Simulating Powder X-ray Diffraction Patterns of Two-Dimensional Materials.

Powder X-ray diffraction (PXRD) is widely used to study atomic arrangements in ordered materials. The Bragg equation, which describes diffraction of a three-dimensional crystal, fails in two-dimensional (2D) cases. Complete integration of diffraction signals from a continuum instead of discrete directions in the Bragg equation is thus required for proper data interpretation of 2D materials. Furthermore, modeling of preferred orientation of the 2D crystals as well as geometric disorders are also of vital importance. Here, we present a complete integration method in real space (CIREALS) for PXRD simulation of monolayer or multilayer 2D crystals, especially 2D metal-organic layers and 2D covalent organic frameworks. By working in real space instead of reciprocal space, we can readily capture the 2D geometry and preferred orientation of these materials. The predicted PXRD patterns by CIREALS facilitates structure analysis of these new types of 2D material.