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Acta Metall Sin  2018, Vol. 54 Issue (4): 603-612    DOI: 10.11900/0412.1961.2017.00252
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A First-Principles Study on Basal/Prismatic Reorientation-Induced Twinning Path and Alloying Effect in Hexagonal Metals
Gang ZHOU1,2, Lihua YE1, Hao WANG1(), Dongsheng XU1, Changgong MENG2, Rui YANG1
1 Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China
2 School of Materials Science and Engineering, Dalian University of Technology, Dalian 116024, China
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In hexagonal metals and alloys, deformation twinning plays an important role, because it is closely relevant to the mechanical behaviors. Recent studies have proposed a new twinning mode via direct lattice reorientation, which results in the basal/prismatic boundary, however, some important details remain unanswered, e.g., the twinning path and alloying effect. In this work, first principles calculations were employed to systematically study the reorientation process from basal to prismatic orientation in hexagonal metals and corresponding alloying effect. The result indicates that different activation energies are required to reorient in various hexagonal metals, and among them, the energy in Mg is the lowest and Os is the highest. Shear and shuffle components compose the reorientation process, where the shuffle component always contributes a significant part of the activation energy in Mg, whereas in Ti with sufficient shear strain, subsequent transition becomes energy-downhill. The pure shear was effected by alloying elements in Mg alloys, but pure shuffle in Ti alloys. Under certain shear or shuffle, subsequent activation energy has a complex dependence on alloying elements.

Key words:  hexagonal metal      twinning      first principles calculation      alloying     
Received:  27 June 2017     
ZTFLH:  TG146.2  
Fund: Supported by National Key Research and Development Program of China (No.2016YFB0701304) and National Natural Science Foundation of China (No.51671195)

Cite this article: 

Gang ZHOU, Lihua YE, Hao WANG, Dongsheng XU, Changgong MENG, Rui YANG. A First-Principles Study on Basal/Prismatic Reorientation-Induced Twinning Path and Alloying Effect in Hexagonal Metals. Acta Metall Sin, 2018, 54(4): 603-612.

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Fig.1  Schematics of the initial (a) and final (b) atomic configurations during the basal/prismatic transition
Fig.2  Energy barriers of 19 hexagonal metals during the basal/prismatic transition
Metal Cal. Exp.[21]
Be 1.568 1.574
Mg 1.624 1.623
Sc 1.592 1.555
Ti 1.587 1.584
Y 1.571 1.552
Zr 1.593 1.597
Tc 1.605 1.599
Gd 1.591 1.575
Tb 1.580 1.564
Dy 1.573 1.556
Ho 1.570 1.552
Er 1.569 1.550
Tm 1.570 1.551
Lu 1.583 1.555
Hf 1.581 1.581
Co 1.623 1.615
Ru 1.583 1.576
Re 1.615 1.615
Os 1.606 1.578
Table 1  Calculated and experimental[21] c/a ratios for hexagonal metals
Metal ZPVE Metal ZPVE
meVatom-1 meVatom-1
Be -1.66 Ho 0.14
Mg 0.20 Er 0.17
Sc 0.45 Tm -0.04
Ti -1.21 Lu 0.38
Y 0.02 Hf 0.44
Zr 0.23 Co 0.34
Tc 0.18 Ru 1.44
Gd 1.68 Re -1.61
Tb 1.03 Os 0.96
Dy 0.34
Table 2  Zero-point vibration energy (ZPVE) correction
Fig.3  Relationships of energy barrier and c/a ratio during the basal/prismatic transition in 16 hexagonal metals
Fig.4  Schematics of the shear and shuffle (εy'z'—equivalent shear strain during basal/prismatic transition)(a) the initial and final four-atom supercell shape(b) the four-atom supercell viewed from [12?10]
Fig.5  Reorientation energy maps against the shear and shuffle components in Mg (a) and Ti (b) (The red curves indicate the minimum energy paths of the basal/prismatic transition processes)
Fig.6  Histogram of ΔE in Mg (a) and Ti (b) (ΔE is the shuffle energy at different amount of shear, and the black squares represent the value less than 0)
Fig.7  Reorientation energy maps against the shear and shuffle components in Mg alloyed by Be (a), Al (b), Si (c), La (d), Zr (e) and Mn (f) (The red circles indicate the amount of pure shear given an activation energy of 14 meV/atom)
Fig.8  Reorientation energy maps against the shear and shuffle components Ti alloyed by Al (a), Hf (b), Zr (c), W (d), Cr (e), Nb (f), V (g), Co (h), La (i), Fe (j), Re (k), Os (l), Ru (m) (The red circles indicate the amount of pure shear or pure shuffle given an activation energy of 30 meV/atom)
Fig.9  3D charge density difference maps of initial and 50% basal/prismatic transitional structures with isosurface values of 13 e/nm3 (a~d) and 47 e/nm3 (e~h) in pure Mg (a, b), Mg-La (c, d), pure Ti (e, f) and Ti-La (g, h) (The red circles indicate charge enrichment)
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