Structural Relaxation In Metallic Glasses Research Articles

Stress-annealing induced quasistatic creep recovery in ZrCuAlNi metallic glass

The relationship between the structural relaxation of metallic glasses and their heterogeneous structure, characterized by a weakly bonded region and a strongly bonded region, remains ambiguous. Thus, our study aimed to explore the connection between the heterogeneous structure and structural relaxation by investigating the quasi-elastic and viscoelastic behavior of a Zr55Cu30Ni5Al10 metallic glass. Stress-annealing (SA) treatment was employed to retain elastic strain energy by subjecting the sample to constant stress and temperature. During the reheating of the SA-treated sample, we observed a unique shrinkage and elongation phenomenon in the glassy-solid region, known as creep recovery (CR). To qualitatively describe the mechanisms of elastic strain energy retention and release, we employed the Maxwell model, which accounts for the heterogeneous structure. The residual elastic strain energy was determined by the discrepancy in relaxation ability within the heterogeneous structure, and the shrinkage and elongation of the CR were associated with structural relaxation.

Uncovering metallic glasses hidden vacancy-like motifs using machine learning

Vacancies are a ubiquitous type of defect in crystalline materials that can affect their properties and behavior, including atomic diffusivity, deformation processes, thermal conductivity, and electrical conductivity. While well-defined in crystals, it is challenging to identify such topological footprints in the amorphous structure of metallic glasses (MGs). Here, we uncover an unforeseen vacancy-like structural motif named Q7, which refers to an atomic Voronoi polyhedron with seven quadrangular faces, by investigating MG local atomic configurations with the help of machine learning. The Q7 motif exhibits characteristics similar to crystalline vacancies and plays a significant role in short-range structural disorder in MGs. The atoms at the center of the Q7 motif display larger local entropy, atomic volume, and local tension. Additionally, its concentration follows an Arrhenius-like relationship with temperature, accurately indicating the glass transition temperature, and is strongly correlated with the yield and failure of MGs during mechanical deformation. The discovery of the Q7 motif provides new insights into understanding the intricate relationship between local disorder and structural relaxation in MGs, offering a remarkable ability to predict their thermal and mechanical behavior. This potentially paves the way for enhancements in the design and manufacturing processes of MGs and other amorphous materials.

Thermodynamic approach for the understanding of the kinetics of heat effects induced by structural relaxation of metallic glasses

We present a novel approach to the understanding of heat effects induced by structural relaxation of metallic glasses. The key idea consists in the application of a general thermodynamic equation for the entropy change due to the evolution of a non-equilibrium part of a complex system. This non-equilibrium part is considered as a defect subsystem of glass and its evolution is governed by local thermoactivated rearrangements with a Gibbs free energy barrier proportional to the high-frequency shear modulus. The only assumption on the nature of the defects is that they should provide a reduction of the shear modulus—a diaelastic effect. This approach allows to determine glass entropy change upon relaxation. On this basis, the kinetics of the heat effects controlled by defect-induced structural relaxation is calculated. A very good agreement between the calculation and specially performed calorimetric and shear modulus measurements on three metallic glasses is found.

One-to-one correlation between the kinetics of the enthalpy changes and the number of defects assumed responsible for structural relaxation in metallic glasses

Parallel measurements of the enthalpy and high-frequency shear modulus changes occurring upon structural relaxation of five bulk metallic glasses are performed. An analysis showed that there exists a one-to-one correlation between the change of the molar enthalpy and the alteration of the number of defects calculated within the framework of the Interstitialcy theory on the basis of shear modulus relaxation data. The defect formation enthalpy derived using this correlation agrees quite well with this quantity accepted in the Interstitialcy theory.

Nonmonotonous atomic motions in metallic glasses

Peculiar temporal intermittent microscopic dynamics has been recently reported during structural relaxation in metallic glasses, though its origin is poorly understood. By using x-ray photon correlation spectroscopy, we have investigated the atomic motions in a model system of metallic glass with distinct stability and in situ stress states. We find that the microscopic dynamics can be tuned from dramatically nonmonotonous to monotonous. The intermittent dynamics is always accompanied by the activation of a secondary relaxation process, as indicated by the drop of the initial nonergodic plateau of the intensity-intensity correlation function. Both phenomena depend on the material state and can be suppressed by simultaneously lowering the fictive temperature and external loading, leading the glass in a stationary metastable state which appears independent on the thermal history of the system.

Особенности релаксации сдвиговой упругости металлических стекол

Работа направлена на установление закономерностей изменения сдвиговой упругости, возникающих при структурной релаксации металлических стекол на основе Pd и Zr. Измерения модуля сдвига выполнялись на частотах около 500 кГц. Несмотря на отличия в физических свойствах исследованных металлических стекол (химический состав, стеклообразующая способность, температуры стеклования и др.), наблюдаются определенные общие закономерности релаксации их сдвиговой упругости при термообработке.
 
 ИСТОЧНИК ФИНАНСИРОВАНИЯ
 Работа поддержана грантом Минобрнауки РФ № 3.1310.2017/4.6.
 
 БЛАГОДАРНОСТИ
 Автор выражает благодарность проф. В.А. Хонику за обсуждение статьи
 
 
 ЛИТЕРАТУРА
 
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КОМПЬЮТЕРНОЕ МОДЕЛИРОВАНИЕ СТРУКТУРНЫХ ДЕФЕКТОВ В МОНОКРИСТАЛЛИЧЕСКОМ И АМОРФНОМ АЛЮМИНИИ

The paper covers the study of microscopic mechanisms of melting of metals and the structural relaxation of metallic glasses. Despite the extensive efforts and numerous important results obtained in this field, this task does not have a generally accepted final solution. One of the main issues is the microscopic nature of structural defects in metallic glasses – the nanosized regions, which are responsible for the evolution of their physical properties under the external influence. The interstitialcy theory (IT) proposed by Granato provides the advanced interpretation of nature of such defects. The interstitialcy theory is based on the unique hypothesis of the interstitialcy mechanism for melting of metals and associates heat effects in the glass with the shear elasticity of a maternal crystal. The experimental study and computer simulation of the diaelastic effect near the melting temperature T m of crystalline aluminum provided a strong evidence of the avalanche generation of interstitial dumbbells near T m . In this work, the authors carried out the computer simulation to check the presence of interstitial dumbbells (or similar atomic structures) in the solid glassy state produced in the result of melt- quench. The computer simulation shows that the amorphous aluminum produced by rapid melt quenching contains a significant number of “defects” similar in their properties to the interstitial dumbbells in the crystalline state. Although these “defects” do not have any well-defined uniform topological structure, unlike the defects of crystal, and they can be exactly identified by their basic properties – high sensitivity to shear stresses and typical low/high-frequency peculiarities of the spectrum of the vibrational density of states of the “defective” atoms. Using the methods of molecular dynamics and statics, it is shown that the solid non-crystalline aluminum contains the specific atomic configurations similar to the interstitial dumbbells in the crystalline state, which can be considered as the amorphous structure “defects”.

Sub-Tg relaxation times of the α process in metallic glasses

The current view of structural relaxation in metallic glasses assumes the presence of primary and secondary processes with different activation energies. While the faster, secondary process can be well characterized in the out-of-equilibrium state below the glass transition temperature Tg, the experimental direct determination of the primary process in this temperature region is more difficult due to the long relaxation times. In this work, we merge new and literature data to analyze the temperature behavior of the primary relaxation time below Tg as observed by mechanical spectroscopy and stress relaxation of metallic glasses of different fragility. We compare these results with the microscopic structural relaxation times previously measured with X-ray photon correlation spectroscopy. The coincidence between the macroscopic and microscopic relaxation times allows us to discuss the underlying mechanisms responsible of primary relaxation over different length scales, as well as to propose an overall picture of the primary relaxation behavior in the glassy regime near Tg.

Decoding flow unit evolution upon annealing from fracture morphology in metallic glasses

The intrinsic correlation between the fracture morphology evolution and the structural heterogeneity of flow units in a typical Zr52.5Ti5Cu17.9Ni14.6Al10 (vit105) metallic glass (MG) upon annealing was investigated. By systematically tuning the annealing time at temperature below the glass transition temperature, a series of dimple-like fracture morphology were obtained, which is the unique fingerprint-like pattern for every annealing state. Based on the structural relaxation model of flow units, the evolution of the typical dimple sizes, the largest and smallest dimple size, with annealing were well fitted. Then the evolution of flow unit density was estimated from the fracture morphology evolution, which displays the same evolution trend with that measured from thermal relaxation. A stochastic dynamic model considering the interaction of activated flow units was proposed to analyze the effect of the initial flow unit density and the flow unit interaction intensity on the dynamic evolution of dimple distribution. Our work may provide a novel scheme to investigate the structural fingerprint information on flow units from fracture morphology, and enlighten the microscopic structural origin of the ductile-to-brittle transition during structural relaxation in MGs.

Interrelationship between heat release and shear modulus change due to structural relaxation of bulk metallic glasses

Within the framework of the Interstitialcy theory it is shown that the amount of heat released during structural relaxation of metallic glasses must be proportional to the room-temperature change of the shear modulus. This prediction is verified by using experimental data taken on seven bulk metallic glasses. It is found that the kinetics of exothermal heat flow upon structural relaxation is determined by shear modulus relaxation. The released heat per one kinetic relaxation unit (“defect”) for all glasses practically coincides with the “defect” formation enthalpy calculated using the Interstitialcy theory providing further support for the description of structural relaxation on the basis of this approach.

Symmetry foundations of a polymer model for close-packed metallic liquids and glasses

The atomic packing density of metallic melts and glasses is too high for their structures to be considered as chaotic. To remove this contradiction, we propose to describe the structures of metallic liquids and the glasses that form from them using (i) a base set of three spirals made of regular tetrahedra with specific noncrystallographic symmetry and (ii) combinatorial permutations of the vertices of a set of the coordination polyhedra that describe the polymorphic transformations in metals. The symmetry base of the proposed model of the structures of liquids and glasses is represented by projective linear groups PSL(2, p), where the order of the Galois field is p = 3, 7, and 11. These groups uniquely determine a tetrahedron, the 7-vertex joining of four tetrahedra along their faces (tetrablock), the 11-vertex joining of two tetrablocks into a spiral, and the throwing over of the diagonals in a rhombus from two triangular faces of neighboring tetrahedra. The throwing over of the diagonals in a rhombus is considered as a unit act of any structural transformation and ensures the melt–crystal, melt–glass, and glass-crystal transitions and the structural relaxation of metallic glasses. In terms of the proposed scheme, the high density of melts and glasses is caused by tetrahedral packing (up to 78%), and the absence of a diffraction pattern of melts and glasses is explained by the absence of translation along the spiral axis. The suggested polymer model also explains the collective effects (string vibrations) that were detected upon measuring the shear modulus relaxation of a metallic glass.

Shear modulus and internal friction hystereses during structural relaxation of metallic glasses based on Pd and Zr in the vicinity of the glass transition range

Cooling of metallic glasses based on Pd and Zr from the supercooled liquid state with a low rate causes significant shear modulus and internal friction hystereses, which indicates a long relaxation time in the vicinity of the glass transition range. The nature of the observed phenomenon has been discussed within the interstitialcy theory.

Understanding of the Structural Relaxation of Metallic Glasses within the Framework of the Interstitialcy Theory

A review of the new approach to the understanding of the structural relaxation of metallic glasses based on the interstitialcy theory has been presented. The key hypothesis of this theory proposed by Granato consists of the statement that the thermodynamic properties of crystalline, liquid and glassy states are closely related to the interstitial defects in the dumbbell (split) configuration, called also interstitialcies. It has been argued that structural relaxation of metallic glasses takes place through a change of the concentration of interstitialcy defects frozen-in from the melt upon glass production. Because of a strong interstitialcy-induced shear softening, the defect concentration can be precisely monitored by measurements of the unrelaxed shear modulus. Depending on the relation between the current interstitialcy concentration c and interstitialcy concentration in the metastable equilibrium, different types of structural relaxation (decreasing or increasing c) can be observed. It has been shown that this approach leads to a correct description of the relaxation kinetics at different testing conditions, heat effects occurring upon annealing, shear softening and a number of other structural relaxation-induced phenomena in metallic glasses. An intrinsic relation of these phenomena with the anharmonicity of the interatomic interaction has been outlined. A generalized form of the interstitialcy approach has been reviewed.

Strain Gradient in Micro‐Hardness Testing and Structural Relaxation in Metallic Glasses

An analytical model is proposed to quantitatively describe the depth‐dependence of Vickers micro‐hardness in metallic glasses. The approach is based on a shear bands distribution‐induced strain gradient during testing and was used to analyze thermal relaxation in the Zr55Cu20Al10Ni10Ti5, Ni53Nb20Zr8Ti10Co6Cu3, and Mg65Cu12.5Ni12.5MM10 metallic glasses. It was shown that a decrease of the free volume leads systematically to a decrease of the alloy hardness. This analysis also gives an evaluation of the shear band thickness and the role of the elastic properties in the depth‐dependence of the Vickers micro‐hardness.

Determination of the activation energy spectrum of structural relaxation in metallic glasses using calorimetric and shear modulus relaxation data

We consider two methods for reconstruction of the activation energy spectra of structural relaxation from calorimetric and shear modulus relaxation data. The methods are based on the assumption that structural relaxation of metallic glasses can be understood as a relaxation change of the concentration of frozen-in defects similar to dumbbell interstitials (interstitialcies) in simple crystals. For three Pd- and Zr-based glasses taken as an example, it is shown that both methods give nearly the same results. We calculated a decrease of the defect concentration and showed that the heat of structural relaxation per defect for all three glasses practically coincides with the theoretical value of the interstitialcy formation enthalpy.

Alternative understanding for the enthalpy vs volume change upon structural relaxation of metallic glasses

It has been argued that the densification observed upon structural relaxation of metallic glasses can be explained not by the “free volume annihilation,” as it is custom to consider, but by the annealing of interstitialcy-like “defects” frozen-in upon glass production. A simple expression for the enthalpy release due to relaxation of defect-induced dilatational energy has been proposed. The expression is shown to be in agreement with recent detailed experimental data on the heat release occurring upon structural relaxation of Au-based metallic glass [J. Bünz and G. Wilde, J. Appl. Phys. 114, 223503 (2013)].

Kinetics of isothermal structural relaxation in metallic glasses measured by real-time diffraction using synchrotron radiation

Quantitative measurements of the excess free volume in Pd40Cu30Ni10P20 and Cu55Zr30Ti10Pd5 metallic glasses during in situ isothermal annealing at various temperatures are used to identify physical parameters of structural relaxation in metallic glasses and to discuss proposed models describing this process. The free-volume model is found to provide a simple and predictive description for structural relaxation phenomena. We show that structural relaxation kinetics follows a second-order law in a satisfactory manner. The activation energy for relaxation is found to depend on annealing temperature and the extent of structural relaxation.

Chemical Short-Range-Ordering Effect on Structural Relaxation in Metallic Glasses

A model is proposed to address chemical effects on structural relaxation in metallic glasses. The atomic short range ordering (SRO) is described under the quasi-chemical approximation (QCA). Local chemical deviations from the ideal SRO are considered as an excess enthalpy. The simplified analysis of a disordered region’s evolution is based on the notion of the collective bond exchange between neighboring atoms. The approach suggests a bimolecular mechanism with possibly large apparent activation energy for structural relaxation near the glass transitions.

Evidence of Distributed Interstitialcy-Like Relaxation of the Shear Modulus due to Structural Relaxation of Metallic Glasses

The interstitialcy theory is used to calculate the kinetics of shear modulus relaxation induced by structural relaxation of metallic glasses. A continuous distribution of activation energies is shown to be a salient feature of the relaxation. High precision in situ contactless electromagnetic acoustic-transformation shear modulus (600- kHz) measurements performed on a Zr-based bulk metallic glass are found to strongly support the approach under consideration. It is revealed that the activation energy spectra derived from isothermal and isochronal shear modulus measurements are in good agreement with each other. It is concluded that the increase of the shear modulus during structural relaxation can be understood as a decrease of the concentration of structural defects similar to dumbbell interstitials in simple crystalline metals.

Anomalous Curie-point relaxation in a Cr-containing amorphous alloy

Anomalous (negative) irreversible and reversible Curie-point relaxation was observed in amorphous Fe 76Cr 8B 15Cu 1 alloy. This observation is in line with the results previously found in a FeNiCrSiB alloy series where the Cr-concentration dependence of the normal (positive) reversible Curie-point relaxation could only be explained by assuming two contributions of different signs to the relaxation. The normal contribution is related to the ordering of Fe and Ni atoms while the anomalous one is associated with the Cr atoms. The role of Cr on the resistivity relaxation is also presented. Existing literature results on anomalous structural relaxation of metallic glasses are critically discussed.