Crystal Symmetry and Forbidden Reflections: From Structure Factors to Multiple Diffraction

A diffraction maximum at a nominally forbidden reciprocal-space position does not uniquely identify a reduction in crystal symmetry. Its interpretation depends on the origin of the extinction, the scattering interaction, and the availability of indirect diffraction pathways. This article develops a theoretical and computational account connecting structure-factor cancellation with multiple X-ray diffraction. Lattice-centering absences, restrictions associated with screw axes and glide planes, and cancellations specific to an atomic basis are distinguished before the diamond structure is examined explicitly. In the equal spherical atom approximation, the 222 structure factor vanishes, although allowed secondary and coupling reflections can transfer intensity into the same outgoing direction. A reproducible geometric calculation for a diamond-type cubic model with a = 5.431 Å and λ = 1.5406 Å identifies 180 indexed two-step event branches at 168 distinct azimuths. These are candidate geometries, not predicted intensities or measured peaks. Selected counterexamples demonstrate that vector closure, nonzero coupling factors, and simultaneous elastic conditions must be tested separately. The analysis also explains why true centering absences cannot be filled by successive Bragg transfers within the same ideal translation lattice, whereas basis cancellations can be bypassed. Recent developments in dynamical diffraction software, energy-dependent measurements, and diffuse multiple scattering are considered alongside earlier studies of Umweg peak indexing, polarization, and fine structure. A combined interpretation using azimuth, wavelength, polarization, reciprocal-space shape, and structural consistency provides a defensible basis for evaluating apparent violations of reflection conditions.