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Hardening mechanism of twin boundaries during nanoindentation of soft-brittle CdTe crystals
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Scripta Materialia 69 (2013) 457–460 www.elsevier.com/locate/scriptamat
Hardening mechanism of twin boundaries during nanoindentation of soft-brittle CdTe crystals Zhenyu Zhang,a,c,⇑ Xianzhong Zhang,a Xiaoguang Guo,a Fei Yeb and Yanxia Huoa a
Key Laboratory for Precision and Non-Traditional Machining Technology of Ministry of Education, Dalian University of Technology, Dalian 116024, People’s Republic of China b School of Materials Science and Engineering, Dalian University of Technology, Dalian 116024, People’s Republic of China c State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, People’s Republic of China Received 6 May 2013; revised 20 May 2013; accepted 26 May 2013 Available online 4 June 2013
Deformations of cadmium telluride (CdTe) under nanoindentation were simulated by molecular dynamics. CdTe slides along the {1 1 1} planes under nanoindentation through edge dislocations. During loading, the sliding of CdTe was limited at twin boundaries, inducing the pile-up phenomenon. When dislocations transferred across the twin boundary, a sessile dislocation and steps formed. The coherence effect of both twin boundaries locked the dislocations at the twin boundary effectively, indicating a better hardening effect. Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Molecular dynamics; Nanotwinned structure; CdTe; Nanoindentation; Edge dislocation
The nanotwinned structures of metals have attracted great attention, due to their high strength, ductility, as well as electrical conductivity [1–4]. The strength of nanotwinned copper (Cu) is increased up to 10 times compared to that of its coarse-grained counterparts [1]. Molecular dynamics (MD) is widely used to investigate the strengthening and softening mechanisms of nanotwinned Cu [5–8]. Nevertheless, both experimental and theoretical simulations, such as MD, for nanotwinned metals have mainly focused on Cu [7]. Little has been reported for third-generation soft-brittle semiconductors, e.g. cadmium zinc telluride (CdZnTe or CZT). CZT is a representative third-generation soft-brittle semiconductor, and has been widely applied for room-temperature X-ray and gamma-ray detectors, medical imaging, and radiation protection [9–11]. Recently, we found the hardness of nanotwinned CZT to be up to 100 times greater than that of its monocrystalline counterparts
⇑ Corresponding author at: Key Laboratory for Precision and NonTraditional Machining Technology of Ministry of Education, Dalian University of Technology, Dalian 116024, People’s Republic of China; e-mail: [email protected]
[11]. Nonetheless, the hardening mechanism of nanotwinned CZT during nanoindentation is not well understood. It is intriguing to investigate the hardening mechanism of nanotwinned CZT under mechanical loading. As CZT is formed from cadmium telluride (CdTe) by the partial displacement of Cd atoms by Zn atoms, both CZT and CdTe have the same face-centered cubic (fcc) and zinc blende structure. In addition, the Zn content in nanotwinned Cd0.96Zn0.04Te is only 0.04, and therefore CdTe can be used to replace CZT in the nanotwinned structure [12]. This is attributed to the difficulty in obtaining a potential function of CZT. In this study, we report our MD results on the hardening mechanism of nanotwinned CdTe during nanoindentation for third-generation soft-brittle semiconductors. In our previous work for nanotwinned CZT, all the twins were unidirectional and lacked grain boundaries. Nanotwinned CZT exhibits a repeating pattern comprising a bigger twin with thickness >12.7 nm, followed by one or several twins with thicknesses <12.7 nm [11]. As a result, three MD models of CdTe have been proposed, consisting of one single crystal (CdTe-sc), and two nano-
1359-6462/$ - see front matter Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.scriptamat.2013.05.034
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Z. Zhang et al. / Scripta Materialia 69 (2013) 457–460
twinned crystals. One nanotwinned crystal includes two twins with thicknesses of 4 and 22 nm at the top and bottom, respectively, referred to as CdTe-nt-4-22. Another nanotwinned crystal consists of three twins with thicknesses of 4, 6 and 16 nm at, respectively, the higher, medium and lower parts, designated as CdTe-nt-4-6-16. The sizes of the three MD models are 32 nm in length, 9 nm in width, and 29 nm in height. Each MD model simulated had 249,600 atoms. Prior to loading, each model experienced an isothermal-isobaric (NPT) relaxation for 100 ps at 300 K. The MD simulations were carried out under displacement rate-controlled conditions. The time step for the MD simulation was 1 fs. The Stillinger–Weber potential was used to present the twobody and three-body potentials for CdTe [12,13]. W 2 ¼ ef2 ðrij =rÞ
ð1Þ
W 3 ¼ ef3 ðrij =r; rjk =r; rki =rÞ
ð2Þ
( f2 ðrÞ ¼
1
AðBr4 1Þ exp½ðr aÞ ;
r
0;
rPa
ð3Þ
f3 ðrij ; rjk ; rki Þ ¼ hðrij ; rik ; hi Þ þ hðrji ; rjk ; hj Þ þ hðrki ; rkj ; hk Þ ð4Þ ( hðr;s;hÞ ¼
2
kexp½vðr aÞ1 þ vðs aÞ1 ðcos h þ 13Þ ; r < a&s < a 0;
otherwise
ð5Þ
previous experimental results [11]. Another critical line ˚ , again marked with a blue line in Figure 1. After is 34 A this line, CdTe-nt-4-6-16 exhibits higher forces at the same indentation depth until unloading. The residual indentation depth after unloading, hf, of CdTe-sc is ˚ , 34 A ˚ the lowest. Therefore, three snapshots at 20 A and after unloading are presented in this work. Figure 2a–c shows snapshots of the MD simulations for CdTe-sc, CdTe-nt-4-22 and CdTe-nt-4-6-16, respec˚ . All the deformatively, at an indentation depth of 20 A tions of three models slide along the h1 1 2i orientations and parallel to the {1 1 1} planes. The transmission of deformations induced by stress occurs via edge dislocations. The deformation depth of CdTe-sc reaches approximately 17 nm, at about a half of the model, as shown in Figure 2a. Both the deformations of CdTent-4-22 and CdTe-nt-4-6-16 arrive at the twin boundaries, as shown in Figure 2b and c. Two pairs of edge dislocations are observed in both the CdTe-sc and CdTe-nt-4-22 models, and one pair of edge dislocations is depicted in CdTe-nt-4-6-16. Figure 3 shows snapshots of the three MD models at ˚ . The three samples slide an indentation depth of 34 A along the {1 1 1} planes. The deformation depth of CdTe-sc reaches about 27 nm, i.e. to the bottom of the model, as shown in Figure 3a. The deformation of CdTe-nt-4-6-16 is basically locked at the first twin boundary of Figure 3c. The deformation of CdTe-nt-4-22 transfers across the twin boundary to about 3 nm. Three steps are seen in Figure 3b at the twin boundary marked with three white arrows. Four pairs, two pairs and one pair
where e, r, k, a and m are 1.03 eV, 0.251 nm, 25, 1.8 and 1.2, respectively. A is 7.0496, 5.1726 and 8.1415 for Cd– Te, Cd–Cd and Te–Te two-body potentials, respectively. B is 0.6022, 0.8807 and 0.6671 corresponding to Cd–Te, Cd–Cd and Te–Te two-body potentials [12,13]. Nanoindentation was performed with a cylindrical indenter of radius 4 nm. Periodic boundary conditions were employed for the lateral dimensions. The thickness for each MD model was fixed at 1.5 nm at the bottom. Red represents Cd atoms, and blue Te atoms. Twin boundaries are highlighted in light yellow. Figure 1 shows the loading–unloading curves for the CdTe-sc, CdTe-nt-4-22 and CdTe-nt-4-6-16 models obtained by MD simulations. During loading, the three loading curves are in good agreement when the indenta˚ , marked by a red line in Figure 1. tion depth is <20 A After this critical line, both nanotwinned models generate higher forces at the same indentation depth, indicating higher hardness. This is consistent with our
Figure 1. Loading–unloading curves for the CdTe-sc, CdTe-nt-4-22 and CdTe-nt-4-6-16 models obtained by MD simulations.
Figure 2. Snapshots of MD simulations for (a) CdTe-sc, (b) CdTe-nt˚. 4-22 and (c) CdTe-nt-4-6-16 at an indentation depth of 20 A
Z. Zhang et al. / Scripta Materialia 69 (2013) 457–460
Figure 3. Snapshots of MD simulations for (a) CdTe-sc, (b) CdTe-nt˚. 4-22 and (c) CdTe-nt-4-6-16 at an indentation depth of 34 A
of edge dislocations are observed in Figure 3a–c, respectively. Pile-up phenomena appear in nanotwinned MD models, except for the single crystal of CdTe-sc. Figure 4 shows snapshots of the three MD models after unloading. The residual indentation depth of CdTe-sc is the lowest, as shown in Figure 4a. Pile-up phenomena are observed in two nanotwinned MD samples, except for the single-crystal model. The deformation depth of CdTe-sc reaches the bottom of the model (Fig. 4a). One pair of edge dislocations is left in both the CdTe-sc and CdTe-nt-4-6-16 samples (Fig. 4c). Three steps are marked with white arrows in Figure 4b, and the transmission depth across the twin boundary in CdTe-nt-4-22 is about 3 nm. ˚ , the lockBefore the indentation depth reaches 20 A ing effect of twin boundaries on the deformations induced under the indenter is not obvious. This is verified by the absence of pile-up profiles for all three MD models, as shown in Figure 2. Hence, the loading curves are in good agreement for the three MD models, as observed in Figure 1. The deformations slide along the h1 1 2i orientations, and are parallel to the {1 1 1} planes. This is attributed to the fcc and zinc blende structure of CdTe. Moreover, CdTe has a low stacking fault energy [14], and easily slides under inhomogeneous stress produced by nanoindentation. ˚ , a strengthening With an indentation depth of 20 A effect prevails, resulting in hardening for nanoindentation during loading, as shown in Figure 1. The critical thickness of twins in nanotwinned CZT is 12.7 nm [11]. This means that when the thickness of the twins is more than 12.7 nm, a strengthening or hardening
459
Figure 4. Snapshots of MD simulations for (a) CdTe-sc, (b) CdTe-nt4-22 and (c) CdTe-nt-4-6-16 after unloading.
effect dominates; whereas, conversely, when the thickness of twins is less than 12.7 nm, softening prevails [1,5,11]. For CdTe-nt-4-22, the upper twin with a thickness of 4 nm generates a softening effect, and the lower twin with a thickness of 22 nm creates a hardening effect, as shown in Figure 3b. The twin boundary limits the sliding along the {1 1 1} planes [4,15]. The transmission of dislocations was identified through Burgers vectors and along dislocation line directions. When dislocations transmitted across a twin boundary, a sessile dislocation formed and reached a depth of 3 nm, as shown in Figure 3b. As the sliding of CdTe is along the {1 1 1} planes, the stress was divided into rightward horizontal and downward components. Moreover, the upper thickness of the twin has a softening effect, and the sliding could move along the twin boundary, leading to the steps marked with white arrows in Figure 3b [16]. On the other hand, for CdTe-nt-4-6-16 in Figure 3c, the upper two twins have a softening effect, and the lower twin has a hardening effect. The combined effect of the two upper twins with a softening effect creates a better locking function compared to a single twin with a softening effect. The composite structure in CdTe-ne-46-16 appears to have a better gradient plasticity and size effect compared to relatively simple CdTe-nt-4-22 [4,17– 20]. The hardening effect for the nanotwinned structure agrees with the Hall–Petch relationship, and consequently the hardness of a 22 nm thick twin is less than that of a 16 nm thick twin [17,4,18–20]. The deformation is basically locked at the first twin boundary, as shown for CdTe-nt-4-6-16 in Figure 3c, resulting in a better ˚ indentation depth, compared hardening effect after 34 A
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Z. Zhang et al. / Scripta Materialia 69 (2013) 457–460
to CdTe-4-22 (Fig. 1). The impeded sliding of deformations induced at twin boundaries creates a hardening effect for both CdTe-nt-4-22 and CdTe-nt-4-6-16. The sliding of CdTe under stress along the {1 1 1} planes causes pile-up profiles to form due to a locking effect at the twin boundaries. In addition, the pile-up phenomenon is also associated with a highly inhomogeneous stress field generated under an indenter. On the other hand, as there is nothing hindering the transmission of deformations in a single crystal, the transmission depth under nanoindentation is the deepest of the three MD models due to the eight edge dislocations, and the pileup phenomenon is absent (Fig. 3a). During unloading, the deformation of CdTe-sc is able to slide freely along the {1 1 1} planes. This makes six edge dislocations annihilate and disappear, leaving one pair of edge dislocations (Fig. 4a). As the pile-up and steps cause plastic deformation, they remain after unloading within nanotwinned structure, as shown in Figure 4b and c. Consequently, the residual indentation depth of CdTe-sc is the lowest, and those of the other two nanotwinned structures are similar to each other. As the horizontal component of stress along the {1 1 1} planes is in rightwards direction, the deformation areas on the right sides of the indentation for both nanotwinned structures are larger than those of the left sides, as observed in Figure 3b and c. Additionally, there is a small inclined angle after unloading due to the effect of the rightward component of stress parallel to the {1 1 1} planes, as illustrated in Figure 4b and c. In conclusion, two nanotwinned structures of CdTe were constructed to investigate the hardening mechanism of twin boundaries. For comparison, an MD model for a single crystal was also constructed. During nanoindentation, deformation of CdTe slides along the ˚, {1 1 1} planes. At indentation depths of less than 20 A the three loading curves (for the single-crystal and the two nanotwinned structures) are in good agreement. This is attributed to the lack of any impediment to the sliding of CdTe at twin boundaries. When the transmission of sliding was limited at the twin boundaries, pileup phenomena occurred. When the sliding was transmitted across the twin boundaries, a sessile dislocation and steps formed. After unloading, most edge dislocations annihilated and disappeared in the single crystal, resulting in the lowest residual indentation depth. However, pile-up profiles around the indenter and at the steps induced at the twin boundary remain in the nanotwinned structures after unloading.
Z.Z. and X.Z. are grateful to Haofei Zhou and Shaoxing Qu, Zhejiang University and Liang Zhang, DLUT for their kind help with the MD construction and discussions. We would like to acknowledge financial support from the National Natural Science Foundation of China (91123013), the Tribology Science Fund of State Key Laboratory of Tribology (SKLTKF12A08) (Tsinghua University), the Fund of State Key Laboratory of Metastable Materials Science and Technology (201302) (Yanshan University), and the Fundamental Research Funds for the Central Universities (DUT13YQ109). [1] L. Lu, X. Chen, X. Huang, K. Lu, Science 323 (2009) 607. [2] L. Lu, Y.F. Shen, X.H. Chen, L.H. Qian, K. Lu, Science 304 (2004) 422. [3] H.Y. Hsiao, C.M. Liu, H.W. Lin, T.C. Liu, C.L. Lu, Y.S. Huang, C. Chen, K.N. Tu, Science 336 (2012) 1007. [4] M. Dao, L. Lu, R.J. Asaro, J.T.M. De Hosson, E. Ma, Acta Mater. 55 (2007) 4041. [5] X.Y. Li, Y.J. Wei, L. Lu, K. Lu, K, H.J. Gao, Nature 464 (2010) 877. [6] S.X. Qu, H.F. Zhou, Nanotechnology 21 (2010) 335704. [7] T. Zhu, H.J. Gao, Scripta Mater. 66 (2012) 843. [8] D. Xu, W.L. Kwan, K. Chen, X. Zhang, V. Ozolins, K.N. Tu, Appl. Phys. Lett. 91 (2007) 254105. [9] Q. Zheng, F. Dierre, J. Crocco, V. Carcelen, H. Bensalah, J.L. Plaza, E. Dieguez, Appl. Surf. Sci. 257 (2011) 8742. [10] T.E. Schlesinger, J.E. Toney, H. Yoon, E.Y. Lee, B.A. Brunett, L. Franks, R.B. James, Mater. Sci. Eng. R 32 (2001) 103. [11] Z.Y. Zhang, Y.X. Huo, F.W. Huo, X.Z. Zhang, L. Zhang, D.M. Guo, Scripta Mater. 68 (2013) 747. [12] Z.Q. Wang, D. Stroud, A.J. Markworth, Phys. Rev. B 40 (1989) 3129. [13] F.H. Stillinger, T.A. Weber, Phys. Rev. B 31 (1985) 5262. [14] Z.Y. Zhang, C.G. Xu, X.Z. Zhang, D.M. Guo, Scripta Mater. 67 (2012) 392. [15] B.J. Pestman, J.T.M. De Hosson, V. Vitek, F.W. Schapink, Philos. Mag. A 64 (1991) 951. [16] W.A. Soer, J.T.M. De Hosson, A.M. Minor, J.W. Morris, E.A. Stach, Acta Mater. 52 (2004) 5783. [17] J.T.M. De Hosson, W.A. Soer, A.M. Minor, Z.W. Shan, E.A. Stach, S.A.S. Asif, O.L. Warren, J. Mater. Sci. 41 (2006) 7704. [18] J.R. Greer, J.T.M. De Hosson, Prog. Mater. Sci. 56 (2011) 654. [19] W.A. Soer, J.T.M. De Hosson, Mater. Lett. 59 (2005) 3192. [20] M. Martyniuk, R.H. Sewell, C.A. Musca, J.M. Dell, L. Faraone, Appl. Phys. Lett. 87 (2005) 251905.
Scripta Materialia 69 (2013) 457–460 www.elsevier.com/locate/scriptamat
Hardening mechanism of twin boundaries during nanoindentation of soft-brittle CdTe crystals Zhenyu Zhang,a,c,⇑ Xianzhong Zhang,a Xiaoguang Guo,a Fei Yeb and Yanxia Huoa a
Key Laboratory for Precision and Non-Traditional Machining Technology of Ministry of Education, Dalian University of Technology, Dalian 116024, People’s Republic of China b School of Materials Science and Engineering, Dalian University of Technology, Dalian 116024, People’s Republic of China c State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, People’s Republic of China Received 6 May 2013; revised 20 May 2013; accepted 26 May 2013 Available online 4 June 2013
Deformations of cadmium telluride (CdTe) under nanoindentation were simulated by molecular dynamics. CdTe slides along the {1 1 1} planes under nanoindentation through edge dislocations. During loading, the sliding of CdTe was limited at twin boundaries, inducing the pile-up phenomenon. When dislocations transferred across the twin boundary, a sessile dislocation and steps formed. The coherence effect of both twin boundaries locked the dislocations at the twin boundary effectively, indicating a better hardening effect. Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Molecular dynamics; Nanotwinned structure; CdTe; Nanoindentation; Edge dislocation
The nanotwinned structures of metals have attracted great attention, due to their high strength, ductility, as well as electrical conductivity [1–4]. The strength of nanotwinned copper (Cu) is increased up to 10 times compared to that of its coarse-grained counterparts [1]. Molecular dynamics (MD) is widely used to investigate the strengthening and softening mechanisms of nanotwinned Cu [5–8]. Nevertheless, both experimental and theoretical simulations, such as MD, for nanotwinned metals have mainly focused on Cu [7]. Little has been reported for third-generation soft-brittle semiconductors, e.g. cadmium zinc telluride (CdZnTe or CZT). CZT is a representative third-generation soft-brittle semiconductor, and has been widely applied for room-temperature X-ray and gamma-ray detectors, medical imaging, and radiation protection [9–11]. Recently, we found the hardness of nanotwinned CZT to be up to 100 times greater than that of its monocrystalline counterparts
⇑ Corresponding author at: Key Laboratory for Precision and NonTraditional Machining Technology of Ministry of Education, Dalian University of Technology, Dalian 116024, People’s Republic of China; e-mail: [email protected]
[11]. Nonetheless, the hardening mechanism of nanotwinned CZT during nanoindentation is not well understood. It is intriguing to investigate the hardening mechanism of nanotwinned CZT under mechanical loading. As CZT is formed from cadmium telluride (CdTe) by the partial displacement of Cd atoms by Zn atoms, both CZT and CdTe have the same face-centered cubic (fcc) and zinc blende structure. In addition, the Zn content in nanotwinned Cd0.96Zn0.04Te is only 0.04, and therefore CdTe can be used to replace CZT in the nanotwinned structure [12]. This is attributed to the difficulty in obtaining a potential function of CZT. In this study, we report our MD results on the hardening mechanism of nanotwinned CdTe during nanoindentation for third-generation soft-brittle semiconductors. In our previous work for nanotwinned CZT, all the twins were unidirectional and lacked grain boundaries. Nanotwinned CZT exhibits a repeating pattern comprising a bigger twin with thickness >12.7 nm, followed by one or several twins with thicknesses <12.7 nm [11]. As a result, three MD models of CdTe have been proposed, consisting of one single crystal (CdTe-sc), and two nano-
1359-6462/$ - see front matter Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.scriptamat.2013.05.034
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Z. Zhang et al. / Scripta Materialia 69 (2013) 457–460
twinned crystals. One nanotwinned crystal includes two twins with thicknesses of 4 and 22 nm at the top and bottom, respectively, referred to as CdTe-nt-4-22. Another nanotwinned crystal consists of three twins with thicknesses of 4, 6 and 16 nm at, respectively, the higher, medium and lower parts, designated as CdTe-nt-4-6-16. The sizes of the three MD models are 32 nm in length, 9 nm in width, and 29 nm in height. Each MD model simulated had 249,600 atoms. Prior to loading, each model experienced an isothermal-isobaric (NPT) relaxation for 100 ps at 300 K. The MD simulations were carried out under displacement rate-controlled conditions. The time step for the MD simulation was 1 fs. The Stillinger–Weber potential was used to present the twobody and three-body potentials for CdTe [12,13]. W 2 ¼ ef2 ðrij =rÞ
ð1Þ
W 3 ¼ ef3 ðrij =r; rjk =r; rki =rÞ
ð2Þ
( f2 ðrÞ ¼
1
AðBr4 1Þ exp½ðr aÞ ;
r
0;
rPa
ð3Þ
f3 ðrij ; rjk ; rki Þ ¼ hðrij ; rik ; hi Þ þ hðrji ; rjk ; hj Þ þ hðrki ; rkj ; hk Þ ð4Þ ( hðr;s;hÞ ¼
2
kexp½vðr aÞ1 þ vðs aÞ1 ðcos h þ 13Þ ; r < a&s < a 0;
otherwise
ð5Þ
previous experimental results [11]. Another critical line ˚ , again marked with a blue line in Figure 1. After is 34 A this line, CdTe-nt-4-6-16 exhibits higher forces at the same indentation depth until unloading. The residual indentation depth after unloading, hf, of CdTe-sc is ˚ , 34 A ˚ the lowest. Therefore, three snapshots at 20 A and after unloading are presented in this work. Figure 2a–c shows snapshots of the MD simulations for CdTe-sc, CdTe-nt-4-22 and CdTe-nt-4-6-16, respec˚ . All the deformatively, at an indentation depth of 20 A tions of three models slide along the h1 1 2i orientations and parallel to the {1 1 1} planes. The transmission of deformations induced by stress occurs via edge dislocations. The deformation depth of CdTe-sc reaches approximately 17 nm, at about a half of the model, as shown in Figure 2a. Both the deformations of CdTent-4-22 and CdTe-nt-4-6-16 arrive at the twin boundaries, as shown in Figure 2b and c. Two pairs of edge dislocations are observed in both the CdTe-sc and CdTe-nt-4-22 models, and one pair of edge dislocations is depicted in CdTe-nt-4-6-16. Figure 3 shows snapshots of the three MD models at ˚ . The three samples slide an indentation depth of 34 A along the {1 1 1} planes. The deformation depth of CdTe-sc reaches about 27 nm, i.e. to the bottom of the model, as shown in Figure 3a. The deformation of CdTe-nt-4-6-16 is basically locked at the first twin boundary of Figure 3c. The deformation of CdTe-nt-4-22 transfers across the twin boundary to about 3 nm. Three steps are seen in Figure 3b at the twin boundary marked with three white arrows. Four pairs, two pairs and one pair
where e, r, k, a and m are 1.03 eV, 0.251 nm, 25, 1.8 and 1.2, respectively. A is 7.0496, 5.1726 and 8.1415 for Cd– Te, Cd–Cd and Te–Te two-body potentials, respectively. B is 0.6022, 0.8807 and 0.6671 corresponding to Cd–Te, Cd–Cd and Te–Te two-body potentials [12,13]. Nanoindentation was performed with a cylindrical indenter of radius 4 nm. Periodic boundary conditions were employed for the lateral dimensions. The thickness for each MD model was fixed at 1.5 nm at the bottom. Red represents Cd atoms, and blue Te atoms. Twin boundaries are highlighted in light yellow. Figure 1 shows the loading–unloading curves for the CdTe-sc, CdTe-nt-4-22 and CdTe-nt-4-6-16 models obtained by MD simulations. During loading, the three loading curves are in good agreement when the indenta˚ , marked by a red line in Figure 1. tion depth is <20 A After this critical line, both nanotwinned models generate higher forces at the same indentation depth, indicating higher hardness. This is consistent with our
Figure 1. Loading–unloading curves for the CdTe-sc, CdTe-nt-4-22 and CdTe-nt-4-6-16 models obtained by MD simulations.
Figure 2. Snapshots of MD simulations for (a) CdTe-sc, (b) CdTe-nt˚. 4-22 and (c) CdTe-nt-4-6-16 at an indentation depth of 20 A
Z. Zhang et al. / Scripta Materialia 69 (2013) 457–460
Figure 3. Snapshots of MD simulations for (a) CdTe-sc, (b) CdTe-nt˚. 4-22 and (c) CdTe-nt-4-6-16 at an indentation depth of 34 A
of edge dislocations are observed in Figure 3a–c, respectively. Pile-up phenomena appear in nanotwinned MD models, except for the single crystal of CdTe-sc. Figure 4 shows snapshots of the three MD models after unloading. The residual indentation depth of CdTe-sc is the lowest, as shown in Figure 4a. Pile-up phenomena are observed in two nanotwinned MD samples, except for the single-crystal model. The deformation depth of CdTe-sc reaches the bottom of the model (Fig. 4a). One pair of edge dislocations is left in both the CdTe-sc and CdTe-nt-4-6-16 samples (Fig. 4c). Three steps are marked with white arrows in Figure 4b, and the transmission depth across the twin boundary in CdTe-nt-4-22 is about 3 nm. ˚ , the lockBefore the indentation depth reaches 20 A ing effect of twin boundaries on the deformations induced under the indenter is not obvious. This is verified by the absence of pile-up profiles for all three MD models, as shown in Figure 2. Hence, the loading curves are in good agreement for the three MD models, as observed in Figure 1. The deformations slide along the h1 1 2i orientations, and are parallel to the {1 1 1} planes. This is attributed to the fcc and zinc blende structure of CdTe. Moreover, CdTe has a low stacking fault energy [14], and easily slides under inhomogeneous stress produced by nanoindentation. ˚ , a strengthening With an indentation depth of 20 A effect prevails, resulting in hardening for nanoindentation during loading, as shown in Figure 1. The critical thickness of twins in nanotwinned CZT is 12.7 nm [11]. This means that when the thickness of the twins is more than 12.7 nm, a strengthening or hardening
459
Figure 4. Snapshots of MD simulations for (a) CdTe-sc, (b) CdTe-nt4-22 and (c) CdTe-nt-4-6-16 after unloading.
effect dominates; whereas, conversely, when the thickness of twins is less than 12.7 nm, softening prevails [1,5,11]. For CdTe-nt-4-22, the upper twin with a thickness of 4 nm generates a softening effect, and the lower twin with a thickness of 22 nm creates a hardening effect, as shown in Figure 3b. The twin boundary limits the sliding along the {1 1 1} planes [4,15]. The transmission of dislocations was identified through Burgers vectors and along dislocation line directions. When dislocations transmitted across a twin boundary, a sessile dislocation formed and reached a depth of 3 nm, as shown in Figure 3b. As the sliding of CdTe is along the {1 1 1} planes, the stress was divided into rightward horizontal and downward components. Moreover, the upper thickness of the twin has a softening effect, and the sliding could move along the twin boundary, leading to the steps marked with white arrows in Figure 3b [16]. On the other hand, for CdTe-nt-4-6-16 in Figure 3c, the upper two twins have a softening effect, and the lower twin has a hardening effect. The combined effect of the two upper twins with a softening effect creates a better locking function compared to a single twin with a softening effect. The composite structure in CdTe-ne-46-16 appears to have a better gradient plasticity and size effect compared to relatively simple CdTe-nt-4-22 [4,17– 20]. The hardening effect for the nanotwinned structure agrees with the Hall–Petch relationship, and consequently the hardness of a 22 nm thick twin is less than that of a 16 nm thick twin [17,4,18–20]. The deformation is basically locked at the first twin boundary, as shown for CdTe-nt-4-6-16 in Figure 3c, resulting in a better ˚ indentation depth, compared hardening effect after 34 A
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to CdTe-4-22 (Fig. 1). The impeded sliding of deformations induced at twin boundaries creates a hardening effect for both CdTe-nt-4-22 and CdTe-nt-4-6-16. The sliding of CdTe under stress along the {1 1 1} planes causes pile-up profiles to form due to a locking effect at the twin boundaries. In addition, the pile-up phenomenon is also associated with a highly inhomogeneous stress field generated under an indenter. On the other hand, as there is nothing hindering the transmission of deformations in a single crystal, the transmission depth under nanoindentation is the deepest of the three MD models due to the eight edge dislocations, and the pileup phenomenon is absent (Fig. 3a). During unloading, the deformation of CdTe-sc is able to slide freely along the {1 1 1} planes. This makes six edge dislocations annihilate and disappear, leaving one pair of edge dislocations (Fig. 4a). As the pile-up and steps cause plastic deformation, they remain after unloading within nanotwinned structure, as shown in Figure 4b and c. Consequently, the residual indentation depth of CdTe-sc is the lowest, and those of the other two nanotwinned structures are similar to each other. As the horizontal component of stress along the {1 1 1} planes is in rightwards direction, the deformation areas on the right sides of the indentation for both nanotwinned structures are larger than those of the left sides, as observed in Figure 3b and c. Additionally, there is a small inclined angle after unloading due to the effect of the rightward component of stress parallel to the {1 1 1} planes, as illustrated in Figure 4b and c. In conclusion, two nanotwinned structures of CdTe were constructed to investigate the hardening mechanism of twin boundaries. For comparison, an MD model for a single crystal was also constructed. During nanoindentation, deformation of CdTe slides along the ˚, {1 1 1} planes. At indentation depths of less than 20 A the three loading curves (for the single-crystal and the two nanotwinned structures) are in good agreement. This is attributed to the lack of any impediment to the sliding of CdTe at twin boundaries. When the transmission of sliding was limited at the twin boundaries, pileup phenomena occurred. When the sliding was transmitted across the twin boundaries, a sessile dislocation and steps formed. After unloading, most edge dislocations annihilated and disappeared in the single crystal, resulting in the lowest residual indentation depth. However, pile-up profiles around the indenter and at the steps induced at the twin boundary remain in the nanotwinned structures after unloading.
Z.Z. and X.Z. are grateful to Haofei Zhou and Shaoxing Qu, Zhejiang University and Liang Zhang, DLUT for their kind help with the MD construction and discussions. We would like to acknowledge financial support from the National Natural Science Foundation of China (91123013), the Tribology Science Fund of State Key Laboratory of Tribology (SKLTKF12A08) (Tsinghua University), the Fund of State Key Laboratory of Metastable Materials Science and Technology (201302) (Yanshan University), and the Fundamental Research Funds for the Central Universities (DUT13YQ109). [1] L. Lu, X. Chen, X. Huang, K. Lu, Science 323 (2009) 607. [2] L. Lu, Y.F. Shen, X.H. Chen, L.H. Qian, K. Lu, Science 304 (2004) 422. [3] H.Y. Hsiao, C.M. Liu, H.W. Lin, T.C. Liu, C.L. Lu, Y.S. Huang, C. Chen, K.N. Tu, Science 336 (2012) 1007. [4] M. Dao, L. Lu, R.J. Asaro, J.T.M. De Hosson, E. Ma, Acta Mater. 55 (2007) 4041. [5] X.Y. Li, Y.J. Wei, L. Lu, K. Lu, K, H.J. Gao, Nature 464 (2010) 877. [6] S.X. Qu, H.F. Zhou, Nanotechnology 21 (2010) 335704. [7] T. Zhu, H.J. Gao, Scripta Mater. 66 (2012) 843. [8] D. Xu, W.L. Kwan, K. Chen, X. Zhang, V. Ozolins, K.N. Tu, Appl. Phys. Lett. 91 (2007) 254105. [9] Q. Zheng, F. Dierre, J. Crocco, V. Carcelen, H. Bensalah, J.L. Plaza, E. Dieguez, Appl. Surf. Sci. 257 (2011) 8742. [10] T.E. Schlesinger, J.E. Toney, H. Yoon, E.Y. Lee, B.A. Brunett, L. Franks, R.B. James, Mater. Sci. Eng. R 32 (2001) 103. [11] Z.Y. Zhang, Y.X. Huo, F.W. Huo, X.Z. Zhang, L. Zhang, D.M. Guo, Scripta Mater. 68 (2013) 747. [12] Z.Q. Wang, D. Stroud, A.J. Markworth, Phys. Rev. B 40 (1989) 3129. [13] F.H. Stillinger, T.A. Weber, Phys. Rev. B 31 (1985) 5262. [14] Z.Y. Zhang, C.G. Xu, X.Z. Zhang, D.M. Guo, Scripta Mater. 67 (2012) 392. [15] B.J. Pestman, J.T.M. De Hosson, V. Vitek, F.W. Schapink, Philos. Mag. A 64 (1991) 951. [16] W.A. Soer, J.T.M. De Hosson, A.M. Minor, J.W. Morris, E.A. Stach, Acta Mater. 52 (2004) 5783. [17] J.T.M. De Hosson, W.A. Soer, A.M. Minor, Z.W. Shan, E.A. Stach, S.A.S. Asif, O.L. Warren, J. Mater. Sci. 41 (2006) 7704. [18] J.R. Greer, J.T.M. De Hosson, Prog. Mater. Sci. 56 (2011) 654. [19] W.A. Soer, J.T.M. De Hosson, Mater. Lett. 59 (2005) 3192. [20] M. Martyniuk, R.H. Sewell, C.A. Musca, J.M. Dell, L. Faraone, Appl. Phys. Lett. 87 (2005) 251905.