Energy landscape-driven non-equilibrium evolution of inherent structure in disordered material

Time series prediction model using LSTM-Transformer neural network for mine water inflow

Mine flooding accidents have occurred frequently in recent years, and the predicting of mine water inflow is one of the most crucial flood warning indicators. Further, the mine water inflow is characterized by non-linearity and instability, making it difficult to predict. Accordingly, we propose a time series prediction model based on the fusion of the Transformer algorithm, which relies on self-attention, and the LSTM algorithm, which captures long-term dependencies. In this paper, Baotailong mine water inflow in Heilongjiang Province is used as sample data, and the sample data is divided into different ratios of the training set and test set in order to obtain optimal prediction results. In this study, we demonstrate that the LSTM-Transformer model exhibits the highest training accuracy when the ratio is 7:3. To improve the efficiency of search, the combination of random search and Bayesian optimization is used to determine the network model parameters and regularization parameters. Finally, in order to verify the accuracy of the LSTM-Transformer model, the LSTM-Transformer model is compared with LSTM, CNN, Transformer and CNN-LSTM models. The results prove that LSTM-Transformer has the highest prediction accuracy, and all the indicators of its model are well improved.

Mechanical mechanism analysis of rockburst in deep-buried tunnel with high in-situ stress

The Qinling water conveyance tunnel has a large buried depth and high in-situ stress level, and rockburst disasters frequently occurred during excavation. In order to find out the mechanical mechanism of rockburst, the research work in this paper is as follows: (1) In-situ three-dimensional hydraulic fracturing method was used to measure the in-situ stress of the deep buried tunnel crossing the ridge. (2) Based on the measured in-situ stress results, the stress distribution characteristics of the tunnel crossing the ridge were obtained by the multiple linear regression method, and the rockburst tendency during construction was predicted. (3) A three-dimensional numerical model of tunnel excavation was established to analyze the dynamic adjustment characteristics of the surrounding rock stress and elastic strain energy during TBM excavation, and to clarify the mechanical mechanism of rockburst. The research results show that the maximum principal stress of the deep-buried tunnel crossing the ridge of Qinling is 40-66 MPa, which belongs to extremely high in-situ stress level, and medium-strong rockburst may occur during excavation. In the process of TBM excavation, the stress of the surrounding rock in the range of 2.6 times the diameter of the tunnel before and after the working face is adjusted violently, and the concentrated zones after the stress redistribution are mainly distributed in the arch roof and arch bottom, and the stress concentration coefficient can reach 2.06. The arch roof, arch waist, and arch bottom are susceptible to immediate rockburst due to stress transient unloading at the moment of excavation. After the elastic strain energy of the surrounding rock at the arch roof and the arch bottom is released and accumulated, it is easy to cause time delayed rockburst, and the depth of the rockburst pit can reach 3.5 m, which is consistent with the rockburst phenomenon in the field.

Metastable grain boundaries: the roles of structural and chemical disorders in their energetics, non-equilibrium kinetic evolution, and mechanical behaviors

Complex environments in advanced manufacturing usually involve ultrafast laser or ion irradiation which leads to rapid heating and cooling and drives grain boundaries (GBs) to non-equilibrium states, featuring distinct energetics and kinetic behaviors compared to conventional equilibrium or near-equilibrium GBs. In this topical review, we provide an overview of both recent experimental and computational studies on metastable GBs, i.e. their energetics, kinetic behaviors, and mechanical properties. In contrast to GBs at thermodynamic equilibrium, the inherent structure energy of metastable GBs exhibits a spectrum instead of single value for a particular misorientation, due to the existence of microstructural and chemical disorder. The potential energy landscape governs the energetic and kinetic behaviors of metastable GBs, including the ageing/rejuvenating mechanism and activation barrier distributions. The unique energetics and structural disorder of metastable GBs lead to unique mechanical properties and tunability of interface-rich nanocrystalline materials. We also discuss that, in addition to structural disorder, chemical complexity in multi-components alloys could also drive the GBs away from their ground states and, subsequently, significantly impact on the GBs-mediated deformation. And under some extreme conditions such as irradiation, structural disorders and chemical complexity may simultaneously present at interfaces, further enriching of metastability of GBs and their physical and mechanical behaviors. Finally, we discuss the machine learning techniques, which have been increasingly employed to predict and understand the complex behaviors of metastable GBs in recent years. We highlight the potential of data-driven approaches to revolutionize the study of disorder systems by efficiently extracting the relationship between structural features and material properties. We hope this topical review paper could shed light and stimulate the development of new GBs engineering strategies that allow more flexibility and tunability for the design of nano-structured materials.

Universal origin of glassy relaxation as recognized by configuration pattern matching

Relaxation processes are crucial for understanding the structural rearrangements of liquids and amorphous materials. However, the overarching principle that governs these processes across vastly different materials remains an open question. Substantial analysis has been carried out based on the motions of individual particles. Here, as an alternative, we propose viewing the global configuration as a single entity. We introduce a global order parameter, namely the inherent structure minimal displacement (IS Dmin), to quantify the variability of configurations by a pattern-matching technique. Through atomic simulations of seven model glass-forming liquids, we unify the influences of temperature, pressure and perturbation time on the relaxation dissipation, via a scaling law between the mechanical damping factor and IS Dmin. Fundamentally, this scaling reflects the curvature of the local potential energy landscape. Our findings uncover a universal origin of glassy relaxation and offer an alternative approach to studying disordered systems.

Ripples in the bottom of the potential energy landscape of metallic glass

In the absence of periodicity, the structure of glass is ill-defined, and a large number of structural states are found at similar energy levels. However, little is known about how these states are connected to each other in the potential energy landscape. We simulate mechanical relaxation by molecular dynamics for a prototypical [Formula: see text] metallic glass and follow the mechanical energy loss of each atom to track the change in the state. We find that the energy barriers separating these states are remarkably low, only of the order of 1 meV, implying that even quantum fluctuations can overcome these potential energy barriers. Our observation of numerous small ripples in the bottom of the potential energy landscape puts many assumptions regarding the thermodynamic states of metallic glasses into question and suggests that metallic glasses are not totally frozen at the local atomic level.

Relevance of structural defects to the mechanism of mechanical deformation in metallic glasses

It is known that deformation in disordered materials such as metallic glasses and supercooled liquids occurs via the cooperative rearrangement of atoms or constituent particles at dynamical heterogeneities, commonly regarded as point-like defects. We show via molecular-dynamics simulations that there is no apparent relationship between atomic rearrangements and the local atomic environment as measured by the atomic-level stresses, kinetic and potential energies, and the per-atom Voronoi volume. In addition, there is only a weak correlation between atomic rearrangements and the largest and smallest eigenvalues of the dynamical matrix. Our results confirm the transient nature of dynamical heterogeneities and suggest that the notion of defects may be less relevant than that of a propensity for rearrangement.

World beyond the nearest neighbors

The structure beyond the nearest neighbor atoms in liquid and glass is characterized by the medium-range order (MRO). In the conventional approach, the MRO is considered to result directly from the short-range order (SRO) in the nearest neighbors. To this bottom-up approach starting with the SRO, we propose to add a top-down approach in which global collective forces drive liquid to form density waves. The two approaches are in conflict with each other, and the compromise produces the structure with the MRO. The driving force to produce density waves provides the stability and stiffness to the MRO, and controls various mechanical properties. This dual framework provides a novel perspective for description of the structure and dynamics of liquid and glass.

Angell plot from the potential energy landscape perspective

Within the scenario of the potential energy landscape (PEL), a thermodynamic model has been developed to uncover the physics behind the Angell plot. In our model, by separating the barrier distribution in PELs into a Gaussian-like and a power-law form, we obtain a general relationship between the relaxation time and the temperature. The wide range of the experimental data in the Angell plot, as well as the molecular-dynamics data, can be excellently fitted by two characteristic parameters, the effective barrier (ω) and the effective width (σ) of a Gaussian-like distribution. More importantly, the fitted ω and σ^{2} for all glasses are found to have a simple linear relationship within a very narrow band, and fragile and strong glasses are well separated in the ω-σ^{2} plot, which indicates that glassy states appear only in a specific region of the PEL.

Configurational Entropy Effects on Glass Transition in Metallic Glasses

Configurational entropy (S_conf) is known to be a key thermodynamic factor governing a glass transition process. However, this significance remains speculative because S_conf is not directly measurable. In this work, we demonstrate the role of S_conf theoretically and experimentally by a comparative study of a Zr-Ti-Cu-Ni-Be high-entropy metallic glass (HE-MG) with one of its conventional MG counterparts. It is revealed that the higher S_conf leads to a glass that is energetically more stable and structurally more ordered. This is manifested by ab initio molecular dynamics simulations, showing that ∼60% fewer atoms are agitated above T_g, and experimental results of smaller heat capacity jump, inconspicuous stiffness loss, insignificant structural change during glass transition, and a more depressed boson peak in the HE-MG than its counterpart. We accordingly propose a model to explain that a higher S_conf promotes a faster degeneracy-dependent kinetics for exploration of the potential energy landscape upon glass transition.

Medium-range atomic correlation in simple liquids. I. Distinction from short-range order

Physical properties of liquids and glasses are controlled not only by the short-range order (SRO) in the nearest-neighbor atoms but also by the medium-range order (MRO) observed for atoms beyond the nearest neighbors. In this article the nature of the MRO as the descriptor of point-to-set atomic correlation is discussed focusing on simple liquids, such as metallic liquids. Through the results of x-ray diffraction and simulation with classical potentials we show that the third peak of the pair-distribution function, which describes the MRO, shows a distinct change in temperature dependence at the glass transition, whereas the first peak, which represents the SRO, changes smoothly through the glass transition. The result suggests that the glass transition is induced by the freezing of the MRO rather than that of the SRO, implying a major role of the MRO on the viscosity of supercooled liquid.

Emergent Fractal Energy Landscape as the Origin of Stress-Accelerated Dynamics in Amorphous Solids

The ageing dynamics in a multiplicity of metastable glasses are investigated at various thermomechanical conditions. By using data analytics to deconvolute the integral effects of environmental factors (e.g., energy level, temperature, stress), and by directly scrutinizing the minimum energy pathways for local excitations, we demonstrate external shear would make the system's energy landscape surprisingly fractal and create an emergent low-barrier mode with highly tortuous pathways, leading to an accelerated relaxation. This finding marks a departure from the classic picture of shear-induced simple bias of energy landscape. The insights and implications of this study are also discussed.

Tunable Chemical Disorder in Concentrated Alloys: Defect Physics and Radiation Performance

The development of advanced structural alloys with performance meeting the requirements of extreme environments in nuclear reactors has been long pursued. In the long history of alloy development, the search for metallic alloys with improved radiation tolerance or increased structural strength has relied on either incorporating alloying elements at low concentrations to synthesize so-called dilute alloys or incorporating nanoscale features to mitigate defects. In contrast to traditional approaches, recent success in synthesizing multicomponent concentrated solid-solution alloys (CSAs), including medium-entropy and high-entropy alloys, has vastly expanded the compositional space for new alloy discovery. Their wide variety of elemental diversity enables tunable chemical disorder and sets CSAs apart from traditional dilute alloys. The tunable electronic structure critically lowers the effectiveness of energy dissipation via the electronic subsystem. The tunable chemical complexity also modifies the scattering mechanisms in the atomic subsystem that control energy transport through phonons. The level of chemical disorder depends substantively on the specific alloying elements, rather than the number of alloying elements, as the disorder does not monotonically increase with a higher number of alloying elements. To go beyond our knowledge based on conventional alloys and take advantage of property enhancement by tuning chemical disorder, this review highlights synergistic effects involving valence electrons and atomic-level and nanoscale inhomogeneity in CSAs composed of multiple transition metals. Understanding of the energy dissipation pathways, deformation tolerance, and structural stability of CSAs can proceed by exploiting the equilibrium and non-equilibrium defect processes at the electronic and atomic levels, with or without microstructural inhomogeneities at multiple length scales. Knowledge of tunable chemical disorder in CSAs may advance the understanding of the substantial modifications in element-specific alloy properties that effectively mitigate radiation damage and control a material's response in extreme environments, as well as overcome strength-ductility trade-offs and provide overarching design strategies for structural alloys.

Slow stretched-exponential and fast compressed-exponential relaxation from local event dynamics

We propose an atomistic model for correlated particle dynamics in liquids and glasses predicting both slow stretched-exponential relaxation (SER) and fast compressed-exponential relaxation (CER). The model is based on the key concept of elastically interacting local relaxation events. SER is related to slowing down of dynamics of local relaxation events as a result of this interaction, whereas CER is related to the avalanche-like dynamics in the low-temperature glass state. The model predicts temperature dependence of SER and CER seen experimentally and recovers the simple, Debye, exponential decay at high temperature. Finally, we reproduce SER to CER crossover across the glass transition recently observed in metallic glasses.

The energy landscape governs ductility in disordered materials

Based on their structure, non-crystalline phases can fail in a brittle or ductile fashion. However, the nature of the link between structure and propensity for ductility in disordered materials has remained elusive. Here, based on molecular dynamics simulations of colloidal gels and silica glasses, we investigate how the degree of structural disorder affects the fracture of disordered materials. As expected, we observe that structural disorder results in an increase in ductility. By applying the activation-relaxation technique (an open-ended saddle point search algorithm), we demonstrate that the propensity for ductility is controlled by the topography of the energy landscape. Interestingly, we observe a power-law relationship between the particle non-affine displacement upon fracture and the average local energy barrier. This reveals that the dynamics of the particles upon fracture is encoded in the static energy landscape, i.e., before any load is applied. This relationship is shown to apply to several classes of non-crystalline materials (oxide and metallic glasses, amorphous solid, and colloidal gels), which suggests that it may be a generic feature of disordered materials.

Structural relaxation and crystallization in supercooled water from 170 to 260 K

The origin of water's anomalous properties has been debated for decades. Resolution of the problem is hindered by a lack of experimental data in a crucial region of temperatures, T, and pressures where supercooled water rapidly crystallizes-a region often referred to as "no man's land." A recently developed technique where water is heated and cooled at rates greater than 10⁹ K/s now enables experiments in this region. Here, it is used to investigate the structural relaxation and crystallization of deeply supercooled water for 170 K < T < 260 K. Water's relaxation toward a new equilibrium structure depends on its initial structure with hyperquenched glassy water (HQW) typically relaxing more quickly than low-density amorphous solid water (LDA). For HQW and T > 230 K, simple exponential relaxation kinetics is observed. For HQW at lower temperatures, increasingly nonexponential relaxation is observed, which is consistent with the dynamics expected on a rough potential energy landscape. For LDA, approximately exponential relaxation is observed for T > 230 K and T < 200 K, with nonexponential relaxation only at intermediate temperatures. At all temperatures, water's structure can be reproduced by a linear combination of two, local structural motifs, and we show that a simple model accounts for the complex kinetics within this context. The relaxation time, τ _rel , is always shorter than the crystallization time, τ _xtal For HQW, the ratio, τ _xtal /τ _rel , goes through a minimum at ∼198 K where the ratio is about 60.

Bulk Metallic Glasses' Response to Oscillatory Stress Is Governed by the Topography of the Energy Landscape

When subjected to cyclic loading, bulk metallic glasses tend to exhibit fatigue-induced damage. Although fatigue is a key limitation of metallic glasses, its atomic origin remains elusive. Here, based on molecular dynamics simulations, we investigate the response of metallic glasses prepared with varying cooling rates to oscillatory stress. We find that fatigue manifests itself as an accumulation of residual strain, which results from some nonaffine displacement of the atoms. Such local reorganizations are promoted under a high cooling rate. Importantly, we demonstrate that the fatigue-induced dynamics of the atoms is encoded in the topography of the static energy landscape, i.e., before any load is applied.

Origin of liquid fragility

Liquid fragility characterizes how steeply the viscosity of a glass-forming liquid decreases with increasing temperature above the glass transition. It is one of the most fundamental properties of a liquid, with high importance for science and application. Yet, its origin is unclear. Here we show that it is directly related to the structural coherence of the medium-range order (MRO) in liquid defined by the decay of the pair-distribution function with distance. The MRO can also be evaluated from the first peak of the structure function determined by x-ray or neutron diffraction, and it is a measure of the cooperativity of atomic motion in a diffusive event in supercooled liquids. These findings shed light on the mechanism of atomic transport in supercooled liquids.

Why Is the Range of Timescale So Wide in Glass-Forming Liquid?

The viscosity and the relaxation time of a glass-forming liquid vary over 15 orders of magnitude before the liquid freezes into a glass. The rate of the change with temperature is characterized by liquid fragility. The mechanism of such a spectacular behavior and the origin of fragility have long been discussed, but it remains unresolved because of the difficulty of carrying out experiments and constructing theories that bridge over a wide timescale from atomic (ps) to bulk (minutes). Through the x-ray diffraction measurement and molecular dynamics simulation for metallic liquids we suggest that large changes in viscosity can be caused by relatively small changes in the structural coherence which characterizes the medium-range order. Here the structural coherence does not imply that of atomic-scale structure, but it relates to the coarse-grained density fluctuations represented by the peaks in the pair-distribution function (PDF) beyond the nearest neighbors. The coherence length is related to fragility and increases with decreasing temperature, and it diverges only at a negative temperature. This analysis is compared with several current theories which predict a phase transition near the glass transition temperature.

Non-Markovian Methods in Glass Transition

A model for the heterogeneity of local dynamics in polymer and other glass-forming materials is provided here. The fundamental characteristics of the glass transition phenomenology emerge when simulating a condensed matter open cluster that has a strong interaction with its heterogeneous environment. General glass transition features, such as non-exponential structural relaxations, the slowing down of relaxation times with temperature and specific off-equilibrium glassy dynamics can be reproduced by non-Markovian dynamics simulations with the minimum computer resources. Non-Markovian models are shown to be useful tools for obtaining insights into the complex dynamics involved in the glass transition phenomenon, including whether or not there is a need for a growing correlation length or the relationship between the non-exponentiality of structural relaxations and dynamic heterogeneity.

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.

Thermalization of plastic flow versus stationarity of thermomechanical equilibrium in SGR theory

We discuss issues related to thermalization of plastic flow in the context of soft glassy rheology (SGR) theory. An apparent problem with the theory in its current form is that the stationarity of thermomechanical equilibrium obtained by requiring that its flow rule satisfy detailed balance in the absence of applied deformation requires plastic flow to be athermal. This prevents proper application of SGR to small-molecule and polymer glasses where plastic flow is often well thermalized. Clearly, one would like to have a SGR-like theory of thermalized plastic flow that satisfies stationarity. We discuss reasons why such a theory could prove very useful and clarify obstacles that must be overcome in order to develop it.

Predicting Shear Transformation Events in Metallic Glasses

Shear transformation is the elementary process for plastic deformation of metallic glasses, the prediction of the occurrence of the shear transformation events is therefore of vital importance to understand the mechanical behavior of metallic glasses. In this Letter, from the view of the potential energy landscape, we find that the protocol-dependent behavior of shear transformation is governed by the stress gradient along its minimum energy path and we propose a framework as well as an atomistic approach to predict the triggering strains, locations, and structural transformations of the shear transformation events under different shear protocols in metallic glasses. Verification with a model Cu_{64}Zr_{36} metallic glass reveals that the prediction agrees well with athermal quasistatic shear simulations. The proposed framework is believed to provide an important tool for developing a quantitative understanding of the deformation processes that control mechanical behavior of metallic glasses.

Local yield stress statistics in model amorphous solids

We develop and extend a method presented by Patinet, Vandembroucq, and Falk [Phys. Rev. Lett. 117, 045501 (2016)PRLTAO0031-900710.1103/PhysRevLett.117.045501] to compute the local yield stresses at the atomic scale in model two-dimensional Lennard-Jones glasses produced via differing quench protocols. This technique allows us to sample the plastic rearrangements in a nonperturbative manner for different loading directions on a well-controlled length scale. Plastic activity upon shearing correlates strongly with the locations of low yield stresses in the quenched states. This correlation is higher in more structurally relaxed systems. The distribution of local yield stresses is also shown to strongly depend on the quench protocol: the more relaxed the glass, the higher the local plastic thresholds. Analysis of the magnitude of local plastic relaxations reveals that stress drops follow exponential distributions, justifying the hypothesis of an average characteristic amplitude often conjectured in mesoscopic or continuum models. The amplitude of the local plastic rearrangements increases on average with the yield stress, regardless of the system preparation. The local yield stress varies with the shear orientation tested and strongly correlates with the plastic rearrangement locations when the system is sheared correspondingly. It is thus argued that plastic rearrangements are the consequence of shear transformation zones encoded in the glass structure that possess weak slip planes along different orientations. Finally, we justify the length scale employed in this work and extract the yield threshold statistics as a function of the size of the probing zones. This method makes it possible to derive physically grounded models of plasticity for amorphous materials by directly revealing the relevant details of the shear transformation zones that mediate this process.