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 2 × 10^-4.