## 2 Materials and Methods
### Simulation Model Development
Figure 5: The simulated current density distribution with white arrows marking the direction of the current. Figure 6: Simulated distribution of hydrostatic stress. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & _DFlux_ & _PFlux_ & _TFlux_ & _SFlux_ & _Total Flux_ \\  & **(_Norm_)** & **(_Norm_)** & **(_Norm_)** & **(_Norm_)** & **(_Norm_)** \\  & **[1/(m\({}^{2}\)s)]** & **[1/(m\({}^{2}\)s)]** & **[1/(m\({}^{2}\)s)]** & **[1/(m\({}^{2}\)s)]** & **[1/(m\({}^{2}\)s)]** \\ \hline Results & \(5.83\times 10^{4}\) & \(6.05\times 10^{5}\) & \(1.81\times 10^{2}\) & \(5.04\times 10^{4}\) & \(7.14\times 10^{5}\) \\ Normalized & \(8.17\%\) & \(84.73\%\) & \(0.03\%\) & \(7.06\%\) & \(100\%\) \\ results & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The simulation results of the vacancy fluxes and the total vacancy flux—maximum values. Figure 7: The simulation results of the transported vacancy concentration with white arrows marking the vacancy transport vector. Figure 8: Simulation result of vacancy flux due to diffusion (_DFlux_) with white arrows marking vacancy transport vector. Figure 10: Simulation result of vacancy flux due to temperature gradient (_TFlux_) with white arrows marking vacancy transport vector. Figure 9: Simulation result of vacancy flux due to electric field (_PFlux_) with white arrows marking vacancy transport vector. The maximum value of the temperature exceeds 1500 \({}^{\circ}\)C, and as for the experimental results shown in Figure 4, the hottest part is located close to the hotplate. There is a temperature gradient visible along the heater arm. The current density distribution, presented in Figure 5, exhibits high current density at the right side of the structure and shows current concentration at the curved portion of the structure with a maximum of \(1.67\times 10^{10}\frac{\Delta}{\text{m}^{2}}\). The heater arm has an average current density of \(1.34\times 10^{10}\frac{\Delta}{\text{m}^{2}}\). The hydrostatic stress distribution, shown in Figure 6, illustrates the presence of a stress gradient (both positive and negative values of hydrostatic stress are present). The absolute maximum value is located on the curved portion of the structure and has a value of \(2.03\times 10^{8}\frac{N}{m^{2}}\). The negative hydrostatic stress values are located at the bottom of the arm (compression), whereas the positive values are located at the top of the structure (tension). The simulation results of vacancy fluxes and their percentage of the total vacancy flux are summarized in Table 7.  
The transported vacancy concentration is shown in Figure 7. The transported vacancy concentration is the total vacancy concentration times the fraction of vacancies that are mobile. The arrows indicate the movement of the vacancies. The highest vacancy concentration is located in the area of maximum temperature in the left portion of the heater arm. The distribution of the vacancy flux due to diffusion (_DFlux_) is shown in Figure 8. The arrows mark the direction amplitude of vacancy transport caused by diffusion. The maximum of this flux is located in the area of the highest temperature. The diffusive flux contributes to the total vacancy flux by 8.17%. The vacancy flux due to the electric field and its distribution is shown in Figure 9. The maximum of this flux is concentrated in the left portion of the structure in the area of the highest temperature and the point of the highest current density. The arrows indicate vacancy transport related to this flux mechanism. _PFlux_ contributes to the total flux by 84.73%. Figure 10 presents the distribution of the vacancy flux due to the temperature gradient with its concentration located at the place of the existing temperature gradient after the maximum temperature area. _TFlux_ contributes 0.03% to the total vacancy flux, with the directions marked by white arrows.