Deformation mechanisms, microstructural evolution and mechanical properties in small-scaled face-centered-cubic metallic thin films

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Deformation mechanisms, microstructural evolution and mechanical properties in small-scaled face-centered-cubic metallic thin films Jinyu Zhang *, Gang Liu **, Jun Sun *** State Key Laboratory for Mechanical Behavior of Materials, Xi'an Jiaotong University, Xi'an, 710049, People's Republic of China

A R T I C L E I N F O

A B S T R A C T

Keywords: Thin films Deformation mechanisms Microstructural stability Mechanical properties Size effects

Metallic thin films have attracted much attention owing to their unique mechanical properties, which are widely used in micro-/nano-devices. In this review, several key topics about the thin films in the micron to nano-scales are covered. First, the plastic deformation mechanisms in face-centered-cubic (FCC) metals, in particular the sizedependent deformation twinning at small scales, are discussed based on a deformation-mechanism map. Microstructural evolution is then briefly discussed from the perspective of the ratio of effective-to-internal stresses, while the stress-driven grain growth is discussed based on a twinning-mediated mechanism. The last section elucidates the size-dependent mechanical properties of metallic thin films, such as yield strength, ductility and mechanical fatigue behavior.

1. Introduction It is well-realized that when the characteristic length and the size parameter likely overlap, the conventional deformation mechanisms and size laws often break down and even be reversed in small-scaled metallic materials. The metallic thin films is one of representative examples of size effects with the tendency '‘smaller is stronger and smaller is less ductile' [1–4], and often suffer from low microstructural stability (e.g. grain growth) [5–8], even at the room temperature (RT), owing to their large volume fraction of grain boundaries (GBs). During the past two decades, metallic thin films thus have received considerable attention owing to their unique, often desirable properties for micro- and nano-technologies, and many other applications as important structural materials [9,10]. The trend of miniaturizing materials in the micro-electro-mechanical system (MEMS) has led to a strong demand for understanding the correlation between microstructure and mechanical properties of thin films and the underlying deformation mechanisms both for scientific aspects and in the interest of the reliability of MEMS. This review thus mainly focuses on deformation mechanisms, microstructural evolution and mechanical properties of face-centeredcubic (FCC) metallic thin films in micron- and nano-scales, and is divided into three sections. First, the size-dependent deformation mechanisms is introduced based on a deformation mechanism map.

Microstructural evolution, in particular the stable grain size and grain growth, is then discussed in terms of the twinning-mediated mechanism. The last section elucidates the size-dependent properties of metallic thin films, such as yield strength, ductility and mechanical fatigue lifetime. Given most of the studies by far about deformation behavior and mechanical properties of thin films are focused on polycrystalline materials and the grain size often much smaller than the film thickness govern their mechanical response, in what follows we mainly focus on the grain sizedependent deformation behavior of FCC metals. 2. Size-dependent deformation mechanisms In coarse-grained (CG, grain size d
1 μm) even ultrafine-grained (UFG, 1 μm > d > 100 nm) metals, plastic deformation often occurs through the motion and propagation of dislocations generated from the bulk (Frank-Reed) dislocation sources in grain interiors [11]. In a previous in-situ study on UFG Al with grain sizes d > 300 nm undergoing loading–unloading cycles [12], the emission of dislocations from internal sources piling against GBs has been observed. Pile-ups are formed by spiral sources and lead to the incorporation of dislocations into grain boundaries (GBs) during loading. Upon unloading, partial re-emission of dislocations from GBs can be observed. However, because grains were sufficiently large and contained dislocation sources, no intergranular

* Corresponding author. ** Corresponding author. *** Corresponding author. E-mail addresses: [email protected] (J. Zhang), [email protected] (G. Liu), [email protected] (J. Sun). https://doi.org/10.1016/j.nanoms.2019.11.002 Received 27 September 2019; Accepted 6 November 2019 Available online xxxx 2589-9651/© 2019 Chongqing University. Production and hosting by Elsevier B.V. on behalf of KeAi. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Please cite this article as: J. Zhang et al., Deformation mechanisms, microstructural evolution and mechanical properties in small-scaled facecentered-cubic metallic thin films, Nano Materials Science , https://doi.org/10.1016/j.nanoms.2019.11.002

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about the deformation mechanism transition from full dislocations to partial dislocations to GB-mediated processes with decreasing d. In parallel, several theoretical models [20,27,28] were proposed to predict the crossover grain size (dC) for the transition of full to partial dislocations emitted from GBs and explain the observed size-dependent deformation twinning behavior in FCC metals. A simple, realistic model based on dislocations emission from GBs was constructed by Asaro et al. [27], in which the critical stresses needed to move a full dislocation and a partial dislocation are respectively described as follows:

plasticity has been observed. Further reducing the grain size into the nanocrystalline (NC) regime, it is anticipated that plastic deformation proceeds by a mechanism that is intergranular rather than intragranular in nature, since there is insufficient room for the operation of bulk dislocation sources and GBs occupy a significant volume fraction [13,14]. Subsequently, in-situ TEM tensile experiments have been carried out on UFG Al thin films with a mean grain size of around 250 nm. Mompiou et al. [15] uncovered that the intergranular plasticity including nucleation and motion of dislocations inside GBs is controlled by imperfections such as GB grooves rather than by the type of GBs. This mechanism takes place in all types of GBs irrespective of the misorientation. Additionally, Rajagopalan et al. [16] studied of microplasticity and Bauschinger effect in NC Al and Au metals with grain sizes of 65 nm and 50 nm, respectively, recovered a substantial fraction (50–100%) of plastic strain after unloading. They also found that the dislocations can be emitted from a GB and absorbed by the opposite GB [17]. Atomistic simulations suggest that dislocations nucleated at grain boundaries (GBs) carry out plastic deformation in the NC regime; once nucleated, these dislocations travel across the grains and are eventually absorbed in the opposite GB [18,19]. Based on the physics of nucleation and propagation of dislocations in nanocrystalline (NC) FCC metals, Yamakov et al. [20] have built a deformation mechanism map utilizing the molecular dynamics (MD) simulations (see Fig. 1). This mechanism map unveils how the crossover with decreasing grain sizes 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. Also, 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 the lowest stress regime, where no dislocations are present and deformation is controlled by the GB-mediated mechanism (e.g. grain rotation, GB sliding). Although the MD simulations were performed at unrealistically high strain rates (107–109 s1), their predictions consist well with experimental observations [12,21–26]

σ Full ¼

μb d

;

(1a)

α  1 μb 1 γ SF þ ; α d 3 b

(1b)

and

σ Partial ¼

where μ is the shear modulus, b is the magnitude of Burgers vector of the full dislocation, γ SF is the stacking fault energy (SFE), ðα  1Þ =α  1. Considering the stress concentration effect (with a factor n of ~2–4), a transition from full to partial dislocation is thus expected at a grain size dC, dC 

3m  1 μ b2 : 3 γ sf

(1c)

At small grain sizes d < dC, emission of Shockley partials in lieu of full dislocations (when d > dC) from GBs become favorable, which in turn produces deformation twins (and SFs) to accommodate plastic deformation of NC metals. In fact, the single-crystalline films have a favorable microstructure for investigating the scaling behavior of mechanical properties and the underlying deformation mechanisms, without the influence of GB effects. Previously, in-situ transmission electron microscopy straining experiments by Oh et al. [23] were performed on 40, 60, 80 and 160 nm thick single crystalline Au films on polyimide substrates. A transition in deformation mechanisms was observed with decreasing film thickness: the 160 nm thick film deforms predominantly by perfect dislocations while thinner films deform mainly by partial dislocations (as well as deformation twins and SFs). Such film thickness-dependent deformation mechanism transition was further verified by Gruber et al. [29] via the synchrotron-based tensile testing. In polycrystalline FCC metals, the formation of deformation twins via partials emitted from GBs was first predicted by MD simulations [30] and later verified by experimental observations [31–33]. Zhang et al. [25] proposed a stimulated slip concept to elucidate the formation of such deformation twins (in submicron and nano-sized Cu grains), in which Shockley partials need to be emitted from the GBs on successive slip planes one after another in a highly correlated fashion to thicken the twin. Because it is statistically and practically impossible for a partial dislocation to nucleate on every slip plane to grow a single twin, the partial multiplication mechanism(s) [34,35] at a GB that will supply a twinning partial on every successive slip plane for twin nucleation and growth to sustain this plane-to-plane “infection” are required for stimulated slip. Interestingly, there is a double-inverse grain size effect on deformation twinning in NC FCC metals with respect to the normal Hall-Petch (H–P) d-dependence (for CG metals), as uncovered in Cu [25], see Fig. 2. This non-monotonic d-dependence of DT was also explained by Zhang et al. [25,26] via the stimulated slip model in terms of the competition between grain size effects on the emission of the first partial and the plane-to-plane promotion of partial slip afterwards. Although this model was originally proposed to explain the H–P d-dependent twinning in CG metals (e.g. Ti [36]), subsequent in-situ TEM observations in stretched nanowires of Au with low twin-fault energy barriers clearly proved the stimulated slip mechanism of partials is operative in the micron-to nano-scales [37]. However, for the small-scaled FCC metals

Fig. 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 (r0/d). The parameters σ∞ and r0 are functions of the SEF and the elastic properties of the material. Figure is taken from Ref. [18]. 2

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excess energy, small-scaled metals even at RT (RT) often exhibit grain coarsening, but they occasionally exhibit grain refinement under severe plastic deformation conditions [47]. How to tune their microstructural stability of small-scaled materials for mechanical performance optimization becomes a grand challenge in the material community [48,49]. Understanding the grain growth/refinement mechanisms in small-scaled materials is thus quit important for microstructure sensitive design of materials. It is well-known that the CG metals, such as Cu, would refine their grains, while their NC siblings in general coarsen their grains, during plastic deformation at temperatures near the RT [50]. Therefore, it is naturally anticipated that a material has a stable grain size (dS) during plastic deformation, which was previously taken granted as a characteristic of each metal. For the stable grain sizes of metals, Mohamed [51] first thoroughly modeled in terms of various physical parameters, which is further analyzed by Edalati and Horita [52] with respect to the atomic bond energy and related parameters. In Mohamed's model [51], the usage of applied stresses (σ a) lead to the roles of average internal stresses (σ i) driving recovery or average effective stresses (σ e ¼ σ a - σ i) driving dislocation motion played in microstructural evolution can't be distinguished. Thus, some critical information about the physical mechanism(s) for microstructural evolution would be lack, which is unfavorable for us to design a material with the stable grain size via tailoring their initial microstructures and/or processing parameters. In this regard, considering the competition between average effective and internal stresses, Li and coworkers [53] most recently constructed a new dislocation-based model to describe the stable grain size dS for FCC metals as

Fig. 2. The grain-size d effect on the formation of deformation twins in Cu thin films tensile-tested at the strain rate of 102/s. Figure is taken from Ref. [23].

with high twin-fault energy barriers, such as Al and Pt, unlike the above twinning route, deformation twinning initiated through the formation of two SFs separated by a single atomic layer, and proceeded with the emission of a partial dislocation in between these two SFs [38]. Through this route, a three-layer twin was nucleated without a mandatory layer-by-layer twinning process. This route is facilitated by GBs in NC metals that promote the nucleation of separated but closely spaced partials, thus enabling an effective bypassing of the high twin-fault energy barrier [38]. It is reported that the GB-mediated mechanism, such as grain rotation and GB sliding, plays a more important role in plastic deformation of NC metals when their grain size less than the strongest size, on the order of ~15 nm [13]. This is normally anticipated to occur in most metals with extremely small grain sizes (<~15 nm), because activation of ordinary dislocation plasticity in general requires prohibitively high stresses, as predicted from Equations (1) and (2). In this regime, such GB-mediated deformation involving GB sliding and grain rotation [13,39–41], Coble creep-like diffusive processes involving grain growth [42,43], GB migration via atomic shuffling [44,45,46] and stress-coupled GB motion [5,7] can lead to the softening of a material or the so-called inverse H–P behavior. In summary, small-scaled metals manifest the 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 microstructure evolution and mechanical properties addressed below.


   ds ð2 þ υÞM μb μ ¼C 162π Kb2 ω2 θ γ sf b σe

for ðf ¼ 0Þ;

(2a)

and

ds ¼ b

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi    ð4þ2υÞM μb μ ð1  f Þ2 þ C λf 81 σe π Kbω2 θ γ sf 2f

λ 1f λ  b 2f b

for ð0 < f  1Þ; (2b)

where C is a stress-dependent coefficient in-between the growth rate C1 and the refinement rate C2, and a useful representation of the coefficient C as a function of σ e, consisting of C1 and C2 below and above the internal   σ e σ i C1 C2 2 stress σ i, respectively, is C ¼ C1 þC , Δ is a measure of the 2  2 erf Δ extent of the transition region, M is the Taylor factor, μ is the shear modulus, υ is Poisson's ratio, θ 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 ¼ 1 for screw dislocations and K ¼ (1-υ) for edge dislocations). This model captures well with the stable grain size dS obtained from freestanding nanostructured Ni foils at the steady state creep stage at the

3. Microstructure evolution in nanostructured metals Owing to the large volume fraction of high-angle GBs associated with

Fig. 3. Calculated stable grain size ds as a function of effective stress σ e in nanograined Ni with different f (a) and λ (b). Figure is taken from Ref. [53]. 3

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Previous studies about the microstructural stability of NC metals showed that the grain growth is mainly achieved via the GB-related processes, such as grain rotation [14,57] and GB migration [44,58–60]. It is suggested that the grain rotation become quite important only for very small grains and at very high temperatures, and the growth mechanism is associated with gradual GB dissociation caused by dislocation motion [57]. With respect to the GB migration observed in most cases, the motion of a low-angle GB often relate to the collective motion of individual dislocations in these boundaries [59]. While the migration of a high-angle GB via reversible GB fluctuations, typically involving up to several hundred atoms in a cooperative motion manner, is mainly described by the shuffling model [44,45], the shear coupling model [5,7] and the displacement shift complete model [44,61,62]. More details can be referred to these literatures and would not be discussed here. Recently, Luo et al. [58] reported the evident adjustment ability of the local GB structures at atomic scales during self-driven GB migration, simultaneously involving GB dissociation, partial dislocation emission from GB, and faceting/defaceting in NC Cu. Furthermore, they revealed that the fundamental of GB migration ability is closely related to the local structure, i.e., the GB segment consisting of “hybrid” structural units [58]. Actually, in addition to the traditional mechanisms of grain rotation [14,57] and GB migration [44,58–60] mentioned above, deformation twinning also play an important role in grain growth for NC metals [53, 63,64]. Fig. 5 shows that the atomic evidence of twinning-mediated grain growth in free-standing Ni foils, essentially being the consequence of nanotwin-assisted GB dissociation and local grain coarsening [53]. Some nanotwins changed the local orientation of G1 to the same orientation as G2. For this reason, some parts of G1 were transformed into G2 through such multiple formation of nanotwins, leading to some localized segments of GB between G1 and G2 (marked by red asterisks) dissociate gradually (see Fig. 5(b and c)). This process not only stimulates the emission of partials from GBs, but also facilitates the dissociation of GBs and local change of orientations. Thus, the formation of nanotwins likely induces that some local parts of the high-angle GB are transformed into several new low-angle GB segments. These recurrent interactions between partials/twins and GBs would facilitate the two adjacent nanograins to gradually coalesce into one larger grain with nanotwins. Luo et al. [64] studied the mechanism of grain growth in ultrathin NC Au thin films with an initial grain size d of ~19 nm under mechanical fatigue testing and pointed out that there is a great possibility for the present mechanism to occur in G1/G2 with different mutual misorientation (θ) through the rotation around four typical low-index symmetric axes , in particular for θ<111> (θ ¼ 0–10 , 50–70 , 110–130 and 170–180 ) and θ<110> (θ ¼ 0–10 , 29–48.9 , 60.6–80.5 , 99.5–119.4 , 131.1–151 and 170–180 ), as shown in Fig. 5(d). It should be pointed out that although there is small misorientation between G1 and G2, it is

Fig. 4. Schematic illustration of grain growth based on the competition between the σ i and the σ e. The ratio of σ e to σ i, ηStress, is used to evaluate the grain size evolution: ηStress < 1, grains coarsen; ηStress > 1, grains refine; and at ηStress ¼ 1, a stable grain size is reached. Figure is taken from Ref. [53].

RT, as shown in Fig. 3. Interestingly, by postmortem transmission electron microscopy (TEM) observations, Li et al. [53] unveiled that the nanostructured Ni foils with grain orientations prefer to display grain coalescence at low stress ratio ηStress < 1, whereas they prefer to display grain refinement at stress ratio ηStress ¼ σ e =σ i > 1 during the creep test. When the effective stress balances the internal stress, i.e., ηStress ¼ σ e =σ i ¼ 1, these Ni foils manifest stable microstructures, as schematically shown in Fig. 4. These findings are consistent well with the results observed in NC Cu by Hu et al. [22], namely, grain refinement occurs at high strain rates with ηStress > 1 while grain growth occurs at low strain rates with ηStress < 1. Apart from the well-known mechanisms of grain refinement via the formation of dislocation cells or sub-GBs in CG FCC metals, deformation twinning also facilitates refining of grains in materials with low to medium SFE, such as Cu-Zn [54] and Cu–Al [55] alloys and Cu [56]. For example, Wang et al. [54] in high-pressure torsioned CG Cu–Zn alloys showed that stacking faults and twin boundaries play a key role in the grain refinement process such that the smallest achievable grain size is determined by the highest stacking fault and twin density that the system is able to produce. Similar phenomena were observed in CG Cu-Al [55] alloys and Cu [56]. Subsequently, some of the present authors verified that deformation twinning is also an important grain refinement mechanism in NC metals and found that under high deformation rates, the nano-grains of Cu with the average size of ~25 nm can be further reduced to ~18 nm via twin-twin interactions [22].

Fig. 5. (a–c) The TEM images showing nanotwin-assisted grain growth in NT Ni after creep (Figure is taken from Ref. [53].). (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 (Figure is taken from Ref. [64].). The inset shows all the misorientation angles among grains and twins. 4

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possible for them to coalesce, because the transmitting dislocations across the GB would leave residual dislocations at the GB to eliminate the misorientation [65]. Furthermore, they found that the newly formed TBs in fatigued ultrathin NC Au films are mainly incoherent TBs rather than the coherent TBs [64]. This twinning-mediated grain growth was also observed in cyclic compressed bulk NC Cu [22] with an initial grain size d of ~25 nm, which increases to ~34 nm, at the RT. Traditionally, mechanistic descriptions developed to describe NC metals generally consider the GBs to be stable and immortal obstacles to dislocation motion, whereas there are numerous evidences to suggest that this is not always the case [5–8]. In-situ nanoindentation of UFG and NC Al films deposited on specially designed Si wedges demonstrated rapid GB migration and coalescence during deformation [5]. Another representative study reported the grain growth of UFG and NC Cu near the indented region during microhardness testing at both cryogenic and RTs by Zhang et al. [8]. They surprisingly uncovered that the grain growth was found to be faster at the cryogenic temperature compared with that at the RT, implying that grain coarsening was driven primarily by stresses rather than atomic diffusion [8]. Gianola et al. [7] pointed out that the stress-driven grain growth appears to have preceded dislocation activity and involved GB migration and grain coalescence, and can be an active RT deformation mode in abnormally ductile NC Al thin films. However, the twinning-mediated grain growth mechanism uncovered in fatigued Au [64], tensioned Ni [53,65] and compressed Cu [22] is far different from these mechanisms mentioned above. It becomes clear that the excess energy of GBs enable the NC metals suffer from remarkable microstructure evolution via dislocation-GB interactions during plastic deformation even at the RT. To stabilize the microstructure of NC metals, apart from introducing special low energy GBs [66,67], alloying is an effective strategy utilizing dopant segregation at GBs to hinder GB motion. In particular, the immiscible elements tend to strongly segregate to GBs, reducing their free energy and thus the capillary driving force for grain growth [68–72]. They can also reduce GB mobility through the solute drag effect [4,73,74]. Additionally, immiscible elements often form highly dispersed particles/clusters that effectively pin GBs and create strong obstacles to dislocation motion. In such a case, alloying can significantly improve the mechanical properties (e.g. strength, ductility etc) and thermal stability of these NC pure metals by building the hierarchical microstructure via embedding nano-particles/clusters within grain interiors to increase dislocation storage on the one hand and enabling the solute atoms segregated at GBs to restrain the high mobility and thus prevent the grain growth on the other hand. Recent work by Li et al. [69] indeed proved that in the immiscible Cu–Cr alloyed thin films, Cr atoms are more favorable to segregate at the GBs with the segregation width of several nanometers accompanied with Cr clusters inside grain interiors, as shown in Fig. 6. Moreover, an optimum Cr concentration in the range of ~1.1 at.% 3.7 at.% facilitates the formation of nanotwins to significantly enhance their strength. Similar phenomena were further discovered in the immiscible Cu–W [72] and Cu–Mo [75] alloyed thin films as well as the miscible Cu-Ti [75], Cu-Al [76,77] and Cu–Zr [78,79] alloyed thin films.

Fig. 6. The 3DAP analysis of Cu-3.7 at.% Cr thin films, showing Cr segregation at GBs and the Cr concentrations inside grains and at GBs. The red dash dot line indicates the nominal volume concentration of Cr of ~3.7 at.%.

4.1. Yield strength and ductility A striking feature of NC metals is their extraordinary strength compared to corresponding bulk materials. Potential strengthening mechanisms in metallic thin films can be divided into two main categories [81]: (i) glide-controlled mechanisms, e.g., GB strengthening, Taylor hardening and the film thickness effect, and (ii) nucleation-controlled mechanisms, owing to the geometrical constraint on the activation of a dislocation source or the limited number of dislocation sources. The dependence of measured yield strength σ y of Cu thin films on their thickness h and on the grain size d are summarized in Fig. 7 [68,77,82–88]. It appears that, similar to their bulk NC siblings, the yield strength σ y of Cu thin films monotonically increases with decreasing d down to ~20 nm, below which materials softening occurs, as shown in Fig. 7(a). In this strengthening regime (d
~1 μm), the yield strength σ y can be well captured by the empirical H–P relationship, i.e., σ y ∝d0:5 . At small grain sizes (~1 μm > d
~20 nm), the yield strength of UFG/NC Cu thin films can be well captured by Equation (1). This is caused by the transition from intragranular (e.g. F-R sources) to intergranular (GB sources) deformation mechanism. In Fig. 7(b), one can also find that the yield strength σ y first increases with decreasing h down to the nano-scale and then it appears to drop slightly between 20 and 50 nm-thickness. In general, the grain size d often scales with the film thickness h. Therefore, the high yield strength of Cu thin films is a result of the coupling constraining effects of h and d on dislocation nucleation and motion. The attainment of both strength and ductility is a vital requirement for most engineering materials; unfortunately these properties are generally mutually exclusive, known as the strength-ductility tradeoff. This general belief is hold true for these NC metallic thin films, such as Cu and Ni. When the freestanding thin films subjected to a tensile strain, they can deform plastically but cannot harden as their bulk counterparts because the dislocations in thin films are ready to escape due to the limited thickness constraint. It means that the localized necking could cause further intense localized plastic deformation, resulting in fast rupture. In other words, the rupture strain of freestanding films is close to the strain needed to nucleate the microcrack or neck, due to the low hardening capability and small thickness-to-length ratio of the thin films [89]. In particular, the NC thin films with columnar grains are more favorable to exhibit quite limit uniform tensile elongation, because the insufficient room in nanosized grains doesn't permit involving intragranular dislocation interaction and entanglement and cracks are easier to propagate along columnar GBs. This intrinsic limitation promotes plastic instabilities such as necking or cracking. However, when the

4. Size effects on the mechanical properties of pure FCC metals The mechanical behavior of nanostructures are well known to deviate from their CG counterparts, displaying the strong size effects across a wide range of properties. For polycrystalline films, the varying ratio between film thickness and grain size makes it difficult to compare the results from different studies and to separate the effect of film thickness and grain size. Thus in what follows we mainly focus on the FCC with large film thickness-to-grain size ratios (>5), since under this condition this size ratio effect on strength is quite weak and is negligible [80]. The consequence of this size effect is that metallic thin films often exhibit mechanical properties of an increased magnitude: in general the yield strength and fatigue lifetime increase with respect to the bulk materials but the tensile ductility reduces. 5

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Fig. 7. The dependence of yield strength of Cu thin films as a function of (a) grain size d and (b) film thickness h.

Cu thin films different from their bulk counterparts. At the micron-scale (d and/or h > 1 μm), the fatigue deformation is accommodated by the extended dislocation structure (accompanied with extrusions/intrusions) and show the weak size-dependent crack nucleation and propagation behavior [91]. At the submicron-scale, the extended dislocation structure in the fatigued samples is replaced by individual dislocations, and the GBs take over as the preferred site for damage formation [91]. As further scaling the characteristic dimensions, the localized accumulation of plastic strains within grains is hindered, the fatigue damage only manifests the intergranular cracking dominated behavior, owing to the operation of the GB-mediated mechanisms such as GB sliding and grain rotation at the nanoscale [95]. The changes in fatigue damage with length scales (d and/or h) suggest the fatigue mechanism transits from dislocation mediated extrusion formation to intergranular crack formation controlled behavior, which can be attributed to the inhibition of dislocation mobility and the limited activation of dislocation sources on the small length scale [91]. Accompanied with the transition of fatigue mechanisms, the mechanical fatigue lifetime would be anticipated to manifest the strongly size-dependent behavior. Thus, how to accurately determine the fatigue lifetime (Nf) or the cycle-to-damage formation of metallic thin films on compliant substrates is a great challenge. Previously, several studies [80, 84,87,96] focused on the mechanical tensile cyclic deformation behavior in polymer-supported thin metal films, and suggested the corresponding methods based on the criterion for structural instability to determine the fatigue lifetime Nf. For example, one of these methods [84] is that the change in the strain range (Δε) was recorded as a function of the cycle number N for a bare substrate and a sample with a metal film under load control. The strain range for the sample with the film was initially smaller because the sample stiffness is higher due to the contribution from the film. With cyclic straining, the strain range would increase up to the level of the bare substrate, indicating the failure of the film. The fatigue lifetime Nf was defined as the critical cycle number where the Δε vs N curve of the sample dramatically increases [84]. According to this method, the fatigue lifetime Nf of polymer-supported 3 μm-thick Cu thin films has been experimentally determined as a function of the total strain ranges [84]. Another method proposed by Wang et al. [80] was based on the evolution of extrusions of cracks with fatigue cycles in Cu thin films on the polyimide substrate, Nf was defined as the number of cycles when the evolution of extrusions of cracks began to saturate. They found that the fatigue lifetime of Cu thin films was significantly dependent on their thickness, i.e., smaller thickness of the thin films leads to greater fatigue resistance. However, all these methods are not in-situ measurements and are performed with complicated and time-costly data treatment and microstructural analyses. In particular, the fatigue lifetime defined in the above methods was the critical cycle number where the metal films fail mechanically. However, for the metallic thin films used in flexible electronics, their electrical properties are very important. Far before structural instability, the microcracks will be generated in these thin films

metallic thin films are deposited on the compliant substrates, a different scenario often emerges owing to the substrate constraining effect on the necking [90]. For example, Niu et al. [91] studied the tensile ductility of NC Cu thin films deposited on the polyimide substrate characterized by the critical strain to nucleate microcracks via in-situ measurement of the change of relative electrical resistance with the magnitude of plastic deformation. It is revealed that compared with the free-standing thin films, these supported Cu thin films exhibited enhanced tensile ductility, Moreover, the strength-ductility tradeoff still exists, i.e., the Cu thin films manifest enhanced strength but suffer from reduced ductility, as shown in Fig. 8. Notice that for the polymer-supported metal films, the rupture strain is much larger than the critical strain for nucleating microcrack or necking, thus this critical strain should be more meaningful for practical applications because this parameter can be taken as a signature of initial microstructure damage. 4.2. Mechanical fatigue lifetime Although these metallic thin films are excellent in electrical performance, they are relatively stiff and poor in mechanical deformability. This renders the reliability of metal films under the cyclic stress/strain condition becomes the greatest challenge in the application of flexible electronics [92–94]. Therefore, deep understanding of mechanical fatigue behavior of polymer-supported thin films is thus in urgent need. Previously, a number of typical studies of length-scale effects on mechanical fatigue behaviors [80,91,94,95] have been conducted in metallic thin films with the thickness h or the grain size d range spanning from micron to submicron-scale. These experimental results [91] show that, since the geometric and microstructural characteristic dimensions of the materials are in the range of microns to nanometers, the constraints of the characteristic dimensions on dislocation activities and the effects of surface and interfaces in the thin films result in the fatigue behaviors of

Fig. 8. Dependence of the critical strain and the yield strength of Cu thin film on the thickness h. Figure is taken from Ref. [91]. 6

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Fig. 9. (a) Dependence of fatigue lifetime Nf on strain range Δε as a function of film thickness h for Cu thin films, respectively; (b) A comparison of the relationship of Δε - Nf in Cu thin films with different thickness h. Figure is taken from Ref. [73].

Acknowledgements

after a few cycles, which will notably affect their electrical property. Based on these considerations, Sun et al. [95] thus proposed a simple but precise method by in-situ measure the change of electrical resistance of metallic thin films with the number of cyclic loading, in which the fatigue lifetime was defined as the number of cycles when the microcrack nucleation induces the sharply linear increment of electrical resistance. Utilizing this real-time electrical resistance measurement method proposed by Sun et al. [95], Zhang and coworkers [88] investigated the fatigue behavior of NC Cu thin films with thickness spanning from 60 to 700 nm on compliant substrates by Fig. 9(a) clearly shows the dependence of fatigue lifetime Nf of NC Cu films on h at different strain ranges (Δε). It is found that there is a maximum Nf at the critical thickness of h ¼ 100 nm, above which Nf monotonically increases with reducing h at a constant Δε. While below this thickness, 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. [64] recently also pointed out that in addition to the potential contribution from the high strength of nanograins in NC metals (e.g. Au), remarkable improvement in fatigue properties may be closely correlated with the twinning-mediated grain growth. For a given thickness h, a higher Δε leads to a smaller Nf of Cu films. Moreover, all the Cu thin films exhibit the dependence of Nf on Δε that could be well described by the   well-known Coffin–Manson relationship of Δε 2 ¼ εf ð2Nf ÞC , where εf

This work was supported by the National Key Research and Development Program of China (2017YFA0700701, 2017YFB0702301), the National Natural Science Foundation of China (Grant Nos. 51621063, 51722104, 51625103, 51790482, 51761135031 and 51571157), the 111 Project 2.0 of China (BP2018008), the Fok Ying Tong Education Foundation (161096), the Shaanxi Province innovative talents promotion Projects (2018KJXX-004) and the Fundamental Research Funds for the Central Universities. References [1] M. Dao, L. Lu, R.J. Asaro, J.T.M. De Hosson, E. Ma, Acta Mater. (2007), https:// doi.org/10.1016/j.actamat.2007.01.038. [2] H. Gleiter, Prog. Mater. Sci. (1989), https://doi.org/10.1016/0079-6425(89) 90001-7. [3] K.S. Kumar, H. Van Swygenhoven, S. Suresh, Acta Mater. (2003), https://doi.org/ 10.1016/j.actamat.2003.08.032. [4] K. Lucke, K. Detert, Acta Metall. (1957), https://doi.org/10.1016/0001-6160(57) 90109-8. [5] D.S. Gianola, S. Van Petegem, M. Legros, S. Brandstetter, H. Van Swygenhoven, K.J. Hemker, Acta Mater. (2006), https://doi.org/10.1016/j.actamat.2006.01.023. [6] M. Jin, A.M. Minor, E.A. Stach, J.W. Morris, Acta Mater. (2004), https://doi.org/ 10.1016/j.actamat.2004.07.044. [7] T.J. Rupert, D.S. Gianola, Y. Gan, K.J. Hemker, Science (2009), https://doi.org/ 10.1126/science.1178226. [8] K. Zhang, J.R. Weertman, J.A. Eastman, Appl. Phys. Lett. (2005), https://doi.org/ 10.1063/1.2008377. [9] K. Barmak, C. Cabral, K.P. Rodbell, J.M.E. Harper, J. Vac. Sci. Technol. B (2006), https://doi.org/10.1116/1.2357744. [10] S.M. Spearing, Acta Mater. (2000), https://doi.org/10.1016/S1359-6454(99) 00294-3. [11] U.F. Kocks, H. Mecking, Prog. Mater. Sci. (2003), https://doi.org/10.1016/S00796425(02)00003-8. [12] F. Mompiou, D. Caillard, M. Legros, H. Mughrabi, Acta Mater. (2012), https:// doi.org/10.1016/j.actamat.2012.02.049. [13] J. Schiotz, K.W. Jacobsen, Science (2003), https://doi.org/10.1126/ science.1086636. [14] Z.W. Shan, E.A. Stach, J.M.K. Wiezorek, J.A. Knapp, D.M. Follstaedt, S.X. Mao, Science (2004), https://doi.org/10.1126/science.1098741. [15] F. Mompiou, M. Legros, A. Boe, M. Coulombier, J.P. Raskin, T. Pardoen, Acta Mater. (2013), https://doi.org/10.1016/j.actamat.2012.09.051. [16] J. Rajagopalan, J.H. Han, M.T.A. Saif, Science (2007), https://doi.org/10.1126/ science.1137580. [17] J. Rajagopalan, C. Rentenberger, H.P. Karnthaler, G. Dehm, M.T.A. Saif, Acta Mater. (2010), https://doi.org/10.1016/j.actamat.2010.05.013. [18] H. Van Swygenhoven, P.M. Derlet, A.G. Froseth, Acta Mater. (2006), https:// doi.org/10.1016/j.actamat.2005.12.026. [19] V. Yamakov, D. Wolf, S.R. Phillpot, A.K. Mukherjee, H. Gleiter, Nat. Mater. (2002), https://doi.org/10.1038/nmat700. [20] V. Yamakov, D. Wolf, S.R. Phillpot, A.K. Mukherjee, H. Gleiter, Nat. Mater. (2004), https://doi.org/10.1038/nmat1035. [21] Z. Budrovic, H. Van Swygenhoven, P.M. Derlet, S. Van Petegem, B. Schmitt, Science (2004), https://doi.org/10.1126/science.1095071. [22] J.J. Hu, J.Y. Zhang, Z.H. Jiang, X.D. Ding, Y.S. Zhang, S. Han, J. Sun, J.S. Lian, Mater. Sci. Eng. A (2016), https://doi.org/10.1016/j.msea.2015.11.031. [23] S.H. Oh, M. Legros, D. Kiener, P. Gruber, G. Dehm, Acta Mater. (2007), https:// doi.org/10.1016/j.actamat.2007.06.015.

=

and C are the fatigue ductility coefficient and exponent, respectively, as shown in Fig. 9(b). Similar results were observed in Al thin films by Sun and coworkers [95]. 5. Summary The metallic thin films at small scales manifest strong size-dependent behavior, including the transition of deformation mechanisms, microstructural stability and the mechanical properties. While in the conventional coarse grained regime deformation twinning becomes increasingly difficult with smaller grain sizes, in nanocrystalline grains deformation twinning has been found to be a major contributing deformation mechanism again, showing a maximum propensity at the inversion grain size. The excess energy of grain boundaries enable the nanocrystalline metals to suffer from significant microstructure evolution via deformation twinning-mediated processes during plastic deformation even at the room temperature. Manipulation of grain boundary structures via dopants segregation at grain boundaries to inhibit grain coalescence associated with remarkably enhanced mechanical properties can be realized in the binary Cu-based system. Similar to their coarse grained counterparts, these nanocrystalline metallic thin films undergo the well-known strength-ductility tradeoff. The deformation mechanism transition determines the size-dependent fatigue damage, while the combination of strength and ductility governs the fatigue lifetime of thin films.

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