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Formation of {112¯1} twins in polycrystalline cobalt during dynamic plastic deformation
Materials Science and Engineering A 548 (2012) 1–5
Contents lists available at SciVerse ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Formation of {1 1 2¯ 1} twins in polycrystalline cobalt during dynamic plastic deformation Y.T. Zhu, X.Y. Zhang ∗ , H.T. Ni, F. Xu, J. Tu, C. Lou School of Materials Science and Engineering, Chongqing University, Chongqing 400044, China
a r t i c l e
i n f o
Article history: Received 16 September 2011 Received in revised form 12 January 2012 Accepted 7 March 2012 Available online 22 March 2012 Keywords: ¯ deformation twins {1121} Dislocation reaction Cobalt Dynamic plastic deformation
a b s t r a c t ¯ deformation twins in polycrystalline cobalt during dynamic plasThe formation mechanism of the {1121} tic deformation has been proposed in this paper. It is found that the dislocation reactions play important ¯ deformation twins. The basal dislocations dissociate into roles in the nucleation and growth of {1121} ¯ planes and glissile partials glided to nucleate sessile partials pinned at the intersection of two {1121} twins on the (0 0 0 2) planes during the deformation. With the help of the applied stress, the dislocation ¯ deformation twins. reactions can be repeated, resulting in the formation of {1121} © 2012 Elsevier B.V. All rights reserved.
1. Introduction Twinning is the primary deformation mechanism for hexagonal close-packed (hcp) metals due to their lack of sufficient dislocation glide systems [1–4]. The most commonly observed twin modes in hcp metals are at least five compound twin modes as following: tension twins of {1 0 1¯ 2} and {1 1 2¯ 1}, contraction twins of {1 0 1¯ 1}, {1 0 1¯ 3} and {1 1 2¯ 1} [5–8]. Among all of the above modes, tension twins could occur when a compression is applied perpendicular to the c axis of hcp metals, whereas contraction twins could occur when an hcp crystal or grain subject to compression along its c axis [9–12]. The {1 0 1¯ 2} twin is prior to form during the deformation because the twinning shear magnitude (s) of this model is theoretically the lowest. On the other hand, as only two atomic planes on K1 {1 1 2¯ 1} are intersected by 2 (K1 , K2 , 1 and 2 are of four elements to characterize twin property by Miller–Bravis indices [6,7]), all the lattice atoms can be carried to their correct position without atomic shuffling during twinning deformation [8]. The {1 1 2¯ 1} twin can still take place despite that the s of which is the largest in the above twin modes. The earliest observation concerning the nucleation and growth of {1 1 2¯ 1} twins was made by Geach et al. [13] and by Jeffery and Smith [14] working with Re single crystals. These authors have shown that twinning always occurs on the {1 1 2¯ 1} planes when the c axis is close to the tensile axis. Then Akhtar has reported the first-order prismatic slip in the micro-strain region
∗ Corresponding author. Fax: +86 23 65112154. E-mail address: [email protected] (X.Y. Zhang). 0921-5093/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2012.03.017
appears to be responsible for the nucleation of {1 1 2¯ 1} twins in single crystals of Ti [15]. Also, Vaidya and Mahajan have suggested ¯ dislocations and a 1 1¯ 0 0 dislothe reaction of two 1/32¯ 1 1 3 cation would yield a multilayer stacking fault approximating to a thin twin [16]. However, the relationship between the formation of {1 1 2¯ 1} twins and the dislocation dissociations is unclearly. In this paper, the microstructure of a deformed polycrystalline Co is investigated by scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), transmission electron microscopy (TEM) and high resolution TEM (HRTEM) techniques, and the dislocation dissociations in {1 1 2¯ 1} plane are discussed to reveal the formation mechanism of {1 1 2¯ 1} deformation twins based on the dislocation reactions.
2. Experimental procedure Polycrystalline Co (99.9%pure) sheets used in this work were acquired from Goodfellow Company. Specimens with dimensions of about 10 mm × 7 mm × 7 mm were deformed by DPD facility at room temperature (293 K). The strain rate applied to the samples was estimated to be about 2 × 102 –1 × 103 . The deformation strain of each sample was calculated by the reduction of thicknesses, as ε = (L0 − Ld )/L0 , where L0 and Ld were the initial and final thickness of the deformed sample, respectively. These deformed specimens were analyzed by EBSD and TEM measurements. In order to achieve the surface quality required for EBSD examinations, electropolishing was conducted at 20 V/0.5 A and at room temperature for 45 s in a solution consisting of 10 ml glycerinum, 20 ml perchloric acid and 70 ml alcohol. The EBSD characterization was carried out on heat
2
Y.T. Zhu et al. / Materials Science and Engineering A 548 (2012) 1–5
Fig. 1. (a) An EBSD boundary map of polycrystalline Co after DPD to a strain of 8.7%. The {1 1 2¯ 1} twin boundaries have been plotted in red lines. The typical grains A and B are selected in order to express the variation of the {1 1 2¯ 1} twin. The growth of twin T1 obstructed by the presence of twin T2 is identified by the black triangles. (b) and (c) giving the misorientation angle distributions corresponding the twins T1 and T2 of the grain A in Fig. 1a, respectively. (d) The misorientation angle distributions corresponding the twin of the grain B in Fig. 1a. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
treated samples with an FEI NOVA 400 SEM equipped with a field emission gun. The EBSD patterns were recorded by an ultrasensitive CCD camera and processed using the Channel 5 software from HKL technology to determine both the phases and local orientations. For TEM studies, samples of about 0.4 mm thick were sectioned by spark-cutting, thinned by grinding and then electropolished using a twin-jet polisher. TEM observations were carried out with an FEI Tecnai F30-G2 electron microscope operating at 300 kV. 3. Results and discussions The EBSD boundary map for polycrystalline Co deformed to a strain of 8.7% is shown in Fig. 1(a). Most of the boundaries are of high angles (>15◦ ). Thereinto, the {1 1 2¯ 1} twin boundaries have been plotted in red lines. The rest special boundaries corresponding the other types of twin boundaries have been identified in our previous research [8]. Two types of {1 1 2¯ 1} deformation twins (indicated by T1 and T2) are observed in the grain A. The domains of twin T1 and matrix of the grain A are identified to be of the misorientation of about 35◦ /[0 1¯ 1 0] (see the misorientation axis distribution shown in Fig. 1(b)), while the domains of twin T2 and matrix of the grain A are found to have a misorientation of about 35◦ /[0 1 1¯ 0] (see the misorientation axis distribution shown in Fig. 1(c)), indicating that twin T1 and twin T2 have the different habit-planes of the {1 1 2¯ 1} planes. In addition, it can be seen that the growth of twin T1 is obstructed by the presence of twin T2, which is identified by the black triangles. This phenomenon was also observed in single Co by TEM measurement, and it can be attributed to the dislocation reactions or the glide of (c + a) dislocations [16]. In the grain B, only one type of {1 1 2¯ 1} deformation twin is observed, and the domains of twin and matrix are identified to
have a misorientation of about 35◦ /[0 1¯ 1 0] (see the misorientation axis distribution shown in Fig. 1(d)). The discrepancy of exhibition of {1 1 2¯ 1} twin types in the grain A and grain B may be due to the original orientation difference of these two grains [8]. Fig. 2(a) is a cross-sectional bright-field TEM micrograph of the {1 1 2¯ 1} deformation twins in polycrystalline Co during DPD. The corresponding selected-area electron diffraction (SAED) pattern taken using [0 1 1¯ 0] zone axis from the circled area is shown in the bottom-right of Fig. 1(a). From the SEAD pattern, it can be seen that the (0 0 0 2) plane of the twin is rotated about 32◦ around 0 1 1¯ 0 axis from that of the matrix. The error for the misorientation-angle measured by EBSD and TEM is reasonable. Obviously, some dislocations labeled N are observed near the twin boundary (TB). These dislocations are basal dislocations because the dislocations are visible for g = [0 1 1¯ 0] [17]. Fig. 2(b) is the corresponding HRTEM image of the area labeled by the black frame and the letter of b in Fig. 2(a). It can be seen that the TB of {1 1 2¯ 1} twins is straight, which is unlike the TB of {1 0 1¯ 2} twins presented the step-like boundary [18]. Fig. 2(c) shows an enlarged image of the area indicated by the white frame and the letter c in Fig. 2(b). The basal dislocation labeled by T is observed near the TB. The basal dislocations were also observed by Vaidya and Mahajan in single Co when the sample was deformed by exposure to ultrasonic cavitation [16]. In addition, they have observed the (c + a) type dislocations with [2¯ 1 1 3] Burgers vector. However, this type of dislocation is not observed in our research. Fig. 3(a) shows a model involving the primitive hexagonal unit cell with the vector notation for hcp metals. The parallelograms ABCD and A B C D represent the same stacking of close packed planes. The “body” atom A0 is in the left triangular prism ABC. Each edge of the parallelograms represents the Burgers vector of a full
Y.T. Zhu et al. / Materials Science and Engineering A 548 (2012) 1–5
3
Fig. 2. (a) A TEM micrograph showing the {1 0 1¯ 2} deformation twins. The corresponding selected-area electron diffraction pattern taken using [0 1 1¯ 0] zone axis from the circled area is shown in the bottom-right. The basal dislocations labeled N are near the twin boundary. (b) The HRTEM image corresponding the area indicated by the black frame in (a). (c) Magnified map of the area indicated by the white frame in (b). The partial dislocation lying on (0 0 0 2) plane is marked by yellow T. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
dislocation in basal plane, 1/31¯ 1¯ 2 0. The points ˛ and ˇ are at the center point of the triangles ABC and CBD, respectively. The lines linking the corner of triangle and its center, e.g. A␣, represent the Burgers vector of the partial dislocations on the basal (a) slip plane. The vectors a1 , a2 and a3 are referred to three different directions in basal slips, namely 1/3[2 1 1 0], 1/3[1 1 2 0] and 1/3[1 2 1 0]. The vector c represents the [0 0 0 1] direction. The letter A0 represents atom corresponding to another stacking of close packed planes. The lines that link A0 and the corner of triangle represent the Burgers vector of the partial dislocation on the pyramidal (a + c) slip planes. We define the direction of the Burgers vector as from the first letter to the second letter. For example, A␣ represents a vector from the A to ␣. Fig. 3(b) is the schematic of neighboring four hexagonal unit cells for polycrystalline Co. Mendelson [19] has reported that the vectors AB and ␣A0 lie on −
AB → AD + DB → AF + F D + DB
(1)
where and are coefficients. Thus, we postulate that the {1 1 2¯ 1} deformation twins are formed by the reaction and glide of the basal dislocations. With the help of the primitive hexagonal unit cell with the vector notation of hcp metals in Fig. 3(a) and the Eq. (1), we describe the formation mechanism of {1 1 2¯ 1} deformation twins in the following section.
(2)
In the right-hand of Eq. (2), there are three vectors. The first vector, AF = 1/3[1¯ 1¯ 2 6], is the shear direction (1 ) of the invari−
ant plane (K1 = (1 1 2 1)) of the shear. The length of the second vector of dislocation F D is as much again as that of dislocation B D = 1/3[2 1¯ 1¯ 3]. The full dislocation B D can dissociate the sessile and glide partial dislocation as following: B D → B  + D
the {0 1 1¯ 0} plane of shear for the {2 1 1 l} zone giving b0 = [AB + ˛A0 ]
Due to the fact that the dissociation of an AB dislocation can result in the twinning partial dislocation on {1 1 2¯ 1} plane [19], we assume that the AB dislocation can dissociate into the following dislocations under the applied stress:
(3)
Thereinto, the partial B  is the sessile dislocation which cannot move and pin at the intersection of two {1 1 2¯ 1} planes, while the partial D can glide to nucleate a twin on the (0 0 0 2) plane (Fig. 4(a)). The dislocation DB can cross-slip the next intersection of two {1 1 2¯ 1} planes during the deformation. The dislocation reactions are energetically unfavorable and can only proceed with the help of applied stress [16,19,20].
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Y.T. Zhu et al. / Materials Science and Engineering A 548 (2012) 1–5
Fig. 3. (a) A primitive hexagonal unit cell with the vector notation for hcp metals. (b) The schematic of neighboring four hexagonal unit cells for polycrystalline Co.
Fig. 4. Schematics of the nucleation and growth of the {1 1 2¯ 1} deformation twins. (a) Nucleation of a twin on the (0 0 0 2) plane of matrix (or twin). (b) Nucleation of a twin on the next (0 0 0 2) plane of twin (or matrix). (c) The growth of the {1 1 2¯ 1} deformation twins with the partials gliding on the (0 0 0 2) plane. The alternate sessile dislocation ¯ and {1 1 2¯ 1} planes. of B  and B is at the intersection between the (1 1 2¯ 1)
Now DB dissociates into the following dislocations under the applied stress: DB → DA + AB → DF + F A + AB
(4) −−
Thereinto, the vector F A (1/3[1 1 2 6]) is the shear direction −
(1 ) of the invariant plane (K1 = (1 1 2 1)) of the shear. The length of the dislocation DF is as much again as that of dislocation DB −
−
(1/3[2 1 1 3]). Then, the dislocation B D dissociates into two partials on the next (0 0 0 2) plane: DB → D + B
(5)
As shown in Fig. 4(b), the partial B is the sessile and cannot move, while the partial D glides to nucleate a twin on the (0 0 0 2) plane. AB cross-slips the next intersection of two {1 1 2¯ 1} planes and dissociates like Eq. (1). With the repeating dislocation reactions and processes (see Fig. 4(c)), the {1 1 2¯ 1} deformation twins are generated successively. As shown in Fig. 2, the basal dislocations are the trails of the partials D or D which glides on the (0 0 0 2) planes. 4. Conclusions In this paper, the characteristic of the {1 1 2¯ 1} deformation twins and involved formation mechanisms have been investigated. The
results show that the dislocation dissociation plays an important role in the nucleation of {1 1 2¯ 1} deformation twins. With help of the applied stress, the basal full dislocation dissociates into three types of dislocations: (1) a dislocation with the shear direction of the invariant plane; (2) a dislocation dissociated into two partials including a sessile partial pinned at every intersection of the two {1 1 2¯ 1} planes and a glissile partial glided to nucleate a twin on the (0 0 0 2) planes; and (3) a dislocation cross-slipped the next intersection of two {1 1 2¯ 1} planes in order to provide the further dislocation reaction under the applied stress. During the DPD process, the dislocation reactions can be repeated and lead to the formation of the {1 1 2¯ 1} deformation twins. Acknowledgements X.Y. Zhang thanks prof. X.L. Wu for his constructive discussion. This work was supported by National Natural Science Foundation of China (Nos. 51071183, 50890170), the Fundamental Research Funds for the Central Universities (No. CDJXS11132225) and the Major State Basic Research Development Program of China (973 Program) (No. 2010CB631004). References [1] N. Munroe, X.L. Tan, Scr. Mater. 36 (1997) 1383. [2] L. Kucherov, E.B. Tadmor, Acta Mater. 55 (2007) 2065.
Y.T. Zhu et al. / Materials Science and Engineering A 548 (2012) 1–5 [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
G. Proust, C.N. Tome, G.C. Kaschner, Acta Mater. 55 (2007) 2137. L. Capolungo, I.J. Beyerlein, C.N. Tome, Scr. Mater. 60 (2009) 32. M.H. Yoo, Mater. Trans. A 12 (1981) 409. J.W. Christian, S. Mahajan, Prog. Mater. Sci. 39 (1995) 1. M.H. Yoo, J.R. Morris, K.M. Ho, S.R. Agnew, Met. Mater. Trans. A 33 (2002) 813. X.Y. Zhang, Y.T. Zhu, Q. Liu, Scr. Mater. 63 (2010) 387. S. Vaidya, S. Mahajan, Scr. Mater. 14 (1980) 623. L. Jiang, J.J. Jonas, A.A. Luo, A.K. Sachdev, S. Godet, Scr. Mater. 54 (2006) 771. M.R. Barnett, Mater. Sci. Eng. A 464 (2007) 1. M.R. Barnett, Mater. Sci. Eng. A 464 (2007) 8. G.A. Geach, R.A. Jeffery, E. Smith, in: B.W. Gonser (Ed.), Rhenium, Elsevier, Amsterdam, 1962, p. 96.
[14] [15] [16] [17]
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R.A. Jeffery, E. Smith, Philos. Mag. 13 (1966) 1163. A. Akhtar, Met. Trans. A 64 (1975) 1105. S. Vaidya, S. Mahajan, Acta Mater. 28 (1980) 1123. D. Bhattacharyya, E.K. Cerreta, R. McCabe, M. Niewczas, G.T. Gray III, A. Misra, C.N. Tome, Acta Mater. 57 (2009) 305. ¯ [18] Y.T. Zhu, X.Y. Zhang, H.T. Ni, F. Xu, Q. Liu, Characteristic and formation of {1012} twins of polycrystalline cobalt subjected to dynamic plastic deformation, submitted, unpublished results. [19] S. Mendelson, J. Appl. Phys. 41 (1970) 1893. [20] Y.T. Zhu, J. Narayan, J.P. Hirth, S. Mahajan, X.L. Wu, X.Z. Liao, Acta Mater. 57 (2009) 3763.
Contents lists available at SciVerse ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Formation of {1 1 2¯ 1} twins in polycrystalline cobalt during dynamic plastic deformation Y.T. Zhu, X.Y. Zhang ∗ , H.T. Ni, F. Xu, J. Tu, C. Lou School of Materials Science and Engineering, Chongqing University, Chongqing 400044, China
a r t i c l e
i n f o
Article history: Received 16 September 2011 Received in revised form 12 January 2012 Accepted 7 March 2012 Available online 22 March 2012 Keywords: ¯ deformation twins {1121} Dislocation reaction Cobalt Dynamic plastic deformation
a b s t r a c t ¯ deformation twins in polycrystalline cobalt during dynamic plasThe formation mechanism of the {1121} tic deformation has been proposed in this paper. It is found that the dislocation reactions play important ¯ deformation twins. The basal dislocations dissociate into roles in the nucleation and growth of {1121} ¯ planes and glissile partials glided to nucleate sessile partials pinned at the intersection of two {1121} twins on the (0 0 0 2) planes during the deformation. With the help of the applied stress, the dislocation ¯ deformation twins. reactions can be repeated, resulting in the formation of {1121} © 2012 Elsevier B.V. All rights reserved.
1. Introduction Twinning is the primary deformation mechanism for hexagonal close-packed (hcp) metals due to their lack of sufficient dislocation glide systems [1–4]. The most commonly observed twin modes in hcp metals are at least five compound twin modes as following: tension twins of {1 0 1¯ 2} and {1 1 2¯ 1}, contraction twins of {1 0 1¯ 1}, {1 0 1¯ 3} and {1 1 2¯ 1} [5–8]. Among all of the above modes, tension twins could occur when a compression is applied perpendicular to the c axis of hcp metals, whereas contraction twins could occur when an hcp crystal or grain subject to compression along its c axis [9–12]. The {1 0 1¯ 2} twin is prior to form during the deformation because the twinning shear magnitude (s) of this model is theoretically the lowest. On the other hand, as only two atomic planes on K1 {1 1 2¯ 1} are intersected by 2 (K1 , K2 , 1 and 2 are of four elements to characterize twin property by Miller–Bravis indices [6,7]), all the lattice atoms can be carried to their correct position without atomic shuffling during twinning deformation [8]. The {1 1 2¯ 1} twin can still take place despite that the s of which is the largest in the above twin modes. The earliest observation concerning the nucleation and growth of {1 1 2¯ 1} twins was made by Geach et al. [13] and by Jeffery and Smith [14] working with Re single crystals. These authors have shown that twinning always occurs on the {1 1 2¯ 1} planes when the c axis is close to the tensile axis. Then Akhtar has reported the first-order prismatic slip in the micro-strain region
∗ Corresponding author. Fax: +86 23 65112154. E-mail address: [email protected] (X.Y. Zhang). 0921-5093/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2012.03.017
appears to be responsible for the nucleation of {1 1 2¯ 1} twins in single crystals of Ti [15]. Also, Vaidya and Mahajan have suggested ¯ dislocations and a 1 1¯ 0 0 dislothe reaction of two 1/32¯ 1 1 3 cation would yield a multilayer stacking fault approximating to a thin twin [16]. However, the relationship between the formation of {1 1 2¯ 1} twins and the dislocation dissociations is unclearly. In this paper, the microstructure of a deformed polycrystalline Co is investigated by scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), transmission electron microscopy (TEM) and high resolution TEM (HRTEM) techniques, and the dislocation dissociations in {1 1 2¯ 1} plane are discussed to reveal the formation mechanism of {1 1 2¯ 1} deformation twins based on the dislocation reactions.
2. Experimental procedure Polycrystalline Co (99.9%pure) sheets used in this work were acquired from Goodfellow Company. Specimens with dimensions of about 10 mm × 7 mm × 7 mm were deformed by DPD facility at room temperature (293 K). The strain rate applied to the samples was estimated to be about 2 × 102 –1 × 103 . The deformation strain of each sample was calculated by the reduction of thicknesses, as ε = (L0 − Ld )/L0 , where L0 and Ld were the initial and final thickness of the deformed sample, respectively. These deformed specimens were analyzed by EBSD and TEM measurements. In order to achieve the surface quality required for EBSD examinations, electropolishing was conducted at 20 V/0.5 A and at room temperature for 45 s in a solution consisting of 10 ml glycerinum, 20 ml perchloric acid and 70 ml alcohol. The EBSD characterization was carried out on heat
2
Y.T. Zhu et al. / Materials Science and Engineering A 548 (2012) 1–5
Fig. 1. (a) An EBSD boundary map of polycrystalline Co after DPD to a strain of 8.7%. The {1 1 2¯ 1} twin boundaries have been plotted in red lines. The typical grains A and B are selected in order to express the variation of the {1 1 2¯ 1} twin. The growth of twin T1 obstructed by the presence of twin T2 is identified by the black triangles. (b) and (c) giving the misorientation angle distributions corresponding the twins T1 and T2 of the grain A in Fig. 1a, respectively. (d) The misorientation angle distributions corresponding the twin of the grain B in Fig. 1a. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
treated samples with an FEI NOVA 400 SEM equipped with a field emission gun. The EBSD patterns were recorded by an ultrasensitive CCD camera and processed using the Channel 5 software from HKL technology to determine both the phases and local orientations. For TEM studies, samples of about 0.4 mm thick were sectioned by spark-cutting, thinned by grinding and then electropolished using a twin-jet polisher. TEM observations were carried out with an FEI Tecnai F30-G2 electron microscope operating at 300 kV. 3. Results and discussions The EBSD boundary map for polycrystalline Co deformed to a strain of 8.7% is shown in Fig. 1(a). Most of the boundaries are of high angles (>15◦ ). Thereinto, the {1 1 2¯ 1} twin boundaries have been plotted in red lines. The rest special boundaries corresponding the other types of twin boundaries have been identified in our previous research [8]. Two types of {1 1 2¯ 1} deformation twins (indicated by T1 and T2) are observed in the grain A. The domains of twin T1 and matrix of the grain A are identified to be of the misorientation of about 35◦ /[0 1¯ 1 0] (see the misorientation axis distribution shown in Fig. 1(b)), while the domains of twin T2 and matrix of the grain A are found to have a misorientation of about 35◦ /[0 1 1¯ 0] (see the misorientation axis distribution shown in Fig. 1(c)), indicating that twin T1 and twin T2 have the different habit-planes of the {1 1 2¯ 1} planes. In addition, it can be seen that the growth of twin T1 is obstructed by the presence of twin T2, which is identified by the black triangles. This phenomenon was also observed in single Co by TEM measurement, and it can be attributed to the dislocation reactions or the glide of (c + a) dislocations [16]. In the grain B, only one type of {1 1 2¯ 1} deformation twin is observed, and the domains of twin and matrix are identified to
have a misorientation of about 35◦ /[0 1¯ 1 0] (see the misorientation axis distribution shown in Fig. 1(d)). The discrepancy of exhibition of {1 1 2¯ 1} twin types in the grain A and grain B may be due to the original orientation difference of these two grains [8]. Fig. 2(a) is a cross-sectional bright-field TEM micrograph of the {1 1 2¯ 1} deformation twins in polycrystalline Co during DPD. The corresponding selected-area electron diffraction (SAED) pattern taken using [0 1 1¯ 0] zone axis from the circled area is shown in the bottom-right of Fig. 1(a). From the SEAD pattern, it can be seen that the (0 0 0 2) plane of the twin is rotated about 32◦ around 0 1 1¯ 0 axis from that of the matrix. The error for the misorientation-angle measured by EBSD and TEM is reasonable. Obviously, some dislocations labeled N are observed near the twin boundary (TB). These dislocations are basal dislocations because the dislocations are visible for g = [0 1 1¯ 0] [17]. Fig. 2(b) is the corresponding HRTEM image of the area labeled by the black frame and the letter of b in Fig. 2(a). It can be seen that the TB of {1 1 2¯ 1} twins is straight, which is unlike the TB of {1 0 1¯ 2} twins presented the step-like boundary [18]. Fig. 2(c) shows an enlarged image of the area indicated by the white frame and the letter c in Fig. 2(b). The basal dislocation labeled by T is observed near the TB. The basal dislocations were also observed by Vaidya and Mahajan in single Co when the sample was deformed by exposure to ultrasonic cavitation [16]. In addition, they have observed the (c + a) type dislocations with [2¯ 1 1 3] Burgers vector. However, this type of dislocation is not observed in our research. Fig. 3(a) shows a model involving the primitive hexagonal unit cell with the vector notation for hcp metals. The parallelograms ABCD and A B C D represent the same stacking of close packed planes. The “body” atom A0 is in the left triangular prism ABC. Each edge of the parallelograms represents the Burgers vector of a full
Y.T. Zhu et al. / Materials Science and Engineering A 548 (2012) 1–5
3
Fig. 2. (a) A TEM micrograph showing the {1 0 1¯ 2} deformation twins. The corresponding selected-area electron diffraction pattern taken using [0 1 1¯ 0] zone axis from the circled area is shown in the bottom-right. The basal dislocations labeled N are near the twin boundary. (b) The HRTEM image corresponding the area indicated by the black frame in (a). (c) Magnified map of the area indicated by the white frame in (b). The partial dislocation lying on (0 0 0 2) plane is marked by yellow T. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
dislocation in basal plane, 1/31¯ 1¯ 2 0. The points ˛ and ˇ are at the center point of the triangles ABC and CBD, respectively. The lines linking the corner of triangle and its center, e.g. A␣, represent the Burgers vector of the partial dislocations on the basal (a) slip plane. The vectors a1 , a2 and a3 are referred to three different directions in basal slips, namely 1/3[2 1 1 0], 1/3[1 1 2 0] and 1/3[1 2 1 0]. The vector c represents the [0 0 0 1] direction. The letter A0 represents atom corresponding to another stacking of close packed planes. The lines that link A0 and the corner of triangle represent the Burgers vector of the partial dislocation on the pyramidal (a + c) slip planes. We define the direction of the Burgers vector as from the first letter to the second letter. For example, A␣ represents a vector from the A to ␣. Fig. 3(b) is the schematic of neighboring four hexagonal unit cells for polycrystalline Co. Mendelson [19] has reported that the vectors AB and ␣A0 lie on −
AB → AD + DB → AF + F D + DB
(1)
where and are coefficients. Thus, we postulate that the {1 1 2¯ 1} deformation twins are formed by the reaction and glide of the basal dislocations. With the help of the primitive hexagonal unit cell with the vector notation of hcp metals in Fig. 3(a) and the Eq. (1), we describe the formation mechanism of {1 1 2¯ 1} deformation twins in the following section.
(2)
In the right-hand of Eq. (2), there are three vectors. The first vector, AF = 1/3[1¯ 1¯ 2 6], is the shear direction (1 ) of the invari−
ant plane (K1 = (1 1 2 1)) of the shear. The length of the second vector of dislocation F D is as much again as that of dislocation B D = 1/3[2 1¯ 1¯ 3]. The full dislocation B D can dissociate the sessile and glide partial dislocation as following: B D → B  + D
the {0 1 1¯ 0} plane of shear for the {2 1 1 l} zone giving b0 = [AB + ˛A0 ]
Due to the fact that the dissociation of an AB dislocation can result in the twinning partial dislocation on {1 1 2¯ 1} plane [19], we assume that the AB dislocation can dissociate into the following dislocations under the applied stress:
(3)
Thereinto, the partial B  is the sessile dislocation which cannot move and pin at the intersection of two {1 1 2¯ 1} planes, while the partial D can glide to nucleate a twin on the (0 0 0 2) plane (Fig. 4(a)). The dislocation DB can cross-slip the next intersection of two {1 1 2¯ 1} planes during the deformation. The dislocation reactions are energetically unfavorable and can only proceed with the help of applied stress [16,19,20].
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Y.T. Zhu et al. / Materials Science and Engineering A 548 (2012) 1–5
Fig. 3. (a) A primitive hexagonal unit cell with the vector notation for hcp metals. (b) The schematic of neighboring four hexagonal unit cells for polycrystalline Co.
Fig. 4. Schematics of the nucleation and growth of the {1 1 2¯ 1} deformation twins. (a) Nucleation of a twin on the (0 0 0 2) plane of matrix (or twin). (b) Nucleation of a twin on the next (0 0 0 2) plane of twin (or matrix). (c) The growth of the {1 1 2¯ 1} deformation twins with the partials gliding on the (0 0 0 2) plane. The alternate sessile dislocation ¯ and {1 1 2¯ 1} planes. of B  and B is at the intersection between the (1 1 2¯ 1)
Now DB dissociates into the following dislocations under the applied stress: DB → DA + AB → DF + F A + AB
(4) −−
Thereinto, the vector F A (1/3[1 1 2 6]) is the shear direction −
(1 ) of the invariant plane (K1 = (1 1 2 1)) of the shear. The length of the dislocation DF is as much again as that of dislocation DB −
−
(1/3[2 1 1 3]). Then, the dislocation B D dissociates into two partials on the next (0 0 0 2) plane: DB → D + B
(5)
As shown in Fig. 4(b), the partial B is the sessile and cannot move, while the partial D glides to nucleate a twin on the (0 0 0 2) plane. AB cross-slips the next intersection of two {1 1 2¯ 1} planes and dissociates like Eq. (1). With the repeating dislocation reactions and processes (see Fig. 4(c)), the {1 1 2¯ 1} deformation twins are generated successively. As shown in Fig. 2, the basal dislocations are the trails of the partials D or D which glides on the (0 0 0 2) planes. 4. Conclusions In this paper, the characteristic of the {1 1 2¯ 1} deformation twins and involved formation mechanisms have been investigated. The
results show that the dislocation dissociation plays an important role in the nucleation of {1 1 2¯ 1} deformation twins. With help of the applied stress, the basal full dislocation dissociates into three types of dislocations: (1) a dislocation with the shear direction of the invariant plane; (2) a dislocation dissociated into two partials including a sessile partial pinned at every intersection of the two {1 1 2¯ 1} planes and a glissile partial glided to nucleate a twin on the (0 0 0 2) planes; and (3) a dislocation cross-slipped the next intersection of two {1 1 2¯ 1} planes in order to provide the further dislocation reaction under the applied stress. During the DPD process, the dislocation reactions can be repeated and lead to the formation of the {1 1 2¯ 1} deformation twins. Acknowledgements X.Y. Zhang thanks prof. X.L. Wu for his constructive discussion. This work was supported by National Natural Science Foundation of China (Nos. 51071183, 50890170), the Fundamental Research Funds for the Central Universities (No. CDJXS11132225) and the Major State Basic Research Development Program of China (973 Program) (No. 2010CB631004). References [1] N. Munroe, X.L. Tan, Scr. Mater. 36 (1997) 1383. [2] L. Kucherov, E.B. Tadmor, Acta Mater. 55 (2007) 2065.
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