# Exploring Surface-Driven Mechanisms for Low-Temperature Sintering of Nanoscale Copper
## 3 Results and Discussion
### Mechanical Properties of Sintered Samples
#### 3.2.2 Young's Modulus and Tensile Strength  
Then, the uniaxial tensile tests are conducted on samples sintered at various temperatures. The stress-strain data throughout the tensile process is carefully monitored. As illustrated in Figure 9a, all sintered samples exhibit an elastic deformation range during the tensile testing, regardless of the sintering temperature. For samples sintered at temperatures below 700 K, the duration of the elastic deformation range is relatively short, quickly transitioning into the plastic deformation stage due to crack propagation caused by internal defects. In contrast, samples sintered at temperatures above 700 K demonstrate a significantly longer elastic deformation range, with sudden failure occurring at approximately 9%strain. However, these samples do not completely fracture, continuing to undergo plastic deformation in the subsequent range. The data indicate that as the sintering temperature increases, the tensile properties of the sintered samples improve markedly, with the onset of plastic deformation being notably delayed. Failure occurs only when the strain reaches around 9%, with tensile strength approaching 10 GPa. In practical scenarios, copper rods typically fracture at around 5% strain during uniaxial tensile tests, with tensile strength averaging around 380 MPa. This discrepancy arises from the smaller simulated system used, which lacks the numerous grain boundaries present in macroscopic bulk copper, preventing the failure process from initiating at these weak points. The sintered samples in the simulation are nearly perfect single crystals, resulting in significantly higher strength compared to the materials used in experiments. By observing the stage where the strain is less than 1%, it can be noted that as the sintering temperature increases, the slope of the stress-strain curve also rises, corresponding to the material's Young's modulus. Figure 9b illustrates the variation in Young's modulus of the samples obtained from the slope of the stress-strain curve during the phase of strain less than 1% at different sintering temperatures. It is evident that with the increase in temperature, the Young's modulus of the material gradually increases and stabilizes after 900 K. It is also noteworthy that the Young's modulus measured in samples sintered at temperatures above 500 K exceeds the actual Young's modulus value of bulk copper materials (127.1 GPa). This discrepancy arises because the system used in the simulation is relatively small, lacking the numerous grain boundaries present in macroscopic bulk copper; thus, the modulus measured here is nearly that of pure single-crystal copper. Nevertheless, this still reflects the relationship between sintering temperature and sintering quality, indicating that higher sintering temperatures yield samples with greater strength. To provide a more intuitive observation of the deformation process during tensile testing, atomic strain cloud diagrams are plotted during the stretching process, as shown in Figure 10. The lower table of each image represents the simulation step length corresponding to the tensile process at the respective temperature; for instance, 600,000 corresponds to a strain of 0.06. Three representative temperatures are selected: 300 K, 600 K, and 900 K, which correspond to three distinct states of the sintered samples: one with a granular morphology, one with no granular morphology and nearly closed porosity, and one with completely closed porosity. From Figure 10, it can be observed that for the sample sintered at 300 K, there are numerous pores, and the granular morphology remains largely intact. During the stretching process, its load-bearing capacity is weak, and material failure quickly initiates at the interfaces of the particles. As the strain increases, the material enters  
Figure 9: (**a**) The stress–strain relationship of sintered samples obtained at different sintering temperatures during uniaxial tensile testing.