Af. Moodie et Hj. Whitfield, THE REDUCTION OF N-BEAM SCATTERING FORM NONCENTROSYMMETRIC CRYSTALS TO 2-BEAM FORM, Acta crystallographica. Section A, Foundations of crystallography, 50, 1994, pp. 730-736
It is shown that certain noncentrosymmetric seven-beam configurations
can be reduced to two-beam form. This is exemplified for the space gro
up of alpha-quartz, namely P3(1)21, 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 fi
ve zero projectors rather than confluence, although confluence is pres
ent. An exhaustive list of the 15 reducible noncentrosymmetric space g
roups is obtained.