Abstract
The phenomenology of glass-forming liquids is often described in terms of their underlying, high-dimensional potential energy surface. In particular, the statistics of stationary points sampled as a function of temperature provides useful insight into the thermodynamics and dynamics of the system. To make contact with the real space physics, however, analysis of the spatial structure of the normal modes is required. In this work, we numerically study the potential energy surface of a glass-forming ternary mixture. Starting from liquid configurations equilibrated over a broad range of temperatures using a swap Monte Carlo method, we locate the nearby stationary points and investigate the spatial architecture and the energetics of the associated unstable modes. Through this spatially-resolved analysis, originally developed to study local minima, we corroborate recent evidence that the nature of the unstable modes changes from delocalized to localized around the mode-coupling temperature. We find that the displacement amplitudes of the delocalized modes have a slowly decaying far field, whereas the localized modes consist of a core with large displacements and a rapidly decaying far field. The fractal dimension of unstable modes around the mobility edge is equal to 1, consistent with the scaling of the participation ratio. Finally, we find that around and below the mode-coupling temperature the unstable modes are localized around structural defects, characterized by a disordered local structure markedly different from the liquid's locally favored structure. These defects are similar to those associated to quasi-localized vibrations in local minima and are good candidates to predict the emergence of localized excitations at low temperature.
Highlights
2.2.1 Participation ratio 2.2.2 Decay profile 2.2.3 Fractal dimension 2.2.4 Energy profile 2.2.5 One-particle dynamical matrix 2.3 Local structure 2.3.1 Locally favored structures 2.3.2 Structural order parameter
Stationary points of the potential energy surface (PES) are configurations such that the gradient of the total potential energy U vanishes, and correspond to either local minima or saddles. These configurations play an important role in the PES-based description of glass formation. In his seminal work in 1969, Goldstein [8] argued that the dynamics of supercooled liquids is dominated by activated barrier crossing between neighboring local minima below some temperature Tx, at which the structural relaxation time is of order 10−9s
We provide evidence that around and below TMCT localized unstable modes originate from structural defects similar to those associated to the cores of the quasi-localized vibrations (QLVs), or “soft spots”, which have been identified in previous studies on metallic glasses [46]
Summary
Glass formation is driven by the rapid increase of structural relaxation times that takes place when liquids are cooled fast enough to avoid crystallization [1, 2]. These configurations play an important role in the PES-based description of glass formation In his seminal work in 1969, Goldstein [8] argued that the dynamics of supercooled liquids is dominated by activated barrier crossing between neighboring local minima below some temperature Tx , at which the structural relaxation time is of order 10−9s. MCT provides a semi-quantitative description of several non-trivial dynamic features above the critical temperature TMCT, at which the theory predicts a power law divergence of the relaxation times This singularity is smeared out in actual supercooled liquids by the presence of thermally activated processes, which are not accounted for by the theory and turn the transition into a crossover.
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