## 3 Results  
### Hardness  
Figure 2 illustrates the distribution of hardness for irradiated borosilicate glass exposed at the ion fluence of 1.0 \(\times\) 10\({}^{15}\) ions/cm\({}^{2}\). It was observed that the hardness sharply increased along the depth in the surface influence zone area. This phenomenon may be attributed to the blunt tip of the indenter and surface effects [13; 14; 15]. Then, the hardness gradually increased along the glass depth. Compared with published reports in this area [5; 15; 16], hardness of the Ar pre-irradiated samples subjected to the He ion had a plateau-like region, while there was not a similar trend for the hardness of He- and Ar-irradiated specimens made of borosilicate glass.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Ion**} & **Range** & **Sn** & **Se** & **St** & **Flux** & **Fluence** & **Total Displace-** \\  & \(\upmu\)m & **keV/nm** & **keV/nm** & **keV/nm** & **(Ions/cm\({}^{2}\))s** & **Ions/cm\({}^{2}\)** & **ments/Ion** \\ \hline He\({}^{+}\) & 1.9 & \(5\times 10^{-3}\) & 0.5 & 0.5 & \(1.6\times 10^{13}\) & \(5.0\times 10^{14}\)–\(1.0\times 10^{17}\) & 164 \\ Ar\({}^{9+}\) & 1.7 & 0.4 & 1.5 & 1.9 & \(2.1\times 10^{12}\) & \(5.6\times 10^{12}\)–\(1.7\times 10^{16}\) & 5960 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Statistics of ion irradiation in the studied borosilicate glass.  
Figure 1: Distribution of stopping power against the glass depth exposed to 0.5 MeV He and 2 MeV Ar ion irradiation, respectively.  
Figure 2 indicates that the hardness of the irradiated glasses is remarkably less than that of the pristine one. This was especially more pronounced for the Ar-ion-irradiated glass. Since the plastic interaction zone is approximately twice the depth of plastic penetration [5,13,14], the measured values with penetration depths varying from 500 nm to 1000 nm were considered to describe the corresponding mean hardness values of the specimens. Figure 3 reveals that, as the irradiation fluence increased, the corresponding mean hardness of He-ion-irradiated glass reduced. For the ion fluence of 1 \(\times\) 10\({}^{15}\) ions/cm\({}^{2}\) (i.e., \(\mathrm{E_{nucl.}}\) = 1.8 \(\times\) 10\({}^{20}\) keV/cm\({}^{3}\)), the hardness saturated. This is consistent with the published reports for the ion-irradiated borosilicate glass [8,11,12,13,15,17]. The obtained results demonstrated that the maximum hardness reduction was approximately 8.4%. For Ar- ion-irradiated borosilicate glass, the mean hardness decreased first, and when the fluence reached 1.06 \(\times\) 10\({}^{15}\) ions/cm\({}^{2}\), it increased. The maximum reduction was about 17.0%. Moreover, when the ion fluence was set to 7.7 \(\times\) 10\({}^{15}\) ions/cm\({}^{2}\) (i.e., \(\mathrm{E_{nucl.}}\) = 7.6 \(\times\) 10\({}^{22}\) keV/cm\({}^{3}\)), the mean hardness increased first and then saturated. It should be indicated that the hardness of the Ar-ion-irradiated samples had a significant recovery of approximately 6.2%, while there was no similar trend in the He-ion-irradiated samples. This is also consistent with published reports.  
Figure 2: Distribution of hardness against the penetration depth for He and Ar ion-irradiated borosilicate glass.  
It was observed that Ar ions imposed high and intermediate damage levels (i.e., 17.0% and 11.5%, respectively), while He ions imposed a low damage level (i.e., 8.4%). Moreover, Figure 4 indicates that He ions induced different degrees of the recovery effect in the hardness of the Ar pre-irradiated specimens. More specifically, both the maximum and intermediate damage levels recovered to the saturation damage level of He ion irradiation.  
Figure 4: Variations of hardness against the He irradiation in Ar pre-irradiated samples.  
Figure 3: The hardness variation of borosilicate glasses versus the He and Ar ion fluence.