**3.1. Size-dependent deformation mechanisms**

of the driving force for grain growth by segregation of the solutes at the grain-boundaries (GBs), (ii) Kinetic approach: reduction of the GB mobility, by e.g., porosity, solute atoms, and

In this chapter, first, a brief introduction of mechanical stress-driven grain growth in NS Cu and Ni thin films/foils as well as their mechanical properties will be provided in terms of sizedependent deformation mechanisms. Subsequently, dopants segregation at GBs to hinder grain coarsening and enhance mechanical properties via the alloying method is discussed in

three representative binary Cu-based systems, i.e., Cu-Zr, Cu-Al, and Cu-W.

**2. Synthesis, microstructural characterizationw and mechanical tests**

The synthesis of NS metallic thin films can be achieved by several bottom-up techniques, such as physical vapor deposition (PVD) and electrodeposition (ED), in which the choice of deposition conditions has a tremendous influence on the microstructural features and mechanical

PVD is the most common approach to fabricate metallic thin films/foils, including evaporation, sputtering, and less commonly molecular beam epitaxy [16, 17]. Compared with other methods, magnetron sputtering (MS) can clean the substrate by "backsputtering" and generate greater impact angles of the sputtered atoms onto the substrate, resulting in smaller surface roughness of the film by covering the defects and/or step on the substrate [17]. Although, MS increases the possibility of crystal damage due to high impact energies of sputtered atoms,

ED is a technique within the broader group of electrochemical synthesis methods and uses an electric current to deposit pure metals from an aqueous, electrolytic solution [18, 19]. Compared with PVD, ED offers a lower cost and faster low-temperature deposition method. It displays remarkable advantages to synthesize highly dense NC materials with (1) few size and shape limitations, (2) tunable microstructural size parameters, and (3) hierarchical structures, e.g., a bimodal grain size-distribution [20] and NT grains [21], providing potential benefits to mechanical performance. Especially, these nanotwins improve both the mechanical

The crystalline structure, orientation, and grain boundaries within metallic thin films could be experimentally probed by suitable techniques, including X-ray diffraction (XRD), scanning and transmission electron microscopy (SEM and TEM), combining with other more superior appurtenances, such as the electron backscattered diffraction (EBSD) system and the precession-enhanced electron diffraction (PED) system. The chemical conuration of the materials can be characterized by the energy dispersive X-ray (EDX) and the powerful 3-D atom probe

Due to the difficulty in performing the mechanical tests on the free-standing metallic thin films often with thickness of roughly 1 µm or less, researchers put great emphasis on the substrate-supported thin films. For example, the tensile ductility and fatigue lifetime of metallic

precipitates at the GBs, which impose drag forces.

80 Study of Grain Boundary Character

properties of these NS metallic films/foils.

tomography (APT).

it is still the most widely used method to prepare thin films.

strength and ductility, yet maintain high electric conductivity [22].

In coarse-grained (CG) metals (grain size *d* ≥ 1 µm), deformation of the material is believed to occur through the generation and motion of dislocations within the individual grains. As the grain size decreases, it is normally expected that with GBs now occupying a significant volume fraction of the material, deformation proceeds by a mechanism that is intergranular rather than intragranular in nature.

Yamakov and colleagues [25] constructed a deformation mechanism map in NC FCC metals using information obtained from molecular dynamics (MD) simulations (see **Figure 1**), revealing how the crossover with decreasing *d* from dislocation-driven to GB-mediated deformation depends on the stacking-fault energy (SFE, *γ*sf), the elastic properties of the material, and the magnitude of the applied stress. This deformation map can be divided into three regions in light of the competition between the grain size *d* and the dislocation splitting distance *r*. Region I encompasses larger *d* and/or higher *γ*sf, where plastic deformation is dominated by full (perhaps extended) dislocations that nucleate from GBs and propagate across grains. Region II involves smaller *d* and/or lower *γ*sf, where partials nucleate and propagate across grains, associated with production of stacking-faults (SFs) that inhibit subsequent dislocation motion and induce strain hardening. Region III corresponds to the smallest *d* or lowest stress regime, where no dislocations are present and deformation is dominantly controlled by GB-mediated mechanism, resulting in an inverse H-P effect. Although these MD simulations performed at unrealistically large strain rates (10<sup>7</sup> –10<sup>9</sup> s–1), their findings agree well with the experiment observations about the transition from full dislocations to partials and finally to GB-mediated processes.

Where do dislocations in NC metals go if they are the dominant plastic carriers? Actually, in the MD simulations, a key deformation process is dislocation nucleation at a GB, glide across grain interiors that are free of obstacles, and are absorbed by the opposite GB [26, 27].

**Figure 1.** A deformation-mechanism map incorporating the role of the SEF for FCC NC metals at low temperature. The map shows three distinct regions in which either complete extended dislocations (Region I) or partial dislocations (Region II), or no dislocations at all (Region III) exist during the low-temperature deformation of FCC NC metals. The map is expressed in reduced units of stress (*σ*/*σ*∞) and inverse grain size (*r*<sup>0</sup> /*d*).The parameters *σ*∞ and *r*<sup>0</sup> are functions of the SEF and the elastic properties of the material. Figure is taken with permission from Ref. [25].

Both *in situ* and *ex situ* experiments have unambiguously demonstrated that the reversible motion of dislocations emitted from GBs accompanied with weak storage even starvation of dislocations in grain interiors in deformed NC FCC metals, leaving behind deformation twins (terminated at GBs) and SFs in general at upper and lower nanoregime, respectively [28–34]. In this context, GBs act as dislocation sources as well as sinks.

In parallel, several theoretical models have been proposed to predict the crossover grain size (*dC*) between emitted full dislocations and partials from GBs and explain the twinning behavior in NC metals. A simple, realistic model based on dislocations emission from GBs was constructed by Asaro et al. [35], in which the critical stresses needed to move a full dislocation and a partial are described respectively as follows:

$$
\sigma\_{\text{ball}} \propto \frac{\mu b}{d} \tag{1}
$$

and

$$
\sigma\_{\text{Partal}} \propto \left(\frac{1}{3} - \frac{1}{12\pi}\right) \frac{\mu b}{d} + \frac{\mathcal{V}\_{\text{SV}}}{b} \tag{2}
$$

where *μ* is the shear modulus, *b* is the magnitude of Burgers vector of full dislocations, and *γSF* is the stacking fault energy (SFE).

The slip of partials in general triggers the formation of deformation twins and SFs that contribute to the plastic deformation of NC FCC metals. There is a double-inverse grain size effect on deformation twinning in NC metal with respect to the normal Hall-Petch (H-P) *d-*dependence, as uncovered in Ni [30] and Cu [31]. This nonmonotonic *d*-dependence of twinning is explained by Zhang et al. [31] via the stimulated slip model, involving the competing grain size effects on the emission of the first partial, and the plane-to-plane promotion of partial slip afterwards. Though this model was originally proposed to explain the H-P *d-*dependent twinning in CG metals (e.g., Ti), latter *in situ* TEM observations in stretched Au nanowires clearly demonstrated the stimulated slip of partials is operative at nanoregime [36]. Actually, just opposite to the trend of twinning, its reverse process, i.e., detwinning, also manifests the double-inverse *d*-dependence, as revealed in NT Ni [37].

It is conceivable that GB-mediated deformation become more important in NC metals due to a high density of GBs [38, 39]. Typically, this is expected to occur for grain sizes below 15 nm for most metals [38], because ordinary dislocation plasticity requires prohibitively high stresses to switch on, predicted from Eqs. (1) and (2). In this regime, GB-mediated deformation leads to material's softening or the so-called inverse H-P effect [40]. Given the pervasive dislocation nucleation and motion still prevails in such a small size-range, Carlton and Ferreira [41] established an elegant model based on the statistical absorption of dislocations by GBs to explain the inverse H-P effect, showing that the yield strength is dependent on strain rate and temperature and deviates from the H-P relationship below a critical grain size.

Building on these insights from NC metals, it is unexpected that Cu, even high SFE Ni, with submicron grains and a high density of nm-scale twin boundaries (TBs) exhibit the softening behavior deformed at RT. As a matter of fact, in NT FCC metals, the TBs not only serve as deformation barrier for dislocation transmission but also serve as dislocation sources as well as sinks [21, 42, 43]. Concomitantly, NT metals, e.g., Cu, also exhibit the size-dependent deformation mechanisms that transit from dislocation nucleation from steps on the TBs to TB/ GB junctions at a critical twin thickness (*λC*), e.g., *λ<sup>C</sup>* ~18 nm for Cu [43], as shown in **Figure 2**. At this point, the classical H-P type of strengthening due to dislocation pile-up and cutting through twin planes transforms to a dislocation-nucleation controlled softening mechanism with TB migration resulting from nucleation and motion of partials parallel to the twin planes [44]. This mechanism transition size is quantitatively consistent well with the strongest size of ~15 nm determined by mechanical tests [21].

To summarize, NC metals exhibit size-dependent deformation mechanisms at different size regimes that involve GBs as the primary sources and sinks for dislocations as well as diffusive and sliding phenomena, that is to say, the size-dependence itself manifest strong size effects. This would inevitably affect the microstructural evolution and mechanical properties addressed below.

#### **3.2. Microstructure evolution in nanostructured metals**

Both *in situ* and *ex situ* experiments have unambiguously demonstrated that the reversible motion of dislocations emitted from GBs accompanied with weak storage even starvation of dislocations in grain interiors in deformed NC FCC metals, leaving behind deformation twins (terminated at GBs) and SFs in general at upper and lower nanoregime, respectively [28–34].

**Figure 1.** A deformation-mechanism map incorporating the role of the SEF for FCC NC metals at low temperature. The map shows three distinct regions in which either complete extended dislocations (Region I) or partial dislocations (Region II), or no dislocations at all (Region III) exist during the low-temperature deformation of FCC NC metals. The

In parallel, several theoretical models have been proposed to predict the crossover grain size (*dC*) between emitted full dislocations and partials from GBs and explain the twinning behavior in NC metals. A simple, realistic model based on dislocations emission from GBs was constructed by Asaro et al. [35], in which the critical stresses needed to move a full dislocation

> \_1 3 − \_1 <sup>12</sup>*π*) *μb* \_\_\_ *<sup>d</sup>* <sup>+</sup> *γ*\_\_\_*SF*

where *μ* is the shear modulus, *b* is the magnitude of Burgers vector of full dislocations, and *γSF*

*<sup>d</sup>* (1)

/*d*).The parameters *σ*∞ and *r*<sup>0</sup>

are functions of

*<sup>b</sup>* (2)

In this context, GBs act as dislocation sources as well as sinks.

map is expressed in reduced units of stress (*σ*/*σ*∞) and inverse grain size (*r*<sup>0</sup>

82 Study of Grain Boundary Character

the SEF and the elastic properties of the material. Figure is taken with permission from Ref. [25].

and a partial are described respectively as follows:

*<sup>σ</sup>*Full <sup>∝</sup> *μb* \_\_\_

*σ*Partial ∝ (

is the stacking fault energy (SFE).

and

Understanding the underlying physical mechanisms of grain growth/refinement in materials, in particular, for NT metals with simultaneous high strength and good ductility, to manipulate their microstructural stability for performance optimization is a grand challenge in the material community. It is well realized that the CG metals would shrink their grains, whereas

**Figure 2.** (a) Statistical distribution of two types of dislocations in NT Cu with different TB spacing *λ* during *in situ* deformations (left, figure is taken with permission from Ref. [43]). (b) Yield stress of NT Cu as a function of TB spacing *λ* at different grain sizes (right, figure is taken with permission from Ref. [44]).

the NC metals often coarsen their grains during plastic deformation even at low temperature. Similar phenomena were observed in NT metals and alloys, such as Cu. Therefore, it is naturally anticipated that for a metal it has a steady-state grain size (*dS* ) during plastic deformation, which was previously taken granted as a characteristic of each metal.

#### *3.2.1. Steady-state grain size*

So far, the steady-state grain sizes of metals have been thoroughly modeled in terms of various physical parameters by Mohamed [45] and further analyzed by Edalati and Horita [46] with respect to atomic bond energy and related parameters. The usage of applied stress (*σ<sup>a</sup>* ) in Mohamed's model [45] renders the roles of average internal stresses (*σ<sup>i</sup>* ) driving recovery or average effective stresses (*σ<sup>e</sup>* = *σ<sup>a</sup>* – *σ<sup>i</sup>* ) driving dislocation motion played in microstructural evolution during plastic deformation are indistinguishable. This treatment would miss some critical information about the physical mechanism(s) for microstructural evolution, which is unfavorable for us to design an engineering material with the steady-state grain size via tuning their initial microstructures and/or processing parameters. In the light of competition between average effective and internal stresses characterized by the stress ratio *η*Stress = *σ<sup>e</sup>* /*σi* , Li and coworkers [47] most recently constructed a new dislocation-based model to describe the steady-state grain size *dS* for NS metals as

$$\frac{d\_s}{b} = \mathcal{C} \left[ \frac{(2+\upsilon)M}{162\pi K b^2 \omega^2 \varphi} \right] \left( \frac{\mu b}{\mathcal{V}\_{\forall}} \right) \left( \frac{\mu}{\mathcal{O}\_s} \right) \text{ for } \left\{ f = 0 \right\} \tag{3}$$

and

$$\begin{aligned} \min \\ \frac{d\_\*}{b} &= \frac{\sqrt{\left(1-f\right)^2 + C \frac{f}{\lambda} \frac{(4+2\nu)M}{81\pi Rk} \frac{\left(\frac{\mu b}{\lambda}\right) \left(\frac{\mu}{\mathcal{O}\_\*}\right)}{\left(\frac{\mu}{\mathcal{O}\_\*}\right)}}}{2f} \frac{1}{b} - \frac{1-f}{2f} \frac{\lambda}{b} \quad \text{for } \left\{0 < f \le 1\right\} \end{aligned} \tag{4}$$

where *C* is a stress-dependent coefficient in-between the growth rate *C*<sup>1</sup> and the refinement rate *C*<sup>2</sup> , and a useful representation of the coefficient *C* as a function of *σ<sup>e</sup>* , consisting of *C*<sup>1</sup> and *C*<sup>2</sup> below and above the internal stress *σ<sup>i</sup>* , respectively, is C <sup>=</sup> ((*<sup>C</sup>* <sup>1</sup> <sup>+</sup> <sup>C</sup> <sup>2</sup> ) /2 ) −((*<sup>C</sup>* <sup>1</sup> <sup>−</sup> <sup>C</sup> <sup>2</sup> ) /2 ) erf(( *σ <sup>e</sup>* − *σ <sup>i</sup>* ) /Δ ), Δ is a measure of the extent of the transition region, *M* is the Taylor factor, *μ* is the shear modulus, *υ* is Poisson's ratio, *ϕ is* the misorientation angle between neighboring grains, *ω* represents the linear atomic density of the dislocation line, *f* is the number fraction of nanotwins, and *K* is a constant (*K* = 1 for screw dislocations and *K* = (1 − *υ*) for edge dislocations). This model captures well with the steady-state grain size *dS* obtained from free-standing NS Ni foils with *λ* = 38 nm at the steady-state creep stage tested at RT, as shown in **Figure 3**. Interestingly, by postmortem transmission electron microscopy (TEM) observations, Li et al. [47] uncovered that the ED NT Ni foils (with a strong (111) peak and followed by (200) and (311) peaks) prefer to display grain coalescence at low stress ratios *η*Stress < 1, while they prefer to display grain refinement at stress ratios *η*Stress > 1 during the creep test. When the effective stress balances the internal stress, i.e., *η*Stress = 1, these NT Ni foils sustain the stable microstructures. Note that the stress ratio itself is strongly temperature- and strain rate-dependent, in that the internal stress *σ<sup>i</sup>* has contained the contribution of the thermal component. In their work, the grain refinement/growth in the NT Ni is achieved by twinning- or detwinningmediated mechanism via dislocation-boundary interactions. Similar phenomena in cyclically compressed bulk NC Cu with an initial *d* of ~25 nm and in fatigued ultrathin Au thin films with an initial *d* of ~19 nm were observed by Hu et al. [34] and Luo et al. [48], respectively, at RT. The underlying reasons for grain growth are the excessive energy of GBs/TBs and randomly orientated grains [49] in these Ni and Cu nanostructures synthesized by the nonequilibrium deposition.

#### *3.2.2. Mechanisms of grain growth and grain refinement*

the NC metals often coarsen their grains during plastic deformation even at low temperature. Similar phenomena were observed in NT metals and alloys, such as Cu. Therefore, it is natu-

**Figure 2.** (a) Statistical distribution of two types of dislocations in NT Cu with different TB spacing *λ* during *in situ* deformations (left, figure is taken with permission from Ref. [43]). (b) Yield stress of NT Cu as a function of TB spacing

So far, the steady-state grain sizes of metals have been thoroughly modeled in terms of various physical parameters by Mohamed [45] and further analyzed by Edalati and Horita [46] with respect to atomic bond energy and related parameters. The usage of applied stress (*σ<sup>a</sup>*

evolution during plastic deformation are indistinguishable. This treatment would miss some critical information about the physical mechanism(s) for microstructural evolution, which is unfavorable for us to design an engineering material with the steady-state grain size via tuning their initial microstructures and/or processing parameters. In the light of competition between average effective and internal stresses characterized by the stress ratio *η*Stress = *σ<sup>e</sup>*

and coworkers [47] most recently constructed a new dislocation-based model to describe the

\_ *μb γsf*)( *μ*\_ *σe*

> \_\_ *λ <sup>b</sup>* <sup>−</sup> <sup>1</sup> <sup>−</sup> *<sup>f</sup>* \_\_\_ 2*f* \_\_ *λ*

) during plastic deforma-

) driving recovery

/*σi* , Li

) driving dislocation motion played in microstructural

) for (*f* = 0) (3)

*<sup>b</sup>* for (0 <sup>&</sup>lt; *<sup>f</sup>* <sup>≤</sup> <sup>1</sup>) (4)

)

rally anticipated that for a metal it has a steady-state grain size (*dS*

*λ* at different grain sizes (right, figure is taken with permission from Ref. [44]).

*3.2.1. Steady-state grain size*

84 Study of Grain Boundary Character

steady-state grain size *dS*

*<sup>d</sup>*

\_\_*s <sup>b</sup>* <sup>=</sup> <sup>√</sup>

*<sup>d</sup>*

and

or average effective stresses (*σ<sup>e</sup>* = *σ<sup>a</sup>* – *σ<sup>i</sup>*

tion, which was previously taken granted as a characteristic of each metal.

in Mohamed's model [45] renders the roles of average internal stresses (*σ<sup>i</sup>*

for NS metals as

\_\_\_\_\_\_\_\_\_\_\_ (2 + *υ*)*M* 162*πK b*<sup>2</sup> *ω*<sup>2</sup> *ϕ*](

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ (<sup>1</sup> <sup>−</sup> *<sup>f</sup>*) <sup>2</sup>

\_\_\_\_\_\_\_\_\_ (4 + 2*υ*)*M* 81*πKb ω*<sup>2</sup> *ϕ*(

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 2*<sup>f</sup>*

\_ *μb γsf*)( *μ*\_ *σe* )

<sup>+</sup> *<sup>C</sup> <sup>f</sup>* \_\_ *λ*

\_\_*s <sup>b</sup>* <sup>=</sup> *<sup>C</sup>*[ Traditionally, mechanistic descriptions that have been developed to describe NC metals have generally considered the GBs to be stable and immortal obstacles to dislocation motion, whereas there are numerous evidences that suggest that this is not always the case [4–7]. Such materials are often unstable: The NC grains tend to merge and grow larger as subjected to heat or stress. Indeed, *in situ* nanoindentation of ultrafine-grained (UFG)/NC Al films deposited on specially designed Si wedges demonstrated rapid GB migration and coalescence during deformation [4]. Another representative study has reported the grain growth of UFG/NC Cu near the indented region during microhardness testing at both cryogenic temperature and RT by Zhang et al. [5]. They surprisingly uncovered that the grain growth was found to be faster at cryogenic temperature than at RT, implying that the grain coarsening process is driven primarily by stresses rather than diffusion. Gianola et al. [6, 7] concluded that stress-driven grain growth appears to have preceded dislocation activity and involved GB migration and grain coalescence and becomes an active RT deformation mode in abnormally ductile NC Al thin films, based on coupled microtensile thin-film testing, *in situ* synchrotron diffraction experiments, and postmortem TEM observations. However, the twinning-mediated grain grow mechanism unveiled in stretched NT Ni [37, 47] and compressed NT Cu [34] is radically different from these grain growth mechanisms aforementioned above.

**Figure 4** shows the atomic evidence of twinning-mediated grain growth in NT Ni, essentially being the consequence of nanotwin-assisted GB dissociation and local grain coarsening. Because the localized misorientation between two adjacent grains G1 and G2 can be reduced

**Figure 3.** (a) Calculated steady-state grain size ds as a function of average effective stress *σ<sup>e</sup>* in nanograined Ni with different twins' fraction *f* (a) and twin thickness *λ* (b). Figure is taken with permission from Ref. [47].

Grain Boundary Segregation in Nanocrystructured Metallic Materials http://dx.doi.org/10.5772/66598 87

**Figure 4.** The TEM images showing nanotwin-assisted grain growth occurred among three grains (labeled as G1, G2 and G3, respectively) in NT Ni after creep. (b) is the magnified view of blue rectangular region in (a) and (c) is the magnified view of yellow rectangular region in (b) showing grain coalescence between G1 and G2 (left, figure is taken with permission from Ref. [47]). (d) Possibility for nanotwin-assisted grain coalescence. Possible misorientation angle (*φ*) suitable for nanograins G1 and G2 coalescence induced by the present nanotwin-assisted mechanism under different rotation axes <*hkl*> (right, figure is taken with permission from Ref. [48]). The inset shows all the misorientation angles among grains and twins.

by twinning, leading to some parts of G1 being transformed into G2, thus some localized segments of GB coalesce and disappear, see **Figure 4(b)** and **(c)**. Consequently, the repetitive formation of nanotwins induces some local segments of a high-angle GB are transformed into low-angle GB segments by storage of residual dislocations generated from dislocation reactions [37]. These recurrent interactions between partials/twins and GBs would facilitate the two adjacent nanograins to gradually coalesce into one larger grain with nanotwins. Moreover, there is a great possibility for the present mechanism to occur in G1/G2 with different mutual misorientation (*ϕ*) through the rotation around four typical low-index symmetric axes <*hkl*>, in particular, for *ϕ*<*111*> (*ϕ =* 0–10°, 50–70°, 110–130°, and 170–180°) and *ϕ*<*110*> (*ϕ =* 0–10°, 29–48.9°, 60.6–80.5°, 99.5–119.4°, 131.1–151°, and 170–180°) [48], as shown in **Figure 4(d)**.

**Figure 5** displays the TEM observation of detwinning-induced refinement of grains in NT Ni, achieved by interplay between partials and primary TBs. Two typical examples of the interactions are presented in **Figure 5(b)** and **(c)**. It appears that the atomic arrangement is distorted at the intersection region of twins, see **Figure 5(b)**. The presence of SFs in the primary twin implies the gliding of partials created by dislocation-TB reactions [50]. In **Figure 5(c)**, these Shockley partials glide parallel to the CTB, rendering detwinning of the primary twin, as observed in the twins crossed region of R4. As deformation proceeds, these partials stimulate twinning process, resulting in twin interactions to produce abundance of sessile dislocations. As a consequence, CTBs lose their coherency and transform into conventional GBs [51]. Obviously, this mechanism is parallel with other mechanisms for nanoscale structural refinement via twin/matrix lamellae in various FCC metals are identified, such as fragmentation of T/M lamellae, twins intersection, and shear banding [52].

#### **3.3. Size effects on the mechanical properties**

**Figure 3.** (a) Calculated steady-state grain size ds as a function of average effective stress *σ<sup>e</sup>*

86 Study of Grain Boundary Character

different twins' fraction *f* (a) and twin thickness *λ* (b). Figure is taken with permission from Ref. [47].

in nanograined Ni with

Mechanical properties of nanoscale structures are well known for deviating from their CG counterparts, exhibiting size effects across a wide range of properties. These NS metallic

**Figure 5.** The TEM images showing the GB formation for grain refinement via detwinning-induced twin interactions in NT Ni after creep. Figure is taken with permission from Ref. [47].

materials generally fall under the banner of "smaller is stronger." The result of this size effect is that NS thin films often exhibit mechanical properties of an increased magnitude: typically the yield strength, strain rate sensitivity (SRS), and fatigue lifetime all increase with respect to the accepted bulk values.

#### *3.3.1. Strength and ductility*

A striking feature of NS metals is their extraordinary strength compared to corresponding bulk materials. The dependence of measured yield strength *σ<sup>y</sup>* of either substrate supported [23, 53–57] or freestanding [56] Cu on film thickness *h* and on grain size *d* are summarized and shown in **Figure 6(a)** and **(b)**, respectively. It seems that, similar to their bulk NS counterparts, *σ<sup>y</sup>* of Cu thin films also monotonically increases with reducing *d* and shows some-

Grain Boundary Segregation in Nanocrystructured Metallic Materials http://dx.doi.org/10.5772/66598 89

**Figure 6.** The dependence of yield strength of Cu thin films as a function of (a) grain size *d* and (b) film thickness *h*. The lines in (a) are predictions of yield strength from the H-P relationship, partial dislocation model (Eq. (1)) and full/perfect dislocation model (Eq. (2)), respectively.

what drop until *d* reduces down to ~20 nm, as shown in **Figure 6(a)**. In this strengthening regime, *σ<sup>y</sup>* obeys the empirical H-P relationship, i.e., *σ<sup>y</sup>* ∝ *d*-0.5, at *d* ≥ ~800 nm. Below this grain size, the strength of UFG/NC Cu thin films can be well captured by Eqs. (1) and (2). Also, **Figure 6(b)** clearly shows *σ<sup>y</sup>* increases with decreasing *h* down to nanoregime and appears to drop slightly between 20 and 50 nm thickness. In general, *d* trends to scale with *h*. Thus, the strengthening of Cu thin films results from the constraints of both *d* and *h* on dislocation nucleation and motion.

The attainment of both strength and ductility is a vital requirement for most structural materials; unfortunately these properties are generally mutually exclusive. This general belief holds true for these NS metallic thin films/foils, such as Cu and Ni. For example, Niu et al. [23] studied the tensile ductility of NC Cu thin films with thickness spanning from 60 to 700 nm by characterizing the critical strain to nucleate microcracks, and revealed the fashion of "smaller is stronger and smaller is less ductile." The limited tensile ductility in NS thin films can be ascribed to the lack of strain hardening and grain geometry. In particular, the NC thin films with columnar grains are more favorable to exhibit quite limit uniform tensile elongation, because the insufficient room in NC grains does not permit involving intragranular dislocation interaction and entanglement and cracks are easier to propagate along columnar GBs [58]. This intrinsic limitation promotes plastic instabilities such as necking or cracking.

materials generally fall under the banner of "smaller is stronger." The result of this size effect is that NS thin films often exhibit mechanical properties of an increased magnitude: typically the yield strength, strain rate sensitivity (SRS), and fatigue lifetime all increase with respect to

**Figure 5.** The TEM images showing the GB formation for grain refinement via detwinning-induced twin interactions in

A striking feature of NS metals is their extraordinary strength compared to corresponding

[23, 53–57] or freestanding [56] Cu on film thickness *h* and on grain size *d* are summarized and shown in **Figure 6(a)** and **(b)**, respectively. It seems that, similar to their bulk NS coun-

of Cu thin films also monotonically increases with reducing *d* and shows some-

of either substrate supported

bulk materials. The dependence of measured yield strength *σ<sup>y</sup>*

NT Ni after creep. Figure is taken with permission from Ref. [47].

the accepted bulk values.

88 Study of Grain Boundary Character

*3.3.1. Strength and ductility*

terparts, *σ<sup>y</sup>*

By far, three available strategies are presented that demonstrate enhancement of ductility in NC metals, including engineering grain-size distributions [59], embedding growth nanotwins [21], and designing high twinnability NC metals [60]. Gianola et al. [6] has uncovered that the stressassisted grain growth has a dynamic effect on the macroscopic mechanical properties of free-standing NC Al thin films; extended ductility can be realized along with a concurrent loss in strength in comparison to tests in which no grain growth was observed. Therefore, this twinning-mediated grain growth mechanism unveiled in NT Ni [37, 47] seems to synergically combine the merits of (deformation/growth) nanotwins and grain growth mentioned above, being a novel and promising method to enhance the tensile ductility of NS metals for their performance optimization.

#### *3.3.2. Strain-rate sensitivity*

The plastic deformation kinetics in NS metals could be investigated to shed light on the strength-ductility tradeoff. It is well known that a material's strain rate dependence is usually quantified through the power law relationship: *<sup>σ</sup>* <sup>=</sup> *<sup>σ</sup>*<sup>0</sup> *<sup>ε</sup>*˙ *<sup>m</sup>* [61]. The strain-rate sensitivity (SRS) of a material can be characterized by two key kinetic signatures of deformation mechanisms, i.e., SRS index (*m*) and activation volume (*V*\* ), both of which correlated via the expression *<sup>m</sup>* <sup>=</sup> <sup>∂</sup> ln(*σ*) \_\_\_\_\_\_ <sup>∂</sup> ln(*ε*˙) <sup>=</sup> <sup>√</sup> \_\_ 3 *k* <sup>B</sup> *<sup>T</sup>* \_\_\_\_ *<sup>σ</sup> <sup>V</sup>*\* . The former characterizes the rate-controlling process, while the latter characterizes deformation kinetics in a metal. From a series of experiments, the SRS *m* is summarized **Figure 7(a)** and **(b)** for UFG/NC nontwinned [62–69] and NT [37, 70, 71] FCC metals (i.e., Cu and Ni). **Figure 7(a)** shows that *m* for several typical small-scaled Cu materials (e.g., NC Cu, single and multicrystalline Cu micropillars) increases monotonically with decreasing their *size parameters*, with *m* > 0.01 for small-scaled NS Cu. This trend is similar to the *d*-effect in other nontwinned FCC metals, such as Ni [64–67], and to the *λ*-effect in NT Ni foils [37, 71] and bulk NT Cu [70] that are presented in **Figure 7(b)**. The large *m* achieved in both cases can facilitate suppressing localization at high deformation rates. In contrast, the BCC metals in general exhibit the reduced *m* with decreasing *d* [62, 72]. The fundamental difference between FCC and BCC metals can be attributed to their different dislocation core structures.

Insight into the dominant deformation mechanism is often interpreted in terms of the values of activation volume *V*\* for plastic deformation. In CG FCC metals, a typical rate-determining process, such as the intersection of forest dislocations, gives a large *V*\* of the order of several hundred to a few thousand *b*<sup>3</sup> [61, 70]. At another extreme, GB sliding or GB diffusion mediated creep (Coble creep) gives a small *V*\* of less than 1*b*<sup>3</sup> . When the *V*\* is between 1*b*<sup>3</sup> and 100*b*<sup>3</sup> , the rate process typically involves cross-slip or dislocation nucleation from boundaries [70]. Recent findings have shown that there is linear relationship between the activation volume *V*\* and *size parameters*, such as grain size *d*, twin thickness *λ* and pillar diameter *ϕ* in the log-log plots [68, 69].

**Figure 7.** Strain-rate sensitivity of FCC Ni and Cu metals as a function of (a) grain size (*d*) or pillar diameter (*φ*) and (b) twin thickness (*λ*), summarized from available literatures [37, 62–71]. All the curves are visual guides.

#### *3.3.3. Mechanical fatigue lifetime*

*3.3.2. Strain-rate sensitivity*

90 Study of Grain Boundary Character

expression *<sup>m</sup>* <sup>=</sup> <sup>∂</sup> ln(*σ*) \_\_\_\_\_\_

mechanisms, i.e., SRS index (*m*) and activation volume (*V*\*

\_\_ 3 *k* <sup>B</sup> *<sup>T</sup>* \_\_\_\_

<sup>∂</sup> ln(*ε*˙) <sup>=</sup> <sup>√</sup>

ent dislocation core structures.

hundred to a few thousand *b*<sup>3</sup>

ated creep (Coble creep) gives a small *V*\*

of activation volume *V*\*

plots [68, 69].

The plastic deformation kinetics in NS metals could be investigated to shed light on the strength-ductility tradeoff. It is well known that a material's strain rate dependence is usually quantified through the power law relationship: *<sup>σ</sup>* <sup>=</sup> *<sup>σ</sup>*<sup>0</sup> *<sup>ε</sup>*˙ *<sup>m</sup>* [61]. The strain-rate sensitivity (SRS) of a material can be characterized by two key kinetic signatures of deformation

the latter characterizes deformation kinetics in a metal. From a series of experiments, the SRS *m* is summarized **Figure 7(a)** and **(b)** for UFG/NC nontwinned [62–69] and NT [37, 70, 71] FCC metals (i.e., Cu and Ni). **Figure 7(a)** shows that *m* for several typical small-scaled Cu materials (e.g., NC Cu, single and multicrystalline Cu micropillars) increases monotonically with decreasing their *size parameters*, with *m* > 0.01 for small-scaled NS Cu. This trend is similar to the *d*-effect in other nontwinned FCC metals, such as Ni [64–67], and to the *λ*-effect in NT Ni foils [37, 71] and bulk NT Cu [70] that are presented in **Figure 7(b)**. The large *m* achieved in both cases can facilitate suppressing localization at high deformation rates. In contrast, the BCC metals in general exhibit the reduced *m* with decreasing *d* [62, 72]. The fundamental difference between FCC and BCC metals can be attributed to their differ-

Insight into the dominant deformation mechanism is often interpreted in terms of the values

of less than 1*b*<sup>3</sup>

the rate process typically involves cross-slip or dislocation nucleation from boundaries [70]. Recent findings have shown that there is linear relationship between the activation volume *V*\* and *size parameters*, such as grain size *d*, twin thickness *λ* and pillar diameter *ϕ* in the log-log

**Figure 7.** Strain-rate sensitivity of FCC Ni and Cu metals as a function of (a) grain size (*d*) or pillar diameter (*φ*) and (b)

twin thickness (*λ*), summarized from available literatures [37, 62–71]. All the curves are visual guides.

process, such as the intersection of forest dislocations, gives a large *V*\*

*<sup>σ</sup> <sup>V</sup>*\* . The former characterizes the rate-controlling process, while

for plastic deformation. In CG FCC metals, a typical rate-determining

[61, 70]. At another extreme, GB sliding or GB diffusion medi-

. When the *V*\*

), both of which correlated via the

of the order of several

and 100*b*<sup>3</sup>

,

is between 1*b*<sup>3</sup>

The continuing trend of miniaturizing materials in micro- and nanodevices has led to a strong demand for understanding the complex fatigue properties of NS thin films to tailor their internal features to guarantee their reliability. Zhang and coworkers [57] investigated the fatigue behavior of NC Cu thin films with thickness spanning from 60 to 700 nm on compliant substrates by *in situ* measure the change of electrical resistance with the number of cyclic loading, by adopting the method proposed by Sun et al. [24]. **Figure 8(a)** clearly shows the dependence of fatigue lifetime (*Nf* ) of NC Cu films on *h* at different strain ranges (Δ*ε*). It is found that there is a maximum *Nf* at the critical thickness of *h* = 100 nm, above which *Nf* monotonically increases with reducing *h* at a constant Δ*ε*. While below this critical thickness,

**Figure 8.** (a) Dependence of fatigue lifetime *Nf* on strain range Δ*ε* as a function of film thickness *h* for Cu thin films, respectively. (b) A comparison of the relationship of Δ*ε* − *Nf* in Cu thin films with different thickness *h*. Figure is taken with permission from Ref. [57].

*Nf* decreases with further reducing *h*. This is caused by the good combination of high strength (~1050 MPa) and suitable ductility (~5.5%). Luo et al. [48] recently also pointed out that in addition to the potential contribution from the high strength of nanograins (of Au), notable improvement in fatigue properties may be closely associated with twinning-mediated grain growth. For a given *h*, a higher Δ*ε* leads to a smaller *Nf* of the Cu thin film. Moreover, all Cu thin films exhibit the dependence of *Nf* on Δ*ε* that could be well described by the well-known Coffin–Manson relationship: (Δ*ε*/2 ) <sup>=</sup> *<sup>ε</sup><sup>f</sup>* (2 *Nf* ) *C* , where *ε<sup>f</sup>* and *C* are the fatigue ductility coefficient and exponent, respectively, as shown in **Figure 8(b)**. Accordingly, with reduction in *h* from 700 nm with *d* = 220 nm to *h* = 60 nm with *d* = 20 nm, the surface damage morphologies change from extrusion/intrusion to intergranular cracks, due to the transition of deformation mechanism from dislocation-based to GB-mediated. In other words, with decreasing *size parameters* the localized accumulation of plastic strains within grains is hindered and the GBs take over as the preferred site for damage formation, implying the availability and activation of bulk dislocation sources become more limited in NC metals. This is consistent with the postmortem TEM observations by Zhang et al. [73].
