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库提供了一系列模型，用于模拟多种材料结构中热中子的弹性与非弹性散射过程。本文介绍了现有的弹性散射模型，并对其理论背景、实现方式，尤其是验证工作展开了详细讨论。所涵盖的模型既有用于晶体粉末的布拉格衍射模型，也包含非相干弹性散射模型，而研究的核心聚焦于理想缺陷单晶体的布拉格衍射模型：既包含应用最广泛的各向同性高斯镶嵌性模型，也涵盖了适用于热解石墨等材料的层状单晶体专用模型。即便这些单晶体模型在适宜场景下采用了计算效率较高的近似手段，仍充分保障了背散射、前散射以及大镶嵌展宽晶体等极端场景下的结果精确可靠。结合NCrystal库的晶体结构初始化与非弹性物理相关其他功能，本文所介绍的模型可在Geant4、McStas等框架中实现中子散射仪器各类组件的真实建模，涵盖单色器、分析器、滤波器、支撑材料、屏蔽结构以及多种样品。作为本项研究的附带成果，本文还提供了一种改进的近似公式，用于计算具备高斯镶嵌性的各向同性单晶体的散射截面。