattern analysis. Previous approaches mostly rely on the knowledge of unit‐cell parameters and experimental geometry. An auto‐indexing procedure is introduced that is able to find the unknown lattice, its orientation and the indices of the lines. To achieve this, the unbiased extraction of the precise conical geometrical information from the patterns is combined with existing auto‐indexing procedures developed in the field of crystallography. A subsequent lattice‐constrained refinement of all lines to the experimental pattern yields reliable lattice and experimental parameters simultaneously. Beyond providing detailed mathematical formulae, the procedure is also demonstrated on an experimental Kossel line pattern. [ABSTRACT FROM AUTHOR]

In coherent‐diffraction‐imaging experiments X‐ray diffraction patterns of identical particles are recorded. The particles are injected into the X‐ray free‐electron laser (XFEL) beam in random orientations. If the particle has symmetry, finding the orientation of a pattern can be ambiguous. With some modifications, the correlation‐maximization method can find the relative orientations of the diffraction patterns for the case of symmetric particles as well. After convergence, the correlation maps show the symmetry of the particle and can be used to determine the symmetry elements and their orientations. The C factor, slightly modified for the symmetric case, can indicate the consistency of the assembled three‐dimensional intensity distribution. [ABSTRACT FROM AUTHOR]

The short pulses of X-ray free-electron lasers can produce diffraction patterns with structural information before radiation damage destroys the particle. From the recorded diffraction patterns the structure of particles or molecules can be determined on the nano- or even atomic scale. In a coherent diffraction imaging experiment thousands of diffraction patterns of identical particles are recorded and assembled into a three-dimensional distribution which is subsequently used to solve the structure of the particle. It is essential to know, but not always obvious, that the assembled three-dimensional reciprocal-space intensity distribution is really consistent with the measured diffraction patterns. This paper shows that, with the use of correlation maps and a single parameter calculated from them, the consistency of the three-dimensional distribution can be reliably validated. [ABSTRACT FROM AUTHOR]

Very short pulses of X-ray free-electron lasers opened the way to obtaining diffraction signal from single particles beyond the radiation dose limit. For three-dimensional structure reconstruction many patterns are recorded in the object's unknown orientation. A method is described for the orientation of continuous diffraction patterns of non-periodic objects, utilizing intensity correlations in the curved intersections of the corresponding Ewald spheres, and hence named the common arc orientation method. The present implementation of the algorithm optionally takes into account Friedel's law, handles missing data and is capable of determining the point group of symmetric objects. Its performance is demonstrated on simulated diffraction data sets and verification of the results indicates a high orientation accuracy even at low signal levels. The common arc method fills a gap in the wide palette of orientation methods. [ABSTRACT FROM AUTHOR]

The structure of the title compound, 5,6-[(1R,10S)-2,9-dioxatri-cyclo-[8.6.0(3,8).0(11,16)]hexa-decane-1,10-di-yl]-(C60-Ih)[5,6]fullerene methane-dithione 0.1-solvate, C74H10O2·0.1CS2, has tetra-gonal (P42/n) symmetry at 100 K. It has a unique eight-membered ring, with two incorporated O atoms in place of the original central ring of the anthracene. The distortion of the mol-ecular geometry around the cyclo-adduct bonds corresponds to that seen in related fullerene derivatives. Close packing of the adduct forms cavities partially filled with disordered carbon di-sulfide solvent mol-ecule. The 41% occupancy of the cavities yields an overall 1:0.103 adduct-solvent ratio. Reaction steps are described as light-assisted singlet-oxygen generation, peroxide, epoxide and dioxocin derivative formation and the final step of thermally activated cyclo-addition.