Spatial structure of unstable normal modes in a glass-forming liquid

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.

Instantaneous normal modes of glass-forming liquids during the athermal relaxation process of the steepest descent algorithm

“…In the early stage of the dynamics, or the large-W regime, it decays rapidly with distance r from the core. This behavior resembles the unstable localized modes found at saddle points [30]. As W decreases with time, this decay becomes slower.…”

“…Considering the spatial distribution of the eigenenergies of unstable modes, it is possible to investigate the local mechanical stability. Thus, we next study the energy profile Λ(r) [30,49,50] of the most unstable mode. The energy profile is a function of the distance r from the particle that has the most negative local harmonic energy δE i for a given mode [49].…”

“…The energy profile Λ(r) is the partial harmonic energy of the mode integrated from the core to the distance r. In other words, Λ(r) is the harmonic energy that the mode would have if the system were cut at a distance r from the core, and thus Λ(r → ∞) converges to the eigenvalue of the mode, see Refs. [30,49,50] for the complete definition. Figure 8 shows the results for N = 128000 at the same values of W as in Fig.…”

“…Such modes, known as quasilocalized modes, are attributed to several anomalous low-energy properties of glasses, including plastic events under shear [25][26][27] and low-temperature thermal properties [28,29]. Recently, comparing the quasi-localized modes and unstable modes found at saddles, it was also established that these two types of modes are deeply interlinked in terms of their structures [30]. Along these lines, it is meaningful to analyze instantaneous modes during relaxation using the methods adopted to analyze the quasi-localized modes.…”

Correlation between plastic rearrangements and local structure in a cyclically driven glass

“…Predicting plastic re-arrangements based on local structures information is a challenging domain of research (see Ref. 30 and reference therein) that has attracted a lot of interest in recent years [72][73][74][75] . In this paper, we have studied the local structural rearrangements of particles undergoing cyclic shear deformation in a model glass former focusing on local tetrahedrality n tet that we introduced previously 19 and the well known two-body excess entropy S 2 .…”