Acta Metallurgica Sinica (English Letters) ›› 2024, Vol. 37 ›› Issue (3): 537-550.DOI: 10.1007/s40195-023-01547-2
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Yunxuan Zhou1, Wenjun Tian1, Quan Dong1, Hailian Wang1, Jun Tan1,2(), Xianhua Chen1,2(
), Kaihong Zheng3, Fusheng Pan1,2
Received:
2022-11-21
Revised:
2022-12-21
Accepted:
2023-02-09
Online:
2024-03-10
Published:
2023-03-22
Contact:
Jun Tan, Yunxuan Zhou, Wenjun Tian, Quan Dong, Hailian Wang, Jun Tan, Xianhua Chen, Kaihong Zheng, Fusheng Pan. A First-principles Study on the Adhesion Strength, Interfacial Stability, and Electronic Properties of Mg/Mg2Y Interface[J]. Acta Metallurgica Sinica (English Letters), 2024, 37(3): 537-550.
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Fig. 1 Optimized crystalline structures of the bulk Mg a and bulk Mg2Y b. The calculated lattice parameters c and elastic modulus d of the bulk Mg and bulk Mg2Y. (The green and light blue balls represent the Mg and Y atoms)
Different terminations | Interlayer | 3 | 5 | 7 | 9 | 11 | 13 |
---|---|---|---|---|---|---|---|
Mg2Y(0001)_Mg1 | Δ12 | - 0.433 | 0.177 | 0.344 | 0.350 | 0.138 | 0.138 |
Δ23 | - 0.102 | - 0.133 | - 0.162 | - 0.172 | - 0.213 | ||
Δ34 | - 0.094 | - 0.075 | - 0.035 | - 0.017 | |||
Δ45 | 0.164 | 0.053 | 0.110 | ||||
Δ56 | 0.035 | 0.117 | |||||
Δ67 | - 0.017 | ||||||
Mg2Y(0001)_Mg2 | Δ12 | 0.987 | 0.092 | 0.040 | 0.116 | - 0.032 | 0.100 |
Δ23 | - 0.008 | - 0.185 | - 0.374 | - 0.158 | - 0.271 | ||
Δ34 | 0.050 | 0.234 | 0.041 | 0.142 | |||
Δ45 | 0.018 | - 0.027 | 0.016 | ||||
Δ56 | 0.135 | - 0.017 | |||||
Δ67 | 0.108 | ||||||
Mg2Y(0001)_Y | Δ12 | 0.751 | - 0.630 | - 0.598 | - 0.506 | - 0.404 | - 0.531 |
Δ23 | 0.365 | 0.567 | 0.326 | 0.188 | 0.279 | ||
Δ34 | - 0.185 | - 0.111 | - 0.165 | - 0.095 | |||
Δ45 | 0.149 | 0.133 | - 0.007 | ||||
Δ56 | 0.035 | 0.006 | |||||
Δ67 | 0.134 |
Table 1 Convergence of the atomic structures of the Mg2Y(0001) surfaces with different terminations as a function of slab layers
Different terminations | Interlayer | 3 | 5 | 7 | 9 | 11 | 13 |
---|---|---|---|---|---|---|---|
Mg2Y(0001)_Mg1 | Δ12 | - 0.433 | 0.177 | 0.344 | 0.350 | 0.138 | 0.138 |
Δ23 | - 0.102 | - 0.133 | - 0.162 | - 0.172 | - 0.213 | ||
Δ34 | - 0.094 | - 0.075 | - 0.035 | - 0.017 | |||
Δ45 | 0.164 | 0.053 | 0.110 | ||||
Δ56 | 0.035 | 0.117 | |||||
Δ67 | - 0.017 | ||||||
Mg2Y(0001)_Mg2 | Δ12 | 0.987 | 0.092 | 0.040 | 0.116 | - 0.032 | 0.100 |
Δ23 | - 0.008 | - 0.185 | - 0.374 | - 0.158 | - 0.271 | ||
Δ34 | 0.050 | 0.234 | 0.041 | 0.142 | |||
Δ45 | 0.018 | - 0.027 | 0.016 | ||||
Δ56 | 0.135 | - 0.017 | |||||
Δ67 | 0.108 | ||||||
Mg2Y(0001)_Y | Δ12 | 0.751 | - 0.630 | - 0.598 | - 0.506 | - 0.404 | - 0.531 |
Δ23 | 0.365 | 0.567 | 0.326 | 0.188 | 0.279 | ||
Δ34 | - 0.185 | - 0.111 | - 0.165 | - 0.095 | |||
Δ45 | 0.149 | 0.133 | - 0.007 | ||||
Δ56 | 0.035 | 0.006 | |||||
Δ67 | 0.134 |
Fig. 2 Surface configurations of Mg and Mg2Y with different terminations: a Mg(0001) surface slab model, b Mg2Y(0001) surface slab with Mg1 termination, c Mg2Y(0001) surface slab with Mg2 termination, d Mg2Y(0001) surface slab with Y termination
Fig. 3 Calculated surface energy of Mg2Y(0001) surface slab with Mg1, Mg2, and Y terminations as a function of the yttrium chemical potential (${\mu }_{\mathrm{Y}}^{\mathrm{slab}}-{\mu }_{\mathrm{Y}}^{\mathrm{bulk}}$, labeled as $\Delta {\mu }_{\mathrm{Y}}$). Vertical orange dotted lines at the left part of this figure indicate the range of the stability of Mg2Y
Different configurations | a (Å) | b (Å) | γ (°) | Ω (Å2) | A1 (Å2) | A2 (Å2) | |
---|---|---|---|---|---|---|---|
Mg(0001) | 6.229 | 6.230 | 60.024 | 33.614 | |||
Mg2Y(0001)_Mg1 | 5.980 | 5.980 | 59.406 | 30.783 | |||
Mg2Y(0001)_Mg2 | 6.060 | 5.949 | 59.711 | 31.132 | |||
Mg2Y(0001)_Y | 5.989 | 5.989 | 59.627 | 30.946 | |||
Mg1-OT | 6.225 | 6.217 | 59.183 | 33.235 | 33.614 | 30.783 | - 3.217 |
Mg1-MT | 6.158 | 6.163 | 59.730 | 32.780 | 33.614 | 30.783 | - 1.805 |
Mg1-HCP | 6.179 | 6.177 | 59.888 | 33.014 | 33.614 | 30.783 | - 2.534 |
Mg2-OT | 6.217 | 6.190 | 59.590 | 33.187 | 33.614 | 31.132 | - 2.516 |
Mg2-MT | 6.264 | 6.163 | 59.458 | 33.245 | 33.614 | 31.132 | - 2.694 |
Mg2-HCP | 6.257 | 6.166 | 59.522 | 33.248 | 33.614 | 31.132 | - 2.703 |
Y-OT | 6.179 | 6.180 | 59.685 | 32.962 | 33.614 | 30.946 | - 2.112 |
Y-MT | 6.192 | 6.201 | 59.681 | 33.144 | 33.614 | 30.946 | - 2.677 |
Y-HCP | 6.183 | 6.181 | 59.740 | 33.012 | 33.614 | 30.946 | - 2.269 |
Table 2 Surface and interface parameters, interfacial areas (Ω), angle, areas of Mg(0001) (A1) and Mg2Y(0001) slabs (A2), and the interface mismatch ($\xi$) of the Mg(0001)/Mg2Y(0001)
Different configurations | a (Å) | b (Å) | γ (°) | Ω (Å2) | A1 (Å2) | A2 (Å2) | |
---|---|---|---|---|---|---|---|
Mg(0001) | 6.229 | 6.230 | 60.024 | 33.614 | |||
Mg2Y(0001)_Mg1 | 5.980 | 5.980 | 59.406 | 30.783 | |||
Mg2Y(0001)_Mg2 | 6.060 | 5.949 | 59.711 | 31.132 | |||
Mg2Y(0001)_Y | 5.989 | 5.989 | 59.627 | 30.946 | |||
Mg1-OT | 6.225 | 6.217 | 59.183 | 33.235 | 33.614 | 30.783 | - 3.217 |
Mg1-MT | 6.158 | 6.163 | 59.730 | 32.780 | 33.614 | 30.783 | - 1.805 |
Mg1-HCP | 6.179 | 6.177 | 59.888 | 33.014 | 33.614 | 30.783 | - 2.534 |
Mg2-OT | 6.217 | 6.190 | 59.590 | 33.187 | 33.614 | 31.132 | - 2.516 |
Mg2-MT | 6.264 | 6.163 | 59.458 | 33.245 | 33.614 | 31.132 | - 2.694 |
Mg2-HCP | 6.257 | 6.166 | 59.522 | 33.248 | 33.614 | 31.132 | - 2.703 |
Y-OT | 6.179 | 6.180 | 59.685 | 32.962 | 33.614 | 30.946 | - 2.112 |
Y-MT | 6.192 | 6.201 | 59.681 | 33.144 | 33.614 | 30.946 | - 2.677 |
Y-HCP | 6.183 | 6.181 | 59.740 | 33.012 | 33.614 | 30.946 | - 2.269 |
Fig. 4 Master view and top view of different stacking sequences of interface atomic structures of the Mg(0001)/Mg2Y(0001) interface: a OT site, b MT site, and c HCP site for Mg1 termination; d OT site, (e) MT site, and f HCP site for Mg2 termination, and g OT site, h MT site, i HCP site for Y termination. The red dotted line represents the interface, and the top side of interface is Mg2Y(0001) slab, while the bottom of the interface is the Mg(0001) slab)
Fig. 5 Total energy and the ideal Wad as a function of the separation distance between Mg(0001) and Mg2Y(0001) surface slabs for different Mg1, Mg2, and Y terminations in interfacial configurations of the Mg(0001)/Mg2Y(0001) interface
Fig. 6 Actual work of adhesion with different stacking sequences for Mg1, Mg2, and Y terminations in interfacial configurations of Mg(0001)/Mg2Y(0001) interface
Different configurations | Ai (Å2) | Wad (J/m2) | |||
---|---|---|---|---|---|
Mg1-OT | - 40,975.025 | - 27,198.430 | - 13,774.651 | 33.235 | 0.937 |
Mg1-MT | - 40,973.965 | - 27,198.430 | - 13,774.651 | 32.780 | 0.432 |
Mg1-HCP | - 40,977.177 | - 27,198.430 | - 13,774.651 | 33.014 | 1.988 |
Mg2-OT | - 40,976.716 | - 27,198.430 | - 13,774.561 | 33.187 | 1.798 |
Mg2-MT | - 40,976.818 | - 27,198.430 | - 13,774.561 | 33.245 | 1.844 |
Mg2-HCP | - 40,976.773 | - 27,198.430 | - 13,774.561 | 33.248 | 1.823 |
Y-OT | - 40,197.175 | - 27,198.430 | - 12,994.648 | 32.962 | 1.991 |
Y-MT | - 40,197.963 | - 27,198.430 | - 12,994.648 | 33.144 | 2.362 |
Y-HCP | - 40,197.977 | - 27,198.430 | - 12,994.648 | 33.012 | 2.378 |
Table 3 Energy of the Mg(0001) and Mg2Y(0001) slab, the total energy, and Wad of the Mg(0001)/Mg2Y(0001) with different configurations
Different configurations | Ai (Å2) | Wad (J/m2) | |||
---|---|---|---|---|---|
Mg1-OT | - 40,975.025 | - 27,198.430 | - 13,774.651 | 33.235 | 0.937 |
Mg1-MT | - 40,973.965 | - 27,198.430 | - 13,774.651 | 32.780 | 0.432 |
Mg1-HCP | - 40,977.177 | - 27,198.430 | - 13,774.651 | 33.014 | 1.988 |
Mg2-OT | - 40,976.716 | - 27,198.430 | - 13,774.561 | 33.187 | 1.798 |
Mg2-MT | - 40,976.818 | - 27,198.430 | - 13,774.561 | 33.245 | 1.844 |
Mg2-HCP | - 40,976.773 | - 27,198.430 | - 13,774.561 | 33.248 | 1.823 |
Y-OT | - 40,197.175 | - 27,198.430 | - 12,994.648 | 32.962 | 1.991 |
Y-MT | - 40,197.963 | - 27,198.430 | - 12,994.648 | 33.144 | 2.362 |
Y-HCP | - 40,197.977 | - 27,198.430 | - 12,994.648 | 33.012 | 2.378 |
Fig. 7 Interfacial energy as a function of the yttrium chemical potential (${\mu }_{\mathrm{Y}}^{\mathrm{slab}}-{\mu }_{\mathrm{Y}}^{\mathrm{bulk}}$, labeled as $\Delta {\mu }_{\mathrm{Y}}$) with different stacking sequences for Mg1, Mg2, and Y terminations in interfacial configurations of Mg(0001)/Mg2Y(0001) interface
Fig. 8 a Total energy of different terminations of the Mg(0001)/Mg2Y(0001) interface as a function of applied uniaxial tensile strain (the black vertical coordinates represent the total energy of Mg1 and Mg2 terminations, and the blue vertical coordinates represent the total energy value of Y termination), b profiles of tensile stress versus engineering strain of different terminations in interfacial configurations of the Mg(0001)/Mg2Y(0001) interface
Fig. 9 Partial density of states on both sides of the Mg(0001)/Mg2Y(0001) interface with different stacking sequences for Mg1, Mg2, and Y terminations: a Mg1-OT, b Mg1-MT, c Mg1-HCP, d Mg2-OT, e Mg2-MT, f Mg2-HCP, g Y-OT, h Y-MT, i Y-HCP. And the pink dotted lines represent Ef. (1st, 2nd, 3rd, and 4th are the first, second, third, and fourth atoms, and the up arrow is the Mg2Y(0001) slab, and the down arrow is the Mg(0001) slab.)
Fig. 10 Charge density difference of the Mg(0001)/Mg2Y(0001) interface with different terminations: a Mg1-OT, b Mg1-MT, c Mg1-HCP, d Mg2-OT, e Mg2-MT, f Mg2-HCP, g Y-OT, h Y-MT, i Y-HCP
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