Order parameter for structural heterogeneity in disordered solids

The role of excitations in supercooled liquids: Density, geometry, and relaxation dynamics

Low-energy excitations play a key role in all condensed-matter systems, yet there is limited understanding of their nature in glasses, where they correspond to local rearrangements of groups of particles. Here, we introduce an algorithm to systematically uncover these excitations up to the activation energy scale relevant to structural relaxation. We use it in a model system to measure the density of states on a scale never achieved before, confirming that this quantity shifts to higher energy under cooling, precisely as the activation energy does. Second, we show that the excitations' energetic and spatial features allow one to predict with great accuracy the dynamic propensity, i.e., the location of future relaxation dynamics. Finally, we find that excitations have a primary field whose properties, including the displacement of the most mobile particle, scale as a power-law of their activation energy and are independent of temperature. Additionally, they exhibit an outer deformation field that depends on the material's stability and, therefore, on temperature. We build a scaling description of these findings. Overall, our analysis supports that excitations play a crucial role in regulating relaxation dynamics near the glass transition, effectively suppressing the transition to dynamical arrest predicted by mean-field theories while also being strongly influenced by it.

Superionic UO_{2} crystal: How to model its relaxation and diffusion via a microscopic theory of glass-forming liquids

UO_{2} is a crucial nuclear material but its behaviors are elusive due to the impact of superionic diffusion. Herein, we introduce a simple but effective theoretical model to describe the intrinsic superionicity of UO_{2} at the quantitative level. Our idea stems from a close similarity between superionic crystals and supercooled liquids. Namely, we view UO_{2} as a randomly pinned hard-sphere fluid in the framework of the elastically collective nonlinear Langevin equation theory. This treatment allows us to fully evaluate the contribution of local, collective, pinning, and screening effects to the molecular dynamics of UO_{2} without complex computational processes. Finite-temperature factors are considered via volumetric expansion during isobaric heating. On that basis, we satisfactorily explain recent large-scale atomistic simulations on UO_{2} under various thermodynamic conditions. Our calculations also reveal that UO_{2} is equivalent to an intermediate glass former. Its structural relaxation, self-diffusion, and shear deformation are strongly correlated near the onset of superionicity. These intimate correlations are reminiscent of the famed Dyre shoving model in the soft-matter community. Our results promise to facilitate the development of diverse energy applications of UO_{2}.

Machine Learning Classification of Local Environments in Molecular Crystals

Identifying local structural motifs and packing patterns of molecular solids is a challenging task for both simulation and experiment. We demonstrate two novel approaches to characterize local environments in different polymorphs of molecular crystals using learning models that employ either flexibly learned or handcrafted molecular representations. In the first case, we follow our earlier work on graph learning in molecular crystals, deploying an atomistic graph convolutional network combined with molecule-wise aggregation to enable per-molecule environmental classification. For the second model, we develop a new set of descriptors based on symmetry functions combined with a point-vector representation of the molecules, encoding information about the positions and relative orientations of the molecule. We demonstrate very high classification accuracy for both approaches on urea and nicotinamide crystal polymorphs and practical applications to the analysis of dynamical trajectory data for nanocrystals and solid-solid interfaces. Both architectures are applicable to a wide range of molecules and diverse topologies, providing an essential step in the exploration of complex condensed matter phenomena.

Low-frequency vibrational density of states of ordinary and ultra-stable glasses

A remarkable feature of disordered solids distinct from crystals is the violation of the Debye scaling law of the low-frequency vibrational density of states. Because the low-frequency vibration is responsible for many properties of solids, it is crucial to elucidate it for disordered solids. Numerous recent studies have suggested power-law scalings of the low-frequency vibrational density of states, but the scaling exponent is currently under intensive debate. Here, by classifying disordered solids into stable and unstable ones, we find two distinct and robust scaling exponents for non-phononic modes at low frequencies. Using the competition of these two scalings, we clarify the variation of the scaling exponent and hence reconcile the debate. Via the study of both ordinary and ultra-stable glasses, our work reveals a comprehensive picture of the low-frequency vibration of disordered solids and sheds light on the low-frequency vibrational features of ultra-stable glasses on approaching the ideal glass.

Orientational Order in Dense Colloidal Liquids and Glasses

We construct structural order parameters based on local angular and radial distribution functions in dense colloidal suspensions. All the order parameters show significant correlations to local dynamics in the supercooled and glass regime. In particular, the correlations between the orientational order and dynamical heterogeneity are consistently higher than those between the conventional two-body structural entropy and local dynamics. The structure-dynamics correlations can be explained by a excitation model with the energy barrier depending on local structural order. Our results suggest that in dense disordered packings, local orientational order is higher than translational order, and plays a more important role in determining the dynamics in glassy systems.

A general structural order parameter for the amorphous solidification of a supercooled liquid

The persistent problem posed by the glass transition is to develop a general atomic level description of amorphous solidification. The answer proposed in this paper is to measure a configuration's capacity to restrain the motion of the constituent atoms. Here, we show that the instantaneous normal modes can be used to define a measure of atomic restraint that accounts for the difference between fragile and strong liquids and the collective length scale of the supercooled liquid. These results represent a significant simplification of the description of amorphous solidification and provide a powerful systematic treatment of the influence of microscopic factors on the formation of an amorphous solid.

Local-Average Free Volume Correlates with Dynamics in Glass Formers

Glass formers exhibit a pronounced slowdown in dynamics, accompanied by progressive heterogeneity as they approach the glass transition. There is intense debate over whether the dramatic slowdown is caused by dynamical heterogeneity and whether the enhanced dynamical heterogeneity originates from structural causes. However, the connection between dynamical heterogeneity and the spatial distribution of the single-particle free volume (a purely static structural quantity) was found to be rather weak, which raises the question of whether dynamic heterogeneity has a purely structural origin. Here, by introducing the concept of local-average free volume, we present numerical evidence that long-time dynamic heterogeneity shows significantly enhanced correlation with the average local free volume over a length scale of a few neighboring shells. Our results resolve the long-standing controversy about whether free volume plays an important role in particle rearrangements associated with the activated hopping relaxation. The concept of "local average" can be applied to other local structural descriptors to better correlate with dynamic heterogeneity in glass-forming liquids.

Avalanche dynamics in sheared athermal particle packings occurs via localized bursts predicted by unstable linear response

Under applied shear strain, granular and amorphous materials deform via particle rearrangements, which can be small and localized or organized into system-spanning avalanches. While the statistical properties of avalanches under quasi-static shear are well-studied, the dynamics during avalanches is not. In numerical simulations of sheared soft spheres, we find that avalanches can be decomposed into bursts of localized deformations, which we identify using an extension of persistent homology methods. We also study the linear response of unstable systems during an avalanche, demonstrating that eigenvalue dynamics are highly complex during such events, and that the most unstable eigenvector is a poor predictor of avalanche dynamics. Instead, we modify existing tools that identify localized excitations in stable systems, and apply them to these unstable systems with non-positive definite Hessians, quantifying the evolution of such excitations during avalanches. We find that bursts of localized deformations in the avalanche almost always occur at localized excitations identified using the linear spectrum. These new tools will provide an improved framework for validating and extending mesoscale elastoplastic models that are commonly used to explain avalanche statistics in glasses and granular matter.

Revealing the characteristic length of random close packing via critical-like random pinning

By randomly pinning particles in fluidized states and finding the local energy minima, we form static packings of mono-disperse disks that resemble random close packing, when only n_c = 2.6% of the particles are pinned. The packings are isostatic and exhibit typical critical scalings of the jamming transition. The non-triviality of n_c is manifested mainly in two aspects. First, n_c acts as a critical point, leading to bifurcated critical scalings in its vicinity. The criticality of n_c is also demonstrated in the packings of weakly polydisperse disks. Second, n_c sets a length scale in agreement with the characteristic length of random close packing. With robust evidence, we show that this agreement is generally true for both mono- and poly-disperse particles and in both two and three dimensions. The randomness inherited from fluidized states by random pinning thus interprets the randomness of random close packing from a unique perspective.

Searching for structural predictors of plasticity in dense active packings

In amorphous solids subject to shear or thermal excitation, so-called structural indicators have been developed that predict locations of future plasticity or particle rearrangements. An open question is whether similar tools can be used in dense active materials, but a challenge is that under most circumstances, active systems do not possess well-defined solid reference configurations. We develop a computational model for a dense active crowd attracted to a point of interest, which does permit a mechanically stable reference state in the limit of infinitely persistent motion. Previous work on a similar system suggested that the collective motion of crowds could be predicted by inverting a matrix of time-averaged two-particle correlation functions. Seeking a first-principles understanding of this result, we demonstrate that this active matter system maps directly onto a granular packing in the presence of an external potential, and extend an existing structural indicator based on linear response to predict plasticity in the presence of noisy dynamics. We find that the strong pressure gradient necessitated by the directed activity, as well as a self-generated free boundary, strongly impact the linear response of the system. In low-pressure regions the linear-response-based indicator is predictive, but it does not work well in the high-pressure interior of our active packings. Our findings motivate and inform future work that could better formulate structure-dynamics predictions in systems with strong pressure gradients.

Unified quantifier of mechanical disorder in solids

Mechanical disorder in solids, which is generated by a broad range of physical processes and controls various material properties, appears in a wide variety of forms. Defining unified and measurable dimensionless quantifiers, allowing quantitative comparison of mechanical disorder across widely different physical systems, is therefore an important goal. Two such coarse-grained dimensionless quantifiers (among others) appear in the literature: one is related to the spectral broadening of discrete phononic bands in finite-size systems (accessible through computer simulations) and the other is related to the spatial fluctuations of the shear modulus in macroscopically large systems. The latter has been recently shown to determine the amplitude of wave attenuation rates in the low-frequency limit (accessible through laboratory experiments). Here, using two alternative and complementary theoretical approaches linked to the vibrational spectra of solids, we derive a basic scaling relation between the two dimensionless quantifiers. This scaling relation, which is supported by simulational data, shows that the two apparently distinct quantifiers are in fact intrinsically related, giving rise to a unified quantifier of mechanical disorder in solids. We further discuss the obtained results in the context of the unjamming transition taking place in soft sphere packings at low confining pressures, in addition to their implications for our understanding of the low-frequency vibrational spectra of disordered solids in general, and in particular those of glassy systems.

Structural and short-time vibrational properties of colloidal glasses and supercooled liquids in the vicinity of the re-entrant glass transition

We investigate the short-time vibrational properties and structure of two-dimensional, bidisperse, colloidal glasses and supercooled liquids in the vicinity of the re-entrant glass transition, as a function of interparticle depletion attraction strength. The long-time spatiotemporal dynamics of the samples are measured to be non-monotonic, confirming that the suspensions evolve from repulsive glass to supercooled liquid to attractive glass with increasing depletion attraction. Here, we search for vibrational signatures of the re-entrant behavior in the short-time spatiotemporal dynamics, i.e., dynamics associated with particle motion inside its nearest-neighbor cage. Interestingly, we observe that the anharmonicity of these in-cage vibrations varies non-monotonically with increasing attraction strength, consistent with the non-monotonic long-time structural relaxation dynamics of the re-entrant glass. We also extract effective spring constants between neighboring particles; we find that spring stiffness involving small particles also varies non-monotonically with increasing attraction strength, while stiffness between large particles increases monotonically. Last, from study of depletion-dependent local structure and vibration participation fractions, we gain microscopic insight into the particle-size-dependent contributions to short-time vibrational modes in the glass and supercooled liquid states.

Unifying fluctuation-dissipation temperatures of slow-evolving nonequilibrium systems from the perspective of inherent structures

For nonequilibrium systems, how to define temperature is one of the key and difficult issues to solve. Although effective temperatures have been proposed and studied to this end, it still remains elusive what they actually are. Here, we focus on the fluctuation-dissipation temperatures and report that such effective temperatures of slow-evolving systems represent characteristic temperatures of their equilibrium counterparts. By calculating the fluctuation-dissipation relation of inherent structures, we obtain a temperature-like quantity T IS For monocomponent crystal-formers, T IS agrees well with the crystallization temperature T c, while it matches with the onset temperature T on for glass-formers. It also agrees with effective temperatures of typical nonequilibrium systems, such as aging glasses, quasi-static shear flows, and quasi-static self-propelled flows. From the unique perspective of inherent structures, our study reveals the nature of effective temperatures and the underlying connections between nonequilibrium and equilibrium systems and confirms the equivalence between T on and T c.

The dependence of the boson peak on the thickness of Cu50Zr50 film metallic glasses

In this study, intensive calculations were performed to investigate the behavior of the low-temperature excess heat capacity of Cu50Zr50 ultrathin film metallic glasses. Our results show that there is a well-defined boson peak in the film metallic glasses and that the boson peak height exhibits an obvious size-dependent feature. Furthermore, there is a critical thickness dc in the curves between the boson peak height and the thickness, where the boson peak height changes abruptly. Through structural analysis, we found that the low-temperature excess heat capacity of the film metallic glasses is correlated with the density layering structure near the surface. The structural parameter S is defined by atomic density and it was found that the boson peak height is highly correlated with S. Our investigation of ultrathin film metallic glasses provides a deeper understanding about the structural origin of the boson peak in metallic glasses.

Complexity of plastic instability in amorphous solids: Insights from spatiotemporal evolution of vibrational modes

It has been accepted that low-frequency vibrational modes are causally correlated to fundamental plastic rearrangement events in amorphous solids, irrespective of the structural details. But the mode-event relationship is far from clear. In this work, we carry out case studies using atomistic simulations of a three-dimensional Cu₅₀Zr₅₀ model glass under athermal, quasistatic shear. We focus on the first four plastic events, and carefully trace the spatiotemporal evolution of the associated low-frequency normal modes with applied shear strain. We reveal that these low-frequency modes get highly entangled with each other, from which the critical mode emerges spontaneously to predict a shear transformation event. But the detailed emergence picture is event by event and shear-protocol dependent, even for the first plastic event. This demonstrates that the instability of a plastic event is a result of extremely complex multiple-path choice or competition, and there is a strong, elastic interaction among neighboring instability events. At last, the generality of the present findings is shown to be applicable to covalent-bonded glasses.

Soft-Mode Parameter as an Indicator for the Activation Energy Spectra in Metallic Glass

The activation energy (E_A) spectra of the potential energy landscape (PEL) provide a convenient perspective for interpreting complex phenomena in amorphous materials; however, the link between the E_A spectra and other physical properties in metallic glasses is still mysterious. By systematically probing the E_A spectra for numerous metallic glass samples with distinct local geometric ordering, which correspond to broad processing histories, we found that the shear moduli of the samples are strongly correlated with the arithmetic mean of the E_A spectra rather than with the local geometrical ordering. Furthermore, we studied the correlation of the obtained E_A spectra and various well-established physical parameters. The outcome of our research clearly demonstrates that the soft-mode parameter Ψ and the E_A spectrum are correlated; therefore, this could be a good indicator of metallic glass properties and sheds important light on the structure-property relationship in metallic glass through the medium of the PEL.

Emergence and percolation of rigid domains during the colloidal glass transition

Using video microscopy, we measure local spatial constraints in disordered binary colloidal samples, ranging from dilute fluids to jammed glasses, and probe their spatial and temporal correlations to local dynamics during the glass transition. We observe the emergence of significant correlations between constraints and local dynamics within the Lindemann criterion, which coincides with the onset of glassy dynamics in supercooled liquids. Rigid domains in fluids are identified based on local constraints and demonstrate a percolation transition near the glass transition, accompanied by the emergence of dynamical heterogeneities. Our results show that spatial constraint instead of the geometry of amorphous structures is the key that connects the complex spatial-temporal correlations in disordered materials.

Revealing Inherent Structural Characteristics of Jammed Particulate Packings

We look for inherent structural characteristics hidden behind amorphous solid formation by using zero-temperature jammed packings of frictionless particles as models. Differently from previous geometrical approaches, we introduce a microscopic mechanical or vibrational order parameter Ψ, which characterizes the susceptibility of particle motion to infinitesimal thermal excitation. We show that (i) the distribution of Ψ has a power-law tail toward high Ψ and (ii) the spatial organization of Ψ is characterized by a nontrivial scale-free correlation. Both findings (i) and (ii) are regarded as a real-space manifestation of marginal stability due to critical self-organization of jammed packings toward mechanical equilibrium. Furthermore, we find that the power-law exponent of the Ψ distribution tail shows a critical-like scaling behavior toward the unjamming transition, which unveils an intriguing interplay between jamming criticality and marginal stability. Our microscopic order parameter provides new structural insights into the marginal stability and instability of jammed packings and may shed light on the important common structural feature of amorphous solids.

Vibrational Modes and Dynamic Heterogeneity in a Near-Equilibrium 2D Glass of Colloidal Kites

Using video microscopy and particle-tracking techniques developed for dense Brownian systems of polygons, we study the structure-dynamics relationship in a near-equilibrium 2D glass consisting of anisotropic Penrose kite-shaped colloids. Detailed vibrational properties of kite glasses, both translational and rotational, are obtained using covariance matrix techniques. Different from other colloidal glasses of spheres and ellipsoids, the vibrational modes of kite glasses at low frequencies show a strong translational character with spatially localized rotational modes and extended translational modes. Low-frequency quasilocalized soft modes commonly found in sphere glasses are absent in the translational phonon modes of kite glasses. Soft modes are observed predominantly in the rotational vibrations and correlate well with the spatial distribution of Debye-Waller factors. The local structural entropy field shows a strong correlation with the observed dynamic heterogeneity.

Stable small bubble clusters in two-dimensional foams

Key features of the mechanical response of amorphous particulate materials, such as foams, emulsions, and granular media, to applied stress are determined by the frequency and size of particle rearrangements that occur as the system transitions from one mechanically stable state to another. This work describes coordinated experimental and computational studies of bubble rafts, which are quasi-two dimensional systems of bubbles confined to the air-water interface. We focus on small mechanically stable clusters of four, five, six, and seven bubbles with two different sizes with diameter ratio σ_L/σ_S ≃ 1.4. Focusing on small bubble clusters, which can be viewed as subsystems of a larger system, allows us to investigate the full ensemble of clusters that form, measure the respective frequencies with which the clusters occur, and determine the form of the bubble-bubble interactions. We emphasize several important results. First, for clusters with N > 5 bubbles, we find using discrete element simulations that short-range attractive interactions between bubbles give rise to a larger ensemble of distinct mechanically stable clusters compared to that generated by long-range attractive interactions. The additional clusters in systems with short-range attractions possess larger gaps between pairs of neighboring bubbles on the periphery of the clusters. The ensemble of bubble clusters observed in experiments is similar to the ensemble of clusters with long-range attractive interactions. We also compare the frequency with which each cluster occurs in simulations and experiments. We find that the cluster frequencies are extremely sensitive to the protocol used to generate them and only weakly correlated to the energy of the clusters.

Structures of Local Rearrangements in Soft Colloidal Glasses

We image local structural rearrangements in soft colloidal glasses under small periodic perturbations induced by thermal cycling. Local structural entropy S_{2} positively correlates with observed rearrangements in colloidal glasses. The high S_{2} values of the rearranging clusters in glasses indicate that fragile regions in glasses are structurally less correlated, similar to structural defects in crystalline solids. Slow-evolving high S_{2} spots are capable of predicting local rearrangements long before the relaxations occur, while fluctuation-created high S_{2} spots best correlate with local deformations right before the rearrangement events. Local free volumes are also found to correlate with particle rearrangements at extreme values, although the ability to identify relaxation sites is substantially lower than S_{2}. Our experiments provide an efficient structural identifier for the fragile regions in glasses and highlight the important role of structural correlations in the physics of glasses.

Probing the Role of Mobility in the Collective Motion of Nonequilibrium Systems

By systematically varying the mobility of self-propelled particles in a 2D lattice, we experimentally study the influence of particle mobility on system's collective motion. Our system is intrinsically nonequilibrium due to the lack of energy equipartition. By constructing the covariance matrix of spatial fluctuations and solving for its eigenmodes, we obtain the collective motions of the system with various magnitudes. Interestingly, our structurally ordered nonequilibrium system exhibits properties almost identical to disordered glassy systems under thermal equilibrium: the modes with large overall motions are spatially correlated and quasilocalized while the modes with small collective motions are highly localized, resembling the low- and high-frequency modes in glass. More surprisingly, a peak similar to the boson peak forms in our nonequilibrium system as the number of mobile particles increases, revealing the possible origin of the boson peak from a dynamic aspect. We further illustrate that the spatially correlated large-movement modes can be produced by the cooperation of highly active particles above a threshold fraction, while the localized small-movement modes can be created by adding individual inactive particles. Our study clarifies the role of mobility in collective motions, and further suggests a promising possibility of extending the powerful mode analysis approach to nonequilibrium systems.

From Crystals to Disordered Crystals: A Hidden Order-Disorder Transition

To distinguish between order and disorder is of fundamental importance to understanding solids. It becomes more significant with recent observations that solids with high structural order can behave like disordered solids, while properties of disordered solids can approach crystals under certain circumstance. It is then imperative to understand when and how disorder takes effect to deviate the properties of a solid from crystals and what the correct factors are to control the behaviours of solids. Here we answer these questions by reporting the finding of a hidden order-disorder transition from crystals to disordered crystals for static packings of frictionless spheres. While the geometric indicators are mostly blind to the transition, disordered crystals already exhibit properties apart from crystals. The transition approaches the close packing of hard spheres, giving rise to the singularity of the close packing point. We evidence that both the transition and properties of disordered crystals are jointly determined by the structural order and density. Near the transition, the elastic moduli and coordination number of disordered crystals show particular pressure dependence distinct from known behaviours of both crystals and jammed solids. The discovery of the transition therefore reveals some unknown aspects of solids.