**3. Results**

X-ray diffraction spectra were recorded and compared for each sample before and after hydrogen charging. The result of X-ray diffraction only reveals a small shift of the broad maxima characteristic of the nearest neighbor distances. In a sample charged to *c*H > 0.5 H/M (the highest hydrogen content in this work) the position of the broad maxima is shifted to lower 2θ values by 0.5 degrees relative to the as-cast material (see Figure 1a). The lower diffraction angle indicates that on average the hydrogen-charged sample has larger atomic spacing than the uncharged sample. No evidence of hydride formation was found in the samples.

**Figure 1.** (**a**) X-ray diffraction spectra of Vit 105 metallic glass (MG) samples with and without hydrogen charging. The hydrogen content is defined as the hydrogen-to-metal ratio. (**b**) Hardness and modulus (Berkovich indentation) of samples with and without hydrogen charging. The dashed line is to guide the eye.

Modulus and hardness measured by Berkovich indentation on samples with and without hydrogen charging for *c*H > 0.5 H/M are plotted in Figure 1b. The average modulus and hardness of the as-cast sample were 98 ± 3 and 6.6 ± 0.2 GPa, respectively. Although there is considerable scatter in the values, both the modulus and the hardness clearly increase as a result of hydrogen charging, leading to average values of 110 ± 7 and 8.7 ± 0.8 GPa, respectively. The modulus and hardness values in both the uncharged and charged states are linearly correlated with each other, suggesting that both properties are determined by the same features of the structure and short-range chemical ordering. Meanwhile, the wider distribution of modulus and hardness values in the charged state indicates larger variations in local structure (more structural heterogeneities) due to hydrogen incorporation on the micrometer length scale of the Berkovich indents. Some of the data points do not show the linear correlation, in that the modulus is decreased without a significant change in hardness. We attribute this to the formation of surface relaxation or surface cracks which are observed in some regions of the highly charged specimens [28,29].

Mechanical properties of the bulk sample were measured by Berkovich indentation while local plasticity was studied by spherical indentation which is sensitive to early plasticity events in MGs [27]. The first pop-in in the load-displacement curve is attributed to the onset of plasticity and the corresponding maximum shear stress along the shear band trajectory defines the yield stress [22]. Samples were prepared for spherical indentation tests with *<sup>c</sup>*H-values of 0, 0.11, 0.13, and 0.29 H/M. Before indentation tests, the sample surfaces were checked with optical microscopy to make sure there were no cracks. Representative load-displacement curves of indentations from the four di fferent samples are plotted in Figure 2a. Pop-ins can be seen in the data from samples with *<sup>c</sup>*H-values 0, 0.11, and 0.13 H/M. The first pop-in is attributed to the initiation of detectable plasticity [27] and is marked by a solid arrow in each curve. In contrast, the sample with *c*H = 0.29 H/M does not show any pop-ins. In order to further analyze the pop-ins, displacement rates were calculated for each curve (Figure 2b) where pop-ins with a displacement larger than a threshold value can be easily identified. Compared to other samples, displacement rate curves for the sample with *c*H = 0.29 H/M are very smooth. It is worth noting that there is residual plastic deformation in the indents of the 0.29 H/M sample even though no pop-ins are observed. The data point indicated by the arrow in Figure 2a demonstrates that deformation of the material under the indenter is not fully recoverable. Therefore, the deformation during indentation is already beyond the elastic region but is not able to initiate a pop-in. A statistical evaluation shows that 100% of the indents in the uncharged *c*H = 0 H/M sample have pop-ins. This percentage reduces to about 80% in the *<sup>c</sup>*H-value 0.11 and 0.13 H/M samples. In the *c*H = 0.29 H/M sample, there are no pop-ins at all in all indentations demonstrating that local homogeneous deformation is occurring. This result is summarized in Figure 2c.

The strength of the sample is evaluated using the maximum shear stress when the first pop-in occurs. Analysis of elastic stress distribution based on Hertzian contact theory [30] reveals that the maximum stress locates underneath the center of the indenter at a depth of half the contact radius [31]. The maximum shear stress is approximated by:

$$
\pi\_{\text{max}} \approx A P\_{\text{pop}-in} / \left( \pi \times R \times h\_{\text{pop}-in} \right) \tag{2}
$$

with *Ppop*−*in* and *hpop*−*in* being the load and displacement at the onset of the pop-in, respectively, diameter of the spherical diamond tip *R* = 650 nm, and a pre-factor *A* = 0.4413 [27]. Cumulative distributions of the maximum shear stresses at the first pop-ins for the *<sup>c</sup>*H-value 0, 0.11, and 0.13 H/M samples are plotted in Figure 3. The pop-in stresses vary by as much as 2 GPa for a given sample, indicating significant structural heterogeneity on a length scale between the size of the indented volume (ca. 1 μm) and the size of the indent array (ca. 35 μm). The average maximum shear stress for uncharged sample 1 is about 2.9 GPa. A clear shift of maximum shear stresses to higher values is shown in hydrogen-charged samples 2 and 3 compared to sample 1. The average maximum shear stress for the charged sample 3 is about 3.2 GPa, 10% higher than that of sample 1. This result showing hydrogen-induced hardening e ffect is qualitatively consistent with modulus and hardness measurement with Berkovich indentation, as shown in Figure 1b. It can also be noticed that the shape of the distribution curves for samples 2 and 3 is di fferent from that of sample 1. The curve of sample 2 is stretched while the curve of sample 3 is compressed even though they have similar *c*H. This di fference suggests considerable structural heterogeneity in the hydrogen-charged MG over length scales much larger than the array size of ca. 35 μm. There is no cumulative distribution curve for sample 4 because no pop-ins were observed for any of the 144 indentation tests.

**Figure 2.** (**a**) Typical load displacement curves for indents in samples with different hydrogen content (*c*H). The curves are shifted for the sake of clarity. (**b**) Displacement rate as a function of displacement for each curve in (a). The first pop-ins are marked with arrows. The curves are shifted for the sake of clarity. (**c**) The percentage of indents that have no pop-in out of 144 tests in each sample.

**Figure 3.** Cumulative distribution of the first pop-ins against the maximum shear stress of samples with different *c*H.
