Materials Science and Engineering A 459 (2007) 75–81

Ductile–brittle–ductile transition in an electrodeposited 13 nanometer grain sized Ni–8.6 wt.% Co alloy Changdong Gu, Jianshe Lian ∗ , Qing Jiang, Zhonghao Jiang Key Lab of Automobile Materials, Ministry of Education, College of Materials Science and Engineering, Jilin University, Nanling campus, Changchun, 130025, China Received 17 April 2006; received in revised form 15 December 2006; accepted 19 December 2006

Abstract A ductile–brittle–ductile transition in the fracture mode of the Ni–8.6 wt.% Co alloy with an average grain size of 13 nm was observed through increasing the strain rates from 1.04 × 10−5 to 1.04 s−1 at room temperature (RT). The Ni–Co alloy exhibited a limited plastic strain (about 1%) at the intermediate strain rates of 2.08 × 10−3 to 4.17 × 10−2 s−1 , which was attributed to that in this strain rate range less dislocations or GB atoms would be activated. However, a gradual brittle–ductile transition occurred with the strain rate decreasing from 2.08 × 10−3 to 1.04 × 10−5 s−1 . The lower strain rates allow the GB atoms diffuse easily, which would relax the stress concentration and hence enhance the ductility. Another brittle–ductile transition happened with increasing the strain rates from 4.17 × 10−2 to 1.04 s−1 . The enhanced ductility at high strain rate can be explained by stress-assisted activation of GB atoms. © 2007 Published by Elsevier B.V. Keywords: Nanocrystalline material; Deformation mechanism; Tensile test; Strain rate sensitivity; Electrodeposition; Ni–Co alloy

1. Introduction Many scientific and practical investigations are currently focused on the understanding of the atomic-scale deformation mechanisms in nanocrystalline (nc) metals. The grain refinement to the nanometer range (usually less than 100 nm) would lead to the substantial strengthening which is due to that the nucleation and movement of dislocations are difficult in such tiny grains and demand very high stresses [1]. However, it was suggested from lots of experiments [2–4] and molecular dynamics (MD) simulations [5–7] that a reduction of the yield and flow stress would occur with decreasing the grain size below a certain value, named by the critical grain size, for example, 10–12 nm for Ni and Ni–Fe alloy [8], due to the transition in deformation mechanisms from one based on dislocations to one mediated by grain boundary (GB) processes [5,6]. Therefore, it is believed that the maximum strength would be obtained in the materials with the critical grain size [9]. Furthermore, it can be deduced that nc materials with critical grain sizes should possess the competing deformation mechanisms between the

∗

Corresponding author. Fax: +86 431 85095876. E-mail address: [email protected] (J. Lian).

0921-5093/$ – see front matter © 2007 Published by Elsevier B.V. doi:10.1016/j.msea.2006.12.093

processes of the dislocations and the GBs. Recently, an emerging insight is that the strain rates would also have an effect on the deformation mechanism of nc materials [10–13]. Nc materials usually exhibit highly strain-rate sensitive mechanical properties, compared to their microcrystalline counterparts with grain size typically larger than 1 ␮m [14]. A recent results [15] indicated at ultrahigh strain rates (>107 s−1 ), dislocation activity was still a prevalent deformation mechanism for the nc Ni with grain size of 30–100 nm and no deformation twinning was observed even at stresses more than twice the threshold for twin formation in micron-sized polycrystals [15]. Therefore, it would be anticipated that by changing the strain rate a deformation mechanism transition would occur in nc materials with the critical grain size. As to the available techniques for fabricating nc metals, electrodeposition has been demonstrated to be an effective route to produce dense nc sheets for the mechanical measurements due to its low cost, industrial applicability, versatility and high production rates, etc. [16]. In this paper, we fabricated an nc Ni–Co alloy with its average grain size of 13 nm being in the critical size range by a direct-current electrodeposition. More interestingly, a ductile–brittle–ductile transition in the fracture mode of the alloy was observed in the tensile deformation by changing the strain rate in a relative broad range. Its underlying mechanism was discussed by the strain rate

76

C. Gu et al. / Materials Science and Engineering A 459 (2007) 75–81

sensitivity, apparent activation volume, and the microstructure observations. 2. Experimental details Bulk nc Ni–Co alloy with a thickness of about 350 ␮m were electrodeposited from a electrolyte containing nickel sulfate, nickel chloride, boric acid, and saccharin with addition of cobalt sulfate. The similar method was used to fabricate nc Ni and Ni–1.7 wt.% Co alloy, which all exhibited an optimal mechanical properties of high strength and good ductility [17,18]. The microstructure was examined by X-ray diffraction (XRD, D/max 2500PC) and transmission electron microscope (TEM, H-800). The contents of Co and other impurities in the alloy were analyzed by the inductively coupled plasma atomic emission spectrometry (ICP-AES, Plasma/1000). The dog-bone shaped tensile specimens with a gauge cross-section of 2.0 mm × 0.25 ∼ 0.3 mm and a gauge length of 8.0 mm were cut from one Ni–Co alloy sheet by a wire electro-discharging machine and then polished to a mirror-like finish surface. Tensile tests were carried out on MTS-810 system at a broad strain rate range of 1.04 × 10−5 to 1.04 s−1 and RT. The tensile behaviors of nc Cu [19], Ni [18] and Ni–1.7 wt.% Co alloy [17] have been preformed on this testing system at such strain rate range. Tensile elongation in this study was measured through the crosshead movement of the tensile machine. The morphologies of the fracture surfaces were studied by scanning electron microscope (SEM, JSM-5600).

Fig. 1. X-ray and selected area diffractions (inset) patterns of nc Ni–8.6 wt.% Co alloy.

the high magnification showed that the grains were roughly equiaxed. A statistical analysis of ∼500 grains indicated that the Ni–8.6 wt.% Co alloy had an average grain size of about 13 nm and a narrow grain size distribution of 6–20 nm. The well-formed ring patterns of SAD (Fig. 1 inset) also confirmed the very small grain size structure of the nc alloy. The reported critical grain size for Ni and Ni–Fe alloy was about 10–12 nm [8]. Accordingly, the grains of the Ni–8.6 wt.% Co alloy are in the critical size region.

3. Results and discussions 3.1. Chemical composition, texture and microstructure

3.2. Ductile–brittle–ductile transition in the tensile deformation

The Co content in the Ni–Co alloy was detected to be about 8.6 wt.% and the alloy had the main impurities of about 110 ppm S, 560 ppm C, 500 ppm Pb and 100 ppm B. Only the facecentered cubic (fcc) phase was observed in the alloy from the XRD patterns (Fig. 1), with a weakly preferred (2 0 0) crystallographic texture where the basal planes of some grains were preferentially aligned parallel to the surface of the deposit. The electrodeposits were known for giving numerous, welldefined preferred orientations depending on electrodeposition conditions, i.e. electrolyte composition, temperature, pH, current density, stirring and organic additions, etc. [20,21]. The selected area diffraction (SAD) patterns on TEM (see Fig. 1 inset) verified the single-phase, fcc structure of the alloy, which was agreement to the XRD results. The low magnification TEM micrograph of the Ni–8.6 wt.% Co alloy (Fig. 2(a)) showed a very distinguished scene where the traces of grain clusters with a diameter of about 1–2 ␮m and their boundary regions could be clearly observed. The similar grain clusters, as shown in our case, have not been reported in the previous studies of the electrodeposited nc materials. But we think that the forming of grain clusters may be a common phenomenon in the deposition techniques and it might be related to the electrodeposition mechanism. The TEM bright field (Fig. 2(b)) and dark field (Fig. 2(c)) micrographs with

The tensile stress–strain curves for the 13 nm grain sized Ni–Co alloy at different strain rates and RT were shown in Fig. 3(a). Interestingly, the alloy exhibited the ultrahigh stress levels of 2.0–2.6 GPa. Another interesting phenomenon was the evident variation of ductility with varying the strain rate. That is, a ductile–brittle–ductile transition in the fracture mode with increasing the strain rates from 1.04 × 10−5 to 1.04 s−1 was observed. To make a clear display of the mechanical behaviors of the alloy, the varieties of the ultimate tensile strength (UTS) and the plastic strain versus the strain rate were shown in Fig. 3(b). It is shown that the strain rate plays a dominant role in the plastic deformation of the alloy. The strain rate range can be divided into two regions by the dash lines in Fig. 3(b). At the low strain rates of 1.04 × 10−5 to 4.17 × 10−2 s−1 , the nc alloy maintained the same level of UTS (about 2.0 GPa), while the plastic strain decreased dramatically from 4.2 to 1% with increasing the strain rate. At the intermediate strain rates range of 2.08 × 10−3 to 4.17 × 10−2 s−1 , the nc alloy exhibited a very limited plastic strain of about 1%. As the strain rates further increased from 4.17 × 10−2 to 1.04 s−1 , both the UTS and plastic strain were improved obviously. Furthermore, the Ni–Co alloy exhibited a very high strength level of about 2.4 GPa (where the true stress was reached to about 2.6 GPa) and a considerable plastic strain of about 5% when deformed at the highest strain rate of 1.04 s−1 .

C. Gu et al. / Materials Science and Engineering A 459 (2007) 75–81

77

Fig. 2. TEM micrographs of nc Ni–8.6 wt.% Co alloy: bright fields in the low (a) and the high (b) magnifications and (c) dark field, respectively.

To the best of our knowledge, it’s the maximal stress value currently obtained in the quasi-static uniaxial tensile deformation of nc metals at RT. Li and Ebrahimi provided a fundamental understanding of the dependence of fracture of nc metals on the grain size [22]. They fabricated single phase fcc nc metals via electrodepostion with grain size above (44 nm Ni) and below (12 nm Ni–15% Fe) the critical grain size [22]. It was found that the 44 nm Ni fractured in a ductile mode due to the dislocation generation

and motion while the 12 nm Ni–Fe alloy was seen as the typical brittle materials due to the GB-based deformation [22]. The ductile-to-brittle transition in the fracture mechanism with grain size indicates that the grain size do influence the deformation mechanisms. However, in our case we observed a continuous ductile–brittle–ductile transition in the 13 nm grain sized Ni–Co alloy by changing the strain rate, which gave the experimental evidences that the strain rate also influences the deformation mechanism of nc materials.

78

C. Gu et al. / Materials Science and Engineering A 459 (2007) 75–81

was noteworthy that in all cases the sizes (about 1–2 ␮m) of the dimples or the ‘cup’ or ‘cone’ shapes on the fracture surfaces shown in Fig. 4 were similar to those of the grain clusters by TEM observations (Fig. 2 (a)). Furthermore, the resolvable picture elements in Fig. 4, especially of the regions as shown in the down-left insets of (a–c), were in the scale of about 100 nm. These observations suggested that the deformation was involved by the collective grain activities [18,23] and the fracture might be initiated and evolved along the boundaries between the grain clusters (size of about 1–2 ␮m) and/or the tens of neighboring grains (size of about 100 nm). 3.3. Deformation mechanism The thermally activated mechanisms contribution to plastic deformation in nc metals and alloys are often quantitatively interpreted by examining the strain rate sensitivity, m, and the apparent activation volume, v [17,24–28]. The strain rate sensitivity of flow stress is defined as m = ∂ ln σf /∂ ln ε˙ , where σ f and ε˙ is the flow stress and strain rate, respectively. The experimental or apparent activation volume can be given by [24]: v=

Fig. 3. (a) Tensile true stress–strain curves of nc Ni–8.6 wt.% Co alloy at different strain rates and RT. (b) Variations of UTS and plastic strain of nc Ni–8.6 wt.% Co alloy with strain rates, respectively.

Sign of plasticity could be detected on the fracture surfaces of the alloy. Evident dimples morphologies, typical of ductile fracture, were observed on the fracture surface of specimens deformed at both the low and high strain rates of 1.04 × 10−5 and 1.04 s−1 , as shown in the up-left insets of Fig. 4(a and b), respectively. More evidently, deep dimples and significant necking of the cross-section (Fig. 4(b)) could be seen on the latter specimen. In addition, some other regions on both specimens were characteristic of a very rough and irregular surface structure (shown in the down-right insets of Fig. 4(a and b), respectively). Both the rough surface structures and the dimples should be corresponding to the ductile behavior. However, the morphologies on the fracture surfaces of the specimens deformed at the strain rates of 2.08 × 10−3 and 1.04 × 10−2 s−1 showed the mixture characteristic of the ductile and the brittle, which was shown in Fig. 4(c). Some regions on the fracture surface (as shown in the up-left inset of Fig. 4(c)) possessed the ductile feature but with the shallow dimples; some regions (as shown in the down-left inset of Fig. 4(c)) gave the brittle feature, resembling the reported ‘cup’ and ‘cone’ shapes [22]; the other regions (as shown in the down-right inset of Fig. 4(c)) seemed to be less rough than those shown in the down-right insets of Fig. 4(a and b), which should be responsible for the brittle fracture. It

√ ∂ ln ε˙ 3kT ∂σf

(1)

Here, k is the Bolzmann constant and T is the deformation temperature. Indeed, the apparent activation volume, v is related to the strain-rate sensitivity, m, through v = kT/(σf m) [25,26,28]. It is generally accepted that higher m is indicative of a smaller v. A model based on the bow-out of single dislocation from its source was proposed accounting for the relationship between the m and v for fcc metals [29]. In addition, high flow stress levels would also give a smaller v. Asaro and Suresh [24] proposed mechanistic models that sought to rationalize experimentally determined small v associated with the high m of nc metals. They presented models for the emission of partial or perfect dislocations from stress concentrations at GBs, which led to the estimates of v in the range of 3–10b3 for the truly 20 nm grain sized metals, where b is the Burgers vector. The logarithm plot of the flow stress at 0.5% plastic strain σ 0.5% versus the strain rate ε˙ for the nc Ni–8.6 wt.% Co alloy was given in Fig. 5(a). The estimated m value was 0.025, which was slightly higher than that of the 30 nm grained Ni (0.02) [30]. The tiny grain size (13 nm) of the alloy should be responsible for the enhanced strain rate sensitivity. To obtain the v, we plotted the curve of ln ε˙ versus σ 0.5% , as shown in Fig. 5(b). An average apparent activation volume, vave , was estimated to be about 7b3 from the slope of the linear fit (thin line) using Eq. (1). A similar small v of ∼8b3 was obtained in 7 nm grained Cu–Ni–P alloy [31] and 10 nm Cu [32] by nanoindentation techniques, respectively. Enhanced m is usually indicative of a smaller v, whereas the significant solid solution strengthening of Co in the alloy would also bring further decrease of v to extremely small value of about 7b3 . By analyzing the scattered date dots in Fig. 5(b), we believed that it would be more reasonable to adopt the two separated apparent activation volumes, v1 and v2 , corresponding to the low and high strain rate regions divided in Fig. 3(b), respectively. The

C. Gu et al. / Materials Science and Engineering A 459 (2007) 75–81

79

Fig. 4. Morphologies of fracture surface for the tensile specimens deformed at different strain rates: (a) 1.04 × 10−5 s−1 , (b) 1.04 s−1 and (c) 2.08 × 10−3 s−1 .

two separated apparent activation volumes were v1 = 13b3 and v2 = 2b3 , as shown in Fig. 5(b), respectively. The two apparent activation volumes were also distinguished based on the fact that the former (v1 = 13b3 ) corresponded to the relatively low strengths (about 2.0 GPa of UTS) and low ductility (about 1–4% plastic strain) and the latter (v2 = 2b3 ) to the high strengths of 2.4–2.6 GPa and enhanced ductility of about 4–5%.

At the low strain rates, the v1 value of ∼13b3 is corresponding to the activation length of ∼3.2 nm, which is just comparable to the edge length (∼5.5 nm) of a 13 nm octagon grain and reasonably agrees with the length of the preexisting GB dislocation source [5,29]. Numerous experiments and MD simulations suggested that the partial and perfect dislocation were emitted from the GB source (facets, steps and jogs), and traverse the grain

80

C. Gu et al. / Materials Science and Engineering A 459 (2007) 75–81

Fig. 5. (a) Logarithm plots of flow stress at 0.5% plastic strain (σ 0.5% ) as a function of strain rate ε˙ for nc Ni–8.6 wt.% Co alloy. The strain rate sensitivity (m value) was estimated from the slope of the linear fit. (b) Plots of ln ε˙ vs. σ 0.5% transformed from Fig. 5(a). The average activation volume (vave , thin line) and two separated activation volumes (v1 and v2 , dashed lines) were estimated from the slope of linear fit using Eq. (1).

under the applied stress to be re-incorporated into the opposing GB. The process of GB-defect-assisted dislocation generation, which is easier than that of emanating a lattice dislocation out of a GB, can well be a thermally activated process usually with v ≥ 10b3 [30]. As to the 13 nm Ni–8.6 wt.% Co alloy, the preexisting GB dislocation may not be sufficient [28]. Therefore, only small plastic strain (about 1% at strain rates of 10−3 to 10−2 s−1 ) was observed. However, the plastic strain of the alloy increased gradually from 1 to about 4% as the strain rate was decreasing to 1.04 × 10−5 s−1 (shown in Fig. 3). In fact, such increase of ductility in low strain rate range was also observed for 20 nm Ni [33], 12 nm Co [34] and 26 nm Cu [19]. A possible reason for this improvement of plasticity with decreasing the strain rate (i.e. the transition in fracture mode from the brittle to the ductile) is that the dislocation-based deformation accommodated by the GB atoms diffusion would occur in the lower strain rate range (10−4 to 10−5 s−1 ). The lower strain rates would allow the GB atoms diffuse easily. The process of GB atoms diffusion

could relax the local stress concentrations and hence improve the plasticity. The small apparent activation volume of ∼2b3 is readily rationalized to be corresponding to the processes of GBs. In our case, at the high strain rates the activation volume v2 (∼2b3 ) is near to the theoretical estimation value of πb3 , which was deduced from the nucleation and emission of partial dislocation at a very small loop at a GB facet crack tip or triple point, with the possibility of the trailing partial dislocation being emitted at higher levels of stress intensity [24]. In addition, the grain rotation and GB sliding would be operated together with twinning, which was revealed by the cold rolling deformation at a high strain rate of about 0.3 s−1 on the 15 nm Pd [35]. The MD simulations [36] of a 12 nm Ni under uniaxial tension indicated that GB sliding became the predominant deformation mechanism at the high strain rate of ∼107 s−1 . Generally, the high stress values can be obtained in the nc metals at the high strain rates [33,37]. It would be possible for the nucleation of small dislocation loops at GBs in nc grains under such a high stress [24]. In the present case, the Ni–Co alloy exhibited the high stress level of 2.4–2.6 GPa at strain rates of 1.04 × 10−1 to 1.04 s−1 . The level of stress is comparable to that (2.5 GPa) of the 12 nm Ni obtained by the MD simulations [36]. Under such high stresses, the GB or at least the GB defects would be fully activated, which should be corresponding to the smaller v of several b3 . The activation of GB atoms could avoid the local stress concentration at GB which usually leads to the fracture. Therefore, another evident brittle–ductile transition occurred in the nc alloy as the strain rate increased from 4.17 × 10−2 to 1.04 s−1 . The high flow stresses and enhanced ductility were also observed in the dynamic tension tests of the 20 nm Ni and Cu at strain rates of 102 to 103 s−1 [33,37]. The difference in the brittle–ductile transition between the present nc alloy and the 20 nm Ni and Cu is that the present brittle–ductile transition occurs at a lower strain rate range (10−2 to 1.0 s−1 ) due to the small average grain size (13 nm). In another words, the process of the stress-assisted activation of GBs would be easier to take place for the smaller grains. In addition, there is still a question how the Co atoms in the 13 nm grain sized Ni–Co alloy influence the estimation of the activation volume. The further work should be taken on this point. 4. Conclusions 1. The nc Ni–8.6 wt.% Co alloy with an average grain size of 13 nm was fabricated via the direct-current electrodeposition. TEM observations showed that the uniform tiny grains were reunited into 1–2 ␮m sized clusters. 2. The deformation behaviors of the nc Ni–8.6 wt.% Co alloy were strongly depended on the strain rate. Significantly, a ductile–brittle–ductile transition in the fracture mode through increasing the strain rates from 1.04 × 10−5 to 1.04 s−1 was found in the tensile deformation of the nc alloy. Furthermore, the superhigh stress value of ∼2.6 GPa was obtained at a strain rate of 1.04 s−1 and RT in this study. 3. For the 13 nm grain sized alloy, less dislocations or GB atoms would be activated at RT and intermediate strain rate range of 2.08 × 10−3 to 4.17 × 10−2 s−1 , which leads to

C. Gu et al. / Materials Science and Engineering A 459 (2007) 75–81

a brittle fracture with limited plastic strain (∼1%). However, a brittle–ductile transition occurred as the strain rates decreased from 2.08 × 10−3 to 1.04 × 10−5 s−1 . The lower strain rates could allow the GB atoms diffuse easily, which would relax the stress concentrations and hence enhance the ductility. In addition, another brittle-ductile transition occurred at the higher strain rates of 4.17 × 10−2 to 1.04 s−1 , where the stress-assisted activation of GBs would be responsible for the improved plasticity. 4. The tensile tests on the 13 nm Ni–Co alloy gave the solid experimental evidence that the strain rate would influence on the deformation mechanism of nc metals. It is expected that as to the nc metals with the critical grain size, the transition of deformation mechanism would occur by changing the strain rates. More extensive works need to be done to explain the interesting ductile–brittle–ductile transition in the fracture mode along with the strain rates for the nc alloy. Acknowledgements This work was supported by the Foundation of national key basic research and development program No. 2004CB619301 and the Project 985-Automotive Engineering of Jilin University. References [1] E. Ma, Science 305 (2004) 623–624. [2] N. Wang, Z. Wang, K.T. Aust, U. Erb, Mater. Sci. Eng. A 237 (1997) 150–158. [3] A.M. El-Sherik, U. Erb, G. Palumbo, K.T. Aust, Scripta Metall. Mater. 27 (1992) 1185–1188. [4] C.A. Schuh, T.G. Nieh, H. Iwasaki, Acta Mater. 51 (2003) 431–443. [5] D. Wolf, V. Yamakov, S.R. Phillpot, A. Mukherjee, H. Gleiter, Acta Mater. 53 (2005) 1–40. [6] J. Schiotz, K.W. Jacobsen, Science 301 (2003) 1357–1359. [7] H. Van Swygenhoven, M. Spaczer, A. Caro, D. Farkas, Phys. Rev. B 60 (1999) 22–25. [8] H. Li, F. Ebrahimi, Appl. Phys. Lett. 84 (2004) 4307–4309.

81

[9] S. Yip, Nature 391 (1998) 532–533. [10] J. Weissm¨uller, J. Markmann, Adv. Eng. Mater. 7 (2005) 202–207. [11] J. Markmann, P. Bunzel, H. Rosner, K.W. Liu, K.A. Padmanabhan, R. Birringer, H. Gleiter, J. Weissmuller, Scripta Mater. 49 (2003) 637– 644. [12] Y.M. Wang, E. Ma, Appl. Phys. Lett. 83 (2003) 3165–3167. [13] R. Asaro, P. Krysl, B. Kad, Philos. Mag. Lett. 83 (2003) 733–743. [14] R. Schwaiger, B. Moser, M. Dao, N. Chollacoop, S. Suresh, Acta Mater. 51 (2003) 5159–5172. [15] Y.M. Wang, E.M. Bringa, J.M. McNaney, M. Victoria, A. Caro, A.M. Hodge, R. Smith, B. Torralva, B.A. Remington, C.A. Schuh, H. Jamarkani, M.A. Meyers, Appl. Phys. Lett. 88 (2006) 061913–061917. [16] S.C. Tjong, H. Chen, Mater. Sci. Eng. R 45 (2004) 1–88. [17] C. Gu, J. Lian, Z. Jiang, Adv. Eng. Mater. 8 (2006) 252–256. [18] C. Gu, J. Lian, Z. Jiang, Q. Jiang, Scripta Mater. 54 (2006) 579–584. [19] Z. Jiang, X. Liu, G. Li, Q. Jiang, J. Lian, Appl. Phys. Lett. 88 (2006) 143113–143115. [20] A.M. El-Sherik, U. Erb, J. Page, Surf. Coat. Technol. 88 (1997) 70–78. [21] F.J. Czerwinski, J.a. Szpunar, Corros. Sci. 41 (1999) 729–740. [22] H.Q. Li, F. Ebrahimi, Adv. Mater. 17 (2005) 1969–1972. [23] A. Hasnaoui, H. Van Swygenhoven, P.M. Derlet, Science 300 (2003) 1550–1552. [24] R.J. Asaro, S. Suresh, Acta Mater. 53 (2005) 3369–3382. [25] S. Cheng, E. Ma, Y.M. Wang, L.J. Kecskes, K.M. Youssef, C.C. Koch, U.P. Trociewitz, K. Han, Acta Mater. 53 (2005) 1521–1533. [26] L. Lu, R. Schwaiger, Z.W. Shan, M. Dao, K. Lu, S. Suresh, Acta Mater. 53 (2005) 2169–2179. [27] Y.M. Wang, A.V. Hamza, E. Ma, Appl. Phys. Lett. 86 (2005) 241913–241917. [28] Q. Wei, S. Cheng, K.T. Ramesh, E. Ma, Mater. Sci. Eng. A 381 (2004) 71–79. [29] J. Lian, C. Gu, Q. Jiang, Z. Jiang, J. Appl. Phys. 99 (2006) 076103–176103. [30] Y.M. Wang, E. Ma, Appl. Phys. Lett. 85 (2004) 2750–2752. [31] J. Chen, Y. Shi, K. Lu, J. Mater. Res. 20 (2005) 2955–2959. [32] J. Chen, L. Lu, K. Lu, Scripta Mater. 54 (2006) 1913–1918. [33] F. Dalla Torre, H. Van Swygenhoven, M. Victoria, Acta Mater. 50 (2002) 3957–3970. [34] A.A. Karimpoor, U. Erb, K.T. Aust, G. Palumbo, Scripta Mater. 49 (2003) 651–656. [35] H. R˝osner, J. Markmann, J. Weissum¨uller, Philos. Mag. Lett. 84 (2004) 321–334. [36] H. Van Swygenhoven, P.M. Derlet, Phys. Rev. B 64 (2001) 224105–224109. [37] L. Lu, S.X. Li, K. Lu, Scripta Mater. 45 (2001) 1163–1169.