Mechanical glass transition revealed by the fracture toughness of metallic glasses

Hierarchical Surface Pattern on Ni-Free Ti-Based Bulk Metallic Glass to Control Cell Interactions

Ni-free Ti-based bulk metallic glasses (BMGs) are exciting materials for biomedical applications because of their outstanding biocompatibility and advantageous mechanical properties. The glassy nature of BMGs allows them to be shaped and patterned via thermoplastic forming (TPF). This work demonstrates the versatility of the TPF technique to create micro- and nano-patterns and hierarchical structures on Ti40Zr10Cu34Pd14Sn2 BMG. Particularly, a hierarchical structure fabricated by a two-step TPF process integrates 400 nm hexagonal close-packed protrusions on 2.5 µm square protuberances while preserving the advantageous mechanical properties from the as-cast material state. The correlations between thermal history, structure, and mechanical properties are explored. Regarding biocompatibility, Ti40Zr10Cu34Pd14Sn2 BMGs with four surface topographies (flat, micro-patterned, nano-patterned, and hierarchical-structured surfaces) are investigated using Saos-2 cell lines. Alamar Blue assay and live/dead analysis show that all tested surfaces have good cell proliferation and viability. Patterned surfaces are observed to promote the formation of longer filopodia on the edge of the cytoskeleton, leading to star-shaped and dendritic cell morphologies compared with the flat surface. In addition to potential implant applications, TPF-patterned Ti-BMGs enable a high level of order and design flexibility on the surface topography, expanding the available toolbox for studying cell behavior on rigid and ordered surfaces.

Elasticity of self-organized frustrated disordered spring networks

There have been some interesting recent advances in understanding the notion of mechanical disorder in structural glasses and the statistical mechanics of these systems' low-energy excitations. Here we contribute to these advances by studying a minimal model for structural glasses' elasticity in which the degree of mechanical disorder-as characterized by recently introduced dimensionless quantifiers-is readily tunable over a very large range. We comprehensively investigate a number of scaling laws observed for various macro, meso and microscopic elastic properties, and rationalize them using scaling arguments. Interestingly, we demonstrate that the model features the universal quartic glassy vibrational density of states as seen in many atomistic and molecular models of structural glasses formed by cooling a melt. The emergence of this universal glassy spectrum highlights the role of self-organization (toward mechanical equilibrium) in its formation, and elucidates why models featuring structural frustration alone do not feature the same universal glassy spectrum. Finally, we discuss relations to existing work in the context of strain stiffening of elastic networks and of low-energy excitations in structural glasses, in addition to future research directions.

Size-dependent vitrification in metallic glasses

Reducing the sample size can profoundly impact properties of bulk metallic glasses. Here, we systematically reduce the length scale of Au and Pt-based metallic glasses and study their vitrification behavior and atomic mobility. For this purpose, we exploit fast scanning calorimetry (FSC) allowing to study glassy dynamics in an exceptionally wide range of cooling rates and frequencies. We show that the main α relaxation process remains size independent and bulk-like. In contrast, we observe pronounced size dependent vitrification kinetics in micrometer-sized glasses, which is more evident for the smallest samples and at low cooling rates, resulting in more than 40 K decrease in fictive temperature, Tf, with respect to the bulk. We discuss the deep implications on how this outcome can be used to convey glasses to low energy states.

Atomic Structural Origin of Fictive Temperature Revealed by AZnP3 O9 (A=K, Rb) Glasses

The fictive temperature (T_f ) is widely applied to understand the relaxation thermodynamics of a glass; however, its atomic structural origin is still unclear. Here, we report two novel AZnP₃ O₉ glasses obtained by melting the composition identical single crystals. These glasses exhibit structural inheritance within 5 Å from the single crystal counterparts that is quantified by δ=n_glass /n_cry (0≤δ≤1, n is the number of pair correlation functions). Among the available glass-formers, ^glass KZnP₃ O₉ exhibits the highest structural inheritance (δ=1, n_glass =8). More insightfully, a reverse correlation between δ and the relaxation thermodynamic parameters is observed in ^glass AZnP₃ O₉ , revealing for the first time the atomic structural origin of fictive temperature.

Finite-Disorder Critical Point in the Yielding Transition of Elastoplastic Models

Upon loading, amorphous solids can exhibit brittle yielding, with the abrupt formation of macroscopic shear bands leading to fracture, or ductile yielding, with a multitude of plastic events leading to homogeneous flow. It has been recently proposed, and subsequently questioned, that the two regimes are separated by a sharp critical point, as a function of some control parameter characterizing the intrinsic disorder strength and the degree of stability of the solid. In order to resolve this issue, we have performed extensive numerical simulations of athermally driven elastoplastic models with long-range and anisotropic realistic interaction kernels in two and three dimensions. Our results provide clear evidence for a finite-disorder critical point separating brittle and ductile yielding, and we provide an estimate of the critical exponents in 2D and 3D.

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.

Advancing the Mechanical Performance of Glasses: Perspectives and Challenges

Glasses are materials that lack a crystalline microstructure and long-range atomic order. Instead, they feature heterogeneity and disorder on superstructural scales, which have profound consequences for their elastic response, material strength, fracture toughness, and the characteristics of dynamic fracture. These structure-property relations present a rich field of study in fundamental glass physics and are also becoming increasingly important in the design of modern materials with improved mechanical performance. A first step in this direction involves glass-like materials that retain optical transparency and the haptics of classical glass products, while overcoming the limitations of brittleness. Among these, novel types of oxide glasses, hybrid glasses, phase-separated glasses, and bioinspired glass-polymer composites hold significant promise. Such materials are designed from the bottom-up, building on structure-property relations, modeling of stresses and strains at relevant length scales, and machine learning predictions. Their fabrication requires a more scientifically driven approach to materials design and processing, building on the physics of structural disorder and its consequences for structural rearrangements, defect initiation, and dynamic fracture in response to mechanical load. In this article, a perspective is provided on this highly interdisciplinary field of research in terms of its most recent challenges and opportunities.

Low-Frequency Excess Vibrational Modes in Two-Dimensional Glasses

Glasses possess more low-frequency vibrational modes than predicted by Debye theory. These excess modes are crucial for the understanding of the low temperature thermal and mechanical properties of glasses, which differ from those of crystalline solids. Recent simulational studies suggest that the density of the excess modes scales with their frequency ω as ω^{4} in two and higher dimensions. Here, we present extensive numerical studies of two-dimensional model glass formers over a large range of glass stabilities. We find that the density of the excess modes follows D_{exc}(ω)∼ω^{2} up to around the boson peak, regardless of the glass stability. The stability dependence of the overall scale of D_{exc}(ω) correlates with the stability dependence of low-frequency sound attenuation. However, we also find that, in small systems, where the first sound mode is pushed to higher frequencies, at frequencies below the first sound mode, there are excess modes with a system size independent density of states that scales as ω^{3}.

Low-energy quasilocalized excitations in structural glasses

Glassy solids exhibit a wide variety of generic thermomechanical properties, ranging from universal anomalous specific heat at cryogenic temperatures to nonlinear plastic yielding and failure under external driving forces, which qualitatively differ from their crystalline counterparts. For a long time, it has been believed that many of these properties are intimately related to nonphononic, low-energy quasilocalized excitations (QLEs) in glasses. Indeed, recent computer simulations have conclusively revealed that the self-organization of glasses during vitrification upon cooling from a melt leads to the emergence of such QLEs. In this Perspective, we review developments over the past three decades toward understanding the emergence of QLEs in structural glasses and the degree of universality in their statistical and structural properties. We discuss the challenges and difficulties that hindered progress in achieving these goals and review the frameworks put forward to overcome them. We conclude with an outlook on future research directions and open questions.

Predicting Fracture Propensity in Amorphous Alumina from Its Static Structure Using Machine Learning

Thin films of amorphous alumina (a-Al₂O₃) have recently been found to deform permanently up to 100% elongation without fracture at room temperature. If the underlying ductile deformation mechanism can be understood at the nanoscale and exploited in bulk samples, it could help to facilitate the design of damage-tolerant glassy materials, the holy grail within glass science. Here, based on atomistic simulations and classification-based machine learning, we reveal that the propensity of a-Al₂O₃ to exhibit nanoscale ductility is encoded in its static (nonstrained) structure. By considering the fracture response of a series of a-Al₂O₃ systems quenched under varying pressure, we demonstrate that the degree of nanoductility is correlated with the number of bond switching events, specifically the fraction of 5- and 6-fold coordinated Al atoms, which are able to decrease their coordination numbers under stress. In turn, we find that the tendency for bond switching can be predicted based on a nonintuitive structural descriptor calculated based on the static structure, namely, the recently developed "softness" metric as determined from machine learning. Importantly, the softness metric is here trained from the spontaneous dynamics of the system (i.e., under zero strain) but, interestingly, is able to readily predict the fracture behavior of the glass (i.e., under strain). That is, lower softness facilitates Al bond switching and the local accumulation of high-softness regions leads to rapid crack propagation. These results are helpful for designing glass formulations with improved resistance to fracture.

Correlation symmetry analysis of electron nanodiffraction from amorphous materials

Angular symmetry in diffraction reflects rotational symmetry in the sample. We introduce the angular symmetry coefficient as a method to extract local symmetry information from electron nanodiffraction patterns of amorphous materials. Symmetry coefficients are the average of the angular autocorrelation function at the characteristic angles of a particular rotational symmetry. The symmetry coefficients avoid non-structural features arising from Fourier transformation and Friedel symmetry breakdown that affect the angular power spectrum approach to determining angular symmetries in amorphous nanodiffraction. Both methods require thin samples to avoid overlapping diffraction from clusters of atoms separated in the thickness of the sample, but symmetry coefficients are more forgiving. Electron nanodiffraction experiments on a Pd-based metallic glass sample demonstrate both potentially misleading information in angular power spectrum and the utility of symmetry coefficients.

Unified quantifier of mechanical disorder in solids

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

Analysis of lens fracture in precision glass molding with the finite element method

Precision glass molding (PGM) technology has recently emerged as a promising fabrication method for mass-fabricating optical glass lenses with complex surfaces. However, lens fracture as a common problem has not been analyzed in detail. In this paper, the divergent cone cracks in the molded lens were analyzed using the finite element method, because crack propagation cannot be seen in the molding process. A three-dimensional model was established in MSC Marc software for analyzing the temperature, stress components, and principal stress of the glass in different molding stages. The crack paths were analyzed using the simulation results and the fracture basis. Based on the analysis, PGM experiments with different processing parameters were carried out. The appearance of the molded lenses demonstrated the rationality and correctness of the analysis. Thus, analyses of other types of lens fractures can use the analysis method proposed in this paper rather than relying on trial and error.

Fracture toughness of crystalline solids

This paper describes an attempt to construct a first-principles theory of the fracture toughness of crystalline solids. It is based on the thermodynamic dislocation theory (TDT), which starts with the assertion that dislocations in solids must obey the second law of thermodynamics. A second starting assumption is that fracture is initiated when the tip of a notch is driven to undergo a dynamic shape instability. The results of this analysis are developed in comparison with measurements by Gumbsch and colleagues of the notch toughness of both predeformed and non-predeformed tungsten crystals. The theory includes a simple ad hoc conjecture regarding tip dynamics at small dislocation densities. Nevertheless, its predictions agree quantitatively with the experimental data, including both brittle and ductile fracture, over a wide range of temperatures, loading rates, and initial conditions.

Biocompatibility of platinum-based bulk metallic glass in orthopedic applications

Bulk metallic glasses (BMGs) are a class of amorphous metals that exhibit high strength, ductility paired with wear and corrosion resistance. These properties suggest that they could serve as an alternative to conventional metallic implants that suffer wear and failure. In the present study, we investigated Platinum (Pt)-BMG biocompatibility in bone applications. Specifically, we investigated osteoclast formation on flat and nanopatterned Pt_57.5Cu_14.7Ni_5.3P_22.5(atomic percent) as well as titanium (control). Specifically, receptor activator of NF-κB (RANK) ligand-induced murine bone marrow derived mononuclear cell fusion was measured on multiple nanopatterns and was found to be reduced on nanorods (80 and 200 nm in diameter) and was associated with reduced tartrate-resistant acid phosphatase (TRAP) and matrix metalloproteinase (MMP9) expression. Evaluation of mesenchymal stem cell (MSC) to osteoblast differentiation on nanopatterned Pt-BMG showed significant reduction in comparison to flat, suggesting that further exploration of nanopatterns is required to have simultaneous induction of osteoblasts and inhibition of osteoclasts.Invivo studies were also pursued to evaluate the biocompatibility of Pt-BMG in comparison to titanium. Rods of each material were implanted in the femurs of mice and evaluated by x-ray, mechanical testing, micro-computed tomography (micro-CT), and histological analysis. Overall, Pt-BMG showed similar biocompatibility with titanium suggesting that it has the potential to improve outcomes by further processing at the nanoscale.

Relaxation dynamics of Pd-Ni-P metallic glass: decoupling of anelastic and viscous processes

The stress relaxation dynamics of metallic glass Pd₄₀Ni₄₀P₂₀was studied in both supercooled liquid and glassy states. Time-temperature superposition was found in the metastable liquid, implying an invariant shape of the distribution of times involved in the relaxation. Once in the glass state, the distribution of relaxation times broadens as temperature and fictive temperature decrease, eventually leading to a decoupling of the relaxation in two processes. While the slow one keeps a viscous behavior, the fast one shows an anelastic nature and a time scale similar to that of the collective atomic motion measured by x-ray photon correlation spectroscopy (XPCS). These results suggest that the atomic dynamics of metallic glasses, as determined by XPCS at low temperatures in the glass state, can be related to the rearrangements of particles responsible of the macroscopically reversible anelastic behavior.

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.

Internally Stressed and Positionally Disordered Minimal Complexes Yield Glasslike Nonphononic Excitations

Glasses, unlike their crystalline counterparts, exhibit low-frequency nonphononic excitations whose frequencies ω follow a universal D(ω)∼ω^{4} density of states. The process of glass formation generates positional disorder intertwined with mechanical frustration, posing fundamental challenges in understanding the origins of glassy nonphononic excitations. Here we suggest that minimal complexes-mechanically frustrated and positionally disordered local structures-embody the minimal physical ingredients needed to generate glasslike excitations. We investigate the individual effects of mechanical frustration and positional disorder on the vibrational spectrum of isolated minimal complexes, and demonstrate that ensembles of marginally stable minimal complexes yield D(ω)∼ω^{4}. Furthermore, glasslike excitations emerge by embedding a single minimal complex within a perfect lattice. Consequently, minimal complexes offer a conceptual framework to understand glasslike excitations from first principles, as well as a practical computational method for introducing them into solids.

Mechanical disorder of sticky-sphere glasses. II. Thermomechanical inannealability

Many structural glasses feature static and dynamic mechanical properties that can depend strongly on glass formation history. The degree of universality of this history dependence and what it is possibly affected by are largely unexplored. Here we show that the variability of elastic properties of simple computer glasses under thermal annealing depends strongly on the strength of attractive interactions between the glasses' constituent particles-referred to here as glass "stickiness." We find that in stickier glasses the stiffening of the shear modulus with thermal annealing is strongly suppressed, while the thermal-annealing-induced softening of the bulk modulus is enhanced. Our key finding is that the characteristic frequency and density per frequency of soft quasilocalized modes becomes effectively invariant to annealing in very sticky glasses; the latter are therefore deemed "thermomechanically inannealable." The implications of our findings and future research directions are discussed.

Ductile and Brittle Yielding in Thermal and Athermal Amorphous Materials

We study theoretically the yielding of sheared amorphous materials as a function of increasing levels of initial sample annealing prior to shear, in three widely used constitutive models and three widely studied annealing protocols. In thermal systems we find a gradual progression, with increasing annealing, from smoothly "ductile" yielding, in which the sample remains homogeneous, to abruptly "brittle" yielding, in which it becomes strongly shear banded. This progression arises from an increase with annealing in the size of an overshoot in the underlying stress-strain curve for homogeneous shear, which causes a shear banding instability that becomes more severe with increasing annealing. Ductile and brittle yielding thereby emerge as two limiting cases of a continuum of yielding transitions, from gradual to catastrophic. In contrast, athermal systems with a stress overshoot always show brittle yielding at low shear rates, however small the overshoot.

Stable glassy configurations of the Kob-Andersen model using swap Monte Carlo

The swap Monte Carlo algorithm allows the preparation of highly stable glassy configurations for a number of glass-formers but is inefficient for some models, such as the much studied binary Kob-Andersen (KA) mixture. We have recently developed generalizations to the KA model where swap can be very effective. Here, we show that these models can, in turn, be used to considerably enhance the stability of glassy configurations in the original KA model at no computational cost. We successfully develop several numerical strategies both in and out of equilibrium to achieve this goal and show how to optimize them. We provide several physical measurements indicating that the proposed algorithms considerably enhance mechanical and thermodynamic stability in the KA model, including a transition toward brittle yielding behavior. Our results thus pave the way for future studies of stable glasses using the KA model.

Ultrastable Metallic Glasses In Silico

We develop a generic strategy and simple numerical models for multicomponent metallic glasses for which the swap Monte Carlo algorithm can produce highly stable equilibrium configurations equivalent to experimental systems cooled more than 10^{7} times slower than in conventional simulations. This paves the way for a deeper understanding of the thermodynamic, dynamic, and mechanical properties of metallic glasses. As first applications, we considerably extend configurational entropy measurements down to the experimental glass temperature, and demonstrate a qualitative change of the mechanical response of metallic glasses of increasing stability toward brittleness.

Coordinate transformation methodology for simulating quasistatic elastoplastic solids

Molecular dynamics simulations frequently employ periodic boundary conditions where the positions of the periodic images are manipulated in order to apply deformation to the material sample. For example, Lees-Edwards conditions use moving periodic images to apply simple shear. Here, we examine the problem of precisely comparing this type of simulation to continuum solid mechanics. We employ a hypoelastoplastic mechanical model, and develop a projection method to enforce quasistatic equilibrium. We introduce a simulation framework that uses a fixed Cartesian computational grid on a reference domain, and which imposes deformation via a time-dependent coordinate transformation to the physical domain. As a test case for our method, we consider the evolution of shear bands in a bulk metallic glass using the shear transformation zone theory of amorphous plasticity. We examine the growth of shear bands in simple shear and pure shear conditions as a function of the initial preparation of the bulk metallic glass.

Glass Stability Changes the Nature of Yielding under Oscillatory Shear

We perform molecular dynamics simulations to investigate the effect of a glass preparation on its yielding transition under oscillatory shear. We use swap Monte Carlo to investigate a broad range of glass stabilities from poorly annealed to highly stable systems. We observe a qualitative change in the nature of yielding, which evolves from ductile to brittle as glass stability increases. Our results disentangle the relative role of mechanical and thermal annealing on the mechanical properties of amorphous solids, which is relevant for various experimental situations from the rheology of soft materials to fatigue failure in metallic glasses.

Brittle-ductile transitions in a metallic glass

Recent computational and laboratory experiments have shown that brittle-ductile transitions in the notch toughnesses of metallic glasses such as Vitreloy 1 are strongly sensitive to the initial effective disorder (or "fictive") temperature. Glasses with lower effective temperatures are weak and brittle; those with higher effective temperatures are strong and ductile. The analysis of this phenomenon presented here examines the onset of fracture at the tip of a notch as predicted by the shear-transformation-zone theory of spatially varying plastic deformation. The central ingredient of this analysis is an approximation for the dynamics of the plastic zone formed by stress concentration at the notch tip. This zone first shields the tip but then, with increasing stress, expands suddenly, producing a discontinuous transition between brittle and ductile failure in satisfactory agreement with the numerical and experimental observations.

Pinching a glass reveals key properties of its soft spots

It is now well established that glasses feature quasilocalized nonphononic excitations-coined "soft spots"-, which follow a universal [Formula: see text] density of states in the limit of low frequencies ω. All glass-specific properties, such as the dependence on the preparation protocol or composition, are encapsulated in the nonuniversal prefactor of the universal [Formula: see text] law. The prefactor, however, is a composite quantity that incorporates information both about the number of quasilocalized nonphononic excitations and their characteristic stiffness, in an apparently inseparable manner. We show that by pinching a glass-i.e., by probing its response to force dipoles-one can disentangle and independently extract these two fundamental pieces of physical information. This analysis reveals that the number of quasilocalized nonphononic excitations follows a Boltzmann-like law in terms of the parent temperature from which the glass is quenched. The latter, sometimes termed the fictive (or effective) temperature, plays important roles in nonequilibrium thermodynamic approaches to the relaxation, flow, and deformation of glasses. The analysis also shows that the characteristic stiffness of quasilocalized nonphononic excitations can be related to their characteristic size, a long sought-for length scale. These results show that important physical information, which is relevant for various key questions in glass physics, can be obtained through pinching a glass.

Effect of Pinning on the Yielding Transition of Amorphous Solids

Using numerical simulations, we have studied the yielding response, in the athermal quasistatic limit, of a model amorphous material having inclusions in the form of randomly pinned particles. We show that, with increasing pinning concentration, the plastic activity becomes more spatially localized, resulting in smaller stress drops, and a corresponding increase in the magnitude of strain where yielding occurs. We demonstrate that, unlike the spatially heterogeneous and avalanche led yielding in the case of the unpinned glass, for the case of large pinning concentration, yielding takes place via a spatially homogeneous proliferation of localized events.

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.

Critical Analysis of an FeP Empirical Potential Employed to Study the Fracture of Metallic Glasses

An empirical potential that has been widely used to perform molecular dynamics studies on the fracture behavior of FeP metallic glasses is shown to exhibit spinodal decomposition in the composition range commonly studied. The phosphorous segregation induces a transition from ductility to brittleness. During brittle fracture the atomically sharp crack tip propagates along a percolating path with higher P concentration. This embrittlement is observed to occur over a wide range of chemical compositions, and toughness decreases linearly with the degree of compositional segregation over the entire regime studied. Stable glass forming alloys that can be quenched at low quench rates do not, as a rule, exhibit such thermodynamically unstable behavior near to or above their glass transition temperatures. Hence, the microstructures exhibited in these simulations are unlikely to reflect the actual microstructures or fracture behaviors of the glassy alloys they seek to elucidate.

Low-frequency vibrational modes of stable glasses

Unusual features of the vibrational density of states D(ω) of glasses allow one to rationalize their peculiar low-temperature properties. Simulational studies of D(ω) have been restricted to studying poorly annealed glasses that may not be relevant to experiments. Here we report on D(ω) of zero-temperature glasses with kinetic stabilities ranging from poorly annealed to ultrastable glasses. For all preparations, the low-frequency part of D(ω) splits between extended and quasi-localized modes. Extended modes exhibit a boson peak crossing over to Debye behavior (D_ex(ω) ~ ω²) at low-frequency, with a strong correlation between the two regimes. Quasi-localized modes obey D_loc(ω) ~ ω⁴, irrespective of the stability. The prefactor of this quartic law decreases with increasing stability, and the corresponding modes become more localized and sparser. Our work is the first numerical observation of quasi-localized modes in a regime relevant to experiments, and it establishes a direct connection between glasses’ stability and their soft vibrational modes

The nature of the vibrational modes of amorphous solids is of fundamental interest, but assessing them is challenging due to very long equilibrium times involved. Wang et al. numerically model the localized low-frequency vibrational modes in glasses and show the sensitivity of their populations to glass stability.

Fast generation of ultrastable computer glasses by minimization of an augmented potential energy

We present a model and protocol that enable the generation of extremely stable computer glasses at minimal computational cost. The protocol consists of an instantaneous quench in an augmented potential energy landscape, with particle radii as additional degrees of freedom. We demonstrate how our glasses' mechanical stability, which is readily tunable in our approach, is reflected in both microscopic and macroscopic observables. Our observations indicate that the stability of our computer glasses is at least comparable to that of computer glasses generated by the celebrated Swap Monte Carlo algorithm. Strikingly, some key properties support even qualitatively enhanced stability in our scheme: the density of quasilocalized excitations displays a gap in our most stable computer glasses, whose magnitude scales with the polydispersity of the particles. We explain this observation, which is consistent with the lack of plasticity we observe at small stress. It also suggests that these glasses are depleted from two-level systems, similarly to experimental vapor-deposited ultrastable glasses.