Determination of precise X-ray diffraction angles by fast Fourier transform

A new analytical method is presented for the separation of two or more closely overlapping X-ray diffraction lines using the narrowly distributed Gaussian function and one-dimensional fast Fourier transform pair. To test the method, the diffraction lines associated with characteristic Kα1 and Kα2 rays are measured by an X-ray diffractometer using a Brazilian quartz powder as a standard sample. It is found that the observed diffraction lines can be completely separated into Kα1 and Kα2 lines and that the accuracy of those diffraction angles is better than 2x10-4. (orig.)