# Exploring Surface-Driven Mechanisms for Low-Temperature Sintering of Nanoscale Copper
## 3 Results and Discussion
### Sintering of Multiple Copper Nanoparticles
#### 3.1.3 Surface-Driven Atomic Migration  
For individual atoms, spontaneous local position migration is not feasible; they can only rely on overall deformation. Once the sintering temperature exceeds 600 K, the rapid dynamic state of the internal surface of the nanoparticles is activated, allowing the atoms at the internal surface to begin jumping and wandering. This rapid dynamic state facilitates the quick smoothing of sharp features (high-curvature regions) on the internal surface, gradually transforming the original polyhedral morphology of the pores into a shape that approximates a sphere. Consequently, the evolutionary trend of the internal surface area corresponding to the pores begins to align with that of the pore volume. To quantitatively describe this process, displacement data of atoms within the system relative to their positions 50 ps prior is extracted after the nanoparticles were in complete contact. Atoms with displacements greater than 2.5 A (they are set as \"Jumping Atoms\") are selected for statistical analysis, and all data within a duration of 1 ns were averaged. As shown in Figure 5, a significant step change occurs in the line graph during the 500-600 K phase, with the number of jumping atoms at a sintering temperature of 600 K being nearly double that at 500 K. This indicates that at 600 K, the kinetic constraints on the internal surface atoms are significantly weakened, allowing them to freely wander across the surface of the internal pores in search of local energy minima. Through the migration and embedding of atoms between lattice sites, the pores during the sintering process will gradually shrink and smooth out, leading to a notable increase in the overall mechanical strength of the sintered system. When the temperature exceeds 600 K, the surface atomic motion continues to intensify between 600 K and 800 K, but the increase in the number of \"Jumping Atoms\" slows down. It is evident that with the temperature increasing, the surface area (specifically the pore surface) is rapidly decreasing (as illustrated in Figure 4), even though the temperature rise enhances the kinetic energy of the atoms, providing them with greater mobility. In this region, the sintered system becomes more compact, with reduced voids. This also provides us with a unique insight into the durability and reliability. During service, when the temperature exceeds 600 K, this mechanism can inversely exacerbate the expansion of voids under stress, significantly affecting the lifespan of the joints. Therefore, the service conditions need to be controlled at 600 K, according to our simulation results. It is worth mentioning that the data between 900 K and 1000 K in Figure 5 is conspicuously low. This phenomenon is due to the surface melting of nanoparticles occurring during the sintering process at 900 K and 1000 K. Surface melting significantly accelerates the sintering process, resulting in the simulation system completing sintering even before sampling the jumping atoms. Atoms with displacements greater than 2.5 A are predominantly found in the liquid region of the system, where they can move relatively freely due to the loss of lattice constraints. The sintering process at such high temperatures is primarily controlled by the surface melting and plastic flow processes, which are outside the purview of this article. To visually observe the distribution of jumping atoms within the sintering system, the coordinate information of sintering atoms from the simulation system at a sintering temperature of 600 K is extracted in Figure 6. Figure 6a-f are arranged in chronological order according to the sintering process, with the leftmost figure displaying an enlarged view of Figure 6b. The areas where pore bridging occurs are marked to clearly illustrate the distribution of jumping atoms near the bridging regions. Figure 6g,h are the pore volume and internal surface area during the sintering. From Figure 6a-f, it is evident that as the sintering process progresses, the initially larger pore regions gradually diminish.