How thermally activated deformation starts in metallic glass

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.

Intermittent cluster dynamics and temporal fractional diffusion in a bulk metallic glass

Glassy solids evolve towards lower-energy structural states by physical aging. This can be characterized by structural relaxation times, the assessment of which is essential for understanding the glass' time-dependent property changes. Conducted over short times, a continuous increase of relaxation times with time is seen, suggesting a time-dependent dissipative transport mechanism. By focusing on micro-structural rearrangements at the atomic-scale, we demonstrate the emergence of sub-diffusive anomalous transport and therefore temporal fractional diffusion in a metallic glass, which we track via coherent x-ray scattering conducted over more than 300,000 s. At the longest probed decorrelation times, a transition from classical stretched exponential to a power-law behavior occurs, which in concert with atomistic simulations reveals collective and intermittent atomic motion. Our observations give a physical basis for classical stretched exponential relaxation behavior, uncover a new power-law governed collective transport regime for metallic glasses at long and practically relevant time-scales, and demonstrate a rich and highly non-monotonous aging response in a glassy solid, thereby challenging the common framework of homogeneous aging and atomic scale diffusion.

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.

Anomalous temperature dependence of elastic limit in metallic glasses

Understanding the atomistic mechanisms of inelastic deformation in metallic glasses (MGs) remains challenging due to their amorphous structure, where local carriers of plasticity cannot be easily defined. Using molecular dynamics (MD) simulations, we analyzed the onset of inelastic deformation in CuZr MGs, specifically the temperature dependence of the elastic limit, in terms of localized shear transformation (ST) events. We find that although the ST events initiate at lower strain with increasing temperature, the elastic limit increases with temperature in certain temperature ranges. We explain this anomalous behavior through the framework of an energy-strain landscape (ESL) constructed from high-throughput strain-dependent energy barrier calculations for the ST events identified in the MD simulations. The ESL reveals that the anomalous behavior is caused by the transition of ST events from irreversible to reversible with increasing temperature. An analytical formulation is developed to predict this transition and the temperature dependence of the elastic limit.

Elasticity, Facilitation, and Dynamic Heterogeneity in Glass-Forming Liquids

We study the role of elasticity-induced facilitation on the dynamics of glass-forming liquids by a coarse-grained two-dimensional model in which local relaxation events, taking place by thermal activation, can trigger new relaxations by long-range elastically mediated interactions. By simulations and an analytical theory, we show that the model reproduces the main salient facts associated with dynamic heterogeneity and offers a mechanism to explain the emergence of dynamical correlations at the glass transition. We also discuss how it can be generalized and combined with current theories.

Relevance of Shear Transformations in the Relaxation of Supercooled Liquids

While deeply supercooled liquids exhibit divergent viscosity and increasingly heterogeneous dynamics as the temperature drops, their structure shows only seemingly marginal changes. Understanding the nature of relaxation processes in this dramatic slowdown is key for understanding the glass transition. Here, we show by atomistic simulations that the heterogeneous dynamics of glass-forming liquids strongly correlate with the local residual plastic strengths along soft directions computed in the initial inherent structures. The correlation increases with decreasing temperature and is maximum in the vicinity of the relaxation time. For the lowest temperature investigated, this maximum is comparable with the best values from the literature dealing with the structure-property relationship. However, the nonlinear probe of the local shear resistance in soft directions provides here a real-space picture of relaxation processes. Our detection method of thermal rearrangements allows us to investigate the first passage time statistics and to study the scaling between the activation energy barriers and the residual plastic strengths. These results shed new light on the nature of relaxations of glassy systems by emphasizing the analogy between the thermal relaxations in viscous liquids and the plastic shear transformation in amorphous solids.

Liquid-like atoms in dense-packed solid glasses

Revealing the microscopic structural and dynamic pictures of glasses is a long-standing challenge for scientists^1,2. Extensive studies on the structure and relaxation dynamics of glasses have constructed the current classical picture^3-5: glasses consist of some 'soft zones' of loosely bound atoms embedded in a tightly bound atomic matrix. Recent experiments have found an additional fast process in the relaxation spectra^6-9, but the underlying physics of this process remains unclear. Here, combining extensive dynamic experiments and computer simulations, we reveal that this fast relaxation is associated with string-like diffusion of liquid-like atoms, which are inherited from the high-temperature liquids. Even at room temperature, some atoms in dense-packed metallic glasses can diffuse just as easily as they would in liquid states, with an experimentally determined viscosity as low as 10⁷ Pa·s. This finding extends our current microscopic picture of glass solids and might help establish the dynamics-property relationship of glasses⁴.

Nonaffine Strains Control Ductility of Metallic Glasses

The origin of limited plasticity in metallic glasses is elusive, with no apparent link to their atomic structure. We propose that the response of the glassy structure to applied stress, not the original structure itself, provides a gauge to predict the degree of plasticity. We carried out high-energy x-ray diffraction on various bulk metallic glasses (BMGs) under uniaxial compression within the elastic limit and evaluated the anisotropic pair distribution function. We show that the extent of local deviation from the affine (uniform) deformation in the elastic regime is strongly correlated with the plastic behavior of BMGs beyond yield, across chemical compositions and sample history. The results suggest that the propensity for collective local atomic rearrangements under stress promotes plasticity.

Relaxation and Strain-Hardening Relationships in Highly Rejuvenated Metallic Glasses

One way to rejuvenate metallic glasses is to increase their free volume. Here, by randomly removing atoms from the glass matrix, free volume is homogeneously generated in metallic glasses, and glassy states with different degrees of rejuvenation are designed and further mechanically tested. We find that the free volume in the rejuvenated glasses can be annihilated under tensile or compressive deformation that consequently leads to structural relaxation and strain-hardening. Additionally, the deformation mechanism of highly rejuvenated metallic glasses during the uniaxial loading–unloading tensile tests is investigated, in order to provide a systematic understanding of the relaxation and strain-hardening relationship. The observed strain-hardening in the highly rejuvenated metallic glasses corresponds to stress-driven structural and residual stress relaxation during cycling deformation. Nevertheless, the rejuvenated metallic glasses relax to a more stable state but could not recover their initial as-cast state.

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.

Substantially enhanced plasticity of bulk metallic glasses by densifying local atomic packing

Introducing regions of looser atomic packing in bulk metallic glasses (BMGs) was reported to facilitate plastic deformation, rendering BMGs more ductile at room temperature. Here, we present a different alloy design approach, namely, doping the nonmetallic elements to form densely packed motifs. The enhanced structural fluctuations in Ti-, Zr- and Cu-based BMG systems leads to improved strength and renders these solutes' atomic neighborhoods more prone to plastic deformation at an increased critical stress. As a result, we simultaneously increased the compressive plasticity (from ∼8% to unfractured), strength (from ∼1725 to 1925 MPa) and toughness (from 87 ± 10 to 165 ± 15 MPa√m), as exemplarily demonstrated for the Zr₂₀Cu₂₀Hf₂₀Ti₂₀Ni₂₀ BMG. Our study advances the understanding of the atomic-scale origin of structure-property relationships in amorphous solids and provides a new strategy for ductilizing BMG without sacrificing strength.

Effects of Re on Vacancy Mobility in a Ni-Re System: An Atomistic Study

The performance of modern Ni-based superalloys depends critically on the kinetic transport of point defects around solutes such as rhenium. Here, we use atomistic calculations to study the diffusion of vacancy in the low-concentration limit, using the crystalline fcc-framework nickel as a model. On-the-fly kinetic Monte Carlo is combined with an efficient energy-valley search to find energies of saddle points, based on energetics from the embedded atom method. With this technique, we compute the local energy barriers to vacancy hopping, tracer diffusivities, and migration energies of the low-concentration limit of Ni-Re alloys. It was estimated that the computed diffusion rates are comparable to the reported rates. The presence of Re atoms affects the difference between the energy of the saddle point and the initial energy of point defect hopping. In pure Ni, this difference is about 1 eV, while at 9.66 mol% Re, the value is raised to about 1.5 eV. The vacancy migration energy of vacancy in the 9.66 mol % Re sample is raised above that of pure Ni. Our findings demonstrate that even in the low-concentration limit, Re solute atoms continue to play a crucial role in the mobility of the vacancies.

Atomic vibration as an indicator of the propensity for configurational rearrangements in metallic glasses

In a metallic glass (MG), the propensity for atomic rearrangements varies spatially from location to location in the amorphous solid, making the prediction of their likelihood a major challenge. One can attack this problem from the "structure controls properties" standpoint. But all the current structure-centric parameters are mostly based on local atomic packing information limited to short-range order, hence falling short in reliably forecasting how the local region would respond to external stimuli (e.g., temperature and/or stress). Alternatively, one can use indicators informed by physical properties to bridge the static structure on the one hand, and the response of the local configuration on the other. A sub-group of such physics-informed quantities consists of atomic vibration parameters, which will be singled out as the focus of this article. Here we use the Cu₆₄Zr₃₆ alloy to systematically demonstrate the following two points, all using a single model MG. First, we show in a comprehensive manner the interrelation among common vibrational parameters characterizing the atomic vibrational amplitude and frequency, including the atomic mean square displacement, flexibility volume, participation fraction in the low-frequency vibrational modes and boson peak intensity. Second, we demonstrate that these vibrational parameters fare much better than purely static structural parameters based on local geometrical packing in providing correlation with the propensity for local configurational transitions. These vibrational parameters also share a correlation length similar to that in structural rearrangements induced by external stimuli. This success, however, also poses a challenge, as it remains to be elucidated as to why short-time dynamical (vibrational) behavior at the bottom of the energy basin can be exploited to project the height of the energy barrier for cross-basin activities and in turn the propensity for locally collective atomic rearrangements.

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.

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.

Activation Entropy as a Key Factor Controlling the Memory Effect in Glasses

As opposed to the common monotonic relaxation process of glasses, the Kovacs memory effect describes an isothermal annealing experiment, in which the enthalpy and volume of a preannealed glass first increases before finally decreasing toward equilibrium. This interesting behavior has been observed for many materials and is generally explained in terms of heterogeneous dynamics. In this Letter, the memory effect in a model Au-based metallic glass is studied using a high-precision high-rate calorimeter. The activation entropy (S^{*}) during isothermal annealing is determined according to the absolute reaction rate theory. We observe that the memory effect appears only when the second-annealing process has a large S^{*}. These results indicate that a large value of S^{*} is a key requirement for observation of the memory effect and this may provide a useful perspective for understanding the memory effect in both thermal and athermal systems.

Phase transitions, percolation, fracture of materials, and deep learning

Percolation and fracture propagation in disordered solids represent two important problems in science and engineering that are characterized by phase transitions: loss of macroscopic connectivity at the percolation threshold p_{c} and formation of a macroscopic fracture network at the incipient fracture point (IFP). Percolation also represents the fracture problem in the limit of very strong disorder. An important unsolved problem is accurate prediction of physical properties of systems undergoing such transitions, given limited data far from the transition point. There is currently no theoretical method that can use limited data for a region far from a transition point p_{c} or the IFP and predict the physical properties all the way to that point, including their location. We present a deep neural network (DNN) for predicting such properties of two- and three-dimensional systems and in particular their percolation probability, the threshold p_{c}, the elastic moduli, and the universal Poisson ratio at p_{c}. All the predictions are in excellent agreement with the data. In particular, the DNN predicts correctly p_{c}, even though the training data were for the state of the systems far from p_{c}. This opens up the possibility of using the DNN for predicting physical properties of many types of disordered materials that undergo phase transformation, for which limited data are available for only far from the transition point.

Structural relaxation affecting shear-transformation avalanches in metallic glasses

Avalanche behaviors, characterized by power-law statistics and structural relaxation that induces shear localization in amorphous plasticity, play an essential role in deciding the mechanical properties of amorphous metallic solids (i.e., metallic glasses). However, their interdependence is still not fully understood. To investigate the influence of structural relaxation on elementary avalanche behavior, we perform molecular-dynamics simulations for the shear deformation test of metallic glasses using two typical metallic-glass models comprising a less-relaxed (as-quenched) glass and a well-relaxed (well-aged) glass exhibiting a relatively homogeneous deformation and a shear-band-like heterogeneous deformation, respectively. The data on elementary avalanches obtained from both glass models follow the same power-law statistics with different maximum event sizes, and the well-relaxed glass shows shear localization. Evaluating the spatial correlation functions of the nonaffine squared displacements of atoms during each elementary avalanche event, we observe that the shapes of the elementary avalanche regions in the well-relaxed glasses tend to be anisotropic, whereas those in the less-relaxed glasses are relatively isotropic. Furthermore, we demonstrate that a temporal clustering in the direction of the avalanche propagation emerges, and a considerable correlation between the anisotropy and avalanche size exists in the well-relaxed glass model.

Shear transformation zone analysis of anelastic relaxation of a metallic glass reveals distinct properties of α and β relaxations

Metallic glasses with pronounced high-frequency β relaxation in their dynamic-mechanical response have been observed to exhibit large plasticity. Due to their disordered atomic structure, it is challenging to identify the microscopic mechanisms of their relaxation behavior. Quasistatic anelastic relaxation measurements have been performed over 10 orders of magnitude of time on La_{55}Ni_{20}Al_{25} metallic glass, which exhibits a strong β relaxation. The corresponding time-constant spectra were computed from the data-they contain a series of peaks corresponding to an atomically quantized hierarchy of shear transformation zones (STZs), where both the α and β relaxations are consistent with the STZ model. Two different regimes of activation-volume increment between the peaks are observed, suggesting the involvement of different elements in STZs corresponding to α vs β relaxations. Room-temperature structural relaxation significantly affects the former but not the latter.

Intrinsic dissipation mechanisms in metallic glass resonators

Micro- and nanoresonators have important applications including sensing, navigation, and biochemical detection. Their performance is quantified using the quality factor Q, which gives the ratio of the energy stored to the energy dissipated per cycle. Metallic glasses are a promising material class for micro- and nanoscale resonators since they are amorphous and can be fabricated precisely into complex shapes on these length scales. To understand the intrinsic dissipation mechanisms that ultimately limit large Q-values in metallic glasses, we perform molecular dynamics simulations to model metallic glass resonators subjected to bending vibrations at low temperatures. We calculate the power spectrum of the kinetic energy, redistribution of energy from the fundamental mode of vibration, and Q vs the kinetic energy per atom K of the excitation. In the harmonic and anharmonic response regimes where there are no atomic rearrangements, we find that Q → ∞ over the time periods we consider (since we do not consider coupling to the environment). We identify a characteristic K_r above which atomic rearrangements occur, and there is significant energy leakage from the fundamental mode to higher frequencies, causing finite Q. Thus, K_r is a critical parameter determining resonator performance. We show that K_r decreases as a power-law, K_r ∼ N^-k, with increasing system size N, where k ≈ 1.3. We estimate the critical strain ⟨γ_r⟩∼ 10^-8 for micrometer-sized resonators below which atomic rearrangements do not occur in the millikelvin temperature range, and thus, large Q-values can be obtained when they are operated below γ_r. We also find that K_r for amorphous resonators is comparable to that for resonators with crystalline order.

Potential energy landscape activations governing plastic flows in glass rheology

While glasses are ubiquitous in natural and manufactured materials, the atomic-level mechanisms governing their deformation and how these mechanisms relate to rheological behavior are still open questions for fundamental understanding. Using atomistic simulations spanning nearly 10 orders of magnitude in the applied strain rate we probe the atomic rearrangements associated with 3 characteristic regimes of homogeneous and heterogeneous shear flow. In the low and high strain-rate limits, simulation results together with theoretical models reveal distinct scaling behavior in flow stress variation with strain rate, signifying a nonlinear coupling between thermally activated diffusion and stress-driven motion. Moreover, we find the emergence of flow heterogeneity is closely correlated with extreme values of local strain bursts that are not readily accommodated by immediate surroundings, acting as origins of shear localization. The atomistic mechanisms underlying the flow regimes are interpreted by analyzing a distance matrix of nonaffine particle displacements, yielding evidence of various barrier-hopping processes on a fractal potential energy landscape (PEL) in which shear transformations and liquid-like regions are triggered by the interplay of thermal and stress activations.

Effective forces in thermal amorphous solids with generic interactions

In thermal glasses at temperatures sufficiently lower than the glass transition, the constituent particles are trapped in their cages for a sufficiently long time such that their time-averaged positions can be determined before diffusion and structural relaxation takes place. The effective forces are those that hold these average positions in place. In numerical simulations the effective forces F_{ij} between any pair of particles can be measured as a time average of the bare forces f_{ij}(r_{ij}(t)). In general, even if the bare forces come from two-body interactions, thermal dynamics dress the effective forces to contain many-body interactions. Here, we develop the effective theory for systems with generic interactions, where the effective forces are derivable from an effective potential and in turn they give rise to an effective Hessian whose eigenvalues are all positive when the system is stable. In this Rapid Communication, we offer analytic expressions for the effective theory, and demonstrate the usefulness and the predictive power of the approach.

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.

Direct determination of structural heterogeneity in metallic glasses using four-dimensional scanning transmission electron microscopy

We report the first direct quantification of the structural heterogeneity in metallic glasses using intensity variance and angular correlation analyses of the 4-dimensional (4-D) scanning transmission electron microscopy (STEM) data. We demonstrate that the real-space reconstruction and analyses of the 4-D nanodiffraction data acquired using a pixelated fast STEM detector enables quantitative determination of the details of local structural heterogeneity, including the type, size, volume fraction and spatial distribution of local ordering at the nano- to meso-scale, beyond the limits of the previous measurements using conventional detectors. We show that different types of local ordering are present in Zr₅₅Co₂₅Al₂₀ glass, leading to a high degree of structural heterogeneity, with the total volume of locally ordered regions making up to ∼14% of the entire volume. These findings are significant, as the structure-property relationship in metallic glasses and other amorphous materials has been difficult to establish because of the lack of detailed structural information from experiments.

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.

The Stress-Dependent Activation Parameters for Dislocation Nucleation in Molybdenum Nanoparticles

Many specimens at the nanoscale are pristine of dislocations, line defects which are the main carriers of plasticity. As a result, they exhibit extremely high strengths which are dislocation-nucleation controlled. Since nucleation is a thermally activated process, it is essential to quantify the stress-dependent activation parameters for dislocation nucleation in order to study the strength of specimens at the nanoscale and its distribution. In this work, we calculate the strength of Mo nanoparticles in molecular dynamics simulations and we propose a method to extract the activation free-energy barrier for dislocation nucleation from the distribution of the results. We show that by deforming the nanoparticles at a constant strain rate, their strength distribution can be approximated by a normal distribution, from which the activation volumes at different stresses and temperatures are calculated directly. We found that the activation energy dependency on the stress near spontaneous nucleation conditions obeys a power-law with a critical exponent of approximately 3/2, which is in accordance with critical exponents found in other thermally activated processes but never for dislocation nucleation. Additionally, significant activation entropies were calculated. Finally, we generalize the approach to calculate the activation parameters for other driving-force dependent thermally activated processes.

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.

Particle rearrangement and softening contributions to the nonlinear mechanical response of glasses

Amorphous materials such as metallic, polymeric, and colloidal glasses exhibit complex preparation-dependent mechanical response to applied shear. In particular, glassy solids yield, with a mechanical response that transitions from elastic to plastic, with increasing shear strain. We perform numerical simulations to investigate the mechanical response of binary Lennard-Jones glasses undergoing athermal, quasistatic pure shear as a function of the cooling rate R used to prepare them. The ensemble-averaged stress versus strain curve 〈σ(γ)〉 resembles the spatial average in the large size limit, which appears smooth and displays a putative elastic regime at small strains, a yielding-related peak in stress at intermediate strain, and a plastic flow regime at large strains. In contrast, for each glass configuration in the ensemble, the stress-strain curve σ(γ) consists of many short nearly linear segments that are punctuated by particle-rearrangement-induced rapid stress drops. To explain the nonlinearity of 〈σ(γ)〉, we quantify the shape of the small stress-strain segments and the frequency and size of the stress drops in each glass configuration. We decompose the stress loss [i.e., the deviation in the slope of 〈σ(γ)〉 from that at 〈σ(0)〉] into the loss from particle rearrangements and the loss from softening [i.e., the reduction of the slopes of the linear segments in σ(γ)], and then compare the two contributions as a function of R and γ. For the current studies, the rearrangement-induced stress loss is larger than the softening-induced stress loss, however, softening stress losses increase with decreasing cooling rate. We also characterize the structure of the potential energy landscape along the strain direction for glasses prepared with different R, and observe a dramatic change of the properties of the landscape near the yielding transition. We then show that the rearrangement-induced energy loss per strain can serve as an order parameter for the yielding transition, which sharpens for slow cooling rates and in large systems.

Correlation between Local Structure Order and Spatial Heterogeneity in a Metallic Glass

Although nanoscale spatial heterogeneity of metallic glasses has been demonstrated by extensive experimental and theoretical investigations, the nature of spatial heterogeneity remains poorly known owing to the absence of a structural depiction of the inhomogeneity from experimental insight. Here we report the experimental characterization of the spatial heterogeneity of a metallic glass by utilizing state-of-the-art angstrom-beam electron diffraction and scanning transmission electron microscopy. The subnanoscale electron diffraction reveals that the nanoscale spatial heterogeneity and corresponding density fluctuation have a close correlation with the local structure variation from icosahedronlike to tetragonal crystal-like order. The structural insights of spatial heterogeneity have important implications in understanding the properties and dynamics of metallic glasses.

Structural rearrangements governing Johari-Goldstein relaxations in metallic glasses

The Johari-Goldstein secondary (β) relaxations are an intrinsic feature of supercooled liquids and glasses. They are crucial to many properties of glassy materials, but the underlying mechanisms are still not established. In a model metallic glass, we study the atomic rearrangements by molecular dynamics simulations at time scales of up to microseconds. We find that the distributions of single-particle displacements exhibit multiple peaks, whose positions quantitatively match the pair distribution function. These are identified as the structural signature of cooperative string-like excitations. Furthermore, the most probable time of the string-like motions coincides with the β-relaxation time as probed by dynamical mechanical simulations over a wide temperature range and is consistent with a theoretical model. Our results provide insights into the long-standing puzzle regarding the structural origin of β relaxations in glassy metallic materials.

Effect of surface and internal defects on the mechanical properties of metallic glasses

Despite the significance of surface effects on the deformation behaviours of small-scale metallic glasses, systematic investigations on surface states are lacking. In this work, by employing atomistic simulations, we characterise the distributions of local inhomogeneity near surfaces created by casting and cutting, along with internal distributions in pristine and irradiated bulk specimens, and investigate the effects of inhomogeneity on the mechanical properties. The cast surface shows enhanced yield strength and degrees of shear localisation, while the cut surface shows the opposite effects, although the fraction of vibrational soft spots, known to indicate low-energy barriers for local rearrangement, is high near both surfaces. Correspondingly, plastic deformation is initiated near the cut surface, but far from the cast surface. We reveal that improved local orientational symmetry promotes strengthening in cast surfaces and originates from the effectively lower quenching rate due to faster diffusion near the surface. However, a significant correlation among vibrational soft spots, local symmetries, and the degree of shear localisation is found for the pristine and irradiated bulk materials. Our findings reveal the sensitivity of the surface state to the surface preparation methods, and indicate that particular care must be taken when studying metallic glasses containing free surfaces.

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

Complex states in glasses can be neatly expressed by the potential energy landscape (PEL). However, because PEL is highly multi-dimensional it is difficult to describe how the system moves around in PEL. Here we demonstrate that it is possible to predict the evolution of macroscopic state in a metallic glass, such as ageing and rejuvenation, through a set of simple equations describing excitations in the PEL. The key to this simplification is the realization that the step of activation from the initial state to the saddle point in PEL and the following step of relaxation to the final state are essentially decoupled. The model shows that the interplay between activation and relaxation in PEL is the key driving force that simultaneously explains both the equilibrium of supercooled liquid and the thermal hysteresis observed in experiments. It further predicts anomalous peaks in truncated thermal scanning, validated by independent molecular dynamics simulation.

Universal structural parameter to quantitatively predict metallic glass properties

Quantitatively correlating the amorphous structure in metallic glasses (MGs) with their physical properties has been a long-sought goal. Here we introduce ‘flexibility volume' as a universal indicator, to bridge the structural state the MG is in with its properties, on both atomic and macroscopic levels. The flexibility volume combines static atomic volume with dynamics information via atomic vibrations that probe local configurational space and interaction between neighbouring atoms. We demonstrate that flexibility volume is a physically appropriate parameter that can quantitatively predict the shear modulus, which is at the heart of many key properties of MGs. Moreover, the new parameter correlates strongly with atomic packing topology, and also with the activation energy for thermally activated relaxation and the propensity for stress-driven shear transformations. These correlations are expected to be robust across a very wide range of MG compositions, processing conditions and length scales.

Various known structural descriptors of metallic glasses have limitations in quantitatively predicting properties. Here authors define a physically-motivated measure and show it to correlate strongly with elastic properties, local structure and relaxation kinetics over a wide range of simulated compositions.

Structural evolution of nanoscale metallic glasses during high-pressure torsion: A molecular dynamics analysis

Structural evolution in nanoscale Cu₅₀Zr₅₀ metallic glasses during high-pressure torsion is investigated using molecular dynamics simulations. Results show that the strong cooperation of shear transformations can be realized by high-pressure torsion in nanoscale Cu₅₀Zr₅₀ metallic glasses at room temperature. It is further shown that high-pressure torsion could prompt atoms to possess lower five-fold symmetries and higher potential energies, making them more likely to participate in shear transformations. Meanwhile, a higher torsion period leads to a greater degree of forced cooperative flow. And the pronounced forced cooperative flow at room temperature under high-pressure torsion permits the study of the shear transformation, its activation and characteristics, and its relationship to the deformations behaviors. This research not only provides an important platform for probing the atomic-level understanding of the fundamental mechanisms of high-pressure torsion in metallic glasses, but also leads to higher stresses and homogeneous flow near lower temperatures which is impossible previously.

Effects of atomic interaction stiffness on low-temperature relaxation of amorphous solids

While low-temperature relaxations show significant differences among metallic glasses with different compositions, the underlying mechanism remains mysterious. Using molecular dynamics simulation, low-temperature relaxation of amorphous solids is investigated in model systems with different atomic interaction stiffness. It was found that as the interaction stiffness increases, the low-temperature relaxation is enhanced. The fraction of mobile atoms increases with increasing interaction stiffness, while the length scale of dynamical heterogeneity does not change. The enhanced relaxation may be due to increased dynamical heterogeneity. These findings provide a physical picture for better understanding the origin of low-temperature relaxation dynamics in amorphous solids, and the experimentally observed different β-relaxation behaviors in various metallic glasses.

Connecting Local Yield Stresses with Plastic Activity in Amorphous Solids

In model amorphous solids produced via differing quench protocols, a strong correlation is established between local yield stress measured by direct local probing of shear stress thresholds and the plastic rearrangements observed during remote loading in shear. This purely local measure shows a higher predictive power for identifying sites of plastic activity when compared with more conventional structural properties. Most importantly, the sites of low local yield stress, thus defined, are shown to be persistent, remaining predictive of deformation events even after fifty or more such plastic rearrangements. This direct and nonperturbative approach gives access to relevant transition pathways that control the stability of amorphous solids. Our results reinforce the relevance of modeling plasticity in amorphous solids based on a gradually evolving population of discrete and local zones preexisting in the structure.

Unveiling the structural arrangements responsible for the atomic dynamics in metallic glasses during physical aging

Understanding and controlling physical aging, that is, the spontaneous temporal evolution of out-of-equilibrium systems, represents one of the greatest tasks in material science. Recent studies have revealed the existence of a complex atomic motion in metallic glasses, with different aging regimes in contrast with the typical continuous aging observed in macroscopic quantities. By combining dynamical and structural synchrotron techniques, here for the first time we directly connect previously identified microscopic structural mechanisms with the peculiar atomic motion, providing a broader unique view of their complexity. We show that the atomic scale is dominated by the interplay between two processes: rearrangements releasing residual stresses related to a cascade mechanism of relaxation, and medium range ordering processes, which do not affect the local density, likely due to localized relaxations of liquid-like regions. As temperature increases, a surprising additional secondary relaxation process sets in, together with a faster medium range ordering, likely precursors of crystallization.

Glass aging is one of unsolved problems during glass processing and annealing, partly due to the lack of the mechanistic understanding on microscales. Here, the authors show how local stresses and their evolution affect structural relaxation at an atomic level in a metallic glass system.

Interatomic repulsion softness directly controls the fragility of supercooled metallic melts

We present an analytic scheme to connect the fragility and viscoelasticity of metallic glasses to the effective ion-ion interaction in the metal. This is achieved by an approximation of the short-range repulsive part of the interaction, combined with nonaffine lattice dynamics to obtain analytical expressions for the shear modulus, viscosity, and fragility in terms of the ion-ion interaction. By fitting the theoretical model to experimental data, we are able to link the steepness of the interionic repulsion to the Thomas-Fermi screened Coulomb repulsion and to the Born-Mayer valence electron overlap repulsion for various alloys. The result is a simple closed-form expression for the fragility of the supercooled liquid metal in terms of few crucial atomic-scale interaction and anharmonicity parameters. In particular, a linear relationship is found between the fragility and the energy scales of both the screened Coulomb and the electron overlap repulsions. This relationship opens up opportunities to fabricate alloys with tailored thermoelasticity and fragility by rationally tuning the chemical composition of the alloy according to general principles. The analysis presented here brings a new way of looking at the link between the outer shell electronic structure of metals and metalloids and the viscoelasticity and fragility thereof.

Unusual fast secondary relaxation in metallic glass

The relaxation spectrum of glassy solids has long been used to probe their dynamic structural features and the fundamental deformation mechanisms. Structurally complicated glasses, such as molecular glasses, often exhibit multiple relaxation processes. By comparison, metallic glasses have a simple atomic structure with dense atomic packing, and their relaxation spectra were commonly found to be simpler than those of molecular glasses. Here we show the compelling evidence obtained across a wide range of temperatures and frequencies from a La-based metallic glass, which clearly shows two peaks of secondary relaxations (fast versus slow) in addition to the primary relaxation peak. The discovery of the unusual fast secondary relaxation unveils the complicated relaxation dynamics in metallic glasses and, more importantly, provides us the clues which help decode the structural features serving as the ‘trigger' of inelasticity on mechanical agitations.

Mechanical relaxation processes in glasses can provide information on the structural and mechanical properties of glasses. Here, the authors observe a fast secondary relaxation process in La-based metallic glasses, providing information on the inelasticity of metallic glasses.

Crossover from Localized to Cascade Relaxations in Metallic Glasses

Thermally activated deformation is investigated in two metallic glass systems with different cooling histories. By probing the atomic displacements and stress changes on the potential energy landscape, two deformation modes, a localized process and cascade process, have observed. The localized deformation involves fewer than 30 atoms and appears in both systems, and its size is invariant with cooling history. However, the cascade deformation is more frequently observed in the fast quenched system than in the slowly quenched system. The origin of the cascade process in the fast quenched system is attributed to the higher density of local minima on the underlying potential energy landscape.

Microscopic description of flow defects and relaxation in metallic glasses

The anelastic relaxation behavior of amorphous Al86.8Ni3.7Y9.5 was characterized in prolonged, quasistatic measurements, up to 1.1×10(8) s. The size-density distribution of potential shear transformation zones was determined from the data. We derive an expression for the distribution, based on a free-volume criterion for an atomic cluster being a potential shear transformation zone. The model is shown to be consistent with experiment.