# Role of Multi-Scale Microstructure in the Degradation of AI Wire for Power Transmission
## 4 Discussion
### Evolution of Strength-Electrical Conductivity Relation  
With the increasing annealing temperature, the increase of EC and the decrease of yield strength were observed both for the CPAWs and the AFWs. The difference is that the EC of the CPAW is always higher than that of the AFW when the yield strength of the CPAW is the same as that of AFW.  
According to [PERSON]'s rule, the resistivity of the Al wire can be estimated by the following equation [27,28]:  
\[\rho=\rho_{\rm Al}+\rho_{\rm gb}+\rho_{\rm d}+\rho_{\rm vac}+\rho_{\rm s}+\rho _{\rm P}, \tag{7}\]  
where \(\rho_{\rm Al}\) is the resistivity of the pure Al (\(2.655\times 10^{-8}\)\(\Omega\)-m at room temperature); \(\rho_{\rm gb}\), \(\rho_{\rm d}\), \(\rho_{\rm vac}\), \(\rho_{\rm s}\) and \(\rho_{\rm P}\) are the resistivities caused by grain boundaries, dislocations, vacancies, solute atoms and precipitates, respectively.  
For the CPAW and the AFW, there is no dissolution and formation of precipitates during the annealing process. As a result, the resistivities of the precipitates and the solute atoms need not to be taken into account for the CPAWs and the AFWs. The recovery of defects including dislocations and vacancies in the cold-drawn CPAW and the cold-drawn AFW could lead to the decrease of resistivities and the increase of EC for the annealed CPAWs and the annealed AFWs. Additionally, the evolution of grains is also closely related to the change of EC. As shown in Figure 8a, the grain widths of the CPAWs and the AFWs obviously increase with the annealing temperature, which leads to the decrease of the fraction of grain boundary per unit volume. Furthermore, the grain lengths of the CPAWs and the AFWs slightly decrease with the annealing temperature. Therefore, the significant increase of grain width could reduce the probability of electron scattering during the current transmission, leading to the increase of EC. In addition, on the one hand, the grain lengths of the CPAWs annealed at 90 \({}^{\circ}\)C and annealed at 250 \({}^{\circ}\)C are about twice that of the AFWs annealed at 200 \({}^{\circ}\)C and annealed at 250 \({}^{\circ}\)C, respectively. Commonly, longer grains lead to higher EC. On the other hand, the resistivities of precipitates and solute atoms of the AFWs are higher than those of the CPAWs. As a result, the EC of the annealed CPAW is always higher than that of the annealed AFWs.  
Figure 9: The strengths induced by the grain strengthening, the precipitates and the texture of the cold-drawn CPAW, the annealed CPAWs, the cold-drawn AFW and the annealed AFWs.  
In addition to the grain size, the state of grain boundary also influences the EC of Al wires. Previously, [PERSON] et al. [18] studied the effect of grain boundary state on the resistivity of ultrafine grained commercially pure Al processed by HPT. The results show that the resistivity of non-equilibrium grain boundary is about 1.5 times of that of equilibrium grain boundary [18]. Figure 3 shows that the grain boundaries in the cold-drawn CPAW and the cold-drawn AFW are non-equilibrium grain boundaries. However, with the increase of annealing temperature, the non-equilibrium grain boundaries gradually transform into equilibrium grain boundaries, leading to the decrease of resistivities of grain boundaries. Thus, the transformation from non-equilibrium grain boundary to equilibrium grain boundary for the CPAWs and the AFWs during the annealing process could also result in the increase of EC without loss of strength.  
Consequently, the recovery of defects and the significant increase of grain width are the main mechanisms for the increase of EC and the decrease of yield strength for the annealed CPAWs and the annealed AFWs. In addition, the coarsening of the precipitates at the grain boundary could purify the interior of the grains, leading to the increase of EC and the decrease of yield strength for the annealed AFWs.