Universal structural parameter to quantitatively predict metallic glass properties

Revealing the hidden structure of disordered materials by parameterizing their local structural manifold

Durable interest in developing a framework for the detailed structure of glassy materials has produced numerous structural descriptors that trade off between general applicability and interpretability. However, none approach the combination of simplicity and wide-ranging predictive power of the lattice-grain-defect framework for crystalline materials. Working from the hypothesis that the local atomic environments of a glassy material are constrained by enthalpy minimization to a low-dimensional manifold in atomic coordinate space, we develop a generalized distance function, the Gaussian Integral Inner Product (GIIP) distance, in connection with agglomerative clustering and diffusion maps, to parameterize that manifold. Applying this approach to a two-dimensional model crystal and a three-dimensional binary model metallic glass results in parameters interpretable as coordination number, composition, volumetric strain, and local symmetry. In particular, we show that a more slowly quenched glass has a higher degree of local tetrahedral symmetry at the expense of cyclic symmetry. While these descriptors require post-hoc interpretation, they minimize bias rooted in crystalline materials science and illuminate a range of structural trends that might otherwise be missed.

Comprehensive characterization of the structure of Zr-based metallic glasses

Structure of metallic glasses fascinates as the generic amorphous structural template for ubiquitous systems. Its specification necessitates determination of the complete hierarchical structure, starting from short-range-order (SRO) → medium-range-order (MRO) → bulk structure and free volume (FV) distribution. This link has largely remained elusive since previous investigations adopted one-technique-at-a-time approach, focusing on limited aspects of any one domain. Reconstruction of structure from experimental data inversion is non-unique for many of these techniques. As a result, complete and precise structural understanding of glass has not emerged yet. In this work, we demonstrate the first experimental pathway for reconstruction of the integrated structure, forZr 67 Ni 33 andZr 52 Ti 6 Al 10 Cu 18 Ni 14 glasses. Our strategy engages diverse (× 7) multi-scale techniques [XAFS, 3D-APT, ABED/NBED, FEM, XRD, PAS, FHREM] on the same glass. This strategy complemented mutual limitations of techniques and corroborated common parameters to generate complete, self-consistent and precise parameters. Further, MRO domain size and inter-void separation were correlated to identify the presence of FV at MRO boundaries. This enabled the first experimental reconstruction of hierarchical subset: SRO → MRO → FV → bulk structure. The first ever image of intermediate region between MRO domains emerged from this link. We clarify that determination of all subsets is not our objective; the essence and novelty of this work lies in directing the pathway towards finite solution, in the most logical and unambiguous way.

Amorphous alloys surpass E/10 strength limit at extreme strain rates

Theoretical predictions of the ideal strength of materials range from E/30 to E/10 (E is Young's modulus). However, despite intense interest over the last decade, the value of the ideal strength achievable through experiments for metals remains a mystery. This study showcases the remarkable spall strength of Cu50Zr50 amorphous alloy that exceeds the E/10 limit at strain rates greater than 107 s-1 through laser-induced shock experiments. The material exhibits a spall strength of 11.5 GPa, approximately E/6 or 1/13 of its P-wave modulus, which sets a record for the elastic limit of metals. Electron microscopy and large-scale molecular dynamics simulations reveal that the primary failure mechanism at extreme strain rates is void nucleation and growth, rather than shear-banding. The rate dependence of material strength is explained by a void kinetic model controlled by surface energy. These findings help advance our understanding on the mechanical behavior of amorphous alloys under extreme strain rates.

Solid-that-Flows Picture of Glass-Forming Liquids

This perspective article reviews arguments that glass-forming liquids are different from those of standard liquid-state theory, which typically have a viscosity in the mPa·s range and relaxation times on the order of picoseconds. These numbers grow dramatically and become 1012 - 1015 times larger for liquids cooled toward the glass transition. This translates into a qualitative difference, and below the "solidity length" which is roughly one micron at the glass transition, a glass-forming liquid behaves much like a solid. Recent numerical evidence for the solidity of ultraviscous liquids is reviewed, and experimental consequences are discussed in relation to dynamic heterogeneity, frequency-dependent linear-response functions, and the temperature dependence of the average relaxation time.

Depicting Defects in Metallic Glasses by Atomic Vibrational Entropy

Due to the chaotic structure of amorphous materials, it is challenging to identify defects in metallic glasses. Here we tackle this problem from a thermodynamic point of view using atomic vibrational entropy, which represents the inhomogeneity of atomic contributions to vibrational modes. We find that the atomic vibrational entropy is correlated to the vibrational mean-square displacement and polyhedral volume of atoms, revealing the critical role of vibrational entropy in bridging dynamics, thermodynamics, and structure. On this method, the local vibrational entropy obtained by coarse-graining the atomic vibrational entropy in space can distinguish more effectively between liquid-like and solid-like atoms in metallic glasses and establish the correlation between the local vibrational entropy and the structure of metallic glasses, offering a route to predict the plastic events from local vibrational entropy. The local vibration entropy is a good indicator of thermally activated and stress-driven plastic events, and its predictive ability is better than that of the structural indicators.

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.

Machine learning modeling for the prediction of plastic properties in metallic glasses

Metallic glasses are one of the most interesting mechanical materials studied in the last years, but as amorphous solids, they differ strongly from their crystalline counterparts. This matter can be addressed with the development and application of predictive techniques capable to describe the plastic regime. Here, machine learning models were employed for the prediction of plastic properties in CuZr metallic glasses. To this aim, 100 different samples were subjected to tensile tests by means of molecular dynamics simulations. A total of 17 materials properties were calculated and explored using statistical analysis. Strong correlations were found for stoichiometry, temperature, structural, and elastic properties with plastic properties. Three regression models were employed for the prediction of six plastic properties. Linear and Ridge regressions delivered the better prediction capability, with coefficients of determination above [Formula: see text]80% for three plastic properties, whereas Lasso regression rendered lower performance, with coefficients of determination above [Formula: see text]60% for two plastic properties. Overall, our work shows that molecular dynamics simulations together with machine learning models can provide a framework for the prediction of plastic behavior of complex materials.

Shear transformations in metallic glasses without excessive and predefinable defects

Plastic flow in metallic glasses (MGs) is known to be mediated by shear transformations (STs), which have been hypothesized to preferentially initiate from identifiable local "defect" regions with loose atomic packing. Here we show that the above idea is incorrect, i.e., STs do not arise from signature structural defects that can be recognized a priori. This conclusion is reached via a realistic MG model obtained by combining molecular dynamics (MD) and Monte Carlo simulations, achieving liquid solidification at an effective cooling rate as slow as 500 K/s to approach that typical in experiments for producing bulk MGs. At shear stresses before global yielding, only about 2% of the total atoms participate in STs, each event involving typically ~10 atoms. These observations rectify the excessive content of "liquid-like regions" retained from unrealistically fast quench in MD-produced glass models. Our findings also shed light on the indeterministic aspect of the ST sites/zones, which emerge with varying spatial locations and distribution depending on specific mechanical loading conditions.

Crystallization of Flexible Chains of Tangent Hard Spheres under Full Confinement

We present results from extensive Monte Carlo simulations on the crystallization of athermal polymers under full confinement. Polymers are represented as freely jointed chains of tangent hard spheres of uniform size. Confinement is applied through the presence of flat, parallel, and impenetrable walls in all dimensions. We analyze crystallization as the summation of two contributions: one that occurs in the bulk volume of the system (bulk crystallization), and one on the wall surfaces (surface crystallization). Depending on volume fraction initially amorphous (disordered) hard-sphere chain packings transit to the stable crystal phase. The established ordered morphologies consist primarily of hexagonal close-packed (HCP) crystals in the bulk volume and of triangular (TRI) crystals on the surface. As in the case of athermal packings in the bulk (without confinement), a structural competition is observed between the 5-fold local symmetry and the formation of close-packed crystallites. Effectively, the full confinement inside a cube favors the growth of the HCP crystal, as the FCC one is quite incompatible with the imposed spatial constraints. Consequently, we observe the formation of noncompact ordered motifs which grow from the surface to the inner volume of the simulation cell. We further compare the 2D and 3D crystals formed by monomeric hard spheres under the same simulation conditions. Significant differences are observed at low densities that tend to diminish as concentration increases.

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.

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.

Simu-D: A Simulator-Descriptor Suite for Polymer-Based Systems under Extreme Conditions

We present Simu-D, a software suite for the simulation and successive identification of local structures of atomistic systems, based on polymers, under extreme conditions, in the bulk, on surfaces, and at interfaces. The protocol is built around various types of Monte Carlo algorithms, which include localized, chain-connectivity-altering, identity-exchange, and cluster-based moves. The approach focuses on alleviating one of the main disadvantages of Monte Carlo algorithms, which is the general applicability under a wide range of conditions. Present applications include polymer-based nanocomposites with nanofillers in the form of cylinders and spheres of varied concentration and size, extremely confined and maximally packed assemblies in two and three dimensions, and terminally grafted macromolecules. The main simulator is accompanied by a descriptor that identifies the similarity of computer-generated configurations with respect to reference crystals in two or three dimensions. The Simu-D simulator-descriptor can be an especially useful tool in the modeling studies of the entropy- and energy-driven phase transition, adsorption, and self-organization of polymer-based systems under a variety of conditions.

Tension-compression asymmetry in amorphous silicon

Hard and brittle materials usually exhibit a much lower strength when loaded in tension than in compression. However, this common-sense behaviour may not be intrinsic to these materials, but arises from their higher flaw sensitivity to tensile loading. Here, we demonstrate a reversed and unusually pronounced tension-compression asymmetry (tensile strength exceeds compressive strength by a large margin) in submicrometre-sized samples of isotropic amorphous silicon. The abnormal asymmetry in the yield strength and anelasticity originates from the reduction in shear modulus and the densification of the shear-activated configuration under compression, altering the magnitude of the activation energy barrier for elementary shear events in amorphous Si. In situ coupled electrical tests corroborate that compressive strains indeed cause increased atomic coordination (metallization) by transforming some local structures from sp³-bonded semiconducting motifs to more metallic-like sites, lending credence to the mechanism we propose. This finding opens up an unexplored regime of intrinsic tension-compression asymmetry in materials.

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.

Predicting orientation-dependent plastic susceptibility from static structure in amorphous solids via deep learning

It has been a long-standing materials science challenge to establish structure-property relations in amorphous solids. Here we introduce a rotationally non-invariant local structure representation that enables different predictions for different loading orientations, which is found essential for high-fidelity prediction of the propensity for stress-driven shear transformations. This novel structure representation, when combined with convolutional neural network (CNN), a powerful deep learning algorithm, leads to unprecedented accuracy for identifying atoms with high propensity for shear transformations (i.e., plastic susceptibility), solely from the static structure in both two- and three-dimensional model glasses. The data-driven models trained on samples at one composition and a given processing history are found transferrable to glass samples with different processing histories or at different compositions in the same alloy system. Our analysis of the new structure representation also provides valuable insight into key atomic packing features that influence the local mechanical response and its anisotropy in glasses.

Investigation of glass forming ability of Al-based metallic glasses by measuring vaporization enthalpy

The analysis of the enthalpy changes for vaporization (ΔH_vap) of Al-based metallic glass (MG) can provide insight into the origin of the MG’s glass forming ability (GFA). The ΔH_vap of three Al-based MGs, Al_{84.5 ± x}(Y₁₀Ni_5.5)_{15.5 ± x}, Al_{85 ± x}(Y₈Ni₅Co₂)_{15 ± x}, and Al_{86 ± x}(Y_4.5Ni₆Co₂La_1.5)_{14 ± x}, (hereafter referred to as AYN_x, AYNC_x, and AYNCL_x, respectively), is analyzed by measuring their weight losses below their glass transition temperatures. The relationship between ΔH_vap and aluminum concentration exhibit minimum values in the range of 83–85 at.% of Al, and the ΔH_vap increases, becoming saturated at 320–350 kJ/mol, as the percentage of Al deviates from this range. The depth of the enthalpy well, referring to the bottom of the parabolic graph of ΔH_vap against the Al concentration, is proportional to the viscosity of clusters showing liquid-like behavior. The amount of weight loss is proportional to the concentration of these clusters. The cluster viscosity and concentration influences the overall viscosity of the MGs, and thus determines the GFA.

Identification of Local Structure in 2-D and 3-D Atomic Systems through Crystallographic Analysis

In the present work, we revise and extend the Characteristic Crystallographic Element (CCE) norm, an algorithm used to simultaneously detect radial and orientational similarity of computer-generated structures with respect to specific reference crystals and local symmetries. Based on the identification of point group symmetry elements, the CCE descriptor is able to gauge local structure with high precision and finely distinguish between competing morphologies. As test cases we use computer-generated monomeric and polymer systems of spherical particles interacting with the hard-sphere and square-well attractive potentials. We demonstrate that the CCE norm is able to detect and differentiate, between others, among: hexagonal close packed (HCP), face centered cubic (FCC), hexagonal (HEX) and body centered cubic (BCC) crystals as well as non-crystallographic fivefold (FIV) local symmetry in bulk 3-D systems; triangular (TRI), square (SQU) and honeycomb (HON) crystals, as well as pentagonal (PEN) local symmetry in thin films of one-layer thickness (2-D systems). The descriptor is general and can be applied to identify the symmetry elements of any point group for arbitrary atomic or particulate system in two or three dimensions, in the bulk or under confinement.

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.

Precursors to plastic failure in a numerical simulation of CuZr metallic glass

We deform, in pure shear, a thin sample of Cu₅₀Zr₅₀ metallic glass using a molecular dynamics simulation up to, and including, failure. The experiment is repeated ten times in order to have average values and standard deviations. Although failure occurs at the same value of the externally imposed strain for the ten samples, there is significant sample-to-sample variation in the specific microscopic material behavior. Failure can occur along one, two, or three planes, located at the boundaries of previously formed shear bands (SBs). These SBs form shortly before failure. However, well before their formation and at external strains where plastic deformation just begins to be significant, non-affine displacement organizes itself along localized bands. The SBs subsequently form at the edges of these non-affine-displacement-bands, and present an alternating rotation-quadrupole structure, as found previously by Şopu et al (2017 Phys. Rev. Lett. 119 195503) in the case of a notched sample loaded in tension. The thickness of SBs is roughly determined by the available plastic energy. The onset of shear banding is accompanied by a sharp increase in the rate of change of the rotation angle localization, the strain localization, and the non-affine square displacement.

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.

A transferable machine-learning framework linking interstice distribution and plastic heterogeneity in metallic glasses

When metallic glasses (MGs) are subjected to mechanical loads, the plastic response of atoms is non-uniform. However, the extent and manner in which atomic environment signatures present in the undeformed structure determine this plastic heterogeneity remain elusive. Here, we demonstrate that novel site environment features that characterize interstice distributions around atoms combined with machine learning (ML) can reliably identify plastic sites in several Cu-Zr compositions. Using only quenched structural information as input, the ML-based plastic probability estimates ("quench-in softness" metric) can identify plastic sites that could activate at high strains, losing predictive power only upon the formation of shear bands. Moreover, we reveal that a quench-in softness model trained on a single composition and quench rate substantially improves upon previous models in generalizing to different compositions and completely different MG systems (Ni₆₂Nb₃₈, Al₉₀Sm₁₀ and Fe₈₀P₂₀). Our work presents a general, data-centric framework that could potentially be used to address the structural origin of any site-specific property in MGs.

Universal nature of dynamic heterogeneity in glass-forming liquids: A comparative study of metallic and polymeric glass-forming liquids

Glass-formation is a ubiquitous phenomenon that is often observed in a broad class of materials ranging from biological matter to commonly encountered synthetic polymer, as well as metallic and inorganic glass-forming (GF) materials. Despite the many regularities in the dynamical properties of GF materials, the structural origin of the universal dynamical properties of these materials has not yet been identified. Recent simulations of coarse-grained polymeric GF liquids have indicated the coexistence of clusters of mobile and immobile particles that appear to be directly linked, respectively, to the rate of molecular diffusion and structural relaxation. The present work examines the extent to which these distinct types of "dynamic heterogeneity" (DH) arise in metallic GF liquids (Cu-Zr, Ni-Nb, and Pd-Si alloys) having a vastly different molecular structure and chemistry. We first identified mobile and immobile particles and their transient clusters and found the DH in the metallic alloys to be remarkably similar in form to polymeric GF liquids, confirming the "universality" of the DH phenomenon. Furthermore, the lifetime of the mobile particle clusters was found to be directly related to the rate of diffusion in these materials, while the lifetime of immobile particles was found to be proportional to the structural relaxation time, providing some insight into the origin of decoupling in GF liquids. An examination of particles having a locally preferred atomic packing, and clusters of such particles, suggests that there is no one-to-one relation between these populations of particles so that an understanding of the origin of DH in terms of static fluid structure remains elusive.

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.

Machine learning characterization of structural defects in amorphous packings of dimers and ellipses

Structural defects within amorphous packings of symmetric particles can be characterized using a machine learning approach that incorporates structure functions of radial distances and angular arrangement. This yields a scalar field, softness, that correlates with the probability that a particle is about to be rearranged. However, when particle shapes are elongated, as in the case of dimers and ellipses, we find that the standard structure functions produce imprecise softness measurements. Moreover, ellipses exhibit deformation profiles in stark contrast to circular particles. In order to account for the effects of orientation and alignment, we introduce structure functions to recover the predictive performance of softness, as well as provide physical insight into local and extended dynamics. We study a model disordered solid, a bidisperse two-dimensional granular pillar, driven by uniaxial compression and composed entirely of monomers, dimers, or ellipses. We demonstrate how the computation of softness via a support vector machine extends to dimers and ellipses with the introduction of orientational structure functions. Then we highlight the spatial extent of rearrangements and defects, as well as their cross correlation, for each particle shape. Finally, we demonstrate how an additional machine learning algorithm, recursive feature elimination, provides an avenue to better understand how softness arises from particular structural aspects. We identify the most crucial structure functions in determining softness and discuss their physical implications.

Structural Parameter of Orientational Order to Predict the Boson Vibrational Anomaly in Glasses

It has so far remained a major challenge to quantitatively predict the boson peak, a THz vibrational anomaly universal for glasses, from features in the amorphous structure. Using molecular dynamics simulations of a model Cu_{50}Zr_{50} glass, we decompose the boson peak to contributions from atoms residing in different types of Voronoi polyhedra. We then introduce a microscopic structural parameter to depict the "orientational order," using the vector pointing from the center atom to the farthest vertex of its Voronoi coordination polyhedron. This order parameter represents the most probable direction of transverse vibration at low frequencies. Its magnitude scales linearly with the boson peak intensity, and its spatial distribution accounts for the quasilocalized modes. This correlation is shown to be universal for different types of glasses.

Spatial heterogeneity as the structure feature for structure-property relationship of metallic glasses

The mechanical properties of crystalline materials can be quantitatively described by crystal defects of solute atoms, dislocations, twins, and grain boundaries with the models of solid solution strengthening, Taylor strain hardening and Hall-Petch grain boundary strengthening. However, for metallic glasses, a well-defined structure feature which dominates the mechanical properties of the disordered materials is still missing. Here, we report that nanoscale spatial heterogeneity is the inherent structural feature of metallic glasses. It has an intrinsic correlation with the strength and deformation behavior. The strength and Young's modulus of metallic glasses can be defined by the function of the square root reciprocal of the characteristic length of the spatial heterogeneity. Moreover, the stretching exponent of time-dependent strain relaxation can be quantitatively described by the characteristic length. Our study provides compelling evidence that the spatial heterogeneity is a feasible structural indicator for portraying mechanical properties of metallic glasses.

Mechanical glass transition revealed by the fracture toughness of metallic glasses

The fracture toughness of glassy materials remains poorly understood. In large part, this is due to the disordered, intrinsically non-equilibrium nature of the glass structure, which challenges its theoretical description and experimental determination. We show that the notch fracture toughness of metallic glasses exhibits an abrupt toughening transition as a function of a well-controlled fictive temperature (T_f), which characterizes the average glass structure. The ordinary temperature, which has been previously associated with a ductile-to-brittle transition, is shown to play a secondary role. The observed transition is interpreted to result from a competition between the T_f-dependent plastic relaxation rate and an applied strain rate. Consequently, a similar toughening transition as a function of strain rate is predicted and demonstrated experimentally. The observed mechanical toughening transition bears strong similarities to the ordinary glass transition and explains the previously reported large scatter in fracture toughness data and ductile-to-brittle transitions.

Understanding the fracture toughness of metallic glasses remains challenging. Here, the authors show that a fictive temperature controls an abrupt mechanical toughening transition in metallic glasses, and can explain the scatter in previously reported fracture toughness data.

Structural Signature of β-Relaxation in La-Based Metallic Glasses

The secondary β-relaxation is an intrinsic feature in glassy materials. However, its structural origin is still not well understood. Here we report that the β-relaxations in La₅₀Al₁₅Ni₃₅ and La₅₀Al₁₅Cu₃₅ metallic glasses (MGs) mainly depend on the vibration of small Ni and Cu atoms in local cages. By using advanced synchrotron X-ray techniques and theoretical calculations, we elucidate that the tricapped-trigonal-prism-like polyhedra with more large La atoms in shells favor the local vibration of center Ni atoms, leading to the pronounced β-relaxation event. In contrast, the in-cage vibration of Cu atoms is somehow suppressed by the appearance of more shell Cu atoms. Nevertheless, they could easily diffuse out of the cages compared with Ni, thus triggering the onset of α-relaxation. This work provides a pathway to understand the different structural relaxation behaviors in MGs and other disordered materials from their local atomic packing and dynamics points of view.

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.

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.