A Statistical Approach to the Atomic Pair Distribution Function for Total Scattering Data from Microstrip Detectors

One-dimensional microstrip detector has been extensively employed for powder diffraction, while it has the potential for measuring total scattering (both Bragg diffraction and diffuse scattering) to obtain both local and average structural insights from the pair distribution function of crystalline materials. Such detectors, however, have not been recognized as being qualified for the technique. One possible reason is that their total scattering data are subject to the various errors such as the statistical error and the systematic error, especially at backscattering. The main focus of this work was to develop a statistical approach to the problem. The statistics of the data obtained from microstrip detectors are relatively low because only a small part of the Debye–Sherrer ring can be integrated. In microstrip detectors, moreover, the statistical error is easily influenced by not only the Poisson noise but also differences in the X-ray response between channels (DXRC). The present work provides an idea of the “apparent” statistical error, taking account of DXRC to statistically deduce the PDF from total scattering data. On the other hand, backscattering data are prone to the systematic error when converting total scattering data to the structure factor. The present work suggests a quantitative approach to measuring the impact of the systematic error on the structure factor.