Methods of Determining Centroid X-Ray Wavelengths: CuKα and FeKα

Abstract

For an exact solution of the Bragg equation it is necessary that there be a one-to-one correspondence (equivalence) between the angular measure θ and the wavelength measure λ. Because the aberrations inherent in all x-ray diffraction profile measurements distort the profile, it is necessary to correct any given measure (peak, centroid, etc.) for all aberrations. The only angular measure of powder diffractometer profiles that can be corrected to a high degree of accuracy is the centroid. To realize the greater accuracy inherent in the centroid method, accurate centroid spectral wavelengths are required. Centroids of CuKα and FeKα two-crystal spectrometer profiles prepared by Bearden have been calculated and corrected for axial divergence, distortions arising from variation in absorption across the spectral distributions, crystal asymmetry, and other factors. To determine the centroid wavelength it is necessary to truncate the profile; equivalence of λ and θ is maintained by truncating the powder and spectral profiles in the same manner. Four methods for systematically truncating the profiles have been published; the methods are evaluated and the superiority of one of the methods is demonstrated. It is shown that the centroid wavelength is a function of integration (wavelength) range, primarily as a result of inclusion or exclusion of the Kα satellite group within the truncated profile. The two-crystal spectrometer profiles are compared with models based on a Cauchy distribution. The necessity for additional spectral data before reference centroid wavelengths can be established is discussed.