Section 2.3.3.2. Problems arising from the Kα doublet

A common source of error arises from the Kα doublet which produces a pair of peaks for each reflection. The separation of the Cu Kα₁, Kα₂ peaks increases from 0.05° at 20°2θ to 1.08° at 150°2θ. The overlapping is also dependent on the instrument resolution and may cause errors in the peak angles and intensities when strip-chart recording or peak-search methods (described below) are used. The Kα₁ wavelength is generally used to calculate all the d's even when the low-angle peaks are unresolved. In the region where the doublet is only slightly resolved, the apparent Kα₁ peak angle is shifted to higher angles because of the overlapping Kα₂ tail and similarly the peak intensities will be in error. The relative peak intensities of a reflection with superposed doublet compared to a resolved doublet could have an error as large as 50%. Relative peak intensities are used in the ICDD standards file and cause no problem because the unknowns are measured in the same way. The integrated intensity avoids this difficulty but is impractical to use in routine identification.

Rachinger (1948) described a simple graphical procedure for removing Kα₂ peaks. The method causes errors because it makes the incorrect assumption that Kα₂ is the exact half-scale version of Kα₁. Ladell, Zagofsky & Pearlman (1975) developed an exact algorithm using the actual mathematical shapes observed with the user's diffractometer but, with line-profile-fitting programs now available, the Kα₂ component can be modelled precisely along with the Kα₁.

It is possible to isolate the Kα₁ line when using a high-quality incident-beam focusing monochromator as described in Subsection 2.3.1.2, Fig. 2.3.1.12(b), but there may be a loss of intensity. The source size must be narrow and the focal length long enough to separate the components.