Exploring crystal structure by three-dimensional atomic density distribution from molecular dynamics simulations

Predicting crystal structure has been one of the core issues in materials research. X-ray diffraction data can generally be used to fit and refine the positions of atoms within the unit cell. However, for a system with part of its atoms diffusing or hopping below the melting temperature, the atoms inside the crystal begin to vibrate, diffuse, or hop when its temperature gradually rises. Even using the partial-occupancy concept, it becomes difficult or impossible to fit the structure due to the trial-and-error characteristic of refinement. More importantly, the limited partial-occupancy positions are insufficient and inappropriate to describe material systems containing diffusing or hopping atoms. To address this shortcoming, we proposed to perform molecular dynamics simulations and then add up all the positions of diffusing atoms in each time step to form a three-dimensional atomic density distribution into the primitive or conventional unit cell. The maximum atomic density points correspond to the partial-occupancy positions in x-ray diffraction data. The connected atomic density distribution identifies and defines the diffusing paths for mobile atoms within the crystal.