## 3 Results
### Lattice Strain, Crystalline Size, and Dislocation Density  
The nanometric grain sizes were employed to determine the dislocation density variation as a function of processing time. In a previous investigation [27], a simple method as a first approximation was utilized to compute dislocation density. This method assumed that each crystallite had at least one dislocation, since, at quite small grain sizes, there may be lack of space to permit an array of more than 1-2 dislocations, which is hardly a pile-up, and there may also be insufficient space to maintain the core and hardened morphology. In this sense, Equation (1) may be used to calculate dislocation density (\(N\)):  
\[N=(L_{c})^{-2} \tag{1}\]  
In Equation (1), \(L_{c}\) is the crystallite size. Figure 13a,b depicts how dislocation density (cm/cm\({}^{3}\)) varies with processing time. This graph shows that dislocation density tends to grow from the start to the conclusion of ball milling processing periods both in the case of Al-5 Cr and Al-7.5 Cr alloys. This trend is justifiable since dislocations increment is generated by the plastic deformation mechanism induced by the repeated ball-powder-ball collisions that develop during milling. Hence, the augmentation of dislocation density promotes particle hardening throughout the deformation process that happens during ball milling. This results in work hardening, which can often be considered as an advantage, from the point of view that the strength of solids can be controlled by the plastic deformation process. It has been known from the beginning of the formulation of the dislocation theory that work-hardening originates from the interaction of dislocations [28; 29; 30]. Figure 12: X-ray Diffraction patterns of the Al-7.5 Cr sample in consolidated stated. However, in Al-5 Cr alloy, the density of dislocations decreased from the sixth to the tenth hours of the ball milling operation, but subsequently rose again. In addition, in Al-7.5 Cr alloy, dislocation density diminished from the 10 th to 20 th h of milling, but after increased again derive from the sintering treatment applied. This trend could be due to a recovery process of the previously deformed particles. This energy release phenomenon might have been caused by an increase in temperature as the mechanical alloying process progressed. The stored energy of the material is released during the recovery stage by dislocations motion. There are two fundamental processes: dislocation annihilation and dislocation rearrangement to produce lower energy configurations. The glide, climb, and cross-slip of these linear crystal defects enable both processes [31; 32; 33]. However, Figure 13a,b shows that the dislocation density increased after the sintering process. This behavior indicates that there was no annihilation process of dislocations during the sintering treatment, instead a dislocation multiplication mechanism could have been developed. In this case, there is a very low probability that a homogeneous nucleation of dislocations could have occured [34]. Instead, is more reasonable that a dislocation generation at local regions of stress concentration was developed because of the thermal energy provided during sintering process. The following paragraph exemplifies this dislocation multiplication mechanism. [PERSON] [35] added spherical glass inclusions into a crystal of AgCl which was subsequently given a thermal treatment to decrease the dislocation density to a minimum value. The crystal was held at 370 \({}^{\circ}\)C to homogenize the temperature and eliminate any internal strains associated with the impurity particles, afterward, it was chilled to room temperature. The results of the structural characterization of this research revealed that a system of prismatic dislocation loops was generated in a recrystallized, dislocation-free crystal AgCl to relax the strain field in the vicinity of the small glass sphere originated by differential contraction which occurs during cooling.