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

For an exact solution of the Bragg equation it is necessary that there be a one-to-one correspondence (equivalence) between the angnlar measure theta and the wavelength measure lambda . Because the aberrations inherent in all x- ray diffraction profile measurements distont 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 CuK alpha and FeK alpha two-crystal spectrometer profiles prepared by Bearden were 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 lambda and theta 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 amore » result of inclusion or exclusion of the K alpha satellite group within the truncated profile. The twocrystal 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.« less