Vortex structure of excitation fields in a supercooled glass-forming liquid and its relationship with relaxations

Abstract

In the framework of the dynamic facilitation model, a glass former is structured with local cooperative excitations in space and time when approaching the glass transition, which is closely related to dynamic relaxations. We investigate the structure of excitation fields in supercooled ${\mathrm{Cu}}_{50}{\mathrm{Zr}}_{50}$ glass former, and reveal that the excitation fields feature the vortexlike structure beyond the well-known stringlike excitations. The vortex is developed from the stringlike excitations and frequently annihilates via the interactions between vortex and antivortex. The region favored by vortices exhibits percolationlike morphology. We find that the probability distributions of vortex core number are characterized by the discrete multiple mode, which is very analogous to the quantized mode of the slow-\ensuremath{\beta} type relaxation. Furthermore, the relaxation time derived from the formation rate of vortices as well as the corresponding activation energy coincide with the characteristic values of the slow-\ensuremath{\beta} relaxation in metallic glasses. Therefore, it is concluded that the vortex excitation is the origin of the slow-\ensuremath{\beta} relaxation in dynamic space. We further find that the activation energy and relaxation time associated with individual excitations agree well with the Johari-Goldstein \ensuremath{\beta} relaxation. It manifests a more intrinsic structural sign of the Johari-Goldstein \ensuremath{\beta} relaxation than the interpretation based on stringlike excitations.