Extended elastic model for flow in metallic glasses

Abstract

We report that both shear and bulk moduli, not only shear modulus, are critical parameters involved in both homogeneous and inhomogeneous flows in metallic glass.The flow activation energy (∆F) of various glasses when scaled with average molar volume V m , which is defined as flow activation energy density ρ Ε =∆F/V m , can be expressed as: 11The extended elastic model is suggestive for understanding the glass transition and deformation in metallic glasses. The mysterious glass transition phenomenon, which connects the liquid and glassy state, has wide applications in daily life, industry, and organism preservation [1][2][3][4]. In the past decades, intensive efforts have been made to understand the glass transition [1,[5][6][7][8][9]. To understand the flow in supercooled liquid and glass, many models have been proposed. The well-known models are the free volume model, the Adam-Gibbs entropy model, the mode-coupling theory and elastic models [1][2][3][4][5][6]. A successful model of viscous liquids and glasses must explain why the activation energy has such strong temperature dependence and can correlate the activation energy to simple and readily measurable parameter. Among these models, the elastic models link the glass transition and elastic moduli of the glasses [1]. All the elastic models link the activation energy to the readily measurable instantaneous shear modulus G. In metallic glasses, the glass transition temperature (T g ) indeed shows clear correlation with the elastic moduli such as Young's modulus E and G [10][11][12][13][14][15][16][17][18].In this letter, based on the scaling laws between T g and elastic moduli in metallic glasses, we demonstrate that the V m scaled flow activation energy (∆F), that is, flow activation energy density, ρ Ε =∆F/V m , is determined by both G and K in a way of ρ Ε = (10G+K)/11. The physical origin of the extended elastic model is discussed.The temperature dependence of the viscosity of liquids approaching glass transition is [1]: ∆F∝G.Figure 1(a) shows experimental data of E and G versus T g for 46 different kinds of bulk metallic glasses (BMGs) (listed in Table I). These BMGs cover many typical alloy systems, including Zr-, Cu-, Ca-, Mg-, Ni-, Fe-, and rare earth elements Fig. 1(b) confirms that the N involved in the cooperative flow event for various metallic glasses is almost the same.Based on above scaling laws and elastic model, we propose that it is the flow activation energy density (ρ E ), not the flow activation energy itself, correlates with the elastic moduli as:The extended elastic model means that the energy per volume needed in glass transition or in STZ in metallic glass is proportional to the elastic moduli.Previous elastic models [1] suggest that the atoms or atomic groups go through pure shearing displacement which is independent of K, and the ρ E depends only on G.Recent works [18,20] and the jamming model of granular systems [22] find that both shear and dilatation are involved in the flow during glass transition and deformation.Next,...

Correlation between relaxations and plastic deformation, and elastic model of flow in metallic glasses and glass-forming liquids

“…We define the activation energy of a unit volume as the activation energy density (q E ) (Refs. [77][78][79][80][81][82]:…”

“…The definition of activation energy density can directly relate the flow activation event to the elastic moduli. 7,8,18,81,82 We estimate the energy barrier between two potential energy minima from the curvature around the minima. 18,82 Consider the one-dimensional PEL with two minima separated the distance 2r 0 as shown in Fig.…”

“…Figure 8(a) shows the data of (10G þ K)V m /11RT g versus various kinds of MGs. These MGs cover many typical systems including Zr-, Cu-, Ca-, Mg-, Ni-, Fe-, and rare earth elements based MGs, and their thermal, mechanical, and physical properties are markedly different 17,80,81 (as listed in Table VI). Their values of T g , E and Poisson's ratio span from 317 K to 930 K, 23 GPa to 195 GPa, 0.276 to 0.41, respectively.…”

“…16 The Poisson's ratio then can be regarded as an indicator of the glass-forming ability of an alloy. Because the average barrier for flow DE is mainly related to G, 81,82 for the MGforming systems with low G or larger Poisson's ratio, their DE is easy to be surmounted via small strain energy. While surmounting the large energy barrier (small v) will take some finite time and large energy, in order for the system to track the changes in the PEL through structural rearrangements.…”

Atomic-scale structural heterogeneity and elastic modulus for metallic glasses

“…Some of the studies also suggest that the elastic deformation in MGs mainly occurs at solvent-solvent junctions among solute-centered clusters; and the elastic modulus is essentially determined by solvent-solvent bonding [8,9]. However, extensive experiments illustrate that the elastic modulus is very sensitive to the minor change of composition which may lead to the appearance of ASSH in MGs [10]. This induces the following interesting question: how does the ASSH affect the elastic modulus of MGs?…”