Quenched-in liquid in glass

Glasses have long been considered as frozen liquids because of the similarity between their static amorphous structures. While the modern theories about glass transition suggest that glass transition may result from supercooling of a heterogeneous liquid that contains fast and slow regions, it remains unclear whether such a physical picture applies to metallic glasses, which are a densely packed solid glass that was once believed to be a vitrified homogeneous metallic liquid. However, in the recent work published in Nature Materials, Chang et al provide compelling evidence to show that metallic glasses contain liquid-like atoms that behave as a high-temperature liquid in stress relaxation. Being activated under cyclic loading, this quenched-in liquid results in a fast relaxation process, which is discovered in a variety of metallic glasses. Their results are important and deliver a strong message that metallic glasses have a dynamic microstructure containing liquid- and solid-like atoms. Most importantly, the outcome of their research provides physical insight into the nature of glass-transition in metallic glasses, and also helps unravel their structure-property relations.

Understanding the nature of glass and liquid-glass transition is one of the longest-standing yet deepest and most interesting problems in the field of condensed matter physics [1]. In general, a liquid-glass transition can be attributed to the dramatic increase in structural relaxation time t R of a supercooled liquid over many decades upon cooling [2], which leads to * Authors to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. the freezing of a liquid's structure on the laboratory timescale across a narrow temperature range where the characteristic structural relaxation time comes to be of the order of 100 s [3]. Surprisingly, it appears that this huge slowdown of the liquid dynamics does not come about with any notable and significant change in the overall static structure of a supercooled liquid across glass transition, as revealed in many previous studies [4][5][6][7]. Therefore, it was once a popular view that glass transition is purely a dynamic phenomenon and irrelevant to any thermodynamic process that entails the evolution of a heterogeneous liquid structure. In other words, an equilibrium supercooled liquid should be homogeneous as indicated by its static structure, and so should the corresponding glass, particularly for metallic glasses which have long been considered as the simplest form of glasses made up of only atoms, which could be also termed as 'atomic glass' in the literature [8,9].
While the common wisdom suggests that metallic glasses are homogeneous in their lack of any structural heterogeneities, the modern theories about glass transition, such as the random first order transition theory [10], the twinkling fractal theory [11], the two-order parameter theory [12,13] and some others [14][15][16][17][18], all propose that supercooled liquids are heterogeneous in a dynamic sense, containing fast regions of low viscosity and slow regions of high viscosity. It is the evolution of this dynamic heterogeneity that underpins the dynamic slowdown of glass-forming liquids under continuous cooling. To be specific, the dramatic slowdown of liquid dynamics and thus glass transition can be attributed to the percolation of the slow regions according to the thermodynamic models [19,20]. As a consequence of the evolution of the dynamic heterogeneities, the relaxation time of a supercooled liquid can grow in an exponential or, in most cases, a nonexponential fashion, which can be fitted to the well-known empirical Vogel-Fulcher-Tammann function [10,21]. Owing to rapid quenching, glasses can therefore inherit this dynamically heterogeneous structure from their corresponding equilibrium liquids as a 'frozen-in' structure feature. Now there are two different physical pictures about glass transition and the structure of glasses. While the physical picture of homogeneous liquids/glasses was widely accepted in the field of metallic glasses from the 1960s to the 2000s, the evidence in favor of a heterogeneous metallic liquid/glass has mounted up in recent years, either from atomistic simulations [22][23][24] or experiments [25][26][27][28]. These recent studies are not limited to the characterization of well-recognized local geometric features, such as short-or medium-range ordering, which are the notions that can be equally applied to homogeneous liquids/glasses, but extended to the characterization of dynamic features hidden in the static amorphous structure of metallic glasses by means of fluctuation transmission electron microscopy (TEM) [28], dynamic atomic force microscopy [25], dynamical mechanical spectroscopy (DMS) [26,27,29,30], or atomistic simulations [24,31,32].
Through the combined efforts from DMS and atomistic simulations, Chang et al [33] (the research team led by Prof Bai) recently provided critical evidence that furthers our understanding of the structural heterogeneity in metallic glasses. Figure 1 shows a typical relaxation spectrum of a metallic glass over a wide temperature range, which can be resolved into three distinct relaxation processes. At the temperature around the glass transition point (T g ), the α relaxation process can be observed, which is usually associated with the glass-to-liquid transition [34] or considered to be equivalent to overall plastic flows in metallic glasses that are strained beyond their yield point [35]. At an intermediate temperature between T g and the room temperature, there is the β relaxation process that usually appears as the excessive wing of the α relaxation. According to the literature [36], the β relaxation is due to the irreversible string-like motions of atoms [37], which is considered to be equivalent to shear transformation or local plasticity because both events are thermally activated and share the same activation energy of E β = 26 k B T g , where k B is the Boltzmann constant. At a lower temperature well below room temperature, there is a fast relaxation process with the activation energy E f = 12 k B T g . In the prior works by Wang et al [38,39], this fast process was also observed, and it was then believed that both the fast and β relaxation process arose from thermally activated events in supercooled liquids. According to their activation energies extracted from DMS [38], the fast process can be viewed as a 'reversible' process involving only local topological changes, such as the alteration of local bond orientation, and the β relaxation as an 'irreversible' process involving atomic bond breakage. However, Chang et al [33] provide compelling evidence to show that this fast process shares the same activation energy with the high-temperature liquid (figure 2), therefore implying that some high-temperature liquid must remain in the corresponding glass even after glass transition. This discovery is of great importance, delivering a strong message that a supercooled metallic liquid is intrinsically heterogeneous and, despite supercooling, a fraction of it still retains the fast atomic mobility or the low viscosity that conforms to the high-temperature liquid. As a result of rapid quenching, the metallic glasses retain the intrinsically heterogeneous structure, containing both liquid-like and solid-like atoms as illustrated by the inset of figure 2.
This quenched-in dynamic 'microstructure' also helps us unravel the structure-property relations of metallic glasses [40]. It is well known that being out-of-equilibrium, metallic glasses undergo thermal evolution below T g like all other glasses. Many of their physical properties (e.g. dynamical and elastic modulus) depend on their thermal history and evolve with time, which is also termed as physical aging. While physical aging is ubiquitous for glassy materials, which can significantly affect their slow β relaxation behaviors [41][42][43], the discovery of a fast process raises other critical questions: how is physical aging initiated in metallic glasses and is it possibly Figure 2. The schematic diagram of viscosity versus the inverse of temperature that can be keyed to different relaxation processes. The insets illustrate the evolution of the dynamic microstructure as a homogeneous high-temperature liquid turns to a heterogeneous supercooled liquid, and finally to a heterogeneous solid glass that contains the fast regions or liquid-like atoms inherited from the homogeneous high-temperature liquid. coupled with the fast process? This is a fundamental issue yet to be understood.
Because the liquid-like atoms of a low viscosity can easily relax nearby mechanical stresses upon loading, the quasistatic elastic modulus of metallic glasses could be considerably lower than that obtained at a fast-loading rate [44]. This rate dependence of elastic modulus can be formulated in terms of glassy rheology [45], which has been exploited to extrapolate the viscosity of the liquid-like atoms [44,46] or rationalize the room-temperature anelasticity [46]. Aside from elastic modulus, the Poisson's ratio of metallic glasses can be related to liquid-like atoms as well. The work of Sun et al [47] suggested that there could be two types of liquid-like atoms in terms of their susceptibility to different stress components. Although the fraction of liquid-like atoms decreases with thermal annealing, the Poisson's ratio of a metallic glass decreases if the liquid-like atoms are more susceptible to a shear stress and increases if the liquid-like atoms are more susceptible to a pressure. This interesting behavior provides a physical insight into a feasible correlation between the Poisson's ratio and plasticity of metallic glasses [48]: i.e. if a plastic flow is really initiated from the liquid-like atoms (also termed as the 'soft spots' in some other works [49]) that are activated by a shear stress, one can envision that the more of those liquid-like atoms, the more plastic a metallic glass would appear. However, it still remains unclear whether the liquid-like atoms can be considered as the initiation sites for local plasticity.
As aforementioned, local plasticity has long been considered to be associated with the β relaxation [36] rather than the fast process [38]. According to the prior works [38,39] and the recent finding of Chang et al [33], the β relaxation corresponds to local stress relaxation in the supercooled liquid and the fast process to local stress relaxation in the high-temperature liquid. Therefore, it is unlikely or would be very intriguing to see a coupling between the β relaxation and the fast process. From the perspective of the dynamic microstructure, a likely physical scenario for plasticity in metallic glasses is that yielding results from microstructure evolution rather than the activation of a typical flow defect in an amorphous structure being analogous to dislocations in crystals. In such a case, plasticity in metallic glasses entails all possible relaxation processes in its course and can be considered as strain-induced glass transition [50], which also obeys the universal laws of glass rheology [35]. Finally, it is worth mentioning that the liquid-like atoms also explain the phenomenon of ultrasound plasticity in metallic glasses [51]. When they were activated under cyclic loading at the ultrasound frequency or the cyclic period matching their relaxation time, it was discovered that the solid-like amorphous structure became unstable and collapsed, turning into a liquid below T g even at the stress level far below the yield strength of the metallic glass. This phenomenon is called 'ultrasound plasticity' and has been exploited in metallic-glass based manufacturing [51,52].
To summarize, the recent work of Chang et al [33] provides key evidence to deepen our understanding of structural heterogeneity in metallic glasses as well as the nature of glass transition in metallic liquids. Although metallic liquids have long been considered as homogeneous, it is clear to us with the mounted evidence that supercooled metallic liquids are intrinsically heterogeneous in a dynamic sense. After glass transition, metallic glasses inherit the quenched-in dynamic microstructure and exhibit a fast process that can be linked with the quenched-in liquid-like atoms. In retrospect, this dynamic microstructure can help us understand many unexpected mechanical behaviors of metallic glasses, such as the Poisson's ratio behavior, ultrasound plasticity, etc. Looking ahead, we believe that the outcome of the current research can surely help us to establish the structure-property relation for metallic glasses and ultimately, to enable the design of metallic glasses with desired properties.