Anisotropic structural predictor in glassy materials

Abstract

There is a growing evidence that relaxation in glassy materials, both spontaneous and externally driven, is mediated by localized soft spots. Recent progress made it possible to identify the soft spots inside glassy structures and to quantify their degree of softness. These softness measures, however, are typically scalars, not taking into account the tensorial/anisotropic nature of soft spots, which implies orientation-dependent coupling to external deformation. Here we derive from first principles the linear response coupling between the local heat capacity of glasses, previously shown to provide a measure of glassy softness, and external deformation in different directions. We first show that this linear response quantity follows an anomalous, fat-tailed distribution related to the universal ω 4 density of states of quasilocalized, nonphononic excitations in glasses. We then construct a structural predictor as the product of the local heat capacity and its linear response to external deformation, and show that it offers enhanced predictability of plastic rearrangements under deformation in different directions, compared to the purely scalar predictor.Introduction.-At the heart of resolving the glass mystery resides the need to quantify the disordered structures inherently associated with glasses and to relate them to glass properties and dynamics, most notably spontaneous and driven structural relaxation [1,2]. Numerous attempts to address and meet this grand challenge have been made [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], aiming at defining structural indicators with predictive powers. Achieving this goal would constitute major progress in understanding glassiness and would provide invaluable insight for developing macroscopic theories of deformation and flow of glasses.Recently accumulated evidence suggests that spatially localized soft spots are the loci of glassy relaxation, and hence are highly relevant for glass dynamics. These localized soft spots have been related to quasilocalized, nonphononic excitations in glasses [4][5][6], whose universal ω 4 density of states (ω is the vibrational frequency) has been also established recently [20][21][22][23]. Among the structural predictors proposed, most relevant here is the normalized local thermal energy [6], which quantifies the interparticle interaction contribution to the zero-temperature heat capacity, termed hereafter the local heat capacity (LHC) c α (α is the interaction index).The LHC c α is a general (system/model-independent), first principles statistical mechanical quantity that reveals soft spots in glassy materials [6]. Yet, the LHC is a scalar that quantifies the resistance to motion in some unknown direction. That is, like previously proposed structural predictors in glasses (with the exception of [15][16][17]), the LHC misses important tensorial/anisotropic information about the coupling to deformation in a certain direction. For example, an extremely soft spot can be completely decoupled from external forces applied in ...

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