The reduction of N-beam scattering from noncentrosymmetric crystals to two-beam form

It is shown that certain noncentrosymmetric seven-beam configurations can be reduced to two-beam form. This is exemplified for the space group of a-quartz, namely P3₁21, with the incident beam along [001]. Explicit eigenvalues and eigenvectors are given for this case and it is shown that the two-beam form is independent of the imaginary parts of the structure amplitudes. The reduction is shown to result from five zero projectors rather than confluence, although confluence is present. An exhaustive list of the 15 reducible noncentrosymmetric space groups is obtained.