03 Fakultät Chemie
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Item Open Access Two-dimensional X-ray powder diffraction(2007) Hinrichsen, Bernd; Dinnebier, Robert E. (Prof. Dr.)The combination two-dimensional detectors, powder diffraction and synchrotron light sources has been staggeringly successful, opening doors to many new experiments. The great advantages of such data collection lie in the short exposure times as well as in the huge redundancy. A large angular region of the Bragg cone is recorded in a single exposure; indeed most detectors are set up perpendicular and centrally to the primary beam, intercepting the Bragg cone over the entire azimuthal range. The standard practice is to integrate the image along the ellipses described by the intersection of the cone with the planar detector to a conventional powder pattern. This commonly reduces the amount of information by the square root of the number of pixels. Does this represent the gamut of information contained in a powder diffraction image? A glance at an image from a calibration standard might lend itself to such a conclusion. Less perfect samples, as well as sample environments leave distinctive artefacts on images. How can they be extracted, filtered or interpreted? Methods offering answers to these questions are introduced. The origins of powder diffraction were based on diffraction images, however with the onset of equatorial electronic point detectors all high quality powder diffraction experiments switched to this method. It has remained the experimental doctrine to this day. Only recently have powder diffraction scientists rediscovered the allure of diffraction images. Indeed high pressure powder diffraction experiments are unthinkable without two-dimensional detectors. What seems like such a positive development does, on closer inspection have its problems. Two dimensional correction factors effectively do not exist for powder diffraction experiments. All commonly used Lorentz and polarization (LP) corrections are meaningless outside the thin equatorial strip for which they were determined. Furthermore various other detector and geometry dependent factors have to be considered should a high quality powder diffraction pattern be extracted from the image. The first chapter of this thesis takes on this challenge and presents all applicable two-dimensional correction factors, as well as the basis for their application: the experimental set-up. Determining the geometry to the highest possible precision is paramount to the quality of the experiment. How can one achieve this goal, without losing oneself in diverging refinements and renitent analysis software? Pattern recognition methods and whole image refinement have been used to solve the two main problems of calibration and are presented in the second chapter. The first global search gives sensible starting values for what is probably the most extreme refinement single pattern powder diffraction has to offer: whole image refinement. Here the entire two-dimensional image is rebuilt, based on the initial values, and subtracted from the experimental image. This residual is then minimized using a Levenberg-Marquardt non-linear least squares refinement algorithm. This method leads to calibrations that are at least one order of magnitude more precise than traditional calibration routines. This is of fundamental importance for the effective use of future high resolution area detectors. A perfect calibration does not suffice to ensure a successful data reduction. Especially in situ experiments - the forte of two-dimensional detectors cause intensity aberrations that need to be removed before the image can successfully be integrated to a conventional powder diffractogram. The source of deviations can be sorted into two camps: those originating from the sample environment and those emanating from the sample itself. Of course the former is both more easily recognized visually and also removed more simply by the fractile filters presented in the third chapter. When intensity deviations originate from the sample the matter becomes far more complex. A new distribution function, the normal Pareto function, has been shown to describe the intensity distribution that results from small sample amounts without substantial sample rotation, as is the case in high pressure powder diffraction. The great benefit of this function is that it opens the possibility of extracting a fractional filtering setting which ultimately leads to normally distributed intensities. Structural analysis from diffraction data is always connected to a plethora of reliability values, describing the raw data as well as the refinement quality. Powder diffraction images completely lack any numerical estimation of their quality. Functions giving universally comparable, detector independent reliability values for images can be found in chapter four.