## 4 Results of Numerical Simulation
As the distance from the grain boundary increased, the concentration of zinc in the amorphous phase decreased. At the end of the computational domain, the zinc concentrations were almost identical. With increasing annealing temperature, the increase in the zinc concentration in both the grain and the amorphous phase near the grain boundary was observed. At higher annealing temperatures, faster grain growth was observed. At a higher growth rate, the remaining elements in the amorphous phase were pushed by the grain, causing an increase in their concentrations in the phase that surrounded the grain. The diffusion rates in the crystalline and amorphous phases remained constant, resulting in a higher element concentration at the grain boundary because grain growth was faster. It is worth mentioning that mass conservation was ensured during each simulation. Additionally, as the annealing temperature increased, an increase in zinc concentration in the grain was observed. This phenomenon was even more visible for longer annealing times. At an annealing temperature of 350 K and an annealing time of 300 s, the zinc concentration in the grain was approximately 3.52 wt.%, and at an annealing temperature of 354 K and an annealing time of 300 s, it was about 3.58 wt.%. A similar trend was observed for the amorphous phase near the grain boundary. At an annealing temperature of 350 K and an annealing time of 300 s, the zinc concentration was about 28.6 wt.%, and at an annealing temperature of 354 K and an annealing time of 300 s, the zinc concentration near the grain boundary reached almost 29.4 wt.%. Figure 6: _Cont._  
The results of the numerical simulation in Figure 7 show the extent of grain growth in the amorphous phase at various temperature values, with time values ranging from 50 s to 300 s, changing every 50 s. The grain grew the fastest at the highest isothermal annealing temperature of 354 K and the slowest at the lowest isothermal annealing temperature of 350 K. Therefore, it can be concluded that as the value of the isothermal annealing temperature decreased, the grain growth rate also decreased. This phenomenon is related to the fact that the diffusion process, which depends on the temperature value, plays a decisive role during grain growth. Figure 7 depicts the results of the numerical simulation, showing the influence of annealing temperature on the grain growth rate and the zinc concentration within the computational domain. After the given annealing times, grains of different radii were obtained. Across all annealing times, the largest grains were obtained at an annealing temperature of 354 K, whereas the smallest grains were obtained at 350 K. Taking all of the presented results into account, it can be stated that higher annealing temperatures yield larger grains. Similarly, as shown in Figure 6, for larger grains, more zinc was present in the grains. Also, for longer annealing times, the zinc concentration in the grain was higher. The same was observed for the zinc concentration near the grain boundary. For longer annealing times, more zinc was pushed off the added grain volume, and the zinc concentration near the grain boundary increased. The subsequent diffusion within the amorphous phase distributed this element throughout the subdomain; however, this phenomenon was not fast enough to avoid Zn accumulation at the grain boundary region. At maximum, it could be greater than 29 wt.% after 300 s of annealing. Figure 6: Simulation results of grain growth over annealing time at chosen isothermal annealing temperature values: T = 350 K, T = 352 K, T = 353 K, T = 353.5 K, and T = 354 K.  
Another interesting observation was the impact of annealing temperature on the zinc concentration in the grain. When the annealing temperature increased, its impact on the zinc concentration did not show a clear trend.