**4. Discussion**

The deformation behavior of MGs is often discussed in terms of a distribution of activation energies for atomic rearrangements [32]. Underlying this distribution of activation energies is the potential energy landscape of the disordered structure [33]. When atomic rearrangements occur, either due to deformation or structural relaxation, they change the glass structure by shifting potential and activation energies. Similarly, hydrogen solid-solution charging of an MG results in local atomic rearrangements and a *<sup>c</sup>*H-dependent increase of the interatomic distances [28,29,34], thereby also

locally shifting potential and activation energies. In the beginning of hydrogen charging, the favored or so-called trapping sites for hydrogen are those with high local potential energies, such as sites with large free volume [35], or geometrically unfavored motifs (GUMs) [36]. Hydrogen also has been found to fill interstitial sites of loosely packed Zr-rich tetrahedral-like sites (t-sites) [3,34,37,38]. These trapping sites are stabilized by the hydrogen [39], lowering the local potential energy and generally resulting in an increase in the local activation energies for atomic rearrangements, thereby restricting deformation [11].

The study here reveals a clear increase in both modulus and hardness due to hydrogen charging. The linear relation between modulus and hardness suggests that the underlying mechanisms controlling sti ffness and deformation by atomic rearrangemen<sup>t</sup> depend on the same aspects of the atomic structure. A similar correlation between the sti ffness and barrier height for local shear rearrangements has been thoroughly investigated and discussed for metallic glass-forming liquids [33]. Furthermore, the fact that the modulus and hardness have the same relation in the uncharged and charged states indicates that the structural changes introduced by hydrogen do not produce fundamentally di fferent mechanical responses than the structural heterogeneities already present in the uncharged disordered structure. The simplest explanation for our observations is that the hydrogen stabilizes regions of low shear modulus, thus increasing the sti ffness and hindering atomic rearrangements.

Both increases and decreases of modulus and hardness have been observed in the literature due to hydrogen charging, depending on the alloy composition. MGs with a high Zr composition consistently show increases in mechanical properties on charging, likely because the Zr-rich clusters are made more stable by the inclusion of hydrogen [11,18,40] due to the large negative mixing enthalpy. The incorporation of hydrogen in these clusters presumably makes them more resistant to deformation, increasing the modulus and hardness, as well as the pop-in stress of the MG. On the contrary, hydrogen incorporated into a stable icosahedron cluster may raise the potential energy and make the cluster less stable to atomic rearrangements. As a result, the MG may appear to be softened by hydrogen addition [20].

Beyond the increase in hardness and modulus, the most noticeable e ffect of hydrogen charging in this study is the replacement of pop-ins by stable or homogeneous flow. The improved ductility and malleability of MGs induced by hydrogen has usually been attributed to an increase in structural heterogeneities in the literature, although an exact mechanism has not been discussed [16,18,20]. There is no doubt that the hydrogen addition changes local environments in the MGs, thereby changing the potential energy distribution which likely accounts for changes in hardness and modulus. In addition to the change in the potential energy distribution, the spatial distribution of sites with di fferent potential energy should be considered. Our recent work suggests an increase of correlation length of medium-range order in a Zr51Cu49 MG during hydrogen loading [41]. The spatial correlation of the heterogeneities may play a decisive role in the ductility of MGs. In a simulation study by Wang et al. [21], the mechanical properties of samples with the same potential energy distribution but di fferent correlation lengths for the local shear modulus are compared. To first order, the correlation length simply describes the size and spacing of potential STZs (elastically soft sites) in the MG. Their results reveal that when the correlation length increases from 0.5 to 5 nm, a transition in deformation mechanism from "stress-dictated" shear band nucleation and growth to a "structural-dictated" strain percolation occurs [21]. This is associated with a decrease in the tendency for strain localization and an increase in the plastic strain to failure. The basic understanding of this observation is that more widely spaced STZs cannot easily interact through their stress fields, thus hindering the formation of shear bands through collective excitation. Building on the model of Wang et al., we propose that hydrogen stabilization of STZs decreases their density, thereby increasing the correlation length and hindering strain localization and pop-in instabilities. We further sugges<sup>t</sup> that the high mobility of the hydrogen may allow it to change sites in response to changing strain fields, thus inhibiting propagation of excitations between STZs and hindering pop-in formation. If hydrogen is able to move in response

to strain fields introduced by other hydrogen atoms, some form of self-organization of the hydrogen is expected to be active.

Potential sites that can be filled with hydrogen are limited in MGs since the maximum solubility of hydrogen is low. When the sample is overcharged with hydrogen [28,29], cracks presumably form due to hydrogen-induced expansion and the possible motion of hydrogen in the resultant strain fields. Precise control of *c*H will be required when using hydrogen to optimize the mechanical behavior of MGs.

Heterogeneities at various length scales have been discussed here, ranging from the flexibility volumes, free volume defects, STZs, and GUMs at the nanometer scale up to the observed variations in modulus, hardness, and pop-in stresses at the micrometer scale. Whether the hydrogen-induced changes in nanometer scale heterogeneities can result in the observed micrometer-scale variations will depend on the distribution of spatial correlations as well as the ability of hydrogen to move in response to the hydrogen-induced strain fields. Confirmation of the nanometer-scale heterogeneity changes as well as evidence for possible self-organization due to hydrogen charging remain elusive due to technical limitations. However, state-of-the-art methods such as fluctuation electron microscopy [42,43] may open the possibility to track the evolution of nanoscale heterogeneities during hydrogen charging.
