Elastic neutron scattering models for NCrystal

The NCrystal library provides a range of models for simulation of both elastic and inelastic scattering of thermal neutrons in a range of material structures. This article presents the available models for elastic scattering, and includes detailed discussion of their theoretical background, their implementation, and in particular their validation. The lineup includes a model for Bragg diffraction in crystal powders as well as one for incoherent elastic scattering, but the main focus is given to models of Bragg diffraction in ideally imperfect single crystals: both for the most widely applicable model of isotropic Gaussian mosaicity, and for a more specific model of layered single crystals which is relevant for materials such as pyrolytic graphite. Although these single crystal models are utilising computationally efficient approximations where appropriate, attention is given to the provision of precise and trustworthy results also for the extreme cases of back-scattering, forward-scattering, and crystals with very large mosaic spreads. Together with NCrystal's other features for crystal structure initialisation and inelastic physics, the presented models enable realistic modelling of components at neutron scattering instruments in frameworks like Geant4 and McStas, including monochromators, analysers, filters, support materials, shielding, and many kinds of samples. As a byproduct of the work, an improved formula for approximating cross sections in isotropic single crystals with Gaussian mosaicity is provided.

NCrystal库提供了多种模型，用以模拟热中子在多种材料结构中发生的弹性散射和非弹性散射。本文阐述了弹性散射的可用模型，并对其理论背景、实现方式及验证进行了深入讨论。模型系列中包括晶粉中的布拉格衍射模型以及非相干弹性散射模型，但主要关注的是理想单晶中的布拉格衍射模型：既包括最广泛应用的各向同性高斯镶嵌模型，也包括适用于类似焦炭石墨等材料的层状单晶的特定模型。尽管这些单晶模型在适当的情况下利用了计算效率较高的近似方法，但仍注重提供精确且可靠的极端情况结果，如反向散射、正向散射以及具有非常宽镶嵌散布的晶体。与NCrystal的其他晶体结构初始化和弹性物理特性相结合，这些模型使得在Geant4和McStas等框架中模拟中子散射仪器组件成为可能，包括单色器、分析器、过滤器、支撑材料、屏蔽材料以及多种样品。作为本工作的副产品，还提供了一种改进的高斯镶嵌性各向同性单晶截面近似公式。