Triplet-phase measurements using reference-beam X-ray diffraction

Reference-beam diffraction (RBD) is a recently developed phase-sensitive X-ray diffraction technique that incorporates the principle of multiple-beam diffraction into the standard oscillating-crystal data-collection method [Shen (1998). Phys. Rev. Lett. 80, 3268-3271]. Using this technique, a large number of multiple-beam interference profiles can be recorded simultaneously on an area detector, from which a large number of triplet phases of Bragg reflections can be determined in a crystallography experiment. In this article, both the theoretical developments and the experimental procedures of the RBD technique are described in detail. Approximate theoretical approaches for RBD are outlined and simple analytical expressions are obtained that provide the basis for an automated data-analysis procedure that can be used to extract triplet phases from a large number of measured reference-beam diffraction profiles. Experimental examples are given for a variety of crystals including GaAs, tetragonal lysozyme and AlPdMn quasicrystal, using both image plates and a charge-coupled device (CCD) as the area detector. Possible uses of the measured phases for crystal structure determination are discussed as well as future prospects of the RBD technique.