**3.3. Grain boundary migration-theoretical model**

Although the mechanical grain growth has been experimentally observed under various mechanical conditions, the underlying microstructural and atomic scale mechanisms are still open for debate. As mentioned in the introduction section, in an NC material, the fraction of atom residing at the GBs increases as the grain size decreases. Thus, GBs in NC materials promote the total free energy of the system. The reduction of this excess free energy through the removal of grain boundary area represents a large driving force for the grain growth. Grain growth in NC materials can be due to the rotation and coalescence of adjacent grains, as well as normal grain boundary movements. There are several theoretical models that have been proposed to describe the mechanically driven grain growth behavior, for example, stresscoupled GB migration [51–56] and grain rotation-induced grain coalescence [57].

The stress-coupled GB migration model is based on the argument that shear stress causes tangential movement of grains along GBs (GB sliding), and this produces a coupling with the normal motion of GBs (GB migration) [51]. Gutkin and Ovid'ko proposed a continuum disclination model for describing the stress-induced cooperative migration of an arbitrary tile GB [53–55]. The migrating GB was approximated by partial wedge disclination that can move under the applied shear stress, as shown in **Figure 6**. In the initial state, these GBs form two triple junctions. Under an applied shear stress, migration of GB3 from their initial position AB to a new position A′B′ occurs. Stress-induced migration of low-angle tilt GB3 results in the formation of two new triple junctions, A′ and B′. Straight-line defects (junctions) A, B, B′, and A′ are characterized by the disclination strength ±*ω*. The motion of the disclination produces rotational plastic deformation. The same is true for migration of two high-angle tile GBs with large angle gaps. It was shown that there is two critical stress, *τ*c1 and *τ*c2, that controls the GB migration behavior. When the applied stress *τ* reaches *τ*c1, the GB can migrate in the stable mode and their equilibrium position is determined by the level of *τ*. When *τ* > *τ*c2, the GB migration becomes unstable when the GB propagation does not depend on the level of *τ*. In all cases, GB migration leads to the unstable growth of a grain at the expense of its neighbors. Energy methods calculation indicates that critical shear stresses strongly depend on the elastic modulus of the material, as well as on the strength of disclination-like defects appearing at the GB junctions in the process of GB migration.

For the case where the translational mode is mainly represented by GB sliding, Wang et al. suggested a theoretical model which describes the cooperative action of GB sliding and grain rotational deformation in mechanically loaded NC materials, as shown in **Figure 7** [25]. The grain rotation-induced grain coalescence model can be understood as follows [57]: with the applied force, GB dislocations glide results in the relative translational motion of GBs. However, the triple junctions impede the motion of GB dislocation. The blocked GB

Grain Boundary Effects on Microstructural Stability of Nanocrystalline Metallic Materials http://dx.doi.org/10.5772/66426 151

the mean grain size of both the as-deposited and annealed Cu samples increase after the fatigue test, as shown in **Figure 5**. However, the grain growth is greatly suppressed in the annealed NC Cu film, which leads to the enhanced resistance to the fatigue cracking as compared with that of the as-deposited one. The enhanced fatigue strength of Cu film after annealing may be

Although the mechanical grain growth has been experimentally observed under various mechanical conditions, the underlying microstructural and atomic scale mechanisms are still open for debate. As mentioned in the introduction section, in an NC material, the fraction of atom residing at the GBs increases as the grain size decreases. Thus, GBs in NC materials promote the total free energy of the system. The reduction of this excess free energy through the removal of grain boundary area represents a large driving force for the grain growth. Grain growth in NC materials can be due to the rotation and coalescence of adjacent grains, as well as normal grain boundary movements. There are several theoretical models that have been proposed to describe the mechanically driven grain growth behavior, for example, stress-

The stress-coupled GB migration model is based on the argument that shear stress causes tangential movement of grains along GBs (GB sliding), and this produces a coupling with the normal motion of GBs (GB migration) [51]. Gutkin and Ovid'ko proposed a continuum disclination model for describing the stress-induced cooperative migration of an arbitrary tile GB [53–55]. The migrating GB was approximated by partial wedge disclination that can move under the applied shear stress, as shown in **Figure 6**. In the initial state, these GBs form two triple junctions. Under an applied shear stress, migration of GB3 from their initial position AB to a new position A′B′ occurs. Stress-induced migration of low-angle tilt GB3 results in the formation of two new triple junctions, A′ and B′. Straight-line defects (junctions) A, B, B′, and A′ are characterized by the disclination strength ±*ω*. The motion of the disclination produces rotational plastic deformation. The same is true for migration of two high-angle tile GBs with large angle gaps. It was shown that there is two critical stress, *τ*c1 and *τ*c2, that controls the GB migration behavior. When the applied stress *τ* reaches *τ*c1, the GB can migrate in the stable mode and their equilibrium position is determined by the level of *τ*. When *τ* > *τ*c2, the GB migration becomes unstable when the GB propagation does not depend on the level of *τ*. In all cases, GB migration leads to the unstable growth of a grain at the expense of its neighbors. Energy methods calculation indicates that critical shear stresses strongly depend on the elastic modulus of the material, as well as on the strength of disclination-like defects appearing at

For the case where the translational mode is mainly represented by GB sliding, Wang et al. suggested a theoretical model which describes the cooperative action of GB sliding and grain rotational deformation in mechanically loaded NC materials, as shown in **Figure 7** [25]. The grain rotation-induced grain coalescence model can be understood as follows [57]: with the applied force, GB dislocations glide results in the relative translational motion of GBs. However, the triple junctions impede the motion of GB dislocation. The blocked GB

coupled GB migration [51–56] and grain rotation-induced grain coalescence [57].

related to the GB structure readjustment during the annealing process.

**3.3. Grain boundary migration-theoretical model**

150 Study of Grain Boundary Character

the GB junctions in the process of GB migration.

**Figure 6.** Schematic of stress-induced grain boundary (GB) migration (a and b) low-angle and (c and d) high-angle GB (GB3) by grain rotation through the glide of lattice dislocations (b) or motion of a dipole of wedge disclinations (d), respectively [54].

dislocation dissociates from the two climbing GB dislocation at the triple junction. With further plastic deformation, the dislocation split process happens repeatedly and the climbing GB dislocations form two dislocation walls along the GBs, which results in the rotation of the central NC grain. Multiple rotations bring the orientation of abutting grains closer together and reduce the GB misorientation angles, and even eliminate the GBs, leading to coalescence of smaller grains into larger ones.

**Figure 7.** Combined grain boundary (GB) sliding and rotational deformation mode. (a) The GB of the nanocrystalline (NC) Ni dominated by high-angle GBs. (b) dislocations motion along GB impeded by the triple junction resulted in climbing GB dislocations, which caused the rotation of grain 3. (c) Repeated grain rotations leading to grain coalescence. (d) The formation of a larger grain with subGBs (highlighted by dotted line) [25].

#### **3.4. Grain boundary migration-atomic scale mechanisms**

Although theoretical models give some clues about the grain growth processes during mechanical deformation of NC materials, the exact microstructural scale and atomic scale mechanisms of the GB migration is still unclear. Quantitative information aimed to identify atomic scale mechanisms that reveal the influences of GB structure on the GB migration can be obtained by using in situ HRTEM and molecular dynamics (MD) simulation methods. Haslam et al. explored how grain rotation can induce grain coarsening [58]. They found that grain rotation decomposes a GB into multiple but distinct dislocations, which can then move by dislocation slip; these dislocations can annihilate at GBs or remain embedded within grains if the applied stress is relieved. The grain rotation mechanism purports that only some grains are able to rotate and thus coarsened grains can maintain their outer boundaries. This is consistent with the experimental result that GB of coarsened grain is characterized by low-angle boundaries [43, 44]. MD simulation of nanoindentation of NC Al films with a mean grain size of 7 nm showed that the grain rotation may be competing with the GB migration and the GB migration is likely dominant, as shown in **Figure 8** [59]. During cyclic deformation of 20-nm-thick Au thin film, Luo et al. found that grain growth of NC Au is closely correlated with twin formation [60]. Based on the atomic scale observations, as shown in **Figure 9**, they revealed that the formation of nanotwins is an effective way to assist grain coarsening. The grain coarsening process can be described as follows: the mutual nucleation of nanotwins near the GB changes the local Grain Boundary Effects on Microstructural Stability of Nanocrystalline Metallic Materials http://dx.doi.org/10.5772/66426 153

**3.4. Grain boundary migration-atomic scale mechanisms**

152 Study of Grain Boundary Character

(d) The formation of a larger grain with subGBs (highlighted by dotted line) [25].

Although theoretical models give some clues about the grain growth processes during mechanical deformation of NC materials, the exact microstructural scale and atomic scale mechanisms of the GB migration is still unclear. Quantitative information aimed to identify atomic scale mechanisms that reveal the influences of GB structure on the GB migration can be obtained by using in situ HRTEM and molecular dynamics (MD) simulation methods. Haslam et al. explored how grain rotation can induce grain coarsening [58]. They found that grain rotation decomposes a GB into multiple but distinct dislocations, which can then move by dislocation slip; these dislocations can annihilate at GBs or remain embedded within grains if the applied stress is relieved. The grain rotation mechanism purports that only some grains are able to rotate and thus coarsened grains can maintain their outer boundaries. This is consistent with the experimental result that GB of coarsened grain is characterized by low-angle boundaries [43, 44]. MD simulation of nanoindentation of NC Al films with a mean grain size of 7 nm showed that the grain rotation may be competing with the GB migration and the GB migration is likely dominant, as shown in **Figure 8** [59]. During cyclic deformation of 20-nm-thick Au thin film, Luo et al. found that grain growth of NC Au is closely correlated with twin formation [60]. Based on the atomic scale observations, as shown in **Figure 9**, they revealed that the formation of nanotwins is an effective way to assist grain coarsening. The grain coarsening process can be described as follows: the mutual nucleation of nanotwins near the GB changes the local

**Figure 7.** Combined grain boundary (GB) sliding and rotational deformation mode. (a) The GB of the nanocrystalline (NC) Ni dominated by high-angle GBs. (b) dislocations motion along GB impeded by the triple junction resulted in climbing GB dislocations, which caused the rotation of grain 3. (c) Repeated grain rotations leading to grain coalescence.

**Figure 8.** Atomic-level detail of the coalescence of grains. Deformation of Al film with grain size of 7 nm. (a) Contact zone before indentation simulation. (b–d) Rotation of grain 1 due to grain boundary (GB) sliding and transformation of the structure of the GBs. (e) Dissociation and migration of the GB between grains 1 and 2 [59].

grain misorientation and results in the GB dissociated into smaller segments, which is more mobile than their parent one.

Recently, by using in situ HRTEM, Luo et al. have reported the adjustment of GB structures of Cu film during a self-driven GB migration, which involves GB dissociation, partial dislocation emission from GB, and faceting/defaceting [61]. Furthermore, they revealed that GB migration ability is closely related to the local GB segment consisting of "hybrid" structural units.

**Figure 9.** GB dissociation induced by twin formation. (a and d) TEM images of two typical examples of large grains with parallel multi-twins in the fatigued samples. (b and c) and (e and f) The corresponding details of the microstructures, respectively. Scale bars: (a and d–f) 5 nm, (b and c) 1 nm [60].
