J. Mater. Sci. Technol. ›› 2021, Vol. 74: 27-34.DOI: 10.1016/j.jmst.2020.10.010
• Research Article • Previous Articles Next Articles
Hai-Le Yana,*(
), Hao-Xuan Liua, Ying Zhaoa, Nan Jiab, Jing Baic, Bo Yanga, Zongbin Lia, Yudong Zhangd, Claude Eslingd, Xiang Zhaoa,*(), Liang Zuoa
Received:2020-07-01
Revised:2020-08-29
Accepted:2020-09-04
Published:2021-05-30
Online:2020-10-10
Contact:
Hai-Le Yan,Xiang Zhao
About author:zhaox@mail.neu.edu.cn (X. Zhao).Hai-Le Yan, Hao-Xuan Liu, Ying Zhao, Nan Jia, Jing Bai, Bo Yang, Zongbin Li, Yudong Zhang, Claude Esling, Xiang Zhao, Liang Zuo. Impact of B alloying on ductility and phase transition in the Ni-Mn-based magnetic shape memory alloys: Insights from first-principles calculation[J]. J. Mater. Sci. Technol., 2021, 74: 27-34.
Fig. 1. Compressive fracture strain ε and fracture stress σ for the B-alloyed and the B-freed Ni-Mn-based alloys. Data are extracted from the literature as follows: a Ref. [12], b Ref. [13], c Ref. [18], d Ref. [14], e Ref. [15], f Ref. [16], and g Ref. [17].
Fig. 2. Illustration of L21 crystal structure of Ni2MnGa. T, O-I and O-II indicate the tetragonal and the two octahedral interstices, respectively.
Fig. 3. Illustrations of the Ni-BNi (a1), the Ni-BMn (a2) and the Ni-BGa (a3) structural models for the (Ni1.75B0.25)MnGa alloy. (b) Formation energies Ef of various occupation models for the (Ni1.75B0.25)MnGa, Ni2(Mn0.75B0.25)Ga, Ni2Mn(Ga0.75B0.25), (Ni2MnGa)0.94B0.06 alloys. Evolution Ef and C' for the Ni2-xBxMnGa alloys with the Ni-BNi occupation (c1), the Ni2Mn1-xBxGa alloys with the Mn-BMn occupation (c2), and the Ni2MnGa1-xBx alloys with the Ga-BGa occupation (c3) as a function of the B content.
| Alloying systems | Concentration x | Ef (meV/atom) | C11 (GPa) | C12 (GPa) | C44 (GPa) | C' (GPa) | a0 (Å) | |
|---|---|---|---|---|---|---|---|---|
| (Ni2-xBx)MnGa | 0 | Our work | -295.0 | 163.6 | 155.4 | 106.7 | 4.1 | 5.8024 |
| PAW [ | - | 163.0 | 152.0 | 107.0 | 5.5 | 5.8120 | ||
| EMTO [ | - | 168.0 ± 0.47 | 152.2 ± 0.23 | 107.0 ± 0.69 | 7.9 ± 0.35 | 5.8208 | ||
| PP [ | - | 153 ± 2 | 148 ± 2 | - | 2.5 ± 2 | - | ||
| Exp. [ | - | 152.0 | 143.0 | 103.0 | 4.5 | - | ||
| Exp. [ | - | 136 ± 3 | - | 102 ± 3 | 22 ± 2 | - | ||
| 0.25 | -150.5 | 169.8 | 165.4 | 98.9 | 2.2 | 5.7686 | ||
| 0.5 | -17.3 | 177.8 | 170.3 | 93.4 | 3.8 | 5.7247 | ||
| 0.75 | 145.4 | 152.2 | 157.7 | 68.7 | -2.8 | 5.6758 | ||
| 1 | 303.0 | 170.2 | 168.8 | 38.6 | 0.7 | 5.6218 | ||
| Ni2(Mn1-xBx)Ga | 0 | -295.0 | 163.6 | 155.4 | 106.7 | 4.1 | 5.8024 | |
| 0.25 | -167.8 | 176.2 | 171.0 | 104.2 | 2.6 | 5.7360 | ||
| 0.5 | -62.0 | 198.7 | 186.8 | 98.1 | 5.9 | 5.6590 | ||
| 0.75 | 20.2 | 196.0 | 175.4 | 9.5 | 10.3 | 5.5731 | ||
| 1 | 70.4 | 215.6 | 190.2 | -65.7 | 12.2 | 5.4737 | ||
| Ni2Mn(Ga1-xBx) | 0 | -295.0 | 163.6 | 155.4 | 106.7 | 4.1 | 5.8024 | |
| 0.25 | -145.1 | 171.1 | 156.0 | 85.3 | 7.5 | 5.7244 | ||
| 0.5 | -18.7 | 177.9 | 170.8 | 47.3 | 3.5 | 5.6373 | ||
| 0.75 | 79.3 | 173.1 | 193.5 | 12.0 | -10.2 | 5.5426 | ||
| 1 | 141.5 | 176.4 | 219.9 | -59.1 | -21.8 | 5.3908 | ||
| (Ni2MnGa)1-xBx | 0 | -295.0 | 163.6 | 155.4 | 106.7 | 4.1 | 5.8024 | |
| 0.0078 | -198.3 | 257.9 | 89.6 | 119.3 | 84.1 | 5.8363 | ||
| 0.06 | -140.0 | 90.5 | 131.5 | 63.9 | -20.5 | 6.0234 | ||
Table 1 Formation energy, elastic constant Cij and equilibrium lattice parameter a0 of the Ni2-xBxMnGa (x = 0, 0.25, 0.5, 0.75 and 1), Ni2Mn1-xBxGa(x = 0.25, 0.5, 0.75 and 1), Ni2MnGa1-xBx (x = 0, 0.25, 0.5, 0.75 and 1) and (Ni2MnGa)1-xBx (x = 0, 0.0078 and 0.06) alloys.
| Alloying systems | Concentration x | Ef (meV/atom) | C11 (GPa) | C12 (GPa) | C44 (GPa) | C' (GPa) | a0 (Å) | |
|---|---|---|---|---|---|---|---|---|
| (Ni2-xBx)MnGa | 0 | Our work | -295.0 | 163.6 | 155.4 | 106.7 | 4.1 | 5.8024 |
| PAW [ | - | 163.0 | 152.0 | 107.0 | 5.5 | 5.8120 | ||
| EMTO [ | - | 168.0 ± 0.47 | 152.2 ± 0.23 | 107.0 ± 0.69 | 7.9 ± 0.35 | 5.8208 | ||
| PP [ | - | 153 ± 2 | 148 ± 2 | - | 2.5 ± 2 | - | ||
| Exp. [ | - | 152.0 | 143.0 | 103.0 | 4.5 | - | ||
| Exp. [ | - | 136 ± 3 | - | 102 ± 3 | 22 ± 2 | - | ||
| 0.25 | -150.5 | 169.8 | 165.4 | 98.9 | 2.2 | 5.7686 | ||
| 0.5 | -17.3 | 177.8 | 170.3 | 93.4 | 3.8 | 5.7247 | ||
| 0.75 | 145.4 | 152.2 | 157.7 | 68.7 | -2.8 | 5.6758 | ||
| 1 | 303.0 | 170.2 | 168.8 | 38.6 | 0.7 | 5.6218 | ||
| Ni2(Mn1-xBx)Ga | 0 | -295.0 | 163.6 | 155.4 | 106.7 | 4.1 | 5.8024 | |
| 0.25 | -167.8 | 176.2 | 171.0 | 104.2 | 2.6 | 5.7360 | ||
| 0.5 | -62.0 | 198.7 | 186.8 | 98.1 | 5.9 | 5.6590 | ||
| 0.75 | 20.2 | 196.0 | 175.4 | 9.5 | 10.3 | 5.5731 | ||
| 1 | 70.4 | 215.6 | 190.2 | -65.7 | 12.2 | 5.4737 | ||
| Ni2Mn(Ga1-xBx) | 0 | -295.0 | 163.6 | 155.4 | 106.7 | 4.1 | 5.8024 | |
| 0.25 | -145.1 | 171.1 | 156.0 | 85.3 | 7.5 | 5.7244 | ||
| 0.5 | -18.7 | 177.9 | 170.8 | 47.3 | 3.5 | 5.6373 | ||
| 0.75 | 79.3 | 173.1 | 193.5 | 12.0 | -10.2 | 5.5426 | ||
| 1 | 141.5 | 176.4 | 219.9 | -59.1 | -21.8 | 5.3908 | ||
| (Ni2MnGa)1-xBx | 0 | -295.0 | 163.6 | 155.4 | 106.7 | 4.1 | 5.8024 | |
| 0.0078 | -198.3 | 257.9 | 89.6 | 119.3 | 84.1 | 5.8363 | ||
| 0.06 | -140.0 | 90.5 | 131.5 | 63.9 | -20.5 | 6.0234 | ||
Fig. 4. Ductile-brittle diagram (a), isotropic Young's modulus EH (b) and shear modulus GH (c) of (Ni2-xBx)MnGa (x = 0, 0.25 and 0.5), Ni2(Mn1-xBx)Ga (x = 0, 0.25 and 0.5), Ni2Mn(Ga1-xBx) (x = 0, 0.25 and 0.5) and (Ni2MnGa)1-xBx (x = 0 and 0.0078) alloys.
Fig. 5. ELF distributions on ($1\bar{1}0$) and |IpCOHP| values of Ni-Ga, Ni-B, Mn-Ga, Mn-B for the Ni2Mn(Ga0.75B0.25) (a1 and a2) and the (Ni2MnGa)0.94B0.06 (b1 and b2) alloys.
Fig. 6. Tetragonal ratio (c/a) dependence of the ground-state energy E(c/a) for the Ni2MnGa1-xBx (x = 0, 0.25 and 0.5) alloys. For clarity, the energy of the austenite (c/a = 1) for the different compositions are normalized to be zero. (b) Variations of energy difference between the austenite and the martensite ΔE and the c/a values of martensite with respect to the B content. Total and atom-resolved magnetic moments for the austenite (c1) and the martensite (c2).
Fig. 7. Density of states of the Ni2MnGa1-xBx (x = 0, 0.25 and 0.5) alloys for the austenite (a1) and the martensite (a2). (b) Enlarged minority-spin electron DOS near the Fermi energy EF.
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