Vlieg Elias, Tinnemans Paul, de Gelder René
Radboud University, Institute for Molecules and Materials, Heyendaalseweg 135, Nijmegen, 6525AJ, The Netherlands.
Acta Crystallogr A Found Adv. 2025 Jul 1;81(Pt 4):306-316. doi: 10.1107/S2053273325000762. Epub 2025 May 27.
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, 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.
大约十年前，富斯特提出了“一种新的X射线衍射理论”，以解释来自晶体极少的样品的粉末衍射图谱的完整性，声称在布拉格散射角2θ处发现了额外的强度，即使晶粒未处于布拉格条件下的取向，还声称这是一种新的X射线散射方法[富斯特（2014年）。《晶体学报》。A70，257 - 282]。弗雷泽和沃克[《晶体学报》（2018年），A74，447 - 456]详细阐述了富斯特方法中的错误和问题，但情况似乎仍未确定。为了解决这个问题，我们采用了不同的视角，基于传统散射理论，并在倒易空间中使用更简单的描述，而不是富斯特以及弗雷泽和沃克所使用的角空间。这使我们能够关注所提出理论中的关键概念性错误。我们表明，富斯特实际上并不是在提出一种新理论，而是由于程长计算中的错误发现了与传统理论不一致的效应。我们还广泛讨论了倒易空间中远离布拉格峰且由晶体终止引起的残余强度的影响。我们表明，残余强度对典型粉末衍射图谱的强度没有显著影响。我们希望通过这一阐述，能够结束关于这一新理论的讨论，连同该理论本身一起。
