Dislocation structures of 3 ˆ112‰ twin boundaries in ...

APPLIED PHYSICS LETTERS 95, 021908 共2009兲

Dislocation structures of ⌺3 ˆ112‰ twin boundaries in face centered cubic metals J. Wang,1,a兲 O. Anderoglu,2 J. P. Hirth,1 A. Misra,1 and X. Zhang2 1

Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA Department of Mechanical Engineering, Materials Science and Engineering Program, Texas A&M University, College Station, Texas 77843-3123, USA

2

共Received 3 June 2009; accepted 22 June 2009; published online 16 July 2009兲 High resolution transmission electron microscopy of nanotwinned Cu films revealed ⌺3 兵112其 incoherent twin boundaries 共ITBs兲, with a repeatable pattern involving units of three 兵111其 atomic planes. Topological analysis shows that ⌺3 兵112其 ITBs adopt two types of atomic structure with differing arrangements of Shockley partial dislocations. Atomistic simulations were performed for Cu and Al. These studies revealed the structure of the two types of ITBs, the formation mechanism and stability of the associated 9R phase, and the influence of stacking fault energies on them. The results suggest that ⌺3 兵112其 ITBs may migrate through the collective glide of partial dislocations. © 2009 American Institute of Physics. 关DOI: 10.1063/1.3176979兴 Nanotwinned 共nt兲 metals exhibit an unusual combination of ultrahigh strength, 1⬃1.2 GPa in ultrafine-grained copper1–3 and in Cu foils,4,5 and high ductility 共14% elongation to failure in ultrafine-grained copper兲.2,3 This unusual high strength originates from ⌺3 共111兲 coherent twin boundaries 共CTBs兲 that act as strong barriers for slip transfer of single dislocations. Atomistic simulations have provided insight into the interactions of TBs with lattice glide dislocations with respect to both the kinetics and energetics of slip transfer across the CTBs.6–9 Apart from ⌺3 兵111其 CTBs, ⌺3 兵112其 incoherent TBs 共ITBs兲 were recently observed in epitaxial nt Cu films.5 ITBs in fcc metals have been studied with high resolution transmission electron microscopy 共HRTEM兲10,11 and molecular statics simulations.12 The results show that ⌺3 兵112其 ITBs can dissociate into two tilt walls bounding a 9R phase.11,12 However, these studies did not completely address the structure of the ITBs at an atomic scale. Moreover, the mobility of ITBs has not been studied yet. In this letter, we report microstructural characteristics of ⌺3 兵112其 ITBs in Cu studied at the atomic length scale by means of HRTEM. Topological analysis and atomistic simulations are performed to explore the structure and energetics of ⌺3 兵112其 ITBs in fcc Cu and Al. Finally, we discuss the mobility of the ITBs and draw conclusions. A Cu 共99.999% purity兲 target was sputtered to produce 1.5 ␮m thick Cu films on a 10% HF etched Si 共110兲 substrate, kept at ambient temperature during deposition.5 X-ray diffraction experiments were performed on a commercial Rigaku Ultima III x-ray diffractometer at room temperature. HRTEM was performed on a JEOL 3000F microscope operated at 300 kV. Figure 1共a兲 shows a cross-sectional HRTEM micrograph of epitaxial nt Cu films examined along a Cu 具110典 zone axis. The Cu film has an average columnar domain size of 70 nm with a high density of 兵111其 growth twins. Two types of boundaries are observed: ⌺3 兵111其 CTBs oriented normal to the growth direction, and ⌺3 兵112其 ITBs parallel to the a兲

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growth direction. Selected area diffraction pattern 共SAD兲 of the same specimen taken from a SAD aperture covering a larger imaging area 关Fig. 1共b兲兴 confirms the formation of ⌺3 兵111其 CTBs and also shows extra diffraction spots corresponding to a periodicity of three times the interplanar spacing of Cu 兵111其. Figure 1共d兲 is a HRTEM micrograph showing a narrow and straight ITB outlined by a box in Fig. 1共c兲. Figure 1共e兲 is a HRTEM micrograph showing a wide and diffuse ITB between twin and matrix in adjacent columns. A repeatable pattern is clearly observed in both the straight 关Fig. 1共d兲兴 and diffuse 关Fig. 1共e兲兴 boundaries, which has a unit involving three 兵111其 planes. However, the detailed dislocation structures of the ITBs are not resolved in these micrographs.

FIG. 1. 共a兲 Cross-sectional TEM micrograph of epitaxial nt Cu sputter deposited on a Si 共110兲 substrate. 共b兲 SAD pattern reveals extra diffraction spots at 1/3共111兲 positions in the reciprocal space. 共c兲 HRTEM micrograph of grain boundaries. 共d兲 Magnified HRTEM micrograph showing narrow and straight ⌺3 兵112其 ITBs. 共e兲 Magnified view of wide and diffuse ⌺3 兵112其 ITBs. A periodic array of defects is observed with a repeat unit of three 兵111其 planes in both 关共d兲 and 共e兲兴.

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FIG. 2. 共Color online兲 Dichromatic pattern of a 关110兴⌺3兵112其 储 兵112其 twin boundary showing two types of atomic structure of the boundary. 共a兲 Type-I boundary containing a set of partial dislocations on every 共111兲 plane with a repetitive sequence b2 : b1 : b3 and 共b兲 type-II boundary containing a set of partial dislocations on every 共111兲 plane with a repetitive sequence b1 : −2b1 : b1. b1 is a pure edge dislocation; b2 and b3 are mixed partial dislocations with opposite sign screw components. The length units are 兩a / 2关112兴兩 for x-axis and 兩a / 3关111兴兩 for y-axis. The solid symbols represent atoms in grain-␣ and the empty symbols represent atoms in grain-␤. The repeatable pattern with a unit involving three 兵111其 planes is delineated by solid lines. Relaxed atomic structures of incoherent ⌺3 兵112其 grain boundaries in Cu under zero applied stress, showing 共c兲 atomic structure of a type-I boundary, 共d兲 disregistry plots of the three partial dislocations in the type-I boundary, 共e兲 atomic structure of a type-II boundary, and 共f兲 disregistry plots of the three partial dislocations in the type-II boundary. Different atom colors represent different excess potential energies.

To understand the defect structure of ITBs, we construct a dichromatic pattern of a 具110典⌺3兵112其 储 兵112其 ITB 共Fig. 2兲. ¯ 10兴 direction pointing out The zone axis is parallel to the 关1 of the paper. Since planes with normal direction along the z-axis have a repeatable stacking sequence ¯abab¯, we present atoms in the a-plane as circles and atoms in the b-plane as triangles. The selection of different cut planes results in two types of grain boundaries with different atomic structures labeled as type-I 关Fig. 2共a兲兴 and type-II 关Fig. 2共b兲兴, respectively. The left crystal of the cut plane is from grain-␣ and the right crystal of the cut plane is from grain-␤. The topological studies reveal a repeatable unit in both type of boundaries 共as outlined by solid lines in Fig. 2兲 involving three adjacent 兵111其 planes. Since the change of 兵111其-plane stacking can be accomplished by the glide of any of the three Shockley partial dislocations,6 the type-I boundary can be created by the glide of a set of partial dislocations with a repeatable sequence b2 : b1 : b3 on every 共111兲 plane in half of a perfect crystal, and type-II can be created by the glide of a set of partial dislocations with a repeatable sequence b1 : −2b1 : b1 on every ¯兴 , 共111兲 plane in half of a perfect crystal. b1 is equal to 61 关112 ␣ a pure edge partial dislocation; b2 and b3 are equal to 1 ¯ 1 ¯ 6 关211兴␣ and 6 关121兴␣, respectively, both of which are mixed partial dislocations with opposite sign of screw components. The subscript ␣ means that all vectors are defined with respect to grain-␣. The finding of a repeat unit involving three

Appl. Phys. Lett. 95, 021908 共2009兲

FIG. 3. 共Color online兲 共a兲 Projection of 共111兲 plane showing layer stacking positions for the ¯ABCABC¯ fcc stacking. The change of plane stacking can be accomplished by the glide of any of the three Shockley partial dis1 1 ¯ ¯ 兴, 1 关2 ¯ locations with Burgers vectors 6 关112 6 11兴, or 6 关121兴. 共b兲 Partials glide on planes represented by dashed lines, creating the stacking of the 9R structure. 共c兲 Atomic structure of the dissociated ⌺3 兵112其 ITBs in Cu under applied shear stress, and 共d兲 shear stress and dissociation distance of the emitted partial dislocation from the initial boundary as a function of applied displacement gradients. Atoms are colored by common-neighbor-analysis. The red atoms represent stacking faults, relative to fcc, in the 9R phase 共dissociated region兲 that, if removed would convert it to fcc. The angle ␪ is 13.0°.

共111兲 atomic planes is consistent with the HRTEM observations. Furthermore, the sum of the Burgers vectors of the three partial dislocations in one unit is equal to zero. Atomistic simulations were then performed to calculate the excess potential energy of ⌺3 兵112其 ITBs for the two types of atomic structures with the empirical embedded atom method 共EAM兲 potential for Cu.13–18 We created the two types of ITBs from a perfect crystal by gliding a set of partial dislocations on every 共111兲 plane. The model is periodic along both the z-axis and the y-axis. The fully relaxed atomic structures of the two types of TBs are shown in Figs. 2共c兲 and 2共e兲. Figures 2共d兲 and 2共f兲 show disregistry plots across three different 共111兲 planes with respect to dislocations in type-I and type-II ITBs, respectively.17,18 The above analysis shows that 共1兲 both types of ITB are stable energetically. 共2兲 The excess potential energy, which includes the fault energy in the nascent dissociation, of type-I boundary 共590 mJ/ m2兲 is lower than that of type-II boundary 共714 mJ/ m2兲. 共3兲 The ITBs dissociate over a finite width, 0.80 nm in type-I and 0.85 nm in type-II, as measured from disregistry plots. 共4兲 The dissociation of the ITBs is ascribed to a decrease in elastic energy and the low stacking fault energy of Cu, resulting in the emission of one partial dislocation in each set of three from the initial compact ITB. The type-I ITB should be more prevalent than the type-II boundary because of its lower boundary energy. The repeatable pattern observed in the HRTEM images is a result of the emission of a Shockley partial dislocation on every three 共111兲 planes from the initial compact ITB. This emission changes the 兵111其 plane stacking19 as shown in Fig. 3. A new phase 9R structure is created from the normal fcc stacking to the 9R phase stacking by the passage of any

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one among the three partials b1, b2, or b3 关Fig. 3共b兲兴. The 9R phase forms because the dissociation is favored by the accompanying decrease in elastic energy: an interesting and seldom encountered category of phase formation. The bicrystal model with the ITB of type-I is homogeneously, gradually sheared by the application of displacement gradients to the simulation cell, with one nonzero term ⳵v / ⳵x.17 The results are plotted in Figs. 3共c兲 and 3共d兲 and reveal that 共1兲 The width of the 9R phase region and the shear stresses on the bicrystal both increase nonlinearly with the accumulated displacement gradient component due to the nonlinear interaction forces of the three dislocations. 共2兲 The width of the 9R phase region increases linearly corresponding to the applied force balancing the constant attractive force ␥SF and the shear stresses remain constant because of the transfer of applied elastic shear strains to plastic phase transformation strains in the 9R phase when the accumulated ⳵v / ⳵x exceeds 0.023. 共3兲 The other two partial dislocations b2 and b3 remain at their initial positions during the growth of the 9R phase, implying that the summed Peierls barrier for the glide of the two paired partial dislocations b2 and b3 is higher than that for the partial dislocation b1. 共4兲 As a result of the emission of partial dislocations on every third 共111兲 plane, the 共111兲 planes in the left grain-␣ of the ITB tilt about the left dissociated boundary in an up-down sense from the left with an angle of 13.0° measured from the simulated structure, which is approximately equal to the theoretical estimate of 13.28°. These tilts are not observed in the HRTEM images because of compatibility constraints. Similar results are obtained for the type-II structure. Again, a 9R phase is formed because one of the two partial dislocations b1 glides away from the initial compact ITB. Hence dissociated ITBs observed in Cu films should be mainly of the type-I structure containing three different partial dislocations b2 : b1 : b3, because the type-I structure has a lower interface energy than that for the type-II structure. However the type-II structure is stable and some ITBs of this type could be present. The width difference of the dissociated ITBs in Figs. 1共d兲 and 1共e兲 can be ascribed to different local stress states, in particular compatibility constraints on the twin boundary arising from the compliance of the matrix. In contrast to Cu, ⌺3 兵112其 ITBs in Al were studied using molecular statics calculations and using an empirical EAM potential Al.20 The results show that 共1兲 the two types of structures are stable; 共2兲 the excess potential energy of the type-I structure 共357 mJ/ m2兲 is lower than that of the type-II structure 共484 mJ/ m2兲. 共3兲 Both energies are lower for Al than for Cu. 共4兲 ⌺3 兵112其 ITBs in Al do not dissociate beyond the spacing of a single dislocation core 共less than 0.30 nm兲. The narrower ITBs compared to Cu are a consequence of the higher stacking fault energy, preventing the emission of partial dislocations from the ITBs. Even when shear stresses up to 0.5 GPa are applied, the partial dislocation b1 does not glide away from the ITB. Therefore, the 9R phase does not appear in Al. The ⌺3 兵112其 ITBs could migrate at a finite temperature since kink formation and motion are easier at elevated temperatures, i.e., the Peierls force is small or zero, and since the boundaries contain lattice glide dislocations on every 共111兲

glide plane. The partial dislocation b1 in the type-I structure is initially more mobile than the other two partial dislocations. As a result, after an initial transient, the partial b1 can move under an applied force equal to ␥SF. In this regime, the repulsive interaction force on the two paired partial dislocations b2 and b3 approaches zero. The applied force on the paired partials 共acting to the left in Fig. 2兲 is nearly balanced by the ␥SF force 共acting to the right兲. Hence, particularly if b2 and b3 dissociate in this situation, the three dislocations may move together. In summary, the structures of ⌺3 兵112其 ITBs have been studied in an atomistic simulation, giving results consistent with HRTEM observations. Two types of atomic structures of ITBs are identified by topology and both types of boundaries are shown to be stable in Cu and Al. The 9R phase is created when the compact ITB dissociates into two tilt walls. This occurs in the lower stacking fault energy Cu, but not in Al. The extent of the 9R phase can be increased under an applied shear stress. The ITBs may migrate at finite temperature through the collective glide of partial dislocations with a minimum unit of three 共111兲 atomic planes. This work was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences. X.Z. acknowledges financial support by the NSF-DMR Metallic Materials and Nanostructures program under Grant No. 0644835 and access to the Center for Integrated Nanotechnologies at Los Alamos National Laboratory through a user program. L. Lu, X. Chen, X. Huang, and K. Lu, Science 323, 607 共2009兲. L. Lu, Y. F. Shen, X. H. Chen, L. H. Qian, and K. Lu, Science 304, 422 共2004兲. 3 E. Ma, Y. M. Wang, Q. H. Lu, M. L. Sui, L. Lu, and K. Lu, Appl. Phys. Lett. 85, 4932 共2004兲. 4 X. Zhang, H. Wang, X. H. Chen, L. Lu, K. Lu, R. G. Hoagland, and A. Misra, Appl. Phys. Lett. 88, 173116 共2006兲. 5 O. Anderoglu, A. Misra, H. Wang, F. Ronning, M. F. Hundley, and X. Zhang, Appl. Phys. Lett. 93, 083108 共2008兲. 6 J. Wang and H. Huang, Appl. Phys. Lett. 88, 203112 共2006兲. 7 T. Zhu, J. Li, A. Samanta, H. G. Kim, and S. Suresh, Proc. Natl. Acad. Sci. U.S.A. 104, 3031 共2007兲. 8 K. A. Afanasyev and F. Sansoz, Nano Lett. 7, 2056 共2007兲. 9 X. Zhang, A. Misra, H. Wang, A. L. Lima, M. F. Hundley, and R. G. Hoagland, J. Appl. Phys. 97, 094302 共2005兲. 10 D. Hofmann and F. Ernst, Ultramicroscopy 53, 205 共1994兲. 11 J. D. Rittner, D. N. Seidman, and K. L. Merkle, Phys. Rev. B 53, R4241 共1996兲. 12 G. Lucadamo and D. L. Medlin, Science 300, 1272 共2003兲. 13 Y. Mishin, M. Mehl, D. Papaconstantopoulos, A. F. Voter, and J. D. Kress, Phys. Rev. B 63, 224106 共2001兲. 14 J. Wang, R. G. Hoagland, and A. Misra, Appl. Phys. Lett. 94, 131910 共2009兲. 15 J. Wang and H. Huang, Appl. Phys. Lett. 85, 5983 共2004兲. 16 J. Wang, R. G. Hoagland, J. P. Hirth, and A. Misra, Acta Mater. 56, 3109 共2008兲. 17 J. Wang, R. G. Hoagland, J. P. Hirth, and A. Misra, Acta Mater. 56, 5685 共2008兲. 18 J. Wang, H. Huang, S. V. Kesapragada, and D. Gall, Nano Lett. 5, 2505 共2005兲. 19 J. P. Hirth and J. Lothe, Theory of Dislocations 共Krieger, Melbourne, FL, 1992兲. 20 Y. Mishin, D. Farkas, M. Mehl, and D. Papaconstantopoulos, Phys. Rev. B 59, 3393 共1999兲. 1 2

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