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Magnesium and aluminum are abundant metals in the Earth’s crust and widely utilized in industrial engineering. Under high pressure, these elements can form elemental compounds into single substances, resulting in a variety of crystal structures and electronic properties. In this study, the possible structures of magnesium-aluminum alloys are systematically investigated in a pressure range of 0–500 GPa by using the first-principles structure search method, with energy and electronic structure calculations conducted using the VASP package. Bader charge analysis elucidates atomic and interstitial quasi-atom (ISQ) valence states, while lattice dynamics are analyzed using the PHONOPY package via the small-displacement supercell approach. Eight stable phases(MgAl3-Pm${\bar {3}} $m, MgAl3-P63/mmc, MgAl-P4/mmm, MgAl-Pmmb, MgAl-Fd${\bar {3}} $m, Mg2Al-P${\bar {3}} $m1, Mg3Al-P63/mmc, Mg3Al-Fm${\bar {3}} $m) and two metastable phases (Mg4Al-I4/m, Mg5Al-P${\bar {3}} $m1) are identified. The critical pressures and stable intervals for phase transitions are precisely determined. Notably, MgAl-Fd${\bar {3}} $m, Mg2Al-P${\bar {3}} $m1, Mg4Al-I4/m and Mg5Al-P${\bar {3}} $m1 represent newly predicted structures. Analysis of electronic localization characteristics reveals that six stable structures (MgAl3-Pm${\bar {3}} $m, MgAl3-P63/mmc, MgAl-Pmmb, MgAl-Fd${\bar {3}} $m, Mg2Al-P${\bar {3}} $m1 and Mg3Al-P63/mmc) exhibit electronic properties of electrides. The ISQs primarily originate from charge transfer of Mg atoms. In the metastable phase Mg4Al-I4/m, Al atoms are predicted to achieve an Al5–valence state, filling the p shell. This finding demonstrates that by adjusting the Mg/Al ratio and pressure conditions, a transition from traditional electrides to high negative valence states can be realized, offering new insights into the development of novel high-pressure functional materials. Furthermore, all Mg-Al compounds display metallic behaviors, with their stability attributed to Al-p-d orbital hybridization, which significantly contributes to the Al-3p/3d orbitals near the Fermi level. Additionally, LA-TA splitting is observed in MgAl3-Pm${\bar {3}} $m, with a splitting value of 45.49 cm–1, confirming the unique regulatory effect of ISQs on lattice vibrational properties. These results elucidate the rich structural and electronic properties of magnesium-aluminum alloys as electrodes, offering deeper insights into their behavior under high pressure and inspiring further exploration of structural and property changes in high-pressure alloys composed of light metal elements and p-electron metals.
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Keywords:
- magnesium-aluminum alloys /
- high-pressure structure and phase transition /
- electrides /
- density functional theory
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图 1 MgmAln 体系在给定压强下的形成焓(热力学稳定的化合物用实心符号表示)
Figure 1. Formation enthalpy of the MgmAln system at a given pressure. Thermodynamically stable compounds are indicated by solid symbols.
图 2 MgmAln化合物的压力-组分相图(黑色斜线区域表明对应的相在该压强范围是亚稳态)
Figure 2. Pressure-composition phase diagram of MgmAln compounds, with the black hatched line area indicating that the corresponding phase is metastable within this pressure range.
图 3 (a) MgAl3的P63/mmc相对于Pm${\bar {3}} $m相在0—500 GPa范围内的焓差曲线; (b) MgAl的Pmmb相和Fd${\bar {3}} $m相对于P4/mmm相在0—500 GPa范围内的焓差曲线; (c) Mg3Al的Fm${\bar {3}} $m相对于P63/mmc相在0—500 GPa范围内的焓差曲线
Figure 3. (a) Enthalpy difference curve of the P63/mmc phase of MgAl3 relative to the Pm${\bar {3}} $m phase within the range of 0−500 GPa; (b) the enthalpy difference curves of the Pmmb phase and Fd${\bar {3}} $m phase of MgAl relative to the P4/mmm phase within the range of 0−500 GPa; (c) the enthalpy difference curve of the Fm${\bar {3}} $m phase of Mg3Al relative to the P63/mmc phase within the range of 0−500 GPa.
图 4 稳定MgmAln化合物的晶体结构图(橙色和蓝色球分别代表Mg原子和Al原子) (a) MgAl3-Pm${\bar {3}} $m在100 GPa的结构; (b) MgAl3-P63/mmc在200 GPa的结构; (c) MgAl-P4/mmm在40 GPa的结构; (d) MgAl-Pmmb在95 GPa的结构; (e) MgAl-Fd${\bar {3}} $m在350 GPa的结构; (f) Mg2Al-P${\bar {3}} $m1在500 GPa的结构; (g) Mg3Al-P63/mmc在50 GPa的结构; (h) Mg3Al-Fm${\bar {3}} $m在350 GPa的结构
Figure 4. Crystal structure of the predicted stable MgmAln compounds: (a) MgAl3-Pm${\bar {3}} $m at 100 GPa; (b) MgAl3-P63/mmc at 200 GPa; (c) MgAl-P4/mmm at 40 GPa; (d) MgAl-Pmmb at 95 GPa; (e) MgAl-Fd${\bar {3}} $m at 350 GPa; (f) Mg2Al-P${\bar {3}} $m1 at 500 GPa; (g) Mg3Al-P63/mmc at 50 GPa; (h) Mg3Al-Fm${\bar {3}} $m at 350 GPa. Orange and blue spheres represent Mg and Al atoms, respectively.
图 5 高压下MgmAln 结构的声子色散曲线 (a), (b) 在0 GPa和100 GPa下的MgAl3-Pm${\bar {3}} $m结构; (c)—(e) 在100 GPa, 200 GPa 和250 GPa下的MgAl3-P63/mmc结构; (f), (g) 在0 GPa和40 GPa下的MgAl-P4/mmm结构; (h)—(j) 在50 GPa, 95 GPa和150 GPa下的MgAl-Pmmb结构; (k)—(m) 在150 GPa, 350 GPa和500 GPa下的MgAl-Fd${\bar {3}} $m结构; (n), (o) 在55 GPa和500 GPa下的Mg2Al-P${\bar {3}} $m1结构; (p), (q) 在0 GPa和50 GPa下的Mg3Al-P63/mmc结构; (r)—(t) 在60 GPa, 350 GPa和500 GPa下的Mg3Al-Fm${\bar {3}} $m结构; (u), (v) 在0 GPa和500 GPa下的Mg4Al-I4/m结构; (w), (x) 在35 GPa和500 GPa下的Mg5Al-P${\bar {3}} $m1结构
Figure 5. Phonon dispersion curves of the predicted MgmAln structures under high pressure: (a), (b) MgAl3-Pm${\bar {3}} $m at 0 GPa and 100 GPa; (c)–(e) MgAl3-P63/mmc at 100 GPa, 200 GPa and 250 GPa; (f), (g) MgAl-P4/mmm at 0 GPa and 40 GPa; (h)–(j) MgAl-Pmmb at 50 GPa, 95 GPa and 150 GPa; (k)–(m) MgAl-Fd${\bar {3}} $m at 150 GPa, 350 GPa and 500 GPa; (n), (o) Mg2Al-P${\bar {3}} $m1 at 55 GPa and 500 GPa; (p), (q) Mg3Al-P63/mmc at 0 GPa and 50 GPa; (r)–(t) Mg3Al-Fm${\bar {3}} $m at 60 GPa, 350 GPa and 500 GPa; (u), (v) Mg4Al-I4/m at 0 GPa and 500 GPa; (w), (x) Mg5Al-P${\bar {3}} $m1 at 35 GPa and 500 GPa.
图 6 MgmAln化合物的原子间距离直方图 (a) 100 GPa的MgAl3-Pm${\bar {3}} $m结构; (b) 200 GPa的MgAl3-P63/mmc结构; (c) 40 GPa的MgAl-P4/mmm结构; (d) 95 GPa的MgAl-Pmmb结构; (e) 350 GPa的MgAl-Fd${\bar {3}} $m结构; (f) 500 GPa的Mg2Al-P${\bar {3}} $m1结构; (g) 50 GPa的Mg3Al-P63/mmc结构; (h) 350 GPa的Mg3Al-Fm${\bar {3}} $m结构
Figure 6. Histograms of interatomic distances for MgmAln structures: (a) MgAl3-Pm${\bar {3}} $m at 100 GPa; (b) MgAl3-P63/mmc at 200 GPa; (c) MgAl-P4/mmm at 40 GPa; (d) MgAl-Pmmb at 95 GPa; (e) MgAl-Fd${\bar {3}} $m at 350 GPa; (f) Mg2Al-P${\bar {3}} $m1 at 500 GPa; (g) Mg3Al-P63/mmc at 50 GPa; (h) Mg3Al-Fm${\bar {3}} $m at 350 GPa.
图 7 稳定的MgmAln化合物的电子局域化函数(ELF)图 (a) 100 GPa的MgAl3-Pm${\bar {3}} $m结构, ELF等值面为0.65; (b) 200 GPa的MgAl3-P63/mmc结构, 等值面为0.70; (c) 40 GPa的MgAl-P4/mmm结构, 等值面为0.70; (d) 95 GPa的MgAl-Pmmb结构, 等值面为0.70; (e) 350 GPa的MgAl-Fd${\bar {3}} $m结构, 等值面为0.70; (f) 500 GPa的Mg2Al-P${\bar {3}} $m1结构, 等值面为0.70; (g) 50 GPa的Mg3Al-P63/mmc结构, 等值面为0.60; (h) 350 GPa的Mg3Al-Fm${\bar {3}} $m结构, 等值面为0.65. 橙色球和蓝色球分别代表Mg原子和Al原子, 粉色小球代表间隙准原子中心
Figure 7. Electron localization function (ELF) isosurface of stable MgmAln compounds: (a) MgAl3-Pm${\bar {3}} $m structure at 100 GPa, ELF isosurface is 0.65; (b) MgAl3-P63/mmc structure at 200 GPa, isosurface is 0.70; (c) MgAl-P4/mmm structure at 40 GPa, isosurface is 0.70; (d) MgAl-Pmmb structure at 95 GPa, isosurface is 0.70; (e) MgAl-Fd${\bar {3}} $m structure at 350 GPa, isosurface is 0.70; (f) Mg2Al-P${\bar {3}} $m1 structure at 500 GPa, isosurface is 0.70; (g) Mg3Al-P63/mmc structure at 50 GPa, isosurface is 0.60; (h) Mg3Al-Fm${\bar {3}} $m structure at 350 GPa, isosurface is 0.65. Orange and blue spheres represent Mg and Al atoms respectively, and pink small spheres represent the center of interstitial quasiatoms.
图 8 100 GPa压力下MgAl3-Pm${\bar {3}} $m结构的声子色散曲线, 图中蓝色点线是不考虑间隙电子影响的结果, 红色点划线是考虑了Bader电荷近似作为原子/ISQ有效电荷引起的库仑长程相互作用导致的LA-TA劈裂结果
Figure 8. Phonon dispersion curves of the MgAl3-Pm${\bar {3}} $m structure at 100 GPa. The blue dotted lines in the figure represent the results without considering the influence of interstitial electrons, while the red dashed lines show the LA-TA splitting induced by the long-range interaction of approximating Bader charges of atom/ISQ.
图 9 稳定的MgmAln化合物的电子投影态密度(PDOS)图 (a) 100 GPa的 MgAl3-Pm${\bar {3}} $m结构; (b) 200 GPa的MgAl3-P63/mmc结构; (c) 40 GPa的 MgAl-P4/mmm结构; (d) 95 GPa的 MgAl-Pmmb结构; (e) 350 GPa的MgAl-Fd${\bar {3}} $m结构; (f) 500 GPa的 Mg2Al- P${\bar {3}} $m1结构; (g) 50 GPa的Mg3Al-P63/mmc结构; (h) 350 GPa的 Mg3Al-Fm${\bar {3}} $m结构
Figure 9. Electronic projected density of states (PDOS) diagrams of stable MgmAln compounds: (a) MgAl3-Pm${\bar {3}} $m at 100 GPa; (b) MgAl3-P63/mmc at 200 GPa; (c) MgAl-P4/mmm at 40 GPa; (d) MgAl-Pmmb at 95 GPa; (e) MgAl-Fd${\bar {3}} $m at 350 GPa; (f) Mg2Al-P${\bar {3}} $m1 at 500 GPa; (g) Mg3Al-P63/mmc at 50 GPa; (h) Mg3Al-Fm${\bar {3}} $m at 350 GPa.
图 10 稳定的 MgmAln化合物的能带图 (a) 100 GPa的MgAl3-Pm${\bar {3}} $m结构; (b) 200 GPa的MgAl3-P63/mmc结构; (c) 40 GPa的MgAl-P4/mmm结构; (d) 95 GPa的MgAl-Pmmb结构; (e) 350 GPa的MgAl-Fd${\bar {3}} $m结构; (f) 500 GPa的Mg2Al-P${\bar {3}} $m1结构; (g) 50 GPa的Mg3Al-P63/mmc结构; (h) 350 GPa的Mg3Al-Fm${\bar {3}} $m结构
Figure 10. Band structure of stable MgmAln compounds: (a) MgAl3-Pm${\bar {3}} $m at 100 GPa; (b) MgAl3-P63/mmc at 200 GPa; (c) MgAl-P4/mmm at 40 GPa; (d) MgAl-Pmmb at 95 GPa; (e) MgAl-Fd${\bar {3}} $m at 350 GPa; (f) Mg2Al- P${\bar {3}} $m1 at 500 GPa; (g) Mg3Al-P63/mmc at 50 GPa; (h) Mg3Al-Fm${\bar {3}} $m at 350 GPa.
表 1 给定压强下 MgAl3-Pm${\bar {3}} $m, MgAl3-P63/mmc, MgAl-P4/mmm, MgAl-Pmmb, MgAl-Fd${\bar {3}} $m, Mg2Al-P${\bar {3}} $m1, Mg3Al-P63/mmc和Mg3Al-Fm${\bar {3}} $m中Mg, Al原子的价态、间隙准原子的电荷量(e/site)和总的局域电荷量(e/cell)
Table 1. Valence state of Mg and Al atoms and the charge quantity per site (e/site) of interstitial quasiatom, as well as the total local charge quantity per cell (e/cell) in MgAl3-Pm${\bar {3}} $m, MgAl3-P63/mmc, MgAl-P4/mmm, MgAl-Pmmb, MgAl-Fd${\bar {3}} $m, Mg2Al-P${\bar {3}} $m1, Mg3Al-P63/mmc and Mg3Al-Fm${\bar {3}} $m at given pressure.
Phase Mg/atom Al/atom ISQ/(e·site–1) ISQ/(e·cell–1) Pm${\bar {3}} $m MgAl3 (100 GPa) +1.48 +1.07 0.39 4.68 P63/mmc MgAl3 (200 GPa) +1.45 +1.65 ISQ1: 1.69; ISQ2: 1.57;
ISQ3: 1.60; ISQ4: 1.5612.81 P4/mmm MgAl (40 GPa) +1.47 –1.47 — — Pmmb MgAl (95 GPa) +1.44 –0.40 ISQ1: 0.53; ISQ2: 0.51 2.09 Fd${\bar {3}} $m MgAl (350 GPa) +1.36 +1.53 1.44 23.07 P${\bar {3}} $m1 Mg2Al (500 GPa) +1.32 +0.70 ISQ1: 0.35; ISQ2: 0.26 3.33 P63/mmc Mg3Al (50 GPa) +1.37 –3.96 0.15 0.30 Fm${\bar {3}} $m Mg3Al (350 GPa) +1.31 –3.95 — — I4/m Mg4Al (300 GPa) +1.23 –4.91 — — I4/m Mg4Al (350 GPa) +1.23 –1.76 0.79 6.32 
DownLoad: CSV
表 A1 MgAl3-Pm${\bar {3}} $m, MgAl3-P63/mmc, MgAl-P4/mmm, MgAl-Pmmb, MgAl-Fd${\bar {3}} $m, Mg2Al-P${\bar {3}} $m1, Mg3Al-P63/mmc, Mg3Al-Fm${\bar {3}} $m, Mg4Al-I4/m和Mg5Al-P${\bar {3}} $m1在给定压强下的晶格参数和原子位置
Table A1. Lattice parameters and atomic coordinates of MgAl3-Pm${\bar {3}} $m, MgAl3-P63/mmc, MgAl-P4/mmm, MgAl-Pmmb, MgAl-Fd${\bar {3}} $m, Mg2Al-P${\bar {3}} $m1, Mg3Al-P63/mmc, Mg3Al-Fm${\bar {3}} $m, Mg4Al-I4/m and Mg5Al-P${\bar {3}} $m1 at given pressure.
Phase Lattice
parameters/ÅAtom Site Atomic coordinates Pm${\bar {3}} $m MgAl3
(100 GPa)a = b = c = 3.4807,
α = β = γ = 90°Mg 1a (0.00000 0.00000 0.00000) Al 3c (0.50000 0.50000 0.00000) P63/mmc MgAl3
(200 GPa)a = b = 4.6192, c = 3.7511,
α = β = 90°, γ = 120°Mg 2d (0.33333 0.66667 0.75000) Al 6h (0.16575 0.33150 0.25000) P4/mmm MgAl
(40 GPa)a = b = 2.6468, c = 3.8386,
α = β = γ = 90°Mg 1d (0.50000 0.50000 0.50000) Al 1a (0.00000 0.00000 0.00000) Pmmb MgAl
(95 GPa)a = 4.0475, b = 2.4798, c = 4.3490,
α = β = γ = 90°Mg 2f (0.25000 0.50000 0.33732) Al 2e (0.25000 0.00000 0.83940) Fd${\bar {3}} $m MgAl
(350 GPa)a = b = c = 4.8837,
α = β = γ = 90°Mg 8a (0.50000 0.50000 0.00000) Al 8b (0.50000 0.00000 0.00000) P${\bar {3}} $m1 Mg2Al
(500 GPa)a = b = 3.3248, c = 2.0093,
α = β = 90°, γ = 120°Mg 2d (0.33333 0.66667 0.49763) Al 1a (0.00000 0.00000 0.00000) P63/mmc Mg3Al
(50 GPa)a = b = 5.3284, c = 4.3022,
α = β = 90°, γ = 120°Mg 6h (0.16784 0.83216 0.25000) Al 2d (0.66667 0.33333 0.25000) Fm${\bar {3}} $m Mg3Al
(350 GPa)a = b = c = 4.8981,
α = β = γ = 90°Mg 4b (0.50000 0.50000 0.50000) 8c (0.75000 0.75000 0.75000) Al 4a (0.00000 0.00000 0.00000) I4/m Mg4Al
(500 GPa)a = b = 4.4643, c = 3.2322,
α = β = γ = 90°Mg 8h (0.09518 0.70193 0.50000) Al 2a (0.00000 0.00000 0.00000) P${\bar {3}} $m1 Mg5Al
(500 GPa)a = b = 3.3132, c = 4.0870,
α = β = 90°, γ = 120°Mg 2d (0.66667 0.33333 0.31434) 2d (0.66667 0.33333 0.81145) 1a (0.00000 0.00000 0.00000) Al 1b (0.00000 0.00000 0.50000)
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