## 2 Experimental Procedure
### Creep Assessment Calculation Framework  
To evaluate the creep response of the system via nanoindentation, the mathematical frameworks referenced in studies [5; 12; 22; 23] were utilized. These frameworks detail the calculations necessary for understanding the system's behavior under specific conditions.  
In a typical nanoindentation experiment using a Berkovitch indenter, the expressed strain rate (\(\dot{\epsilon}\)) and hardness (\(H\)) values are determined as follows:  
\[\dot{\epsilon}=\frac{1}{h}\frac{dh}{dt}=\frac{\dot{h}}{h} \tag{1}\]  
\[H=\frac{P}{24.5\dot{h}^{2}} \tag{2}\]  
where \(\dot{h}\) is the rate of change of the indentation depth, and \(P\) represents the applied load as a function of time.  
In this study, the creep stage was initiated when the indentation depth reached the preset values (1000, 1500, and 2000 nm). Following this, a holding stage of 10 or 30 s at the maximum load (Pmax) was applied. The depth caused by creep during this holding stage is modeled as follows:  
\[h(t)_{creep}=at^{p}+kt. \tag{3}\]  
where \(t\) represents the holding time, and \(a\), \(p\), and \(k\) are the fitting parameters determined experimentally.  
The total indentation depth, accounting for both the loading and creep stages, is thus calculated as  
\[h(total)=h_{0}+at^{p}+kt \tag{4}\]  
where \(h_{0}\) is the indentation depth at the start of the creep stage, achieved upon reaching the preset depth.  
Following the empirical power law described by [PERSON] et al. [7] and [PERSON] et al. [24], the strain rate (\(\dot{\epsilon}\)) obeys the equation  
\[\dot{\epsilon}=A\sigma^{n}\ exp\ (-\frac{Q}{RT}) \tag{5}\]  
where \(A\) is a constant, \(n\) the creep stress exponent, \(\sigma\) the applied stress, and \(Q\) the activation energy. Given that these experiments were conducted at room temperature, the exponential factor \(\exp(-Q/RT)\) is considered a constant, simplifying Equation (5) to  
\[\dot{\epsilon}=\lambda\sigma^{n} \tag{6}\]  
Taking logarithms on both sides of this equation, we obtain  
\[ln(\dot{\epsilon})=ln(\lambda)+nln(\sigma) \tag{7}\]  
A similar treatment at the very first equation gives  
\[ln\big{(}\dot{\epsilon}\big{)}=ln\bigg{(}\frac{1}{h}\frac{dh}{dt}\bigg{)} \tag{8}\]  
Additionally, the relationship between applied stress \(\sigma\) and hardness H is represented by  
\[\sigma=\mathrm{kH} \tag{9}\]  
where \(k\) is a material constant, as proposed by [PERSON] et al. [5] and [PERSON] et al. [12; 23].  
Plotting \(ln(\dot{\epsilon})\) against \(ln(H)\) allows for the derivation of the creep stress exponent \(n\) from the slope and, subsequently, the strain rate sensitivity \(m\), defined as \(m=1/n\).  
To calculate the critical volume for dislocation nucleation (\(V_{cr}\)), the formulas provided by [PERSON] et al. [6], [PERSON] et al. [9], and [PERSON] et al. [23] are applied, yielding  
\[V_{cr}=\frac{kT}{\tau_{max}m} \tag{10}\]  
where \(T\) is the temperature in Kelvin (298 K in this study), \(m\) is the strain rate sensitivity, \(k\) is the Boltzmann constant, and \(\tau_{max}\) is the maximum shear stress during the creep stage.  
The maximum shear stress (\(\tau_{max}\)) is estimated as  
\[\tau_{max}=\frac{H_{max}}{3\sqrt{3}} \tag{11}\]  
where the maximum hardness (\(H_{max}\)) is calculated using the maximum load experienced at the preset indentation depth, according to  
\[H_{max}=\frac{P_{max}}{24.5h_{0}^{2}} \tag{12}\]  
This comprehensive mathematical approach allows for a detailed analysis of the system's creep response via nanoindentation, providing valuable insights into the material's mechanical properties under various loading conditions.