Tensile plasticity in metallic glasses with pronounced β relaxations

Microscopic Observation of the Anisotropy of the Johari-Goldstein-β Process in Cross-Linked Polybutadiene on Stretching by Time-Domain Interferometry

The strain dependence of the Johari-Goldstein (JG)-β relaxation time, as well as the directional dependence, was systematically investigated for stretched cross-linked polybutadiene using time-domain interferometry. We found that the strain dependence of the JG-β relaxation time is directionally dependent, contrary to expectation: the relaxation time of the JG-β motion, whose displacement is perpendicular to the stretching direction, decreases with stretching, whereas the relaxation time of the parallel JG-β motion changes little. This result is distinct from the previously reported strain dependence of the α relaxation time, where the relaxation time increases isotropically with stretching. Thus, the difference in the strain dependence of the relaxation time between the α and JG-β processes suggests a microscopic origin and requires the modification of the conventional dynamic picture for stretched polymers.

Unveiling the Structural Origins of Dynamic Diversity in Pd-Based Metallic Glasses

The β-relaxation is one of the major dynamic behaviors in metallic glasses (MGs) and exhibits diverse features. Despite decades of efforts, the understanding of its structural origin and contribution to the overall dynamics of MG systems is still unclear. Here two palladium-based Pd─Cu─P and Pd─Ni─P MGs are reported with distinct different β-relaxation behaviors and reveal the structural origins for the difference using the advanced X-ray photon correlation spectroscopy and absorption fine structure techniques together with the first-principles calculations. The pronounced β-relaxation and fast atomic dynamics in the Pd─Cu─P MG mainly come from the strong mobility of Cu atoms and their locally favored structures. In contrast, the motion of Ni atoms is constrained by P atoms in the Pd─Ni─P MG, leading to the weakened β-relaxation peak and sluggish dynamics. The correlation of atomic dynamics with microscopic structures provides a way to understand the structural origins of different dynamic behaviors as well as the nature of aging in disordered materials.

Beam Effects on Atomic Dynamics in Metallic Glasses Studied With Electron Correlation Microscopy

Electron correlation microscopy (ECM) is used to investigate atomic dynamics in metallic glasses (MG) close to metastable equilibrium. It temporally correlates diffracted intensities of a time series of dark-field images to deduce a metric for structural decays. The measurement parameters, such as time and temperature, must be chosen according to the material of interest. In this work, ECM was extended to measurements at room temperature. To ensure, or select, a time window with quasi-thermodynamic equilibrium/steady-state measurement conditions, two-time correlation functions of diffracted intensities were calculated. The dynamics at room temperature are partly driven by the electron beam, thus affecting the material and the results. A systematic analysis of the influence of the electron beam is presented, revealing an inverse relation between electron dose rate and intensity correlation decay times at 300 kV acceleration voltage. However, the underlying dynamical mechanisms, described by a stretching exponent, are found to be independent of the applied electron dose rate for a Pd40Ni40P20 MG. An extrapolation of the results to infinite long measurement times and zero dose rate agrees with X-ray photon correlation spectroscopy data and justifies the application of beam-driven ECM at room temperature to study the dynamics of disordered systems.

Detecting the exponential relaxation spectrum in glasses by high-precision nanocalorimetry

Nonexponential relaxations are universal characteristics for glassy materials. There is a well-known hypothesis that nonexponential relaxation peaks are composed of a series of exponential events, which have not been verified. In this Letter, we discover the exponential relaxation events during the recovery process using a high-precision nanocalorimetry, which are universal for metallic glasses and organic glasses. The relaxation peaks can be well fitted by the exponential Debye function with a single activation energy. The activation energy covers a broad range from α relaxation to β relaxation and even the fast γ/β' relaxation. We obtain the complete spectrum of the exponential relaxation peaks over a wide temperature range from 0.63Tg to 1.03Tg, which provides solid evidence that nonexponential relaxation peaks can be decomposed into exponential relaxation units. Furthermore, the contribution of different relaxation modes in the nonequilibrium enthalpy space is measured. These results open a door for developing the thermodynamics of nonequilibrium physics and for precisely modulating the properties of glasses by controlling the relaxation modes.

Highly tunable β-relaxation enables the tailoring of crystallization in phase-change materials

In glasses, secondary (β-) relaxations are the predominant source of atomic dynamics. Recently, they have been discovered in covalently bonded glasses, i.e., amorphous phase-change materials (PCMs). However, it is unclear what the mechanism of β-relaxations is in covalent systems and how they are related to crystallization behaviors of PCMs that are crucial properties for non-volatile memories and neuromorphic applications. Here we show direct evidence that crystallization is strongly linked to β-relaxations. We find that the β-relaxation in Ge15Sb85 possesses a high tunability, which enables a manipulation of crystallization kinetics by an order of magnitude. In-situ synchrotron X-ray scattering, dielectric functions, and ab-initio calculations indicate that the weakened β-relaxation intensity stems from a local reinforcement of Peierls-like distortions, which increases the rigidity of the bonding network and decreases the dynamic heterogeneity. Our findings offer a conceptually new approach to tuning the crystallization of PCMs based on manipulating the β-relaxations.

Relaxation and Amorphous Structure of Polymers Containing Rigid Fumarate Segments

The physical properties of polymers are significantly affected by relaxation processes. Recently, we reported that poly(diethyl fumarate) (PDEF) shows two thermal anomalies on DSC measurement, despite the fact that it is a homopolymer. We attribute these two relaxations α relaxation and β relaxation, respectively. In this study, we investigate the two relaxations of fumarate-containing polymers by DSC, solid-state NMR, and X-ray scattering. The two relaxations are present even in a copolymer of diethyl fumarate and ethyl acrylate with fumarate segments of 30%. We used poly(methyl methacrylate) (PMMA) as a model polymer for comparison, since there are detailed investigations of its dynamics and physical properties. Solid-state NMR indicates that the very local relaxation of poly(fumarate)s is not significantly different from that of PMMA. The tensile test showed that PDEF is still brittle at above β relaxation temperature and below α relaxation temperature. It was revealed that a structural anisotropy appeared when PDEF was extended at around α relaxation temperature. We discuss the effect of the glassy packing of the rigid polymer chain including the DEF segments on the strong β relaxation behavior. Our data provide insight into the microscopic mechanism of β relaxation of vinyl polymers.

Intrinsic Correlation between the Fraction of Liquidlike Zones and the β Relaxation in High-Entropy Metallic Glasses

Lacking the structural information of crystalline solids, the origin of the relaxation dynamics of metallic glasses is unclear. Here, we report the evolution of stress relaxation of high-entropy metallic glasses with distinct β relaxation behavior. The fraction of liquidlike zones, determined at each temperature by the intensity of stress decay, is shown to be directly related to both the aging process and the spectrum of relaxation modes obtained by mechanical spectroscopy. The results shed light on the intrinsic correlation between the static and dynamic mechanical response in high-entropy and conventional metallic glasses, pointing toward a sluggish diffusion high-entropy effect in the liquid dynamics.

Anisotropic correlations of plasticity on the yielding of metallic glasses

We report computer simulations on the shear deformation of CuZr metallic glasses at zero and room temperatures. Shear bands emerge in athermal alloys at strain γ_{c}, with a finite-size effect found. The correlation of nonaffine displacement exhibits an exponential decay even after yielding in thermal alloys, but transits to a power law at γ>γ_{c} in athermal ones. The algebraic exponent is around -1 for the decay inside shear bands, consistent with the theoretical prediction in random elastic media. We quantify the anisotropic correlation with harmonic projection, finding the spectrum is weak in the exponential-decay regime, while it displays a strong polar and quadrupolar symmetry in the power-law regime. The nonvanishing quadrupolar symmetry at long distance signifies the nonlocality of plastic correlation in the athermal alloys. In contrast, the plastic correlation was found to be isotropic and localized at the yielding in the thermal alloys without shear bands.

Review of the Recent Development in Metallic Glass and Its Composites

Metallic glasses are known for their mechanical properties but lack plasticity. This could be prevented by combining them with other materials or by inducing a second phase to form a composite. These composites have enhanced thermo-physical properties. The review paper aims to outline a summary of the current research done on metallic glass and its composites. A background in the history, properties, and their applications is discussed. Recent developments in biocompatible metallic glass composites, fiber-reinforced metallic glass, ex situ and in situ, are discussed.

Metallic Nanoglasses with Promoted β-Relaxation and Tensile Plasticity

The secondary (β) relaxation is an intrinsic feature of glassy systems and is crucial for the mechanical properties of metallic glasses. However, it remains puzzling what structural features control the β-relaxation fundamentally. Here, we use the recently developed nanoglasses exhibiting well-defined structural features at the nanometer scale to interrogate such structure-dynamics relations. We show that an electrodeposited Ni_77.5P_22.5 nanoglass exhibits promoted β-relaxation and enhanced microscale tensile plasticity over the most rapidly melt-quenched metallic glass with the same composition. Structurally, the β-relaxation is sensitive to the interfacial regions among grains in the nanoglasses. Our results reveal a clear correlation between the amorphous nanostructures and the β-relaxation. It seems that the nanostructuring represents a novel route to obtain high-energy glassy states, that is, the inverse problem of the ultrastable glass.

Decoupling between calorimetric and dynamical glass transitions in high-entropy metallic glasses

Glass transition is one of the unresolved critical issues in solid-state physics and materials science, during which a viscous liquid is frozen into a solid or structurally arrested state. On account of the uniform arrested mechanism, the calorimetric glass transition temperature (Tg) always follows the same trend as the dynamical glass transition (or α-relaxation) temperature (Tα) determined by dynamic mechanical analysis (DMA). Here, we explored the correlations between the calorimetric and dynamical glass transitions of three prototypical high-entropy metallic glasses (HEMGs) systems. We found that the HEMGs present a depressed dynamical glass transition phenomenon, i.e., HEMGs with moderate calorimetric Tg represent the highest Tα and the maximum activation energy of α-relaxation. These decoupled glass transitions from thermal and mechanical measurements reveal the effect of high configurational entropy on the structure and dynamics of supercooled liquids and metallic glasses, which are associated with sluggish diffusion and decreased dynamic and spatial heterogeneities from high mixing entropy. The results have important implications in understanding the entropy effect on the structure and properties of metallic glasses for designing new materials with plenteous physical and mechanical performances.

β-Relaxation and Crystallization Behaviors in a Pulse-Current-Thermoplastic-Formed La-Based Bulk Metallic Glass

We use the pulse current thermoplastic forming technique based on joule heating to rejuvenate the atomic structure of a La₆₂Al₁₄Ag_2.34Ni_10.83Co_10.83 bulk metallic glass (BMG). The pulse-formed sample exhibits more pronounced β-relaxation than the as-cast one due to the increased free volume. Instead, the sub-T_g annealing clearly weakens the β-relaxation and also makes it more isolated from the α-relaxation, showing contributions from free volume and preferred structure. However, both treatments exhibit little influence on the following α-relaxation and high temperature crystallization kinetics. Our results open an effective way to rejuvenate the structure of BMGs and provide an in-depth understanding of the relationship between structural relaxations and crystallization kinetics of BMGs.

Correlation between High Temperature Deformation and β Relaxation in LaCeBased Metallic Glass

High-temperature deformation around the glass transition temperature T_g and the dynamic mechanical behavior of La₃₀Ce₃₀Al₁₅Co₂₅ metallic glass were investigated. According to dynamic mechanical analysis (DMA) results, La₃₀Ce₃₀Al₁₅Co₂₅ metallic glass exhibits a pronounced slow β relaxation process. In parallel, strain-rate jump experiments around the glass transition temperature were performed in a wide range of strain rate ranges. The apparent viscosity shows a strong dependence on temperature and strain rate, which reflects the transition from non-Newtonian to Newtonian flow. At low strain or high temperature, a transition was observed from a non-Newtonian viscous flow to Newtonian viscous flow. It was found that the activation volume during plastic deformation of La₃₀Ce₃₀Al₁₅Co₂₅ metallic glass is higher than that of other metallic glasses. Higher values of activation volume in La₃₀Ce₃₀Al₁₅Co₂₅ metallic glass may be attributed to existence of a pronounced slow β relaxation. It is reasonable to conclude that slow β relaxation in La₃₀Ce₃₀Al₁₅Co₂₅ metallic glass corresponds to the “soft” regions (structural heterogeneities) in metallic glass.

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

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

Intrinsic dissipation mechanisms in metallic glass resonators

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

A microscopic look at the Johari-Goldstein relaxation in a hydrogen-bonded glass-former

Understanding the glass transition requires getting the picture of the dynamical processes that intervene in it. Glass-forming liquids show a characteristic decoupling of relaxation processes when they are cooled down towards the glassy state. The faster (βJG) process is still under scrutiny, and its full explanation necessitates information at the microscopic scale. To this aim, nuclear γ-resonance time-domain interferometry (TDI) has been utilized to investigate 5-methyl-2-hexanol, a hydrogen-bonded liquid with a pronounced βJG process as measured by dielectric spectroscopy. TDI probes in fact the center-of-mass, molecular dynamics at scattering-vectors corresponding to both inter- and intra-molecular distances. Our measurements demonstrate that, in the undercooled liquid phase, the βJG relaxation can be visualized as a spatially-restricted rearrangement of molecules within the cage of their closest neighbours accompanied by larger excursions which reach out at least the inter-molecular scale and are related to cage-breaking events. In-cage rattling and cage-breaking processes therefore coexist in the βJG relaxation.

Accelerated discovery and mechanical property characterization of bioresorbable amorphous alloys in the Mg-Zn-Ca and the Fe-Mg-Zn systems using high-throughput methods

Ternary amorphous alloys in the magnesium (Mg)-zinc (Zn)-calcium (Ca) and the iron (Fe)-Mg-Zn systems are promising candidates for use in bioresorbable implants and devices. The optimal alloy compositions for biomedical applications should be chosen from a large variety of available alloys with best combination of mechanical properties (modulus, strength, hardness) and biological response (in situ degradation rates, cell adhesion and proliferation). As a first step towards establishing a database designed to enable such targeted material selection, amorphous alloy composition libraries were fabricated employing a combinatorial magnetron sputtering approach where Mg, Zn, and Ca/Fe are co-deposited from separate sources onto a silicon wafer substrate. Composition analysis using energy dispersive X-ray spectroscopy documented a composition range of ∼15-85 at% Mg, ∼6-55 at% Zn, and ∼5-60 at% Ca for the Mg-Zn-Ca library and ∼26-84 at% Mg, ∼10-61 at% Zn, and ∼7-55 at% Fe for the Fe-Mg-Zn library. X-ray diffraction measurements established that amorphous alloys (i.e., glasses) form in almost the entire range of composition at the high cooling rates during sputtering for both alloy libraries. Finally, the effective material modulus, the Oliver-Pharr hardness, and the yield strength values obtained using nanoindentation reveal a wide range of mechanical properties within both systems.

Flow units as dynamic defects in metallic glassy materials

In a crystalline material, structural defects such as dislocations or twins are well defined and largely determine the mechanical and other properties of the material. For metallic glass (MG) with unique properties in the absence of a long-range lattice, intensive efforts have focused on the search for similar 'defects'. The primary objective has been the elucidation of the flow mechanism of MGs. However, their atomistic mechanism of mechanical deformation and atomic flow response to stress, temperature, and failure, have proven to be challenging. In this paper, we briefly review the state-of-the-art studies on the dynamic defects in metallic glasses from the perspective of flow units. The characteristics, activation and evolution processes of flow units as well as their correlation with mechanical properties, including plasticity, strength, fracture, and dynamic relaxation, are introduced. We show that flow units that are similar to structural defects such as dislocations are crucial in the optimization and design of metallic glassy materials via the thermal, mechanical and high-pressure tailoring of these units. In this report, the relevant issues and open questions with regard to the flow unit model are also introduced and discussed.

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.

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.

Multiscale Relaxation Dynamics in Ultrathin Metallic Glass-Forming Films

The density layering phenomenon originating from a free surface gives rise to the layerlike dynamics and stress heterogeneity in ultrathin Cu-Zr glassy films, which facilitates the occurrence of multistep relaxations in the timescale of computer simulations. Taking advantage of this condition, we trace the relaxation decoupling and evolution with temperature simply via the intermediate scattering function. We show that the β relaxation hierarchically follows fast and slow modes in films, and there is a β-relaxation transition as the film is cooled close to the glass transition. We provide the direct observation of particle motions responsible for the β relaxation and reveal the dominant mechanism varying from the thermal activated to the cooperative jumps across the transition.

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

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

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

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

Structural rearrangements governing Johari-Goldstein relaxations in metallic glasses

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

Pronounced Plasticity Caused by Phase Separation and β-relaxation Synergistically in Zr-Cu-Al-Mo Bulk Metallic Glasses

Bulk metallic glasses (BMGs) are known to have extraordinary merits such as ultrahigh strength and dynamic toughness etc. but tied to the detrimental brittleness, which has become a critical issue to the engineering application and understanding the glass nature. In this article, we report a new class of Zr-Cu-Al-Mo BMGs with extraordinary plastic strain above 20%. "Work-hardening" effect after yielding in a wide range of plastic deformation process has been detected for this kind of BMGs. Compositional heterogeneity, which can be classified into ZrMo- and Cu-rich zones, was differentiated in this kind of BMG. Pronounced humps have been observed on the high frequency kinetic spectrum in Mo containing BMGs, which is the indicator of β-relaxation transition. The underlying mechanism for the excellent plastic deforming ability of this class of BMGs is ascribed to the synergistic effects of soft ZrMo-rich glass formed through phase separation and abundant flow units which related to β-relaxation.

Effects of cooling rate on particle rearrangement statistics: Rapidly cooled glasses are more ductile and less reversible

Amorphous solids, such as metallic, polymeric, and colloidal glasses, display complex spatiotemporal response to applied deformations. In contrast to crystalline solids, during loading, amorphous solids exhibit a smooth crossover from elastic response to plastic flow. In this study, we investigate the mechanical response of binary Lennard-Jones glasses to athermal, quasistatic pure shear as a function of the cooling rate used to prepare them. We find several key results concerning the connection between strain-induced particle rearrangements and mechanical response. We show that the energy loss per strain dU_{loss}/dγ caused by particle rearrangements for more rapidly cooled glasses is larger than that for slowly cooled glasses. We also find that the cumulative energy loss U_{loss} can be used to predict the ductility of glasses even in the putative linear regime of stress versus strain. U_{loss} increases (and the ratio of shear to bulk moduli decreases) with increasing cooling rate, indicating enhanced ductility. In addition, we characterized the degree of reversibility of particle motion during a single shear cycle. We find that irreversible particle motion occurs even in the linear regime of stress versus strain. However, slowly cooled glasses, which undergo smaller rearrangements, are more reversible during a single shear cycle than rapidly cooled glasses. Thus, we show that more ductile glasses are also less reversible.

Single-particle dynamics near the glass transition of a metallic glass

The single-particle dynamics of the glass-forming Cu_{50}Zr_{50} alloy, from the supercooled liquid well above the glass-transition temperature, T_{g} to the glassy state, is studied by using the molecular dynamics simulations. When the liquid is cooled below 1.2T_{g}, the dynamics heterogeneity characterized by the cage-jump motion becomes increasingly pronounced. The analyses based on the continuous time random walk method indicate that the liquid falls out of equilibrium in the present simulation time scale when it is cooled into the regime below 1.02T_{g}. However, we find that the jump length and the jump rate do not display the non-equilibrium behaviors even in the glassy state below T_{g}, which allows us to study the intrinsic dynamic characteristics through T_{g}. The mean waiting time between two successive jumps has a rapid growth following the Vogel-Fulcher-Tammann law as the non-equilibrium regime is approached, in analogy with the temperature behaviors of transport properties for fragile supercooled liquids. In contrast, the jump rate maintains the Arrhenius decay and the jump length has even a weaker temperature dependence when the liquid is cooled into glassy state. We find that a pronounced enhancement of the spatial correlation of jumps occurs accompanied by the glass transition: the string-like cooperative jumps dominate the fast motion instead of the uncorrelated and individual jumps. Our work offers an insight into the equilibrium effect of the single-particle dynamics in glass transition.

The fractal correlation between relaxation dynamics and atomic-level structures observed in metallic glasses by computer simulation

Hierarchical clustering analysis shows that the activating atoms are excited in a cooperative and avalanche-like model to form activating units. Interestingly, a fractal correlation is found between the number and size of the activating units.

Understanding Atomic-Scale Features of Low Temperature-Relaxation Dynamics in Metallic Glasses

Being a key feature of a glassy state, low temperature relaxation has important implications on the mechanical behavior of glasses; however, the mechanism of low temperature relaxation is still an open issue, which has been debated for decades. By systematically investigating the influences of cooling rate and pressure on low temperature relaxation in the Zr₅₀Cu₅₀ metallic glasses, it is found that even though pressure does induce pronounced local structural change, the low temperature-relaxation behavior of the metallic glass is affected mainly by cooling rate, not by pressure. According to the atomic displacement and connection mode analysis, we further demonstrate that the low temperature relaxation is dominated by the dispersion degree of fast dynamic atoms rather than the most probable atomic nonaffine displacement. Our finding provides the direct atomic-level evidence that the intrinsic heterogeneity is the key factor that determines the low temperature-relaxation behavior of the metallic glasses.

Direct visualization of free-volume-triggered activation of β relaxation in colloidal glass

β relaxation, which is predicted by mode coupling theory and involves the localized motions of particles, initiates in a supercooled liquid and continues into glassy state. It correlates essentially with many fundamental properties of amorphous materials. Despite its importance, the underlying mechanisms leading to the β relaxation have remained elusive. As natural heterogeneity, the original distributed free volume has been supposed to be associated with the activation of β relaxation in amorphous solids. However, there has been no direct experimental proof for this hypothesis. Here we used a colloidal glass to directly observe the β relaxation and free-volume distribution. We found a spatial correlation between the β relaxation and free volume. The large free volume regions were observed to possess a low-energy cost of relaxation-induced strain, indicating that the large free volume region presenting a low-energy barrier for structural relaxation benefits the β relaxation.

Local microstructure evolution at shear bands in metallic glasses with nanoscale phase separation

At room temperature, plastic flow of metallic glasses (MGs) is sharply localized in shear bands, which are a key feature of the plastic deformation in MGs. Despite their clear importance and decades of study, the conditions for formation of shear bands, their structural evolution and multiplication mechanism are still under debate. In this work, we investigate the local conditions at shear bands in new phase-separated bulk MGs containing glassy nanospheres and exhibiting exceptional plasticity under compression. It is found that the glassy nanospheres within the shear band dissolve through mechanical mixing driven by the sharp strain localization there, while those nearby in the matrix coarsen by Ostwald ripening due to the increased atomic mobility. The experimental evidence demonstrates that there exists an affected zone around the shear band. This zone may arise from low-strain plastic deformation in the matrix between the bands. These results suggest that measured property changes originate not only from the shear bands themselves, but also from the affected zones in the adjacent matrix. This work sheds light on direct visualization of deformation-related effects, in particular increased atomic mobility, in the region around shear bands.

Intrinsic correlation between β-relaxation and spatial heterogeneity in a metallic glass

β-relaxation has long been attributed to localized motion of constituent molecules or atoms confined to isolated regions in glasses. However, direct experimental evidence to support this spatially heterogeneous scenario is still missing. Here we report the evolution of nanoscale structural heterogeneity in a metallic glass during β-relaxation by utilizing amplitude-modulation dynamic atomic force microscopy. The successive degeneration of heterogeneity during β-relaxation can be well described by the Kohlrausch–Williams–Watts equation. The characteristic relaxation time and activation energy of the heterogeneity evolution are in accord with those of excess enthalpy release by β-relaxation. Our study correlates β-relaxation with nanoscale spatial heterogeneity and provides direct evidence on the structural origins of β-relaxation in metallic glasses.

Beta-relaxation in glasses is commonly attributed to the confined motions of constituent atoms in nanosized domains, but there is no direct evidence so far. Here, Zhu et al. show the correlation between the evolution of spatial heterogeneity at nanoscale and beta-relaxation below glass transition point.

Revealing β-relaxation mechanism based on energy distribution of flow units in metallic glass

The β-relaxation, which is the source of the dynamics in glass state and has practical significance to relaxation and mechanical properties of glasses, has been an open question for decades. Here, we propose a flow unit perspective to explain the structural origin and evolution of β-relaxation based on experimentally obtained energy distribution of flow units using stress relaxation method under isothermal and linear heating modes. Through the molecular dynamics simulations, we creatively design various artificial metallic glass systems and build a direct relation between β-relaxation behavior and features of flow units. Our results demonstrate that the β-relaxation in metallic glasses originates from flow units and is modulated by the energy distribution of flow units, and the density and distribution of flow units can effectively regulate the β-relaxation behavior. The results provide a better understanding of the structural origin of β-relaxation and also afford a method for designing metallic glasses with obvious β-relaxation and better mechanical properties.

Macroscopic tensile plasticity by scalarizating stress distribution in bulk metallic glass

The macroscopic tensile plasticity of bulk metallic glasses (BMGs) is highly desirable for various engineering applications. However, upon yielding, plastic deformation of BMGs is highly localized into narrow shear bands and then leads to the "work softening" behaviors and subsequently catastrophic fracture, which is the major obstacle for their structural applications. Here we report that macroscopic tensile plasticity in BMG can be obtained by designing surface pore distribution using laser surface texturing. The surface pore array by design creates a complex stress field compared to the uniaxial tensile stress field of conventional glassy specimens, and the stress field scalarization induces the unusual tensile plasticity. By systematically analyzing fracture behaviors and finite element simulation, we show that the stress field scalarization can resist the main shear band propagation and promote the formation of larger plastic zones near the pores, which undertake the homogeneous tensile plasticity. These results might give enlightenment for understanding the deformation mechanism and for further improvement of the mechanical performance of metallic glasses.

Suppression of β Relaxation in Vapor-Deposited Ultrastable Glasses

Glassy materials display numerous important properties which relate to the presence and intensity of the secondary (β) relaxations that dominate the dynamics below the glass transition temperature. However, experimental protocols such as annealing allow little control over the β relaxation for most glasses. Here we report on the β relaxation of toluene in highly stable glasses prepared by physical vapor deposition. At conditions that generate the highest kinetic stability, about 70% of the β relaxation intensity is suppressed, indicating the proximity of this state to the long-sought "ideal glass." While preparing such a state via deposition takes less than an hour, it would require ~3500 years of annealing an ordinary glass to obtain similarly suppressed dynamics.

Unusual fast secondary relaxation in metallic glass

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

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

Compositional origin of unusual β-relaxation properties in La-Ni-Al metallic glasses

The β-relaxation of metallic glasses (MGs) bears nontrivial connections to their microscopic and macroscopic properties. In an effort to elucidate the mechanism of the β-relaxation, we studied by dynamical mechanical measurements the change of its properties on varying the composition of La60Ni15Al25 in various ways. The properties of the β-relaxation turn out to be very sensitive to the composition. It is found that the isochronal loss peak temperature of β-relaxation, Tβ,peak, is effectively determined by the total (La + Ni) content. When Cu is added into the alloy to replace either La, Ni, or Al, the Tβ,peak increases with decrease of the (La + Ni) content. The trend is in accordance with data of binary and ternary MGs formed from La, Ni, Al, and Cu. Binary La-Ni MGs have pronounced β-relaxation loss peaks, well separated from the α-relaxation. In contrast, the β-relaxation is not resolved in La-Al and La-Cu MGs, showing up as an excess wing. For the ternary La-Ni-Al MGs, increase of La or Ni content is crucial to lower the Tβ,peak. Keeping the Al content fixed, increase of La content lowers the Tβ,peak further, indicating the more important role La plays in lowering Tβ,peak than Ni. The observed effects on changing the composition of La60Ni15Al25 lead to the conclusion that the properties of the β-relaxation are mainly determined by the interaction between the largest solvent element, La, and the smallest element, Ni. From our data, it is further deduced that La and Ni have high mobility in the MGs, and this explains why the β-relaxation in this La-based MGs is prominent and well resolved from the α-relaxation as opposed to Pd- and Zr-based MGs where the solvent and largest atoms, Pd and Zr, are the least mobile.

The β-relaxation in metallic glasses

Focusing on metallic glasses as model systems, we review the features and mechanisms of the β-relaxations, which are intrinsic and universal to supercooled liquids and glasses, and demonstrate their importance in understanding many crucial unresolved issues in glassy physics and materials science, including glass transition phenomena, mechanical properties, shear-banding dynamics and deformation mechanisms, diffusion and the breakdown of the Stokes–Einstein relation as well as crystallization and stability of glasses. We illustrate that it is an attractive prospect to incorporate these insights into the design of new glassy materials with extraordinary properties. We also outline important questions regarding the nature of β-relaxations and highlight some emerging research directions in this still-evolving field.

Flow unit perspective on room temperature homogeneous plastic deformation in metallic glasses

A mandrel winding method, which can realize remarkable homogeneous plastic deformation at room temperature for various metallic glasses, is applied to characterize plastic flow units and study their relationship with macroscopic deformations and relaxations. The method can provide information on the activation energy, activation time, size, intrinsic relaxation time, distribution, and density of flow units. We find the plasticity of a metallic glass can be controlled through modulating the features of flow units. The results have benefits for better understanding the structural origins of deformations and relaxations, and for designing metallic glasses with improved performances.

Characteristics of the structural and Johari-Goldstein relaxations in Pd-based metallic glass-forming liquids

The dynamics of Pd-based metallic glass-forming liquids (Pd(40)Ni(10)Cu(30)P(20), Pd(42.5)Ni(7.5)Cu(30)P(20), Pd(40)Ni(40)P(20), and Pd(30)Ni(50)P(20)) was studied by mechanical spectroscopy and modulated differential scanning calorimetry (MDSC). We found that the change in composition has a significant effect on the α relaxation dynamics; the largest difference corresponds to an increase of the glass transition temperature Tg of ∼ 15 K, for materials in which 30% Ni was substituted by 30% Cu (i.e., from Pd(40)Ni(40)P(20) to Pd(40)Ni(10)Cu(30)P(20)). We also found that all Pd-based metallic glasses have very similar fragilities, 59 < m < 67, and Kohlrausch stretched exponents, 0.59 < βKWW < 0.60. It is interesting that the values of m and βKWW correlate well with the general relation proposed by Böhmer et al. for nonmetallic glass formers (Böhmer, R.; et al. J. Chem. Phys. 1993, 99, 4201-4209), which for the observed βKWW values predicts 58 < m < 61. From a linear deconvolution of the α and β relaxations, we find that the substitution of the Ni with Cu induced a large change in the time constant of the Johari-Goldstein relaxation, τβ. The activation energy, Uβ, of the β relaxation was largely independent of chemical composition. In all cases, 25 < Uβ/RT < 28, a range in agreement with results for other glass formers (Kudlik, A.; et al. Europhys. Lett. 1997, 40, 649-654 and Ngai, K. L.; et al. Phys. Rev. E 2004, 69, 031501). From the heat capacity and mechanical loss, estimates were obtained for the number of dynamically correlated units, Nc; we find significantly larger values for these metallic glass-forming liquids than Nc for other glass-forming materials.