Bond Orientational Order and Percolation

Crystallization is the ordering of a disordered system. In order to follow this process, it is necessary to label atoms which have a crystalline local environment. This is done by quantifying the directional order of a system of bonds for each atom. Angular correlations at an atomic scale can be achieved by projecting interatomic vectors r, j onto a basis of spherical harmonics Yim (r ), and the order parameter of Steinhardt, Nelson, and Ronchetti has proved to be valuable in several contexts for different symmetries [32], 

13 5sualization of a-d the 460-atom and e-f 648-atom system at different stages of crystallization at 600 K. The atoms with crystaUine local environment are highlighted with ball-and-stick. The fixed cubic seed is at the centre of (a) and (e). Green Ge, purple Sb, and orange Te 

Once we have obtained classification scheme for atoms that have a crystalline local environment, it is useful to analyze their connections between these atoms. In particular, we are interested in continuous paths over these atoms (bonds) which extend over the whole system, i.e. percolation. The connection between statistical mechanics, especially phase transitions, and percolation has a vast literature. In the case of GST, simultaneous measurements of electrical resistivity and optical reflectivity showed a significant influence of percolation on electrical properties, but a negligible influence on optical properties [33]. Here, we have analyzed percolation of the simulation trajectories by locating crystalline atoms as defined above and locating continuous paths of such atoms from an atom / to the same atom in a neighboring ceii in all three Cartesian directions (for bonds of maximum length 3.20 A). 

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