Towards the real structure of quasicrystals and approximants by analysing diffuse scattering and deconvolving the Patterson

Abstract

Methods based on X-ray area detectors are presented for acquiring and analysing single-crystal X-ray diffraction data from quasicrystals and approximants. These methods are complementary to high-resolution diffractometry and fully exploit the possibilities of modern two-dimensional X-ray detector systems (imaging plates and charge coupled devices) such as the on-line read-out capability and the possibility to collect large volumes of reciprocal space in a quantitative and rapid way. In contrast to a classical point detector, area detectors allow the measurement of a very large number of Bragg reflections in a reasonable time scale, as is shown with a large unit-cell periodic approximant in the Al-Co-Ni alloy system. For large approximants exhibiting strong pseudosymmetry, direct methods for structure solution usually fail. Recently implemented Patterson deconvolution techniques are shown to succeed. The extension of techniques for area detectors – beyond the standard application of collecting integrated Bragg intensities – to the quantitative acquisition of continuous and diffuse scattering data is presented with particular emphasis on quasicrystals. One of the key techniques is the quantitative reconstruction of undistorted layers and volumes in reciprocal space. This is crucial for developing and comparing possible models for structural disorder in quasicrystals. Examples for decagonal Al-Co-Ni and icosahedral Al-Mn-Pd are given in respect to possibilities and limitations of X-ray area detectors.