Model Metallic Glass Research Articles

Role of densification in deformation behaviors of model metallic glasses under 3-D nanoindentation studied in molecular dynamics simulation

Under sharp contact loading, glass deforms elastically and then plastically via densification as well as shear flow. Stress build-up during loading, residual stress build-up after unloading, and possible ultimate cracking all depend sensitively on the competition and interplay between densification and shear flow. The crack resistance was shown in experimental studies to generally improve with the increasing contribution of densification in glasses where shear deformation plays a dominant role under indentation. In this work, the role of densification in deformation behaviors of model metallic glasses under sharp contact loading was studied by 3-D nanoindentation tests using indenters with different sharpness in classical molecular dynamics simulations. Starting from a model metallic glass that favors shear deformation, a Lennard-Jones potential was modified to describe model metallic glasses with different abilities of instantaneous densification under compression and permanent densification after decompression. Our studies show that model metallic glass with a higher densification ability under indentation has less stress build-up and less localized shear deformation during loading, as well as smaller residual stress build-up after unloading. However, our study indicates that both instantaneous and permanent densification need to be tuned for designing damage resistant glasses.

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.

The dynamics of shear band propagation in metallic glasses

Understanding the dynamics of shear band propagation in metallic glasses remains elusive due to the limited temporal and spatial scales accessible in experiments. In micron-scale molecular dynamics simulations on two model metallic glasses, we studied the propagation of a dominant shear band under uniaxial tension with a macroscopic strain of 3-5%. For both materials, the shear band can be intersonic with a propagation speed exceeding their respective shear wave speeds. The propagation exhibits intrinsic instability that manifests itself as microbranching and considerable fluctuations in velocity. The shear strain singularity ahead of propagating shear band tip scales as 1/r (r is the distance away from the tip), independent of the macroscopic tensile strain. In addition, we studied the intersection of two shear bands under uniaxial tension, during which path deflection, speed slowing-down, and temperature rise at the junction region were observed. The dynamics of propagating shear band shown here indicate that shear band in metallic glasses can be viewed as shear crack under the framework of weakly nonlinear fracture mechanics theory.

Model Metallic Glasses for Superior Electrocatalytic Performance in a Hydrogen Oxidation Reaction

Metallic glasses or amorphous alloys, with their excellent chemical stability, disordered atomic arrangement, and ability for thermoplastic nanostructuring, show promising performance toward a range of electrocatalytic reactions in proton-exchange membrane fuel cells. However, there are knowledge gaps and a distinct lack of understanding of the role of amorphous alloy chemistry in determining their catalytic activity. Here, we demonstrate the influence of alloy chemistry and the associated electronic structure on the hydrogen oxidation reaction (HOR) activity of a systematic series of Pt42.5-xPdxCu27Ni9.5P21 bulk metallic glasses (BMGs) with x = 0 to 42.5 at%. The HOR activity and electrochemical active surface area as a function of composition were in the form of volcano plots, with a peak around equal proportion of Pt and Pd. The lower relative electron work function and higher binding energy of the Pt core level explain the reduced charge-transfer resistance and improved electrocatalytic activity due to weakened chemisorption of protons in the mid-range composition. Density functional theory calculations show the lower free energy change and higher hydrogen adsorption density for these Pt42.5-xPdxCu27Ni9.5P21 BMGs, suggesting a synergistic effect from the presence of both noble metals, Pt and Pd.

Deformation behaviors of a model metallic glass under 3-D nanoindentation studied in molecular dynamics simulation

In recent years, molecular dynamics (MD) simulation has been used to study the deformation behaviors of glass under nanoindentation, mainly using ideal geometries like a spherical indenter or a 2.5-D sample geometry to simplify post-analysis and save computational costs. To generate stress/strain fields that can be directly compared with experiments, we developed a 3-D nanoindentation protocol in this work to study the deformation behaviors of a model metallic glass under sharp contact loading in MD. Our studies show that the indenter sharpness controls the shear band formation, and the interaction between shear bands dictates the crack initiation in the model metallic glass. Shear bands and residual stress fields in the model metallic glass from our simulated nanoindentation tests are consistent with observations in soda-lime silicate (SLS) glass from the instrumented indentation in experiments, as both of them favor shear deformation under sharp contact loading.

Transient nature of fast relaxation in metallic glass

Metallic glasses exhibit fast mechanical relaxations at temperatures well below the glass transition, one of which shows little variation with temperature known as nearly constant loss (NCL). Despite the important implications of this phenomenon to deformation, the origin of the relaxation is unclear. Through molecular dynamics simulations of a model metallic glass, Cu64.5Zr35.5, we implement molecular dynamics dynamical mechanical spectroscopy (MD-DMS) with system stress decomposed into atomic-level stresses to identify the group of atoms responsible for NCL. This work demonstrates that NCL relaxation is due to transient groups of atoms that revert to the typical atomic-level viscoelastic behavior over picosecond timescales. They are homogenously distributed throughout the glass and have no outstanding features, rather than having defect-like local structure as previously reported.

On the shear modulus and thermal effects during structural relaxation of a model metallic glass: Correlation and thermal decoupling

Pd40Ni40P20 (at.%) samples with different enthalpy states were fabricated through high-pressure torsion or sub-Tg annealing of the as-cast material. Subsequently, the underlying structural relaxation was studied by in-situ shear modulus measurements and modulated differential scanning calorimetry. The results show that high-pressure torsion leads to shear modulus softening and an increase of the nonreversible exothermic enthalpy, indicating a significant structural rejuvenation, while sub-Tg annealing causes shear modulus hardening and a decrease of the nonreversible exothermic enthalpy. The reversible endothermic effect which can reflect the fractional change of supercooled liquid with temperature was found to be almost identical for all samples, and independent of deformation or thermal history. The total heat flow can be well correlated with the shear modulus within the framework of interstitialcy theory. Furthermore, we demonstrate that the structural relaxation below Tg decouples into internal stress relaxation and β-relaxation. In addition, this work indicates that the processes of α-relaxation and β-relaxation in the metallic glass are of similar structural origin but occur on different spatial scales.

A link between mechanical heterogeneity and nontrivial local structural power-law response in a model metallic glass

The structural heterogeneity and mechanical inhomogeneity of metallic glasses at the nanoscale have been demonstrated by extensive experimental investigations, while their inherent correlation remains ambiguous. Based on elasticity theory, a model is developed to describe the local structural response of metallic glasses under hydrostatic deformation. We establish a linear relationship between the local bulk modulus and the nontrivial power-law exponent of the structural response and further verify this relationship by molecular dynamics simulations. The intrinsic link between the local structural response and elastic modulus reveals that the mechanical heterogeneity reflects not only the static atomic packing but also the dynamic evolution of the amorphous structure. Our findings provide direct evidence that mechanical heterogeneity is a feasible indicator for describing the structural heterogeneity of metallic glasses and shed some light on the non-cubic structural power law of disordered materials.

Implementation and calibration of a mesoscale model for amorphous plasticity based on shear transformation dynamics

A mesoscale numerical model based on shear transformation zone (STZ) theory is implemented in a commercial finite element software. The model is designed to predict the (visco)plastic deformation response of amorphous solids at the nano- and microscale. The theoretical framework relies on earlier models developed by Bulatov and Argon (1994a) and of Homer and Schuh (2009). We justify the potential of the computational model by conducting reference calculations for model metallic and polymeric glasses in plane strain compression. Emphasis is placed on the effect of time and space discretisation on the predicted macroscopic response. The dependence of the predicted yield strength upon the values of the fundamental model parameters is analysed via a mean-field approximation. The mean-field approximation is validated based on a series of simulations in model parameter space. We provide guidelines for a straightforward but consistent parameter identification method via the mean-field approximation while starting from experimental data.

On the Shear Modulus and Thermal Effect During Structural Relaxation in a Model Metallic Glass: Correlation and Thermal Decoupling

Pd40 Ni40P20 (at.%) samples with different enthalpy states and relaxation behaviors were fabricated through high-pressure torsion or sub-Tg annealing of the as-cast state. Subsequently, the underlying structural relaxation was studied by investigating the modulus and thermal characteristics using in-situ shear modulus measurement and modulated differential scanning calorimetry. The results show that high-pressure torsion leads to shear modulus softening and an increase of the irreversible exothermic enthalpy, indicating a significant structural rejuvenation, while sub-Tg annealing causes shear modulus hardening and a decrease of the irreversible exothermic enthalpy. Besides, the reversible endothermic effect which reflects the heat capacity was found to be almost identical for all samples, independent on deformation or thermal history. The total heat flow can be well correlated to the shear modulus within the framework of interstitialcy theory. Furthermore, we demonstrate that the structural relaxation below Tg decouples into the internal stress relaxation and β-relaxation. The former is an irreversible process of releasing internal stress, accompanied by an exothermic effect and modulus hardening. The latter is a complex process involving kinetic and thermodynamic components, accompanied by an endothermic effect and modulus softening. Shadow glass transition and glass transition overshoot are related to the activation (cage-breaking) processes in the kinetics of β-relaxation and α-relaxation, respectively. This work indicates that β-relaxation and α-relaxation are kinetically and thermodynamically identical but occur in distinct temperature or frequency domains. Internal stress relaxation as a universal mechanism plays a significant role in the structural relaxation, and simultaneously modulates the diffusive relaxation spectrum.

The critical model size for simulating the structure-dynamics correlation in bulk metallic glasses

Computational simulation provides an effective way of understanding the disordered structure and structure-property relationships for metallic glass systems. Here, we systematically investigated the finite-size effects of the static structure and dynamical behaviors in a three-dimensional Cu50Zr50 model metallic glass via classical molecular dynamics (MD) simulations. It was found that the local structure is insensitive to the system size while the dynamical properties present evident finite-size effects. The decoupling between local structure and relaxation dynamics in the investigated supercooling emerges when the system contains less than ~2000 atoms. However, the collapse can be observed between the structural relaxation time and the dynamical heterogeneity for different sized systems across the whole range of our investigation. Our results support the intrinsic link between the structural relaxation time and dynamic heterogeneity and reveal the critical simulated system size for representing the structural origins of dynamics in bulk metallic glass with ignorable surface effects.

Revealing the ultra-low-temperature relaxation peak in a model metallic glass

By systematically investigating the relaxation behavior of a model metallic glass based on the extensive molecular dynamics (MD) simulations combined with the dynamic mechanical spectroscopy method, a pronounced ultra-low temperature peak on the loss modulus spectrum was discovered for the first time in MD simulations. It was found that the relaxation peak occurs at a much lower temperature than the typical temperature for the conventional β relation peak as reported in the literature. According to the atomic displacement analysis, we unravel that the reversible atomic motions, rather than the thermal vibrations or local structural rearrangements, mainly contribute to this relaxation peak. We further identify the atomic level mechanism of this fast relaxation process by characterizing the local geometrical anisotropy. Furthermore, by tracing the dynamic behaviors of these “reversible” atoms, we demonstrate the intrinsic hierarchy of the relaxation modes, which are triggered by atomic vibrations and gradually developed to include the reversible and irreversible atomic movements. Our findings provide an important piece of the puzzle about the holistic picture of the rich relaxation processes in metallic glasses.

Revealing the Low-Temperature Fast Relaxation Peak in a Model Metallic Glass

By systematically investigating the relaxation behavior of a model metallic glass based on the extensive molecular dynamics (MD) simulations combined with the dynamic mechanical spectroscopy method, a pronounced ultra-low temperature peak on the loss modulus spectrum was discovered for the first time in MD simulations. It was found that the relation peak occurs at a much lower temperature than the typical temperature for the conventional β relation peak as reported in the literature. According to the atomic displacement analysis, we unravel that the atomic motions, rather than the thermal vibrations or local structural rearrangements, mainly contribute to this relaxation peak. We further identify the atomic level mechanism of this fast relaxation process by characterizing the local geometrical anisotropy. Furthermore, by tracing the dynamic behaviors of these reversible atoms, we demonstrate the intrinsic hierarchy of the local relaxation modes, which are triggered by atomic vibrations and gradually developed to the and irreversible atomic movements. Our findings shed light on a general picture of the relaxation processes in metallic glasses.

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 Kr above which atomic rearrangements occur, and there is significant energy leakage from the fundamental mode to higher frequencies, causing finite Q. Thus, Kr is a critical parameter determining resonator performance. We show that Kr decreases as a power-law, Kr ∼ N-k, with increasing system size N, where k ≈ 1.3. We estimate the critical strain ⟨γr⟩∼ 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 γr. We also find that Kr for amorphous resonators is comparable to that for resonators with crystalline order.

Supercluster-Coupled Crystal Growth in Metallic Glass Forming Liquids

While common growth models assume a structure-less liquid composed of atomic flow units, structural ordering has been shown in liquid metals. Here, we conduct in situ transmission electron microscopy crystallization experiments on metallic glass nanorods, and show that structural ordering strongly affects crystal growth and is controlled by nanorod thermal history. Direct visualization reveals structural ordering as densely populated small clusters in a nanorod heated from the glass state, and similar behavior is found in molecular dynamics simulations of model metallic glasses. At the same growth temperature, the asymmetry in growth rate for rods that are heated versus cooled decreases with nanorod diameter and vanishes for very small rods. We hypothesize that structural ordering enhances crystal growth, in contrast to assumptions from common growth models. The asymmetric growth rate is attributed to the difference in the degree of the structural ordering, which is pronounced in the heated glass but sparse in the cooled liquid.

Supercluster-coupled crystal growth in metallic glass forming liquids

While common growth models assume a structure-less liquid composed of atomic flow units, structural ordering has been shown in liquid metals. Here, we conduct in situ transmission electron microscopy crystallization experiments on metallic glass nanorods, and show that structural ordering strongly affects crystal growth and is controlled by nanorod thermal history. Direct visualization reveals structural ordering as densely populated small clusters in a nanorod heated from the glass state, and similar behavior is found in molecular dynamics simulations of model metallic glasses. At the same growth temperature, the asymmetry in growth rate for rods that are heated versus cooled decreases with nanorod diameter and vanishes for very small rods. We hypothesize that structural ordering enhances crystal growth, in contrast to assumptions from common growth models. The asymmetric growth rate is attributed to the difference in the degree of the structural ordering, which is pronounced in the heated glass but sparse in the cooled liquid.

Fundamental Link between β Relaxation, Excess Wings, and Cage-Breaking in Metallic Glasses.

In glassy materials, the Johari-Goldstein secondary (β) relaxation is crucial to many properties as it is directly related to local atomic motions. However, a long-standing puzzle remains elusive: why some glasses exhibit β relaxations as pronounced peaks while others present as unobvious excess wings? Using microsecond atomistic simulation of two model metallic glasses (MGs), we demonstrate that such a difference is associated with the number of string-like collective atomic jumps. Relative to that of excess wings, we find that MGs having pronounced β relaxations contain larger numbers of such jumps. Structurally, they are promoted by the higher tendency of cage-breaking events of their neighbors. Our results provide atomistic insights for different signatures of the β relaxation that could be helpful for understanding the low-temperature dynamics and properties of MGs.

Role of thermal expansion heterogeneity in the cryogenic rejuvenation of metallic glasses

Cryogenic rejuvenation in metallic glasses reported in Ketov et al 's experiment (2015 Nature 524 200) has attracted much attention, both in experiments and numerical studies. The atomic mechanism of rejuvenation has been conjectured to be related to the heterogeneity of the glassy state, but the quantitative evidence is still elusive. Here we use molecular dynamics simulations of a model metallic glass to investigate the heterogeneity in the local thermal expansion. We then combine the resulting spatial distribution of thermal expansion with a continuum mechanics calculation to infer the internal stresses caused by a thermal cycle. Comparing the internal stress with the local yield stress, we prove that the heterogeneity in thermo mechanical response has the potential to trigger local shear transformations, and therefore to induce rejuvenation during a cryogenic thermal cycling.

On measuring the fracture energy of model metallic glasses

We report a heuristic approach to measure the fracture energy of model metallic glasses using molecular dynamics simulation. Specifically, we adopted the Rivlin-Thomas method, simplified by Suo et al., which is applicable even with the presence of plastic flow. We further modified the testing condition with semi-rigid holders in our molecular simulations, to avoid unintended fracture near the holders. This method was first applied in measuring the fracture energy of a brittle model glass, which agrees well with direct KIC and JIC measurements (both measurements are independent of the crack size). Furthermore, the fracture energy values of a family of model metallic glasses, ranging from brittle to ductile (BTD), were measured. The Poisson's ratio-fracture energy (v-G, or v-G/2γ, normalized by the surface energy) relation obtained here exhibits a BTD transition at a critical Poisson's ratio of 0.31–0.32, consistent with experimental results.

Nanomechanics of slip avalanches in amorphous plasticity

Discrete stress relaxations (slip avalanches) in a model metallic glass under uniaxial compression are studied using a metadynamics algorithm for molecular simulation at experimental strain rates. The onset of yielding is observed at the first major stress drop, accompanied, upon analysis, by the formation of a single localized shear band region spanning the entire system. During the elastic response prior to yielding, low concentrations of shear transformation deformation events appear intermittently and spatially uncorrelated. During serrated flow following yielding, small stress drops occur interspersed between large drops. The simulation results point to a threshold value of stress dissipation as a characteristic feature separating major and minor avalanches consistent with mean-field modeling analysis and mechanical testing experiments. We further interpret this behavior to be a consequence of a nonlinear interplay of two prevailing mechanisms of amorphous plasticity, thermally activated atomic diffusion and stress-induced shear transformations, originally proposed by Spaepen and Argon, respectively. Probing the atomistic processes at widely separate strain rates gives insight to different modes of shear band formation: percolation of shear transformations versus crack-like propagation. Additionally a focus on crossover avalanche size has implications for nanomechanical modeling of spatially and temporally heterogeneous dynamics.