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.

Determination of the thermodynamic potentials of metallic glasses and their relation to the defect structure.

We performed calorimetric and shear modulus measurements on four bulk metallic glasses upon heating up to the temperature of the complete crystallization as well as in the fully crystallized state. On the basis of calorimetric experiments, we calculated the excess thermodynamic potentials with respect to the crystalline state-the enthalpy ΔH, entropy ΔSand Gibbs free energy ΔΦ-as functions of temperature. Using high-frequency shear modulus measurements we show that calorimetric determination of ΔH, ΔSand ΔΦ is consistent with the calculation of these potentials within the framework of the interstitialcy theory (IT) within a 15% uncertainty in the worst case for all MGs under investigation. It is concluded that the physical origin of the excess thermodynamic potentials in MGs can be related to a system of interstitial-type defects frozen-in from the liquid state upon melt quenching as suggested by the IT. The estimates of the defect formation enthalpyHfand entropySfshow thatHfscales with the shear modulus whileSfis quite large (10kBto 20kB), in line with the basic assumptions of the IT.

Relation of the fragility and heat capacity jump in the supercooled liquid region with the shear modulus relaxation in metallic glasses.

Fragility constitutes a major parameter of supercooled liquids. The phenomenological definition of this quantity is related to the rate of a change of the shear viscosityηat the glass transition temperature. Although a large number of correlations of the fragility with different properties of metallic glasses were reported, an adequate understanding of its physical nature is still lacking. Attempting to uncover this nature, we performed the calculation of the fragility within the framework of the interstitialcy theory (IT) combined with the elastic shoving model. We derived an analytical expression for the fragility, which shows its relation with the high-frequency shear modulusGin the supercooled liquid state. To verify this result, specially designed measurements ofηandGwere performed on seven Zr-, Cu- and Pd-based metallic glasses. It was found that the fragility calculated from shear modulus relaxation data is in excellent agreement with the fragility derived directly from shear viscosity measurements. We also calculated the heat capacity jump ΔCsqlat the glass transition and showed that it is related to the fragility and, consequently, to shear modulus relaxation. The ΔCsql-value thus derived is in a good agreement with experimental data. It is concluded that the fragility and heat capacity jump in the supercooled liquid state can be determined by the evolution of the system of interstitial-type defects frozen-in from the melt upon glass production, as suggested by the IT. This connection is mediated by the high-frequency shear modulus.

A simple kinetic parameter indicating the origin of the relaxations induced by point(-like) defects in metallic crystals and glasses.

Computer simulation shows that an increase of the volume V due to point defects in a simple metallic crystal (Al) and high entropy alloy (Fe20Ni20Cr20Co20Cu20) leads to a linear decrease of the shear modulus G. This diaelastic effect can be characterized by a single dimensionless parameter K = dln G/dln V. For dumbbell interstitials in single crystals K ≈ -30 while for vacancies the absolute K-value is smaller by an order of magnitude. In the polycrystalline state, K ≈ -20 but its the absolute value remains anyway 5-6 times larger than that for vacancies. The physical origin of this difference comes from the fact that dumbbell interstitials constitute elastic dipoles with highly mobile atoms in their nuclei and that is why produce much larger shear softening compared to vacancies. For simulated Al and high entropy alloy in the glassy state, K equals to -18 and -12, respectively. By the absolute magnitude, these values are by several times larger compared to the case of vacancies in the polycrystalline state of these materials. An analysis of the experimental data on isothermal relaxations of G as a function of V for six Zr-based metallic glasses tested at different temperatures shows that K is time independent and equals to ≈-43, similar to interstitials in single-crystals. It is concluded that K constitutes a important simple kinetic parameter indicating the origin of relaxations induced by point(-like) defects in the crystalline and glassy states.

Interstitial clustering in metallic systems as a source for the formation of the icosahedral matrix and defects in the glassy state.

The paper presents molecular dynamics and -statics simulations of a prototypical mono-atomic metallic system (aluminum) and its defects in the crystalline and glassy states. It is shown that there is a thermodynamic driving force for the association of dumbbell interstitials in the crystalline lattice into clusters consisting of different amounts of defects. Clusters containing seven interstitials constitute perfect icosahedra. Within the general framework of the interstitialcy theory, melting of simple metallic crystals is intrinsically related to a rapid increase of the concentration of dumbbell interstitials, which remain identifiable structural units in the liquid state. Then, the glass produced by rapid melt quenching contains interstitial-type defects. The idea of the present work is to argue that the major structural feature of many metallic glasses-icosahedral ordering-originates from the clustering of interstitial-type defects frozen-in upon melt quenching. Separate defects and their small clusters represent the defect part of the glassy structure.

Identification of interstitial-like defects in a computer model of glassy aluminum.

Computer simulation shows that glassy aluminum produced by rapid melt quenching contains a significant number of 'defects' similar to dumbbell (split) interstitials in the crystalline state. Although these 'defects' do not have any clear topological pattern as opposed to the crystal, they can be uniquely identified with the same properties which are characteristic of these defects in the crystalline structure, i.e. strong sensitivity to applied shear stress, specific local shear strain fields and distinctive low-/high-frequency peculiarities in the vibration spectra of 'defective' atoms. This conclusion provides new support for the interstitialcy theory, which was found to give consistent and verifiable explanations for a number of relaxation phenomena in metallic glasses and their relationship with the maternal crystalline state.

Experimental evidence for thermal generation of interstitials in a metallic crystal near the melting temperature.

The only intrinsic point defects of simple crystalline metals known from solid state physics are vacancies and interstitials. It is widely believed that while vacancies play a major role in crystal properties and their concentration reaches relatively big values near the melting temperature T m, interstitials essentially do not occur in thermodynamic equilibrium and their influence on properties is minor. Here, taking aluminum single crystals as an example, we present compelling experimental evidence for rapid thermoactivated growth of interstitial concentration upon approaching T m. Using high precision measurements of the shear modulus we found a diaelastic effect of up to [Formula: see text] near T m. It is argued that this effect is mostly due to the generation of dumbbell (split) interstitials. The interstitial concentration c i rapidly increases upon approaching T m and becomes only 2-3 times smaller than that of vacancies just below T m. The reason for this c i -increase is conditioned by a decrease of the Gibbs free energy with temperature, which in turn originates from the high formation entropy of dumbbell interstitials and a decrease of their formation enthalpy at high c i . Special molecular dynamic simulation confirmed all basic aspects of the proposed interpretation. The results obtained (i) demonstrate the significance of interstitial concentration near T m that could lead to the revaluation of vacancy concentration at high temperatures, (ii) suggest that dumbbell interstitials play a major role in the melting mechanism of monatomic metallic crystals and (iii) support a new avenue for in-depth understanding of glassy metals.

Towards understanding of heat effects in metallic glasses on the basis of macroscopic shear elasticity.

It is shown that all heat effects taking place upon annealing of a metallic glass within the glassy and supercooled liquid states, i.e. heat release below the glass transition temperature and heat absorption above it, as well as crystallization-induced heat release, are related to the macroscopic shear elasticity. The underlying physical reason can be understood as relaxation in the system of interstitialcy-type "defects" (elastic dipoles) frozen-in from the melt upon glass production.

On the nature of the shear viscosity and shear modulus relaxation in metallic glasses.

Analysis of independent isothermal and linear heating creep and shear modulus measurements performed on bulk Pd- and Zr-based metallic glasses provides evidence that the relaxation of their viscoelastic and elastic properties is controlled by 'defects', which respond to stress and temperature similarly to dumbbell interstitials in simple crystalline metals.

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.

An interstitialcy theory of structural relaxation and related viscous flow of glasses.

A theory of isothermal structural relaxation and creep of glasses below the glass transition temperature is given. According to the interstitialcy theory, the supercooled liquid state does not exist below a Kauzmann "pseudocritical" temperature T(k), which lies above the temperature T(K), commonly called the "Kauzmann temperature." Structural relaxation is simply a reduction with time of the interstitialcy concentration to the crystalline state for TT(k). The predicted viscosity eta is universal, given by eta=eta(0) + eta(T)t, in agreement with experiment. eta is continuous in T, with eta discontinuous at T(k) but linear in 1/T above and below T(k). The dependence of eta on the shear modulus directly connects kinetic and thermodynamic properties of glasses and liquids.