Dynamic arrest in multicomponent glass-forming alloys

Designing Advanced Amorphous/Nanocrystalline Alloys by Controlling the Energy State

Amorphous alloys, also known as metallic glasses, exhibit many advanced mechanical, physical, and chemical properties. Owing to the nonequilibrium nature, their energy states can vary over a wide range. However, the energy relaxation kinetics are very complex and composed of various types that are coupled with each other. This makes it challenging to control the energy state precisely and to study the energy-properties relationship. This brief review introduces the recent progresses on studying the enthalpy relaxation kinetics during isothermal annealing, for example, the observation of two-step relaxation phenomenon, the detection of relaxation unit (relaxun), the key role of large activation entropy in triggering memory effect, the influence of glass energy state on nanocrystallization. Based on the above knowledge, a new strategy is proposed to design a series of amorphous alloys and their composites consisting of nanocrystals and glass matrix with superior functional properties by precisely controlling the nonequilibrium energy states. As the typical examples, Fe-based amorphous alloys with both advanced soft magnetism and good plasticity, Gd-based amorphous/nanocrystalline composites with large magnetocaloric effect, and Fe-based amorphous alloys with high catalytic performance are specifically described.

Local vs. cooperative: Unraveling glass transition mechanisms with SEER

Which phenomenon slows down the dynamics in supercooled liquids and turns them into glasses is a long-standing question of condensed matter. Most popular theories posit that as the temperature decreases, many events must occur in a coordinated fashion on a growing length scale for relaxation to occur. Instead, other approaches consider that local barriers associated with the elementary rearrangement of a few particles or "excitations" govern the dynamics. To resolve this conundrum, our central result is to introduce an algorithm, Systematic Excitation ExtRaction, which can systematically extract hundreds of excitations and their energy from any given configuration. We also provide a measurement of the activation energy, characterizing the liquid dynamics, based on fast quenching and reheating. We use these two methods in a popular liquid model of polydisperse particles. Such polydisperse models are known to capture the hallmarks of the glass transition and can be equilibrated efficiently up to millisecond time scales. The analysis reveals that cooperative effects do not control the fragility of such liquids: the change of energy of local barriers determines the change of activation energy. More generally, these methods can now be used to measure the degree of cooperativity of any liquid model.

Size-dependent deformation behavior in nanosized amorphous metals suggesting transition from collective to individual atomic transport

The underlying atomistic mechanism of deformation is a central problem in mechanics and materials science. Whereas deformation of crystalline metals is fundamentally understood, the understanding of deformation of amorphous metals lacks behind, particularly identifying the involved temporal and spatial scales. Here, we reveal that at small scales the size-dependent deformation behavior of amorphous metals significantly deviates from homogeneous flow, exhibiting increasing deformation rate with reducing size and gradually shifted composition. This transition suggests the deformation mechanism changes from collective atomic transport by viscous flow to individual atomic transport through interface diffusion. The critical length scale of the transition is temperature dependent, exhibiting a maximum at the glass transition. While viscous flow does not discriminate among alloy constituents, diffusion does and the constituent element with higher diffusivity deforms faster. Our findings yield insights into nano-mechanics and glass physics and may suggest alternative processing methods to epitaxially grow metallic glasses.

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.

Impact of host phonons on interstitial diffusion

The net effect of host phonons on interstitial diffusion has remained as a fundamental knowledge gap in our current theories since the motions of the host atoms and interstitials were coupled in these theories. Here we study this effect through molecular dynamics simulations of hydrogen diffusion in palladium, in which the motions can be decoupled through pinning the host atoms. Mathematically this decoupling corresponds to expanding the total diffusion coefficient into a Taylor series, which separates the phonon contribution from the intrinsic interstitial jumping. Our results clearly show that palladium phonons significantly promote hydrogen diffusion. The phonon contribution, being linear with temperature at high temperatures and exponential at low temperatures, is fitted with Brownian motion model. The total diffusion of interstitials can be understood as the intrinsic interstitial jumping in a pinned host plus phonon-induced Brownian diffusion. The generality of our findings is validated by examining the motion of lithium in manganese oxide and carbon in iron.

The Interplay between the Theories of Mode Coupling and of Percolation Transition in Attractive Colloidal Systems

In the recent years a considerable effort has been devoted to foster the understanding of the basic mechanisms underlying the dynamical arrest that is involved in glass forming in supercooled liquids and in the sol-gel transition. The elucidation of the nature of such processes represents one of the most challenging unsolved problems in the field of material science. In this context, two important theories have contributed significantly to the interpretation of these phenomena: the Mode-Coupling theory (MCT) and the Percolation theory (PT). These theories are rooted on the two pillars of statistical physics, universality and scale laws, and their original formulations have been subsequently modified to account for the fundamental concepts of Energy Landscape (EL) and of the universality of the fragile to strong dynamical crossover (FSC). In this review, we discuss experimental and theoretical results, including Molecular Dynamics (MD) simulations, reported in the literature for colloidal and polymer systems displaying both glass and sol-gel transitions. Special focus is dedicated to the analysis of the interferences between these transitions and on the possible interplay between MCT and PT. By reviewing recent theoretical developments, we show that such interplay between sol-gel and glass transitions may be interpreted in terms of the extended F13 MCT model that describes these processes based on the presence of a glass-glass transition line terminating in an A3 cusp-like singularity (near which the logarithmic decay of the density correlator is observed). This transition line originates from the presence of two different amorphous structures, one generated by the inter-particle attraction and the other by the pure repulsion characteristic of hard spheres. We show here, combining literature results with some new results, that such a situation can be generated, and therefore experimentally studied, by considering colloidal-like particles interacting via a hard core plus an attractive square well potential. In the final part of this review, scaling laws associated both to MCT and PT are applied to describe, by means of these two theories, the specific viscoelastic properties of some systems.

Surface Diffusion Is Controlled by Bulk Fragility across All Glass Types

Surface diffusion is vastly faster than bulk diffusion in some glasses, but only moderately enhanced in others. We show that this variation is closely linked to bulk fragility, a common measure of how quickly dynamics is excited when a glass is heated to become a liquid. In fragile molecular glasses, surface diffusion can be a factor of 10^{8} faster than bulk diffusion at the glass transition temperature, while in the strong system SiO_{2}, the enhancement is a factor of 10. Between these two extremes lie systems of intermediate fragility, including metallic glasses and amorphous selenium and silicon. This indicates that stronger liquids have greater resistance to dynamic excitation from bulk to surface and enables prediction of surface diffusion, surface crystallization, and formation of stable glasses by vapor deposition.

Isomorphs in nanoconfined liquids

We study in this paper the possible existence of Roskilde-simple liquids and their isomorphs in a rough-wall nanoconfinement. Isomorphs are curves in the thermodynamic phase diagram along which structure and dynamics are invariant in suitable nondimensionalized units. Two model liquids using molecular dynamics computer simulations are considered: the single-component Lennard-Jones (LJ) liquid and the Kob-Andersen binary LJ mixture, both of which in the bulk phases are known to have good isomorphs. Nanoconfinement is implemented by adopting a slit-pore geometry with fcc crystalline walls; this implies inhomogenous density profiles both parallel and perpendicular to the confining walls. Despite this fact and consistent with an earlier study [Ingebrigtsen et al., Phys. Rev. Lett., 2013, 111, 235901] we find that these two nanoconfined liquids have isomorphs to a good approximation. More specifically, we show good invariance along the isomorphs of inhomogenous density profiles, mean-square displacements, and higher-order structures probed using the topological cluster classification algorithm. Our study thus provides an alternative framework for understanding nanoconfined liquids.

Ni self-diffusion in glass forming Pd-Ni-S melts

The Ni self-diffusion in glass forming Pd₄₀Ni₄₀S₂₀, Pd₃₇Ni₃₇S₂₆and Pd₃₁Ni₄₂S₂₇melts was probed by incoherent, quasielastic neutron scattering over a temperature range between 773 and 1023 K. The Ni self-diffusion coefficients are on a 10^-10 m² s^-1-10^-9 m² s^-1scale and barely change with composition. Each composition exhibits an Arrhenius-type temperature dependence of the Ni self-diffusion coefficients, which results in activation energies ranging fromE_A= 348 ± 16 meV for Pd₄₀Ni₄₀S₂₀toE_A= 387 ± 6 meV for Pd₃₇Ni₃₇S₂₆. The structural relaxation shows a stretched exponential behavior even far above the liquidus temperatures. In addition, the viscosity of the Pd₃₇Ni₃₇S₂₆melt was measured under reduced gravity conditions. The diffusion calculated from the viscosity reveals a significant deviation from the measured Ni self-diffusion by a factor between 4 and 8. This may indicate a dynamic decoupling between the atoms within the Pd-Ni-S equilibrium melts.

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.

Self-Diffusion in Liquid Copper, Silver, and Gold

The recently developed by us semi-analytical representation of the mean spherical approximation in conjunction with the linear trajectory approximation is applied to the quantitative study of self-diffusivities in liquid Cu, Ag and Au at different temperatures. The square-well model is employed for the description of the interatomic pair interactions in metals under study. It is found that our theoretical results are in good agreement with available experimental and computer-simulation data and can be considered as a prediction when such data are absent.

Deformation-Induced Chemical Inhomogeneity and Short-Circuit Diffusion in Shear Bands of a Bulk Metallic Glass

The compositional changes in shear bands of a Cu_{50}Zr_{50} metallic glass after plastic deformation at room temperature have been monitored by atom probe tomography. Across the width of the shear bands an asymmetry of the enriched and depleted zones of the constituent elements is observed, while no change of the composition within the surrounding matrix occurs. The diffusion coefficients determined from the concentration profiles are orders of magnitude larger than the values of bulk diffusion at room temperature. The asymmetric concentration profiles of the constituent elements (Cu and Zr) remain stable during annealing at a temperature of 543 K, even though fast and preferential diffusion of a Ni tracer has been found along the shear band at the same temperature. The results indicate that the atomic structure and stress distribution within the shear bands is altered from that of the surrounding amorphous matrix. The fact that the shear band structure is unaltered at elevated temperatures and that fast diffusion occurs preferentially within the shear bands leads to the conclusion that they are structurally stable.

Excess-entropy scaling in supercooled binary mixtures

Transport coefficients, such as viscosity or diffusion coefficient, show significant dependence on density or temperature near the glass transition. Although several theories have been proposed for explaining this dynamical slowdown, the origin remains to date elusive. We apply here an excess-entropy scaling strategy using molecular dynamics computer simulations and find a quasiuniversal, almost composition-independent, relation for binary mixtures, extending eight orders of magnitude in viscosity or diffusion coefficient. Metallic alloys are also well captured by this relation. The excess-entropy scaling predicts a quasiuniversal breakdown of the Stokes-Einstein relation between viscosity and diffusion coefficient in the supercooled regime. Additionally, we find evidence that quasiuniversality extends beyond binary mixtures, and that the origin is difficult to explain using existing arguments for single-component quasiuniversality.

Vitrification decoupling from α-relaxation in a metallic glass

Understanding how glasses form, the so-called vitrification, remains a major challenge in materials science. Here, we study vitrification kinetics, in terms of the limiting fictive temperature, and atomic mobility related to the α-relaxation of an Au-based bulk metallic glass former by fast scanning calorimetry. We show that the time scale of the α-relaxation exhibits super-Arrhenius temperature dependence typical of fragile liquids. In contrast, vitrification kinetics displays milder temperature dependence at moderate undercooling, and thereby, vitrification takes place at temperatures lower than those associated to the α-relaxation. This finding challenges the paradigmatic view based on a one-to-one correlation between vitrification, leading to the glass transition, and the α-relaxation. We provide arguments that at moderate to deep undercooling, other atomic motions, which are not involved in the α-relaxation and that originate from the heterogeneous dynamics in metallic glasses, contribute to vitrification. Implications from the viewpoint of glasses fundamental properties are discussed.

Strain perceptibility of elements on the diffusion in Zr-based amorphous alloys

With the discovery of bulk metallic glasses (BMGs), there has been considerable interest in understanding their mechanical behavior. In spite of these previous observations on the relation between plastic deformation of metallic glasses and their diffusion behavior, a detailed understanding on the diffusion of BMGs is still unexplored. We evaluated the contribution of deformation-induced structural transformations (elastic, anelastic, viscoplastic or viscoelastic responsive and plastic strain) on the diffusion of Zr-based bulk metallic glasses in as-cast, elastostatically stressed and plastically deformed states. Experimental investigations of the diffusion process and the elemental distributions in the glassy alloy were performed following plastic deformation by multiple cold rolling and elastostatic cyclic compression, respectively. We compared the vacancy model and the transition state model to verify the diffusion mechanism in the deformed bulk metallic glass. The diffusion of tracer atoms, i.e., Fe, in the bulk metallic glass is affected by viscoelastic responsive strain governing the transition-state model. In contrast, the diffusion of constituent atoms, i.e., Ti, Zr, in the bulk metallic glass is dominantly affected by plastic strain governing the vacancy model. The results reveal that the diffusion behavior of bulk glassy alloys can be changed by variation of the constituent elements and applying different strain modes upon deformation.

Revisiting the Stokes-Einstein relation for glass-forming melts

Molecular dynamics simulations of Ni36Zr64, Cu65Zr35 and Ni80Al20 were carried out over a broad range of temperature (900-3000 K) to investigate the Stokes-Einstein (SE) relation for glass-forming melts. Our results reproduce experimental structural and transport properties. Results show that the breakdown temperature of the SE relation (TSE) equals the dynamical crossover temperature (TA) and both are roughly twice the glass-transition temperature (Tg) for the three glass-forming melts (TSE = TA ≈ 2.0Tg). The product of the individual component self-diffusion coefficient and viscosity Dαη can be roughly regarded as a constant at the transition zone (a small temperature range around TSE) in which the temperature behaviors of self-diffusion coefficient and viscosity switch from high-temperature Arrhenius to a low-temperature VFT behavior. Below TSE, the decoupling of component diffusion coefficients was found. In particular, the decoupling of component diffusion coefficients can be ascribed to the decoupling of the partial pair structural correlation of components, which can be clearly reflected by the intersection of the high-temperature and low-temperature behaviors of the ratio between the partial pair correlation entropy of components (Sβ2/Sα2). Furthermore, the ratio between the partial pair correlation entropy of components may be used to predict the validity of the SE relation, in the absence of both transport coefficients and atomic coordinates.

Self- and interdiffusion in dilute liquid germanium-based alloys

Self- and inter-diffusion coefficients in liquid Ge and dilute Ge-based Ge-Si, Ge-Au, Ge-In, Ge-Ce and Ge-Gd alloys-containing 2 at% additions, respectively, are measured using a comprehensive approach of measuring techniques: quasi-elastic neutron scattering, in situ long-capillary experiments combined with x-ray radiography, and a long-capillary experiment under microgravity conditions. Resulting inter- and Ge self-diffusion coefficients are equal within error bars for each investigated alloy. The interdiffusion coefficients are smaller for the alloys containing Ce and Gd, However, no dependence of the atomic mass of the minor additions, that varies by about a factor of seven between Si and Au, on the diffusion coefficients could be observed. This demonstrates that in a loosely-packed metallic liquid with fast diffusive dynamics the diffusion mechanism is highly collective in nature.

Contrasting Bonding-Interaction-Induced Distinct Relaxation in La65Ni35 and La65Al35 Glass-Forming Alloys

The α and β relaxations are two fundamental processes in glass-forming materials, and quite important for many of the properties. Although intensive studies have found that α and β relaxations can be tuned by changing the constituent elements, the underlying structural basis is still elusive. Here, we explored the effect of two key elements of Al and Ni on distinct β and α relaxations in La₆₅Al₃₅ and La₆₅Ni₃₅ glass-forming alloys via classical and ab initio molecular dynamics simulations combined with dynamical mechanical spectroscopy. Unexpected coupling of relaxation in both β and α relaxation time scales is observed for La and Al atoms in the La₆₅Al₃₅ system, which drastically suppresses the relaxation dynamics. It is revealed that the dynamic coupling of La and Al results from the covalent-like bonding interaction between Al atoms, which connect Al together, forming a network-like structure. The bonding network not only drastically slows down the dynamics of Al but also couples the motion of La and Al together. This finding elucidates the underlying basis of Al and Ni elements for distinct β and α relaxation and sheds light on tuning the formation and properties of metallic glasses by minor alloying.

Breakdown of the Stokes-Einstein relation above the melting temperature in a liquid phase-change material

The dynamic properties of liquid phase-change materials (PCMs), such as viscosity η and the atomic self-diffusion coefficient D, play an essential role in the ultrafast phase switching behavior of novel nonvolatile phase-change memory applications. To connect η to D, the Stokes-Einstein relation (SER) is commonly assumed to be valid at high temperatures near or above the melting temperature T m and is often used for assessing liquid fragility (or crystal growth velocity) of technologically important PCMs. However, using quasi-elastic neutron scattering, we provide experimental evidence for a breakdown of the SER even at temperatures above T m in the high-atomic mobility state of a PCM, Ge1Sb2Te4. This implies that although viscosity may have strongly increased during cooling, diffusivity can remain high owing to early decoupling, being a favorable feature for the fast phase switching behavior of the high-fluidity PCM. We discuss the origin of the observation and propose the possible connection to a metal-semiconductor and fragile-strong transition hidden below T m.

Ultrastable metallic glasses formed on cold substrates

Vitrification from physical vapor deposition is known to be an efficient way for tuning the kinetic and thermodynamic stability of glasses and significantly improve their properties. There is a general consensus that preparing stable glasses requires the use of high substrate temperatures close to the glass transition one, T_g. Here, we challenge this empirical rule by showing the formation of Zr-based ultrastable metallic glasses (MGs) at room temperature, i.e., with a substrate temperature of only 0.43T_g. By carefully controlling the deposition rate, we can improve the stability of the obtained glasses to higher values. In contrast to conventional quenched glasses, the ultrastable MGs exhibit a large increase of T_g of ∼60 K, stronger resistance against crystallization, and more homogeneous structure with less order at longer distances. Our study circumvents the limitation of substrate temperature for developing ultrastable glasses, and provides deeper insight into glasses stability and their surface dynamics.

Producing ultrastable metallic glasses has always been associated with substrates heated close to the glass transition temperature. Here, the authors show that reducing the deposition rate of the metallic glass on a cold substrate produces ultrastable metallic glasses with remarkably improved stability.

Perspective on Structural Evolution and Relations with Thermophysical Properties of Metallic Liquids

The relationship between the structural evolution and properties of metallic liquids is a long-standing hot issue in condensed-matter physics and materials science. Here, recent progress is reviewed in several fundamental aspects of metallic liquids, including the methods to study their atomic structures, liquid-liquid transition, physical properties, fragility, and their correlations with local structures, together with potential applications of liquid metals at room temperature. Involved with more experimentally and theoretically advanced techniques, these studies provide more in-depth understanding of the structure-property relationship of metallic liquids and promote the design of new metallic materials with superior properties.

Structural origin of fractional Stokes-Einstein relation in glass-forming liquids

In many glass-forming liquids, fractional Stokes-Einstein relation (SER) is observed above the glass transition temperature. However, the origin of such phenomenon remains elusive. Using molecular dynamics simulations, we investigate the break- down of SER and the onset of fractional SER in a model of metallic glass-forming liquid. We find that SER breaks down when the size of the largest cluster consisting of trapped atoms starts to increase sharply at which the largest cluster spans half of the simulations box along one direction, and the fractional SER starts to follows when the largest cluster percolates the entire system and forms 3-dimentional network structures. Further analysis based on the percolation theory also confirms that percolation occurs at the onset of the fractional SER. Our results directly link the breakdown of the SER with structure inhomogeneity and onset of the fraction SER with percolation of largest clusters, thus provide a possible picture for the break- down of SER and onset of fractional SER in glass-forming liquids, which is is important for the understanding of the dynamic properties in glass-forming liquids.

Dynamics of highly polydisperse colloidal suspensions as a model system for bacterial cytoplasm

There are various kinds of macromolecules in bacterial cell cytoplasm. The size polydispersity of the macromolecules is so significant that the crystallization and the phase separation could be suppressed, thus stabilizing the liquid state of bacterial cytoplasm. On the other hand, recent experiments suggested that the macromolecules in bacterial cytoplasm should exhibit glassy dynamics, which should be also affected significantly by the size polydispersity of the macromolecules. In this work, we investigate the anomalous and slow dynamics of highly polydisperse colloidal suspensions, of which size distribution is chosen to mimic Escherichia coli cytoplasm. We find from our Langevin dynamics simulations that the diffusion coefficient (D_{tot}) and the displacement distribution functions (P(r,t)) averaged over all colloids of different sizes do not show anomalous and glassy dynamic behaviors until the system volume fraction ϕ is increased up to 0.82. This indicates that the intrinsic polydispersity of bacterial cytoplasm should suppress the glass transition and help maintain the liquid state of the cytoplasm. On the other hand, colloids of each kind show totally different dynamic behaviors depending on their size. The dynamics of colloids of different size becomes non-Gaussian at a different range of ϕ, which suggests that a multistep glass transition should occur. The largest colloids undergo the glass transition at ϕ=0.65, while the glass transition does not occur for smaller colloids in our simulations even at the highest value of ϕ. We also investigate the distribution (P(θ,t)) of the relative angles of displacement for macromolecules and find that macromolecules undergo directionally correlated motions in a sufficiently dense system.

Sucrose diffusion in aqueous solution

The diffusion of sugar in aqueous solution is important both in nature and in technological applications, yet measurements of diffusion coefficients at low water content are scarce. We report directly measured sucrose diffusion coefficients in aqueous solution. Our technique utilises a Raman isotope tracer method to monitor the diffusion of non-deuterated and deuterated sucrose across a boundary between the two aqueous solutions. At a water activity of 0.4 (equivalent to 90 wt% sucrose) at room temperature, the diffusion coefficient of sucrose was determined to be approximately four orders of magnitude smaller than that of water in the same material. Using literature viscosity data, we show that, although inappropriate for the prediction of water diffusion, the Stokes-Einstein equation works well for predicting sucrose diffusion under the conditions studied. As well as providing information of importance to the fundamental understanding of diffusion in binary solutions, these data have technological, pharmaceutical and medical implications, for example in cryopreservation. Moreover, in the atmosphere, slow organic diffusion may have important implications for aerosol growth, chemistry and evaporation, where processes may be limited by the inability of a molecule to diffuse between the bulk and the surface of a particle.

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.

Heterogeneous diffusion, viscosity, and the Stokes-Einstein relation in binary liquids

We investigate the origin of the breakdown of the Stokes-Einstein relation (SER) between diffusivity and viscosity in undercooled melts. A binary Lennard-Jones system, as a model for a metallic melt, is studied by molecular dynamics. A weak breakdown at high temperatures can be understood from the collectivization of motion, seen in the isotope effect. The strong breakdown at lower temperatures is connected to an increase in dynamic heterogeneity. On relevant time scales some particles diffuse much faster than the average or than predicted by the SER. The van Hove self-correlation function allows one to unambiguously identify slow particles. Their diffusivity is even less than predicted by the SER. The time span of these particles being slow particles, before their first conversion to be a fast one, is larger than the decay time of the stress correlation. The contribution of the slow particles to the viscosity rises rapidly upon cooling. Not only the diffusion but also the viscosity shows a dynamically heterogeneous scenario. We can define a "slow" viscosity. The SER is recovered as the relation between slow diffusivity and slow viscosity.

X-Ray Photon Correlation Spectroscopy Reveals Intermittent Aging Dynamics in a Metallic Glass

We use coherent x rays to probe the aging dynamics of a metallic glass directly on the atomic level. Contrary to the common assumption of a steady slowing down of the dynamics usually observed in macroscopic studies, we show that the structural relaxation processes underlying aging in this metallic glass are intermittent and highly heterogeneous at the atomic scale. Moreover, physical aging is triggered by cooperative atomic rearrangements, driven by the relaxation of internal stresses. The rich diversity of this behavior reflects a complex energy landscape, giving rise to a unique type of glassy-state dynamics.

Communication: Non-monotonic evolution of dynamical heterogeneity in unfreezing process of metallic glasses

The relaxation dynamics in unfreezing process of metallic glasses is investigated by the activation-relaxation technique. A non-monotonic dynamical microstructural heterogeneities evolution with temperature is discovered, which confirms and supplies more features to flow units concept of glasses. A flow unit perspective is proposed to microscopically describe this non-monotonic evolution of the dynamical heterogeneities as well as its relationship with the deformation mode development of metallic glasses.

Evidence of liquid-liquid transition in glass-forming La50Al35Ni15 melt above liquidus temperature

Liquid-liquid transition, a phase transition of one liquid phase to another with the same composition, provides a key opportunity for investigating the relationship between liquid structures and dynamics. Here we report experimental evidences of a liquid-liquid transition in glass-forming La50Al35Ni15 melt above its liquidus temperature by (27)Al nuclear magnetic resonance including the temperature dependence of cage volume fluctuations and atomic diffusion. The observed dependence of the incubation time on the degree of undercooling is consistent with a first-order phase transition. Simulation results indicate that such transition is accompanied by the change of bond-orientational order without noticeable change in density. The temperature dependence of atomic diffusion revealed by simulations is also in agreement with experiments. These observations indicate the need of two-order parameters in describing phase transitions of liquids.

Dynamic decoupling and local atomic order of a model multicomponent metallic glass-former

The dynamics of multicomponent metallic alloys is spatially heterogeneous near glass transition. The diffusion coefficient of one component of the metallic alloys may also decouple from those of other components, i.e., the diffusion coefficient of each component depends differently on the viscosity of metallic alloys. In this work we investigate the dynamic heterogeneity and decoupling of a model system for multicomponent Pd43Cu27Ni10P20 melts by using a hard sphere model that considers the size disparity of alloys but does not take chemical effects into account. We also study how such dynamic behaviors would relate to the local atomic structure of metallic alloys. We find, from molecular dynamics simulations, that the smallest component P of multicomponent Pd43Cu27Ni10P20 melts becomes dynamically heterogeneous at a translational relaxation time scale and that the largest major component Pd forms a slow subsystem, which has been considered mainly responsible for the stabilization of amorphous state of alloys. The heterogeneous dynamics of P atoms accounts for the breakdown of Stokes-Einstein relation and also leads to the dynamic decoupling of P and Pd atoms. The dynamically heterogeneous P atoms decrease the lifetime of the local short-range atomic orders of both icosahedral and close-packed structures by orders of magnitude.

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.

Decoupling of component diffusion in a glass-forming Zr(46.75)Ti(8.25)Cu(7.5)Ni(10)Be(27.5) melt far above the liquidus temperature

We report (95)Zr and (57)Co radiotracer diffusivities and viscosity data in the equilibrium liquid state of a bulk metallic glass forming Zr(46.75)Ti(8.25)Cu(7.5)Ni(10)Be(27.5) melt (Vitreloy 4) far above the liquidus temperature T(l) that are not affected by convection, as evidenced via quasielastic neutron scattering. Zr diffusion is strongly decoupled from diffusion of the smaller components by more than a factor of 4 at T(l), although it obeys the Stokes-Einstein equation. The results suggest that, in the present Zr-based metallic glass forming systems, diffusion and viscous flow start to develop solidlike, i.e., energy-landscape-controlled, features already in the stable liquid state more than 300 K above the mode coupling temperature T(c).

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.

Microrheology of colloidal systems

Microrheology was proposed almost twenty years ago as a technique to obtain rheological properties in soft matter from the microscopic motion of colloidal tracers used as probes, either freely diffusing in the host medium, or subjected to external forces. The former case is known as passive microrheology, and is based on generalizations of the Stokes-Einstein relation between the friction experienced by the probe and the host-fluid viscosity. The latter is termed active microrheology, and extends the measurement of the friction coefficient to the nonlinear-response regime of strongly driven probes. In this review article, we discuss theoretical models available in the literature for both passive and active microrheology, focusing on the case of single-probe motion in model colloidal host media. A brief overview of the theory of passive microrheology is given, starting from the work of Mason and Weitz. Further developments include refined models of the host suspension beyond that of a Newtonian-fluid continuum, and the investigation of probe-size effects. Active microrheology is described starting from microscopic equations of motion for the whole system including both the host-fluid particles and the tracer; the many-body Smoluchowski equation for the case of colloidal suspensions. At low fluid densities, this can be simplified to a two-particle equation that allows the calculation of the friction coefficient with the input of the density distribution around the tracer, as shown by Brady and coworkers. The results need to be upscaled to agree with simulations at moderate density, in both the case of pulling the tracer with a constant force or dragging it at a constant velocity. The full many-particle equation has been tackled by Fuchs and coworkers, using a mode-coupling approximation and the scheme of integration through transients, valid at high densities. A localization transition is predicted for a probe embedded in a glass-forming host suspension. The nonlinear probe-friction coefficient is calculated from the tracer's position correlation function. Computer simulations show qualitative agreement with the theory, but also some unexpected features, such as superdiffusive motion of the probe related to the breaking of nearest-neighbor cages. We conclude with some perspectives and future directions of theoretical models of microrheology.

Relaxation processes in liquids: variations on a theme by Stokes and Einstein

We investigate numerically the temperature and density dependence of the Stokes-Einstein ratio, Dη∕T, and of two commonly-used variants thereof, Dτ and Dτ∕T, where D is a diffusivity, η the shear viscosity, and τ a structural relaxation time. We consider a family of atomic binary mixtures with systematically-softened repulsive interactions, and the Lewis-Wahnström model of ortho-terphenyl (OTP). The three quantities grow significantly as the temperature decreases in the supercooled regime, a well-known phenomenon. At higher temperatures, Dτ exhibits negative violations of Stokes-Einstein behavior, i.e., decrease upon cooling, for the atomic systems, though not for OTP. We consider two choices for the relaxation time, one based on the decay of the self-intermediate scattering function, and the other on the integral of the stress autocorrelation function. The instantaneous shear modulus exhibits appreciable temperature dependence for the two classes of systems investigated here. Our results suggest that commonly-invoked assumptions, such as τ ∼ η and τ ∼ η∕T, should be critically evaluated across a wide spectrum of systems and thermodynamic conditions. We find the Stokes-Einstein ratio, Dη∕T, to be constant across a broad range of temperatures and densities for the two classes of systems investigated here.

An explanation of the differences in diffusivity of the components of the metallic glass Pd43Cu27Ni10P20

Bartsch et al. [Phys. Rev. Lett. 104, 195901 (2010)] reported measurements of the diffusivities of different components of the multi-component bulk metallic glass Pd43Cu27Ni10P20. The diffusion of the largest Pd and the smallest P was found to be drastically different. The Stokes-Einstein relation breaks down when considering the P constituent atom, while the relation is obeyed by the Pd atom over 14 orders of magnitude of change in Pd diffusivity. This difference in behavior of Pd and P poses a problem challenging for explanation. With the assist of a recent finding in metallic glasses that the β-relaxation and the diffusion of the smallest component are closely related processes by Yu et al. [Phys. Rev. Lett. 109, 095508 (2012)], we use the Coupling Model to explain the observed difference between P and Pd quantitatively. The same model also explains the correlation between property of the β-relaxation with fragility found in the family of (CexLa1-x)68Al10Cu20Co2 with 0 ≤ x ≤ 1.

Correlation between β relaxation and self-diffusion of the smallest constituting atoms in metallic glasses

In multicomponent metallic glasses, we demonstrate that diffusion and secondary (β) relaxation are closely related. The diffusion motion of the smallest constituting atoms takes place within the temperature and time regimes where the β relaxations are activated, and, in particular, the two processes have similar activation energies. We suggest cooperative stringlike atomic motion plays an important role in both processes. This finding provides additional insights into the structural origin of the β relaxations as well as the mechanisms of diffusions in metallic glasses.

Tracer measurements of atomic diffusion inside shear bands of a bulk metallic glass

Atomic diffusion in deformed Pd(40)Ni(40)P(20) bulk metallic glass containing a single family of deformation-induced shear bands was measured by the radiotracer technique. The significant, by orders of magnitude, enhancement of the diffusion rate with respect to that in the untransformed matrix suggests that the shear bands represent short-circuit diffusion paths. Correlations between diffusivity, viscosity, and the excess free volume distribution inside of shear bands are discussed.

Relation between self-diffusion and viscosity in dense liquids: new experimental results from electrostatic levitation

By using the technique of electrostatic levitation, the Ni self-diffusion, density, and viscosity of liquid Zr(64)Ni(36) have been measured in situ with high precision and accuracy. The inverse of the viscosity, η, measured via the oscillating drop technique, and the self-diffusion coefficient D, obtained from quasielastic neutron scattering experiments, exhibit the same temperature dependence over 1.5 orders of magnitude and in a broad temperature range spanning more than 800 K. It was found that Dη=const for the entire temperature range, contradicting the Stokes-Einstein relation.

The role of the dynamic crossover temperature and the arrest in glass-forming fluids

We discuss the role of the dynamic glass-forming fragile-to-strong crossover (FSC) in supercooled liquids. In the FSC, significant dynamic changes such as the decoupling (the violation of the Stokes-Einstein relation) of homologous transport parameters, e.g., the density relaxation time τ and the viscosity η, occur at a characteristic temperature T(c). We study the FSC using a scaling law approach. In particular, we use both forms of the mode-coupling theory (MCT): the original (ideal) and the extended form, which explicitly describes energy hopping processes. We demonstrate that T(c) plays the most important physical role in understanding dynamic arrest processes.

Glassy relaxation and excess wing in mode-coupling theory: the dynamic susceptibility of propylene carbonate above and below T(c)

We explore the possibility of describing experimental susceptibility spectra of the glass former propylene carbonate with a two-component schematic model of mode-coupling theory (MCT) from above the melting point down to temperatures far below the critical temperature of MCT. By introducing a phenomenological time-dependent hopping rate, the spectra are reproduced in the full frequency and temperature range available. Literature data of dielectric susceptibilities and depolarized Brillouin light-scattering spectra are combined with our measurements of photon correlation spectroscopy to cover up to 18 decades in frequency of spectra for two different dynamical variables. A consistent description of all data sets is obtained by adjusting only a few physically motivated parameters. In particular the excess wing or slow β-relaxation commonly observed in the susceptibility spectra can consistently be modeled as originating from a coupling of the individual experimental probe correlator to the collective density fluctuations.