Defects in liquid selenium

We use the data generated in recent first-principles molecular-dynamics simulations of liquid selenium at the temperatures 570, 870, and 1370 K to investigate defects in the liquid. The defects represent disruptions of the chain structure associated with onefold and threefold atoms ${(C}_{1}$ and ${C}_{3}$ defects). We stress that for a full understanding we need to analyze the defects from the viewpoints of atomic coordination, defect dynamics, and electronic structure, and we develop analysis techniques to do this. We find that localized electronic states at the top of the valence band and the bottom of the conduction band are associated with ${C}_{1}$ and ${C}_{3}$ defects, respectively. At 570 K, the concentration of defects is very low, and they exist as ${C}_{1}$ and ${C}_{3}$ defects in bound pairs (intimate valence-alternation pairs), but at high temperatures the defects are isolated and are mainly of ${C}_{1}$ type. The defect concentrations are used to determine the mean length of Se chains, which we find to be much smaller than the values deduced from NMR measurements at lower temperatures, but in reasonable agreement at 1370 K. Analysis of the defect dynamics shows that the residence time of defects on individual atoms becomes extremely short---comparable with the vibrational period---at high temperature.