Characterization of local structures with bond-order parameters and graphs of the nearest neighbors,a comparison

We compare two methods for the characterization of local order in samples undergoing crystal nucleation and growth. Particles with a crystal-like surrounding need to be identified to follow the nucleation process. Both methods are based on the knowledge of the particle positions in a small volume of the sample. (i) Local bond-order parameters are used to quantify the orientation of the nearest neighbors of a particle, while (ii) the graph method determines the topological arrangement of the nearest neighbors and the bonds between them. Both methods are used to detect crystal-like particles and crystal nuclei in a supercooled fluid surrounding and to determine the structure of small crystal nuclei. The properties of these nuclei are of great interest for a deeper understanding of crystal nucleation, and they can be studied in detail in colloidal model systems that allow to follow the evolution of the nuclei with single particle resolution.