An analytical expression of diffraction line profiles of spherical hollow nanocrystals (NCs) is derived. The particular features of the profile lines, enhanced peak tail intensity, are analyzed and discussed as a function of the NC size parameters (outer and inner radius, shell thickness). The explicit formula for the integral breadth, the Fourier particle size, and the Scherrer constants are also obtained and discussed in detail. The diffraction line profiles of hollow CdS NCs of zincblende and wurtzite crystallographic structure are calculated and compared with Debye scattering profiles. The diffraction profiles of both approaches exhibit an enhanced peak tail intensity that can be considered as a fingerprint of the hollow NC structure.

中文翻译：

---

球形空心纳米晶体的衍射线轮廓

推导出球形空心纳米晶体 (NC) 的衍射线轮廓的分析表达式。作为 NC 尺寸参数（外半径和内半径、壳厚度）的函数，分析和讨论了轮廓线的特殊特征、增强的峰尾强度。还获得并详细讨论了积分宽度、傅立叶粒度和谢乐常数的显式公式。计算了闪锌矿和纤锌矿晶体结构的空心 CdS NC 的衍射线轮廓，并与德拜散射轮廓进行了比较。两种方法的衍射曲线都表现出增强的峰尾强度，可以将其视为中空 NC 结构的指纹。