Refuting `a new theory for X-ray diffraction' - a reciprocal-space approach

Some ten years ago, Fewster proposed `a new theory for X-ray diffraction' in order to explain the completeness of powder diffraction patterns from samples with very few crystals, claiming to find extra intensity at Bragg scattering angles 2θ_B, even when a grain was not oriented in the Bragg condition, and claiming this to be a new approach to X-ray scattering [Fewster (2014). Acta Cryst. A70, 257-282]. Fraser & Wark [Acta Cryst. (2018), A74, 447-456] gave a detailed account of the errors and issues in the approach by Fewster, but the situation appears to be still undecided. To address this issue, we use a different perspective, based on conventional scattering theory and using a simpler description in reciprocal space, rather than the angular space used by Fewster and by Fraser & Wark. This allows us to focus on the crucial conceptual errors in the proposed theory. We show that Fewster is in fact not proposing a new theory, but finds effects that disagree with conventional theory because of errors in the path length calculation. We also discuss extensively the effect of residual intensity in reciprocal space, away from the Bragg peaks, and caused by the termination of crystals. We show that the residual intensity has no significant effect on the intensity of typical powder diffraction patterns. We hope that, with this account, we can put the discussion about the new theory to rest, along with the theory itself.