Letter pubs.acs.org/NanoLett
Experimental Quantification of Resolved Shear Stresses for Dislocation Motion in TiN N. Li,*,† A. Misra,†,§ S. Shao,† and J. Wang*,‡ †
Materials Physics and Applications Division, MPA-CINT and ‡Materials Science and Technology Division, MST-8, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States § Department of Materials Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States S Supporting Information *
ABSTRACT: Experimental quantification of the critical resolved shear stress (CRSS) at the level of unit dislocation glide is still a challenge. By using in situ nanoindentation in a high-resolution transmission electron microscope and strain analysis of the acquired structural images, the CRSS for the motion of individual dislocations on {110}⟨011⟩ slip system and glide dislocation re-emission from a tilt grain boundary in TiN are quantified. This work offers an approach to measure the local stresses associated with dislocation motion in highstrength materials. KEYWORDS: In situ HRTEM, strain mapping, resolved shear stress, dislocation motion, TiN
N
a model system for a high Peierls stress material. Under a gradient stress field generated beneath the indenter, we observed that dislocations glide away from the indenter and stop at a point where presumably the local stress drops below the CRSS. The local strains where the dislocation comes to a stop are measured from the high-resolution (HR)TEM images and used to compute the local stresses. TiN is one of most thoroughly investigated transition metal nitrides17−21 and was chosen to be a representative material for the demonstration of our approach. These compounds are brittle at room temperature and show no evidence of measurable plasticity.22 However, the transition-metal carbonitrides are widely used to synthesize metal−ceramic composites that exhibit high hardness, high melting point, low thermal conductivity, high shock and wear resistance even at high temperatures,23,24 and high resistance to radiation damage.25 Particularly, it has been shown that in nanolayered metal− ceramic composites such as Al-TiN, the confined ceramic nanolayer can plastically codeform with the metallic nanolayer.17,26−29 Therefore, optimizing the strength and ductility of metal−ceramic nanocomposites requires better understanding of the active slip systems and critical stresses for dislocation glide in ceramics at room temperature.17,27 There is less experimental measurement of the stresses required for nucleation and glide of dislocations in ceramics. Such experimental measurements are often carried out for a small volume of materials at a high stress under a simple loading (e.g., uniaxial tension and compression) or inden-
ucleation, motion, and reaction of dislocations in crystalline materials are the elementary unit processes for understanding mechanical properties. Experimental measurements of the resolved shear stresses for nucleation and motion of individual dislocations in crystalline materials, although essential for integration with atomistic modeling to enable materials design from first-principles, remain elusive. Nucleation of dislocations is a thermally activated process, and the resolved shear stress (RSS) associated with dislocation nucleation varies with the nucleation sources or sites, the temperature, and the loading condition. At finite temperatures, the critical resolved shear stress (CRSS) associated with the onset of dislocation glide on a given slip system is often inferred from experimentally determined yield strengths of oriented single crystals.1,2 Corresponding to the inherent stochastic nature of dislocation nucleation at finite temperatures, accurate measurement of the dislocation nucleation stress is challenging experimentally due to the complicated stress state in the nucleation domain. When the complexity is ignored, an estimate may be made through elasticity theory (for instance, Hertzian elastic contact theory) corresponding to the loading condition and the tested sample geometry.3−8 CRSS can be calculated or estimated for specific loading and sample geometry without considering temperature effect from Peierls−Nabarro model at continuum scale,9−11 molecular statics modeling,12−15 and first-principles density functional theory calculations.16 However, the CRSS associated with the glide of dislocations could be measured if the dislocation motion was observed under an imposed gradient stress field. In this work, we demonstrate an approach utilizing in situ nanoindentation in a transmission electron microscope (TEM) to measure the CRSS for dislocation motion in TiN, © XXXX American Chemical Society
Received: February 26, 2015 Revised: June 2, 2015
A
DOI: 10.1021/acs.nanolett.5b00791 Nano Lett. XXXX, XXX, XXX−XXX
Letter
Nano Letters tations.3−8,30 For metals that have relatively low yield strength and highly mobile dislocations, uniaxial tension or compression tests are able to explore dislocation activity.4−8 However, uniaxial tension or compression tests are not suitable for measuring the nucleation and motion of dislocations in high strength crystalline materials such as ceramics because of fracture prior to plastic yield.22 Alternatively, nanoindentation can locally achieve a high stress to enable nucleation and motion of dislocations. At room temperature, Oden et al.18 reported evidence for dislocation motion in the TiN indentation tests. By analyzing the postindentation microstructures of TiN, they characterized the dislocations to be 1/ 2{110̅ } and estimated the critical resolved shear stresses for nucleation of dislocations to be 3.7 GPa at the load when pop-in occurs based on a Hertzian elastic contact. Minor et al.19 reported evidence of dislocation-based plasticity in TiN/MgO thin films at room temperature according to in situ indentation tests in a TEM, but they did not measure the CRSS associated with the motion of dislocations. By using in situ indentation in a HRTEM, the dislocation activity in terms of the nucleation, motion, and reactions has been characterized.5−8,18,19 Benefiting from the development of quantitative TEM/scanning TEM (STEM) analysis,31 quantitative measurements of displacement fields near defects can be estimated.32−36 In this work, we extended such effort to study the CRSS associated with dislocation motion in a high strength crystalline material, TiN, at room temperature using in situ indentation in a HRTEM. The primary glide dislocations were characterized to be 1/2{11̅0}. Local strains were calculated from the measured displacements corresponding to the atomic-column positions in HRTEM images and used to compute the resolved stress for the glide of a dislocation in the crystal and near a grain boundary. The TiN films were grown epitaxially on a single-crystal MgO (001) at 650 °C. TEM foils of the TiN were prepared by traditional preparation method: mechanical polishing plus ion milling. The foil is attached to a piezo-operated scanning tunneling microscope (STM) probe with silver paint, which served as one end of a Nanofactory TEM−STM platform. A chemical etched spherical tungsten tip with diameter of 50−100 nm was the other end of the platform.37,38 The STM probe with the tungsten tip was compressed onto the TEM foil. With indentation direction perpendicular to the (001) surface, four of six slip systems {110} could be favorably activated with positive Schmid’s factor. With the electron beam direction along [100], the dislocations on 1/2{110̅ } slip systems can be directly captured from the HRTEM images under the phase contrast mode. In situ nanoindentation studies were conducted at room temperature with a Nanofactory STM platform inside a Tecnai G(2) F30 TEM. A Gatan chargecoupled device (CCD) camera was used to capture deformation of the specimen during indentation with a rate of three frames/s. The compressive displacement rate is ∼0.1 nm/s to minimize sample vibration during indentation. Figure 1, panels a and b show two HRTEM images before loading and after unloading during the indentation test. Nucleation, glide, and pileup of dislocations were recorded in Supplementary Movie 1 of the Supporting Information and are summarized as follows. The dislocations nucleate from surfaces in contact with the indenter and glide into the sample. These dislocations stop at a certain distance from the indenter, pile up, and form a grain boundary. On the basis of the faceted morphology of the boundary, we marked it as three segments,
Figure 1. (a) HRTEM image before the indentation test. The loading direction is perpendicular to TiN (001) plane. (b) HRTEM image of the nucleated GB after retracting the indenter. Three segments are marked as GB-I, GB-II, and GB-III. Detailed structure analysis of GBII is presented in Figure 2, and that of GB-I and GB-III is presented in the Supporting Information.
GB-I, GB-II, and GB-III, as shown in Figure 1, panel b. The diffraction pattern inserted in Figure 1, panel b indicates that the grain boundary is a low angle tilt boundary around the tilt axis of [001]. The observed dislocations and the grain boundary are further characterized in the HRTEM images according to Burgers circuits39 (GB-I and GB-III can be found in Supplementary Figures S1 and S2 of the Supporting Information). Taking the GB-II as an example, the GB-II is characterized to be a low angle tilt grain boundary around the tilt axis [001] with the habit plane of (011) and the tilt angle of 14°. By drawing the Burgers circuit around the defects along the GB-II, we determine two components of a Burgers vector associated with each dislocation. Since the TEM image was taken with the e-beam direction along TiN [100], the shortest distances between the adjacent atoms that are projected on the (100) plane are associated with 1/2 and 1/2. We thus draw the Burgers circuit on the HRTEM images along the and . As shown in Figure 2, panels I−L, three types of dislocations are identified. When the Burgers circuit is closed with two additional vectors 1/2[001̅] and 1/2[01̅0] (Figure 2I,J), the dislocation thus has the Burgers vector 1/ 2[01̅1̅] and is referred to be bf. The glide plane is determined to be (01̅1). When the Burgers circuit is closed with only one additional vector 1/2[001̅] (referred to as bp1 and marked in Figure 2L), the vector bp1 is one component of a dislocation with the Burgers vector 1/2 or 1/2 on the glide plane (101̅) or (101). As schematically shown in Figure 2, panel b, the Burgers vector of the dislocations 1/2(1̅01) and 1/2(101) has only one component 1/2 that is B
DOI: 10.1021/acs.nanolett.5b00791 Nano Lett. XXXX, XXX, XXX−XXX
Letter
Nano Letters
projected on the (100) plane. When the Burgers circuit is closed with only one additional vector 1/2[01̅0] (referred to as bp2 and marked in Figure 2L), the vector bp2 is one component of a dislocation with the Burgers vector 1/2 or 1/2 on the glide plane (11̅0) or (110). In the observed region, the habit plane of the GB-II is close to (011). Corresponding to crystallography of TiN and characterization of dislocations along the GB, the formation of the GB can be described based on the formation of dislocations pileup. The full dislocation, bf = 1/2[01̅1̅], glide on (01̅1) and stop where the stress decreases below the CRSS, resulting in a pile up on the (011) plane and the formation of a tilt grain boundary. The average spacing between the adjacent dislocations along the GB is measured to be L = 1.3 nm. According to Frank’s formula,40,41 we obtained the tilt angle θ = sin−1(bf/L) = 13.4°, where bf = 0.299 nm associated with a full dislocation 1/2, consistent with the experimental measurement (14°). After the indenter was removed from contact (Figure 1b), a grain boundary was clearly discerned at a distance of 25 nm away from the surface, and analysis of HRTEM images revealed the GB to be composed of an array of glide dislocations on the (011) plane. The GB formation at a characteristic distance below the indenter contact is attributed to the gradient stress field generated by the indentation and the low mobility of dislocations in TiN at room temperature. We extracted the critical strains and resolved shear stresses corresponding to the point where the glide dislocations come to a stop from an analysis of the acquired HRTEM images, as described further. Before we discuss the CRSS estimation, we describe the essential details of strain analysis method. Figure 3, panel a shows a HRTEM image that was taken from an undeformed TiN film. A rectangle outlines a region around a center at the atom r0 = (x0,y0). There are N+1 numbers of atoms inside the rectangle. By using the peak pairs analysis (PPA), the ith atom positions with the vector ri with respect to the center. We first calculate the strains εijk at ri, for i = 0...N. The volume average strains at r0 are calculated according to ε̂rjk0 = (1/(N + 1))∑iN= 0εijk. Figure 3, panel b shows the unit cell for calculation of the strains εijk. Around the atom at ri, we search for eight neighbors when the distance |rij| (rij = rj − ri) is less than (2 + √2)a/4, where a is the lattice constant of TiN. With the ideal
Figure 2. (a) Magnified atomic configuration of GB-II. The GB-II is a low angle tilt grain boundary with the habit plane of (011) and the tilt angle of 14°. (b) Schematic illustration of slip systems {110}. (I−L) Magnified atomic structures showing three types of dislocations identified by drawing the Burgers circuit. The dislocation bf has the Burgers vector 1/2[011]. The dislocations bp1 and bp2 own vectors 1/ 2[001̅] and 1/2[01̅0] on [100] projection view. They are one component of a dislocation with the Burgers vector 1/2.
Figure 3. (a) A representative HRTEM image in which a rectangle outlines a region around a center at the atom r0 = (x0,y0). The ith atom positions with the vector ri with respect to the center. (b) The unit cell for calculation of the strains εijk at the ith atom position. Strain fields of strain components (c) ε̂xx and (d) ε̂yy in the HRTEM image. Gaussian distributions of the strains (e) ε̂xx and (f) ε̂yy. C
DOI: 10.1021/acs.nanolett.5b00791 Nano Lett. XXXX, XXX, XXX−XXX
Letter
Nano Letters lattice as the reference, we calculated the strains εijk using the least-squares determination of the strain ellipsoid described by Hoagland et al.42 (also see the details in the Supporting Information). Figure 3, panels c and d show the strain fields of two components, ε̂xx and ε̂yy, that are calculated using the aforementioned method with respect to the HRTEM image in Figure 3, panel a. It was noticed that the strain field is spatially nonuniform, but the mean strain in the region is close to zero. Figure 3, panels e and f show Gaussian distributions of the strains in the region ε̂xx and ε̂yy, respectively. The mean strains are equal to zero, and the standard deviation is about 0.005. To determine the critical resolved shear stress associated with the glide of 1/2{110̅ } dislocations, we analyze the strains in the HRTEM image where part of the GB forms and stops migration during continuous indentation. In Figure 4,
panel a, the red dashed line indicates the stable GB that does not migrate during continuous indentation. For reference, the yellow dashed line indicates the final GB after the indenter is removed. We magnified the region (marked in a white square) in Figure 4, panels b and c with respect to the time. When the indenter makes contact with the surface (Figure 4b), the strains analyzed with the aforementioned method are close to zero with the error bar of 0.5% (Figure 4d). Figure 4, panel e shows the variation of the strains with distance from the contact as the GB forms. Both strains εxx and εyy are compressive. The strain εxy is oscillatory around zero and thus ignored in the stress analysis. By using the linear elasticity theory with the measured strains, we calculate the CRSS associated with the 1/2[01̅1̅] (01̅1) slip system. As plotted in Figure 4, panel c, we found that the CRSS at the GB (10 nm from the contact) is close to 2.0 ± 0.5 GPa. This is in good agreement with the Peierls stress of 1.45 GPa calculated from the first-principles density functional theory.43 It is worth pointing out that the interaction force due to multiple dislocations in the formation of the GB was ignored in our analysis since it decays exponentially with distance from the GB and is insignificant in magnitude compared to the Peierls stress contribution to CRSS. The mechanical response of the GB under continuous indentation is shown in the Supplementary Movie 2 of the Supporting Information. Figure 5, panel a shows the structure
Figure 5. Snapshots of the GB-II under compression with respect to the elapsing time of (a) 5.3 and (b) 13 s, respectively. (c) Strains εxx, εyy, and εxy and the corresponding resolved shear stress in the region marked as a red rectangle in panel a. (d) Schematic illustrating the migration behavior of GB-II.
of the GB at 5.3 s. The tilt angle between the two grains increases from 14° to 16.3°. This is ascribed to dislocation activities in the grain-II, as observed in the Supplementary Movie 2 of the Supporting Information. In the first 5.3 s, dislocations nucleate from surfaces, glide toward the GB-II, and are blocked at the GB-II. As a consequence, dislocation density at the GB-II and the tilt angle increase. Most importantly, the nucleation and glide of dislocations in the grain-I were not observed; instead, Moiré fringes were observed near the GB. The formation of Moiré fringes results from the overlap of two different grains along the electron beam direction.44 With continuous indentation, Moiré pattern expands in the grain-I, as
Figure 4. (a) A HRTEM snapshot taken from Supplementary Movie 1 in the Supporting Information, in which part of the GB formed and stopped migration during continuous indentation. The red dashed line indicates the stable GB compared to the yellow dashed line (the final GB position). Magnified image of the region in the white square in panel a with respect to the elapsing time of (b) 1 s and (c) 31 s, respectively. (d) Strain components (εxx, εyy, and εxy) in panel b with the distance from the contact to the indenter. (e) Strain components (εxx and εyy) in panel c with the distance from the contact to the indenter. εxy is not shown with relatively smaller value compared to εxx or εyy. D
DOI: 10.1021/acs.nanolett.5b00791 Nano Lett. XXXX, XXX, XXX−XXX
Letter
Nano Letters
angle tilt grain boundary at room temperature. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.5b00791.
shown in Figure 5, panel b. The average spacing between two adjoining fringes is measured to be ∼1.2 nm, corresponding to a ∼10.1° tilt between the two overlapped grains. It is worth mentioning that the tilt angle between the two grains across the Moiré fringe region remains the same (16.3°). Thus, we proposed a possible mechanism as illustrated in Figure 5, panel c based on the motion of GB dislocations to account for the response of the GB.45,46 In Figure 5, panel c, the two light brown planes represent the front and back surfaces of the TEM foil. The e-beam direction is perpendicular to the two planes of the foil. Before the formation of Moiré fringes, all GB dislocations align on the (011) plane, showing a sharp low angle tilt grain boundary (light blue plane and marked as GBII). Under indentation, GB dislocations start to glide away from the GB-II. Because of the nonuniform pinning effect of surfaces and possible dislocation intersections,46−48 GB dislocations may not fully move away from the GB-II. Part of a GB dislocation may glide away from the GB-II plane, schematically shown in Figure 5, panel c. As a result, the sharp GB-II plane partially migrates and forms a curved GB plane (the blue plane and several red dislocation lines on it in Figure 5d), which results in the formation of Moiré fringes during in situ TEM observation. We further studied the critical activation stress corresponding to the formation of Moiré fringes, that is, the glide of grain boundary dislocations. We calculated strains in the region beneath the boundary (marked as a red rectangle in Figure 5a). Figure 5, panel c shows strains εxx, εyy, and εxy in the region. The average strains εxx, εyy, and εxy in the region are −2%, −3.5%, and 0.0%, respectively. Corresponding to the glide of 1/2[01̅1̅] dislocations on (01̅1) plane, we calculated the resolved shear stress in the region, and the average RSS is approximately 4 GPa. This is much higher than the CRSS of 2 GPa for an isolated dislocation, which implies a strong pinning effect due to the like-sign dislocation array along the GB. Such RSS is equivalent to a uniaxial compression or tension stress along at the onset of yield of ∼4 GPa based on single dislocation CRSS of ∼2 GPa, and ∼8 GPa based on CRSS of ∼4 GPa for dislocation emission from tilt boundary. Typically, bulk TiN cannot approach such high tension or compression yield stress without cracking, although room-temperature plasticity of TiN has been inferred in nanolayered Al-TiN composites.17,27 In summary, we have characterized plastic deformation of TiN at room temperature with the glide of 1/2{110̅ } dislocations that nucleate from surfaces beneath an indenter. The CRSS corresponding to the glide of an isolated dislocation was estimated to be ∼2 GPa, and the CRSS corresponding to the emission of dislocations from the low angle tilt grain boundary is ∼4 GPa. More importantly, we demonstrated the possibility to experimentally measure the critical stresses associated with the glide and emission of dislocations in TiN at room temperature using in situ indentation in a HRTEM. This approach is applicable for crystalline materials that have high strength and are brittle at room temperature.
■
■
AUTHOR INFORMATION
Corresponding Authors
*Phone: +1 505 665 1857. E-mail:
[email protected]. *Phone: +1 505 667 1238. E-mail:
[email protected]. Author Contributions
N.L. performed in situ indentation experiments. N.L., S.S. and J.W. performed theoretical analysis. A.M. and J.W. supervised the entire project. All authors commented on the manuscript. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS This work was supported by the U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences. This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. DOE, Office of Science. Los Alamos National Laboratory is operated by Los Alamos National Security, LLC, for the National Nuclear Security Administration of the U.S. DOE under Contract No. DE-AC52-06NA25396. We appreciated the valuable discussion with Prof. J.P. Hirth and R.G. Hoagland at Los Alamos National Laboratory.
■
REFERENCES
(1) Kang, K.; Bulatov, V. V.; Cai, W. Proc. Natl. Acad. Sci. U. S. A. 2012, 109, 15174−15178. (2) Lu, G.; Kioussis, N.; Bulatov, V. V.; Kaxiras, E. Philos. Mag. Lett. 2000, 80, 675−682. (3) Maughan, M. R.; Bahr, D. F. Mater. Res. Lett. 2015, 3, 58−64. (4) Li, N.; Wang, J.; Huang, J. Y.; Misra, A.; Zhang, X. Scripta Mater. 2010, 63, 363−366. (5) Bufford, D.; Liu, Y.; Wang, J.; Wang, H.; Zhang, X. Nat. Commun. 2014, 5, 4864. (6) Shan, Z. W. JOM 2012, 64, 1229−1234. (7) Maaß, R.; Derlet, P. M.; Greer, J. R. Small 2015, 11, 341−351. (8) Liu, L.; Wang, J.; Gong, S. K.; Mao, S. X. Sci. Rep. 2014, 4, 4397. (9) Nabarro, F. R. N. Philos. Mag. A 1997, 75, 703−711. (10) Kashyap, K. T.; Bhat, A.; Koppad, P. G.; Puneeth, K. B. Comput. Mater. Sci. 2012, 56, 172−173. (11) Davidson, D. L. Mater. Sci. Eng., A 2000, 293, 281−291. (12) Woodward, C.; Rao, S. I. Phys. Rev. Lett. 2002, 88, 216402. (13) Ito, K. Philos. Mag. A 2001, 81, 1387−1407. (14) Liu, X. L.; Golubov, S. I.; Woo, C. H.; Huang, H. C. Mater. Sci. Eng., A 2004, 365, 96−100. (15) Wang, J.; Beyerlein, I. J.; Hirth, J. P.; Tomé, C. N. Acta Mater. 2011, 59, 3990−4001. (16) Yadav, S. K.; Liu, X. Y.; Wang, J.; Ramprasad, R.; Misra, A.; Hoagland, R. G. Philos. Mag. 2014, 94, 464−475. (17) Li, N.; Wang, H.; Misra, A.; Wang, J. Sci. Rep. 2014, 4, 6633. (18) Oden, M.; Ljungcrantz, H.; Hultman, L. J. Mater. Res. 1997, 12, 2134−2142. (19) Minor, A. M.; Stach, E. A.; Morris, J. W., Jr.; Petrov, I. J. Elec. Mater. 2003, 32, 1023−1027. (20) Toth, L. E. Transition Metal Carbides and Nitrides; Academic Press: New York, 1971. (21) Ljungcrantz, H.; Oden, M.; Hultman, L.; Greene, J. E.; Sundgren, J. E. J. Appl. Phys. 1996, 80, 6725−6733. (22) Williams, W. S. Progress in Solid State Chemistry; Pergamon Press: New York, 1971. (23) Barnett, S. A.; Madan, A. Scripta Mater. 2004, 50, 739−744. (24) Sinnott, S. B.; Dickey, E. C. Mater. Sci. Eng. R 2003, 43, 1−59.
ASSOCIATED CONTENT
S Supporting Information *
HRTEM images of GB-I and GB-III in the TiN. Strain analysis method. In situ indentation of the single crystal, TiN, played at 15× speed (3 frames/sec) and showing the nucleation, glide, and pileup of lattice dislocations at room temperature. In situ indentation of the bicrystal, TiN, played at 10× speed (3 frames/sec) and showing the mechanical response of the low E
DOI: 10.1021/acs.nanolett.5b00791 Nano Lett. XXXX, XXX, XXX−XXX
Letter
Nano Letters (25) Salehinia, I.; Shao, S.; Wang, J.; Zbib, H. M. JOM 2014, 66, 2078−2085. (26) Bhattacharyya, D.; Mara, N. A.; Dickerson, P.; Hoagland, R. G.; Misra, A. Acta Mater. 2011, 59, 3804−3816. (27) Wang, J.; Misra, A. Curr. Opin. Solid State Mater. Sci. 2014, 18, 19−28. (28) Salehinia, I.; Wang, J.; Bahr, D. F.; Zbib, H. M. Int. J. Plast. 2014, 59, 119−132. (29) Embury, J. D.; Hirth, J. P. Acta Metall. Mater. 1994, 42, 2051− 2056. (30) Brenner, S. S. J. Appl. Phys. 1956, 27, 1484−1491. (31) Kret, S.; Ruterana, P.; Rosenauer, A.; Gerthsen, D. Phys. Status Solidi B 2001, 227, 247−295. (32) Hÿtch, M. J.; Putaux, J. L.; Penisson, J. M. Nature 2003, 423, 270−273. (33) Johnson, C. L.; Snoeck, E.; Ezcurdia, M.; Rodríguez-González, B.; Pastoriza-Santos, I.; Liz-Marzán, L. M.; Hÿtch, M. J. Nat. Mater. 2008, 7, 120−124. (34) Chung, J.; Rabenberg, L. Appl. Phys. Lett. 2007, 91, 231902. (35) Zheng, S. J.; Beyerlein, I. J.; Carpenter, J. S.; Kang, K. W.; Wang, J.; Han, W. Z.; Mara, N. A. Nat. Commun. 2013, 4, 1696. (36) Wang, S. J.; Wang, H.; Du, K.; Zhang, W.; Sui, M. L.; Mao, S. X. Nat. Commun. 2014, 5, 3433. (37) Li, N.; Wang, J.; Misra, A.; Huang, J. Y. Microsc. Microanal. 2012, 18, 1155−1162. (38) Li, N.; Wang, J.; Misra, A.; Zhang, X.; Huang, J. Y.; Hirth, J. P. Acta Mater. 2011, 59, 5989−5996. (39) Hirth, J. P.; Pond, R. C.; Hoagland, R. G.; Liu, X.-Y.; Wang, J. Prog. Mater. Sci. 2013, 58, 749−823. (40) Hirth, J. P.; Lothe, J. Theory of Dislocations; John Wiley and Sons: New York, 1992. (41) Wang, J.; Hirth, J. P.; Pond, R. C.; Howe, J. M. Acta Mater. 2011, 59, 241−251. (42) Hoagland, R. G.; Daw, M. S.; Hirth, J. P. J. Mater. Res. 1991, 6, 2565−2577. (43) Yadav, S. K.; Ramprasad, R.; Misra, A.; Liu, X.-Y. Acta Mater. 2014, 74, 268−277. (44) Fultz, B.; Howe, J. M. Transmission Electron Microscopy and Diffractometry of Materials; Springer-Verlag Berlin Heidelberg: New York, 2002. (45) Spearot, D. E.; Jacob, K. I.; McDowell, D. L. Acta Mater. 2005, 53, 3579−3589. (46) Wang, J.; Beyerlein, I. J.; Tomé, C. N. Int. J. Plast. 2014, 56, 156−172. (47) Wang, J.; Misra, A.; Hoagland, R. G.; Hirth, J. P. Acta Mater. 2012, 60, 1503−1513. (48) Zhang, R. F.; Wang, J.; Beyerlein, I. J.; Misra, A.; Germann, T. C. Acta Mater. 2012, 60, 2855−2865.
F
DOI: 10.1021/acs.nanolett.5b00791 Nano Lett. XXXX, XXX, XXX−XXX
