Inverse problems arise frequently in physics: The magnitude of the Fourier transform of some function is measurable, but not its phase. The "phase problem" in crystallography arises because the number of discrete measurements (Bragg peak intensities) is only half the number of unknowns (electron density points in space). Sayre first proposed that oversampling of diffraction data should allow a solution, and this has recently been demonstrated. Here we report the successful phasing of an oversampled hard x-ray diffraction pattern measured from a single nanocrystal of gold.
The structures of the liquid crystalline chiral subphases exhibited by several materials containing either a selenium or sulphur atom have been investigated using a resonant x-ray scattering technique. This technique provides a unique structural probe for the ferroelectric, ferrielectric, antiferroelectric, and SmC(*)(alpha) phases. An analysis of the scattering features allows the structural models of the different subphases to be distinguished, in addition to providing a measurement of the helical pitch. This paper reports resonant scattering features in the antiferroelectric hexatic phase, the three- and four-layer intermediate phases, the antiferroelectric and ferroelectric phases and the SmC(*)(alpha) phase. The helicoidal pitch has been measured from the scattering peaks in the four-layer intermediate phase as well as in the antiferroelectric and ferroelectric phases. In the SmC(*)(alpha) phase, an investigation into the helical structure has revealed a pitch ranging from 5 to 54 layers in different materials. Further, a strong resonant scattering signal has been observed in mixtures of a selenium containing material with as much as 90% nonresonant material.
High-resolution resonant polarized x-ray diffraction experiments near the sulfur K edge have been performed on free-standing liquid crystal films exhibiting the chiral smectic-C*FI2 phase. It is widely accepted that this phase has a four-layer repeat unit, but the internal structure of the repeat unit remains controversial. We report different resolved features of the resonant x-ray diffraction peaks associated with the smectic-C*FI2 phase that unambiguously demonstrate that the four-layer repeat unit is locally biaxial about the layer normal and that the measured angle, describing the biaxiality, is in good agreement with optical measurements.
Obtaining accurate structural information on epitaxial films and interfaces is nowhere more critical than in semiconductor passivation layers, where details of the atomic structure and bonding determine the nature of the interface electronic states. Various non-destructive methods have been used to investigate the structure of films and interfaces, but their interpretation is model-dependent, leading occasionally to wrong conclusions. We have developed a new X-ray method for the direct determination of epitaxial structures, coherent Bragg rod analysis (COBRA). The usefulness of our technique is demonstrated by mapping, with atomic precision, the structure of the interfacial region of a Gd2O3 film grown epitaxially on a (100) GaAs substrate. Our findings reveal interesting behaviour not previously suggested by existing structural methods, in particular a lock-in of the in-plane Gd atomic positions to those of the Ga/As atoms of the substrate. Moreover, we find that the bulk stacking of the Gd2O3 atomic layers is abandoned in favour of a new structure that is directly correlated with the stacking sequence of the substrate. These results have important implications for Gd2O3 as an effective passivation layer for GaAs (ref. 7). Our work shows that the COBRA technique, taking advantage of the brilliance of insertion device synchrotron X-ray sources, is widely applicable to epitaxial films and interfaces.
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