Response to Fraser & Wark's comments on A new theory for X-ray diffraction.

Paul F Fewster

doi:10.1107/s2053273318007489

Abstract

The criticisms of my theory, as given by Fraser & Wark [(2018), Acta Cryst. A74, 447-456], are built on a misunderstanding of the concept and the methodology I have used. The assumption they have made rules out my description from which they conclude that my theory is proved to be wrong. They assume that I have misunderstood the diffraction associated with the shape of a crystal and my calculation is only relevant to a parallelepiped and even that I have got wrong. It only appears wrong to Fraser & Wark because the effect I predict has nothing to do with the crystal shape. The effect though can be measured as well as the crystal shape effects. This response describes my reasoning behind the theory, how it can be related to the Ewald sphere construction, and the build-up of the full diffraction pattern from all the scatterers in a stack of planes. It is the latter point that makes the Fraser & Wark analysis incomplete. The description given in this article describes my approach much more precisely with reference to the Ewald sphere construction. Several experiments are described that directly measure the predictions of the new theory, which are explained with reference to the Ewald sphere description. In its simplest terms the new theory can be considered as giving a thickness to the Ewald sphere surface, whereas in the conventional theory it has no thickness. Any thickness immediately informs us that the scattering from a peak at the Bragg angle does not have to be in the Bragg condition to be observed. I believe the conventional theory is a very good approximation, but as soon as it is tested with careful experiments it is shown to be incomplete. The new theory puts forward the idea that there is persistent intensity at the Bragg scattering angle outside the Bragg condition. This intensity is weak (∼10-5) but can be observed in careful laboratory experiments, despite being on the limit of observation, yet it has a profound impact on how we should interpret diffraction patterns.

Highlights

The new theory of X-ray diffraction arose from trying to account for inexplicable experimental observations
My questioning of conventional theory started in the 1990s when using the nearperfect diffraction space probe (Fewster, 1989) to study polycrystalline materials and perfect semiconductors, with work on a different description beginning in the mid-2000s
The crystal shape will modify the intensity close to the Bragg peak, which was recognized by Fewster (2014) p. 262: ‘ a powder sample that has a distribution of orientations will create fringes associated with its size and surface shape and an enhancement at 2B for each crystallite plane’

Summary

Introduction

The new theory of X-ray diffraction arose from trying to account for inexplicable experimental observations. For a real experiment the data will have a finite dynamic range and only the strong features are likely to be observed (Fig. 2b) These simulations reveal the fringing due to the crystal surface boundary conditions (the shape transform) and if a fringe is close to the Ewald sphere it could be more intense than the associated Bragg peak that is more remote, e.g. The new theory predicts that a scan in 2 over a large range at a fixed incident angle would encounter a peak at 2s corresponding to the specular condition (e.g. crystal truncation rod) and at 2B (the enhancement or persistent peak) This is exactly what was observed by Fewster (2016) and further clearer examples are given, including the measurement of the predicted arc in Fig. 1 [example (iv) in x4]. It indicates how a full two-dimensional diffraction space map can be simulated

The impact of crystal shape

The difficulties with ‘conventional theory’

Conclusions