Abstract:

This paper provides a concise overview of three commonly employed methods for the determination of crystal structures from powder diffraction data, each exemplified with a specific case study. The first method is the single-crystal-like direct methods, leveraging reciprocal space information to construct the structure model. The second approach involves simulated annealing, which performs a global optimization of randomly generated models in real space to identify the structure. The third is the charge flipping method in which modifications to structure factors in reciprocal space and charge densities in real space are made, leading to the determination of the structure model through Fourier cycling switching back and forth between the two spaces. The presented examples are Ba₃BPO₇, MgSO₄·2H₂O and MgSO₄·2.5H₂O, respectively.

Key words: Crystal structure analysis, X-ray powder diffraction, Direct methods, Simulated annealing, Charge flipping