J. Mater. Sci. Technol. ›› 2021, Vol. 66: 28-35.DOI: 10.1016/j.jmst.2020.06.017
• Research Article • Previous Articles Next Articles
Huhu Sua, Xinzhe Zhoua, Shijian Zhengb, Hengqiang Yea,c, Zhiqing Yanga,*(
)
Received:2020-06-11
Accepted:2020-06-18
Published:2021-03-10
Online:2021-04-01
Contact:
Zhiqing Yang
About author:* E-mail address: yangzq@imr.ac.cn (Z. Yang).Huhu Su, Xinzhe Zhou, Shijian Zheng, Hengqiang Ye, Zhiqing Yang. Atomic-resolution studies on reactions between basal dislocations and $\left\{ 10\bar{1}2 \right\}$ coherent twin boundaries in a Mg alloy[J]. J. Mater. Sci. Technol., 2021, 66: 28-35.
Fig. 1. (a) and (b) Optical micrograph and EBSD band contrast image of forged samples, respectively. (c) Distribution of misorientation at GBs and TBs for the region shown in (b). (d)-(f) Bright-field TEM image, selected-area electron diffraction pattern and atomic-resolution Z-contrast image for $\left\{ 10\bar{1}2 \right\}$ TBs.
Fig. 2. (a) and (d) Atomic-resolution Z-contrast images for steps at $\left\{ 10\bar{1}2 \right\}$ CTBs. (b) and (e) Circuit mapping analyses for steps shown in (a) and (d), respectively. Hexagonal unit cells are indicated by rectangles in both white and black lattices. (c) Schematic illustration showing formation of a step along a TB through its reaction with one incident dislocation. (f) Schematic illustration showing formation of a step along a TB through its reaction simultaneously with one dislocation from the upper crystal and the other from the bottom crystal. Basal $\langle {{\mathbf{a}}_{60}}\rangle $, residual and twinning dislocations are denoted as black, red and white “⊥”, respectively.
| Vectors | t(λ) | t(μ) | ${{\mathbf{b}}_{\text{p}/\text{q}}}$ | $|{{\mathbf{b}}_{\text{p q}}}|$ |
|---|---|---|---|---|
| ${{\mathbf{b}}_{2/2}}$ | $[000\bar{1}]$ | $[10\bar{1}0]$ | $(\Lambda^\text{2}-2)/(\Lambda^\text{2}+2)\left[ 10\bar{1}\bar{1} \right]$ | 0.15a |
| ${{\mathbf{b}}_{5/3}}$ | $1/3[\bar{2}11\bar{6}]$ | $1/3[41\bar{5}0]$ | $1/(\lambda^\text{2}+2)\left[ \Lambda^\text{2}-4,0,4-\Lambda^\text{2},6-6\Lambda^\text{2} \right]$ | 2.22a |
| $1/3[\bar{1}\bar{1}2\bar{6}]$ | $1/3[5\bar{1}\bar{4}0]$ | |||
| $1/(3\Lambda^\text{2}+6)[8\Lambda^\text{2}-8,-\Lambda^\text{2}-2,10-7\Lambda^\text{2},12-6\Lambda^\text{2}]$ | 0.84a | |||
| $1/3[11\bar{2}\bar{6}]$ | $[20\bar{2}0]$ | $1/(3\Lambda^\text{2}+6)[7\Lambda^\text{2}-10,\Lambda^\text{2}+2,8-8\Lambda^\text{2},12-6\Lambda^\text{2}]$ | ||
| ${{\mathbf{b}}_{5/6}}$ | $1/3[2\bar{1}\bar{1}\bar{9}]$ | $[30\bar{3}0]$ | $1/(3\Lambda^\text{2}+6)[11\Lambda^\text{2}-14,-\Lambda^\text{2}-2,16-10\Lambda^\text{2},18-9\Lambda^\text{2}]$ | 0.79a |
| $1/3[11\bar{2}\bar{9}]$ | $[30\bar{3}0]$ | $1/(3\Lambda^\text{2}+6)[10\Lambda^\text{2}-16,\Lambda^\text{2}+2,14-11\Lambda^\text{2},18-9\Lambda^\text{2}]$ | ||
| ${{\mathbf{b}}_{-7/-8}}$ | $[000\bar{4}]$ | 0.78a | ||
| $[000\bar{4}]$ | ||||
| ${{\mathbf{b}}_{-9/-10}}$ | $[000\bar{5}]$ | 0.79a | ||
| $[000\bar{5}]$ | ||||
| ${{\mathbf{b}}_{-13/-13}}$ | $1/3[2\bar{1}\bar{1}\bar{2}\bar{1}]$ | 0.18a | ||
| $1/3[11\bar{2}\bar{2}\bar{1}]$ |
Table 1 Topological parameters of interfacial dislocations at $\left\{ 10\bar{1}2 \right\}$ TBs in Mg predicted by the topological theory (Λ= $\sqrt{2/3}$ (c/a), a = 0.321 nm and c = 0.521 nm).
| Vectors | t(λ) | t(μ) | ${{\mathbf{b}}_{\text{p}/\text{q}}}$ | $|{{\mathbf{b}}_{\text{p q}}}|$ |
|---|---|---|---|---|
| ${{\mathbf{b}}_{2/2}}$ | $[000\bar{1}]$ | $[10\bar{1}0]$ | $(\Lambda^\text{2}-2)/(\Lambda^\text{2}+2)\left[ 10\bar{1}\bar{1} \right]$ | 0.15a |
| ${{\mathbf{b}}_{5/3}}$ | $1/3[\bar{2}11\bar{6}]$ | $1/3[41\bar{5}0]$ | $1/(\lambda^\text{2}+2)\left[ \Lambda^\text{2}-4,0,4-\Lambda^\text{2},6-6\Lambda^\text{2} \right]$ | 2.22a |
| $1/3[\bar{1}\bar{1}2\bar{6}]$ | $1/3[5\bar{1}\bar{4}0]$ | |||
| $1/(3\Lambda^\text{2}+6)[8\Lambda^\text{2}-8,-\Lambda^\text{2}-2,10-7\Lambda^\text{2},12-6\Lambda^\text{2}]$ | 0.84a | |||
| $1/3[11\bar{2}\bar{6}]$ | $[20\bar{2}0]$ | $1/(3\Lambda^\text{2}+6)[7\Lambda^\text{2}-10,\Lambda^\text{2}+2,8-8\Lambda^\text{2},12-6\Lambda^\text{2}]$ | ||
| ${{\mathbf{b}}_{5/6}}$ | $1/3[2\bar{1}\bar{1}\bar{9}]$ | $[30\bar{3}0]$ | $1/(3\Lambda^\text{2}+6)[11\Lambda^\text{2}-14,-\Lambda^\text{2}-2,16-10\Lambda^\text{2},18-9\Lambda^\text{2}]$ | 0.79a |
| $1/3[11\bar{2}\bar{9}]$ | $[30\bar{3}0]$ | $1/(3\Lambda^\text{2}+6)[10\Lambda^\text{2}-16,\Lambda^\text{2}+2,14-11\Lambda^\text{2},18-9\Lambda^\text{2}]$ | ||
| ${{\mathbf{b}}_{-7/-8}}$ | $[000\bar{4}]$ | 0.78a | ||
| $[000\bar{4}]$ | ||||
| ${{\mathbf{b}}_{-9/-10}}$ | $[000\bar{5}]$ | 0.79a | ||
| $[000\bar{5}]$ | ||||
| ${{\mathbf{b}}_{-13/-13}}$ | $1/3[2\bar{1}\bar{1}\bar{2}\bar{1}]$ | 0.18a | ||
| $1/3[11\bar{2}\bar{2}\bar{1}]$ |
| Circuit elements | Vectors |
|---|---|
| SAλ | $[\bar{6}060]$ |
| ABλ | $[\bar{3}033]$ |
| BCλ | $1/3[41\bar{5}0]$ or $1/3[5\bar{1}\bar{4}0]$ |
| SCλ | $1/3[\bar{2}\bar{3}1229]$ or $1/3[\bar{2}\bar{2}\bar{1}239]$ |
| CDμ | $[\bar{6}060]$ |
| DEμ | $[80\bar{8}\bar{8}]$ |
| EFμ | $[10\bar{1}0]$ |
| CFμ | $[30\bar{3}\bar{8}]$ |
| CFλ | $1/(\lambda^\text{2}+2)[13\Lambda^\text{2}+6,0,-13\Lambda^\text{2}-6,4-8\Lambda^\text{2}]$ |
| FS=―(SCλ+CFλ) | $1/3(\lambda^\text{2}+2)[28-16\Lambda^\text{2},-\Lambda^\text{2}-2,17\Lambda^\text{2}-26,15\Lambda^\text{2}-30]~$ or $1/3(\lambda^\text{2}+2)[26-17\Lambda^\text{2},\Lambda^\text{2}+2,16\Lambda^\text{2}-28,15\Lambda^\text{2}-30]$ |
Table 2 Circuit mapping elements for $\langle 1\bar{2}10\rangle $ projection of the ${{\mathbf{b}}_{-9/-10}}$ dislocation shown in Fig. 2(a).
| Circuit elements | Vectors |
|---|---|
| SAλ | $[\bar{6}060]$ |
| ABλ | $[\bar{3}033]$ |
| BCλ | $1/3[41\bar{5}0]$ or $1/3[5\bar{1}\bar{4}0]$ |
| SCλ | $1/3[\bar{2}\bar{3}1229]$ or $1/3[\bar{2}\bar{2}\bar{1}239]$ |
| CDμ | $[\bar{6}060]$ |
| DEμ | $[80\bar{8}\bar{8}]$ |
| EFμ | $[10\bar{1}0]$ |
| CFμ | $[30\bar{3}\bar{8}]$ |
| CFλ | $1/(\lambda^\text{2}+2)[13\Lambda^\text{2}+6,0,-13\Lambda^\text{2}-6,4-8\Lambda^\text{2}]$ |
| FS=―(SCλ+CFλ) | $1/3(\lambda^\text{2}+2)[28-16\Lambda^\text{2},-\Lambda^\text{2}-2,17\Lambda^\text{2}-26,15\Lambda^\text{2}-30]~$ or $1/3(\lambda^\text{2}+2)[26-17\Lambda^\text{2},\Lambda^\text{2}+2,16\Lambda^\text{2}-28,15\Lambda^\text{2}-30]$ |
| Circuit elements | Vectors |
|---|---|
| SAλ | $[\bar{1}\bar{0}0100]$ |
| ABλ | $[\bar{4}044]$ |
| BCλ | $1/3[11\bar{1}\bar{1}\bar{0}0]$ or $1/3[10\bar{1}\bar{1}\bar{1}0]$ |
| SCλ | $1/3[\bar{3}\bar{1}\bar{1}3212]$ or $1/3[\bar{3}\bar{2}13112]$ |
| CDμ | $[\bar{1}\bar{3}0130]$ |
| DEμ | $[110\bar{1}\bar{1}\bar{1}\bar{1}]$ |
| EFμ | $1/3[191\bar{2}\bar{0}0]$ or $1/3[20\bar{1}\bar{1}\bar{9}0]$ |
| CFμ | $1/3[131\bar{1}\bar{4}\bar{3}\bar{3}]$ or $1/3[14\bar{1}\bar{1}\bar{3}\bar{3}\bar{3}]$ |
| CFλ | $1/3(\lambda^\text{2}+2)[52\Lambda^\text{2}+26,\Lambda^\text{2}+2,-53\Lambda^\text{2}-28,12-33\Lambda^\text{2}]$ $1/3(\lambda^\text{2}+2)[53\Lambda^\text{2}+28,-\Lambda^\text{2}-2,-52\Lambda^\text{2}-26,12-33\Lambda^\text{2}]$ |
| FS=―(SCλ+CFλ) | $(12-7\Lambda^\text{2})/(\Lambda^\text{2}+2)[10\bar{1}\bar{1}]$ |
Table 3 Circuit mapping elements for the ${{\mathbf{b}}_{-13/-13}}$ dislocation shown in Fig. 2(d).
| Circuit elements | Vectors |
|---|---|
| SAλ | $[\bar{1}\bar{0}0100]$ |
| ABλ | $[\bar{4}044]$ |
| BCλ | $1/3[11\bar{1}\bar{1}\bar{0}0]$ or $1/3[10\bar{1}\bar{1}\bar{1}0]$ |
| SCλ | $1/3[\bar{3}\bar{1}\bar{1}3212]$ or $1/3[\bar{3}\bar{2}13112]$ |
| CDμ | $[\bar{1}\bar{3}0130]$ |
| DEμ | $[110\bar{1}\bar{1}\bar{1}\bar{1}]$ |
| EFμ | $1/3[191\bar{2}\bar{0}0]$ or $1/3[20\bar{1}\bar{1}\bar{9}0]$ |
| CFμ | $1/3[131\bar{1}\bar{4}\bar{3}\bar{3}]$ or $1/3[14\bar{1}\bar{1}\bar{3}\bar{3}\bar{3}]$ |
| CFλ | $1/3(\lambda^\text{2}+2)[52\Lambda^\text{2}+26,\Lambda^\text{2}+2,-53\Lambda^\text{2}-28,12-33\Lambda^\text{2}]$ $1/3(\lambda^\text{2}+2)[53\Lambda^\text{2}+28,-\Lambda^\text{2}-2,-52\Lambda^\text{2}-26,12-33\Lambda^\text{2}]$ |
| FS=―(SCλ+CFλ) | $(12-7\Lambda^\text{2})/(\Lambda^\text{2}+2)[10\bar{1}\bar{1}]$ |
Fig. 3. (a) Atomic-resolution Z-contrast image showing a region with a $\left\{ 10\bar{1}2 \right\}$ CTB and a LAGB. Misfit dislocations are denoted as yellow “⊥”. (b) Schematic illustration for reaction between a $\left\{ 10\bar{1}2 \right\}$ CTB and a LAGB composed of basal $\langle {{\mathbf{a}}_{60}}\rangle $ dislocations. Only one “⊥” is indicated for TDs at each PB facet. (c) An enlarged image for a step at region “C” indicated in (a). (d) Circuit mapping analysis for the step shown in (c).
| Circuit elements | Vectors |
|---|---|
| SAλ | $1/3[\bar{5}140]$ or $1/3[\bar{4}\bar{1}50]$ |
| ABλ | $[\bar{4}044]$ |
| BCλ | $[40\bar{4}0]$ |
| SCλ | $1/3[\bar{5}1412]$ or $1/3[\bar{4}\bar{1}512]$ |
| CDμ | $[\bar{2}020]$ |
| DEμ | $[20\bar{2}\bar{2}]$ |
| EFμ | $1/3[11\bar{1}\bar{1}\bar{0}\bar{0}]$ or $1/3[101\bar{1}\bar{0}0]$ |
| CFμ | $1/3[11\bar{1}\bar{1}\bar{0}\bar{6}]$ or $1/3[101\bar{1}\bar{1}\bar{6}]$ |
| CFλ | $1/3(\lambda^\text{2}+2)[2\Lambda^\text{2}+22,-\Lambda^\text{2}-2,-\Lambda^\text{2}-20,-30-6\Lambda^\text{2}]$ or $1/3(\lambda^\text{2}+2)[\Lambda^\text{2}+20,\Lambda^\text{2}+2,-2\Lambda^\text{2}-22,-30-6\Lambda^\text{2}]$ |
| FS=―(SCλ+CFλ) | $1/(\lambda^\text{2}+2)\left[ \Lambda^\text{2}-4,0,4-\Lambda^\text{2},2-2\Lambda^\text{2} \right]$ |
Table 4 Circuit mapping elements for the ${{\mathbf{b}}_{5/3}}$ dislocation shown in Fig. 3(c).
| Circuit elements | Vectors |
|---|---|
| SAλ | $1/3[\bar{5}140]$ or $1/3[\bar{4}\bar{1}50]$ |
| ABλ | $[\bar{4}044]$ |
| BCλ | $[40\bar{4}0]$ |
| SCλ | $1/3[\bar{5}1412]$ or $1/3[\bar{4}\bar{1}512]$ |
| CDμ | $[\bar{2}020]$ |
| DEμ | $[20\bar{2}\bar{2}]$ |
| EFμ | $1/3[11\bar{1}\bar{1}\bar{0}\bar{0}]$ or $1/3[101\bar{1}\bar{0}0]$ |
| CFμ | $1/3[11\bar{1}\bar{1}\bar{0}\bar{6}]$ or $1/3[101\bar{1}\bar{1}\bar{6}]$ |
| CFλ | $1/3(\lambda^\text{2}+2)[2\Lambda^\text{2}+22,-\Lambda^\text{2}-2,-\Lambda^\text{2}-20,-30-6\Lambda^\text{2}]$ or $1/3(\lambda^\text{2}+2)[\Lambda^\text{2}+20,\Lambda^\text{2}+2,-2\Lambda^\text{2}-22,-30-6\Lambda^\text{2}]$ |
| FS=―(SCλ+CFλ) | $1/(\lambda^\text{2}+2)\left[ \Lambda^\text{2}-4,0,4-\Lambda^\text{2},2-2\Lambda^\text{2} \right]$ |
Fig. 4. (a) Atomic-resolution Z-contrast image showing generation of an asymmetric tilt GB. The inset is an enlarged image for a local region at the asymmetric tilt GB. (b) Circuit mapping analyses for interfacial defects at the asymmetric tilt GB shown in (a). (c) Schematic illustration for the reaction between a $\left\{ 10\bar{1}2 \right\}$ CTB and a LAGB composed of basal $\langle {{\mathbf{a}}_{60}}\rangle $ dislocations. Only one symbol is drawn for TDs at each BP facet.
Fig. 5. (a) and (b) Optical micrographs showing surfaces parallel to the tensile direction for solution-treated and forged samples after tensile fracture, respectively. Insets in (a) and (b) are corresponding EBSD band contrast maps. (c) and (d) SEM images showing fracture morphologies of solution-treated and forged samples, respectively.
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