**4. Mechanism of dislocation slip: physical aspects**

Crystals have different structural arrangements of atoms (**Figure 3**). The directions and planes are determined as per the Miller indices with reference to the unit cell edge vectors *e*i. The slip plane *m*g and direction *s*g in FCC crystal are shown in **Figure 4**. Equivalent families of directions and planes for an FCC are depicted in **Figure 4**. For hexagonal crystals, four indices are often noticed to permit permutations when referring to families, one index along each possible edge direction, being the last one the height c direction, **Figure 3**. The FCC arrangement (**Figure 4a**) has

**Figure 3.**

*BCC = body-Centered cubic. FCC = face-Centered cubic. HCP = hexagonal close-packed. The form ratio for HCP is c/a, ideally c/a = 1.632, but for example, cadmium has c/a = 1.886 and berilium has c/a = 1.586 [28, 29].*

#### **Figure 4.**

*(a, b) Slip plane mg and direction sg in a FCC crystal. (c) Total dislocation in a FCC. (d) Partial dislocation in a FCC lattice, where the dissociation is given as b = c + d = 1/6[* 1 *2* 1 *] + 1/6 [* 2 *11]. Adapted from [28–30]***.**

atoms at the vertices and center of the faces of an ideal hexahedron, resulting in a dense arrangement, and typical of especially ductile materials (e.g., Al, Cu, Au, Ag). FCC crystals have four {111} planes with three <110> directions in each plane, therefore in total have 12 slip systems, referred to as {111} <110>. Body-centered cubic crystals (BCC), (Cr, Fe, W) have atoms in the vertices and in the center of the hexahedron, and usual slip planes in the {110} family and direction < 1 11> (secondary slip systems may become active for some materials and temperatures).

Dislocations are considered as crystal defects that were originated because of the missing of one or few atoms from the regular atomic hierarchy (**Figure 4c** and **d**). The slip is formed due to the sliding of several dislocations, eased by the stress field developed around them. This glide does not occur simultaneously across all the grain but takes place in a worm-like movement. This gliding emphasizes the movement of dislocation concerning a plane that may have both: Burger vector b and its line (**Figure 4c**). The dislocations and their associated local stress fields interact; blocks or auxiliary ease their movement. A slip band is formed because of the accumulation of these multiple displacements. The slip bands may be visualized across the regions of polished samples that might have undergone severe plastic deformation previously.
