Order parameter for structural heterogeneity in disordered solids

Abstract

We construct a new order parameter from the normal modes of vibration, based on the consideration of energy equipartition, to quantify the structural heterogeneity in disordered solids. The order parameter exhibits strong spatial correlations with low-temperature single particle dynamics and local structural entropy. To characterize the role of particles with the most defective local structures identified by the order parameter, we pin them and study how properties of disordered solids respond to the pinning. It turns out that these particles are responsible to the quasilocalized low-frequency vibration, instability, softening, and nonaffinity of disordered solids.PACS numbers: 63.50. Lm,61.43.Bn, The nature of disordered solids, e.g. glasses and sandpiles, remains elusive and a major challenge to condensed matter physics [1][2][3]. Compared to crystalline solids, the absence of long-range structural order makes it difficult to interpret properties of disordered solids analytically. What makes it more difficult is the spatial heterogeneity of the structural disorder. It has been evidenced that the heterogeneous disorder greatly contributes to abnormal properties of disordered materials, e.g. the anomalous low-frequency excitations and consequent unusual thermal properties [4], heterogeneous mechanical response to perturbations [5][6][7], and dynamical heterogeneity of supercooled liquids [8][9][10][11]. Therefore, how to correctly describe the heterogeneous disorder is the key to develop the theory of disordered solids.For crystals, it has been well-known that dislocations are triggers of the instability, which have lower bond orientational order than perfect lattice sites and can thus be easily identified. The bond orientational order has been applied to identify defective spots in weakly disordered solids [10][11][12][13]. However, this approach fails to describe the structural heterogeneity of strongly disordered solids, e.g. systems with large particle size dispersity, in which the locally favored geometric structure is no longer a perfect crystal [11,13]. An alternate order parameter is thus needed to pick out "defective" structures in disordered solids, which must capture the heterogeneous dynamics correctly and be responsible to the special properties of disordered solids.Inspired by recent observations that low-frequency quasilocalized modes of vibration are correlated with particle rearrangements in disordered systems [9, 14-17], we construct an order parameter Ψ at single particle level from normal modes of vibration, based on the assumption of energy equipartition. This new order parameter is validated by showing excellent spatial correlations with low-temperature dynamics and structural entropy. In order to figure out the role of particles with the largest Ψ, i.e. particles with the most defective local structures, we measure the system response to the pinning of these particles. Interestingly, the pinning remarkably eliminates the low-frequency quasilocalized modes, strengthens the system stability ...

Structures of Local Rearrangements in Soft Colloidal Glasses

“…Therefore, the search for "defects" in glasses needs to probe correlations (or lack thereof) on length scales greater than the first-neighbor shell. Recent simulations by Tong et al [15], find strong correlations between the distributions of soft modes in glasses and structural entropy S 2 , raising the possibility that this correlation-based structural parameter may also be able to predict elementary deformations in glasses.…”

“…The most elementary relaxation events in glasses are the local atomic rearrangements that play similar roles in the mechanical properties of glasses as the structural defects in crystals. Local regions prone to rearrangements in glasses are often known as flow units [8,9], shear transformation zones (STZs) [10,11], soft spots [12][13][14][15], or geometrically unfavoured motifs (GUMs) [16]. Unlike crystalline solids whose defects are easily identified from a periodic lattice, no distinguishing structures have been found for the fragile regions of glasses in an apparently disordered background.…”

“…Pair correlation function g(r) is a simple measure of structural correlations in glasses. Using local g(r), the structural entropy of a particle i can be defined as [15,28,49], where µ and ν denote the type of particles (large or small), ρ ν is the number density of ν particles, and g µν i ( r) is the pair correlation function between particle i of type µ and particles of ν type. Structural entropy measures the loss of entropy due to positional correlations [50]; high S 2 values indicate less correlated local structures and vice versa.…”

Stable small bubble clusters in two-dimensional foams

“…STZ theories have been applied to a wide range of materials, including amorphous metals, colloidal glasses, and earthquake faults [28][29][30][31][32][33][34][35][36][37] . Similar descriptions include weak-zone and soft-spot theories, which attempt to iden-1 INTRODUCTION tify regions in a material where non-affine deformation will occur due to mechanical instabilities [38][39][40] .…”

Decoupling between thermodynamics and dynamics during rejuvenation in colloidal glasses

“…Next, we explore the structural origin of the emergence of CRRs. Local structural entropy 2 , a structural parameter highly correlated with particle-level dynamic in binary glasses [35,[48][49][50] , is measured in figure 5 e-f after corresponding thermal groups as in figure 5 a-c. 2…”