High-Pressure Phases and Properties of the Mg3Sb2 Compound.

Pressure always plays an important role in influencing the structure configuration and electronic properties of materials. Here, combining density function theory and structure prediction algorithm, we systematically studied the Mg3Sb2 system from its phase transition to thermodynamic and electronic properties under high pressure. We find that two novel phases, namely Cm and C2/m, are stable under high pressure. Calculation results of phonon dispersions showed that both novel phases have no imaginary frequency, which indicates that the novel phases are thermodynamically stable. Due to the larger ionic radius of Sb compared to N, P, and As elements, the Mg3Sb2 compound shows a different electronic property at high pressure. The electronic calculations show that the novel phases of Cm and C2/m of Mg3Sb2 possess metallic behavior under high pressure. These results provide new insights for understanding the Mg3Sb2 compound.

Introduction

Pressure is one of the most powerful tools, which is frequently used to find and design novel materials with unique properties, as it can influence the geometric configuration, interatomic electrostatic interactions, distance of bonding, and electronic orbitals.[1] For decades, scientists have found and synthesized numbers of materials under high pressure, which are not available at ambient condition.[2−6]

The A3B2-type compounds are usually formed by group II alkaline metal elements and group V elements. As one member of the A3B2-type family, the ground state of Mg3Sb2 compounds at ambient condition possess a typical cubic anti-bixbuite symmetry of the minerals, like (Fe, Mn)2O3.[7] So far, numerous studies both on experiment and theory have been done on these compounds due to their large band gaps. Scientists have shown that the Mg3N2 compound has several phase transitions from ambient condition to high pressure.[8−10] In 2017, a theoretical work reported that the Mg3P2 compound has three stable phases under extreme conditions,[11] while the compound of Ca3N2 in the A3B2-type family, undergoes several phase transformations (like Ia3̅,[12,13]R3̅c,[14,15]Pbcn,[16]C2/m,[17]P3̅m1,[17] and I4̅3d[18]) from experimental and theoretical studies. Recently, Yang. et al. studied the phase transformations and electronic properties of Mg3As2 under high pressure and they found that two novel semiconductor phases are stable under high pressure.[19] As one member of the A3B2-type family, Mg3Sb2 has attracted much focus on its structure configuration and electronic properties. The Mg3Sb2 compound adopts Ia3̅ and P3̅m1 symmetry at ambient conditions and high pressure, which are provided by early works.[20] Specially, the P3̅m1 phase of Mg3Sb2 attracts much attention for its good performance in the thermoelectric material field.[21,22] As one of the element in group VA and compared with N, P, and As atoms, Sb shares the same properties of elements in this group, such as electron distribution outside the nucleus and the chemical reaction characteristics. However, the ionic radius of the Sb element is much larger than the other three elements, which may act as a key factor in making antimonide exhibit different phase transitions, especially at high pressure conditions. Furthermore, A3B2-type compounds always have the Ia3̅ symmetry that is also the favored configuration of rare earth sesquioxides (e.g., Sc2O3,[23] Y2O3,[24] Er2O3,[25] Gd2O3,[26] and In2O3[27]). Thus, it is necessary and important to make a systematical modulation on the Mg3Sb2 system under high pressure.

The intention of our work is therefore to study the phase transformation of the Mg3Sb2 and its electronic properties under high pressure. We perform a systematic theoretical simulation on Mg3Sb2 by combining the technique of structural prediction and density functional theory.The structural predictions are performed at the pressure ranging from ambient to 100 GPa, which is easily reached by experiment. The structural prediction runs use crystal structure analysis by particle swarm optimization (CALYPSO),[28−30] which is one of the most efficient algorithms for crystal structure searching. Its successful stories cover a number of material fields, especially at high pressure conditions,[4,31−36] such as superconductors,[33,37−44] superhard materials,[45−48] metallic carbides,[49] high-energy density materials,[5,6] electrides,[46,50,51] and 2D materials.[52−55] In addition, many high pressure phases that were predicted by using CALYPSO are confirmed by subsequent experiments.[56,57]

Results and Discussion

Starting from structural prediction of the Mg3Sb2 system with a suitable unit-cell size (the maximal formula unites is eight due to the restriction of computer resource) at pressures of 0, 20, 50, and 100 GPa, respectively. Then, we made accuracy structure relaxation for the selected target structures (at least 10 structures that we chose in each prediction). We calculated the relative enthalpy of all structures of the Mg3Sb2 compound relative to the P3̅m1 phase as a function of pressure, which is illustrated in Figure . In addition, we considered some metastable structures with similar energies and the other A3B2 (e.g. Mg3N2,[10] Mg3P2,[11] and Mg3As2,[19]) stable phases, which act as prototype structures for this system. From our calculation, we conclude that the ground state structure of Mg3Sb2 adopts the Ia3̅ symmetry at ambient conditions. With the pressure increasing to 0.25 GPa, a trigonal phase with P3̅m1 becomes stable in energy. This phenomenon is consistent with the previous study and also occurred in the sister systems like Mg3P2.[11] and Mg3As2.[19] Interestingly, when the pressure increases to 5 GPa, we predict that a novel monoclinic phase with the Cm symmetry becomes stable. However, this novel phase is quickly destabilized by pressure and transformed into another monoclinic phase with the C2/m symmetry. The C2/m structure will be stable in large pressures ranging from 12.7 to 100 GPa, which is the maximum pressure we simulated in this work. These results also checked by using SCAN functional.[58] The results show that the phase transition sequence is the same when compared to PBE calculations. Only the transition pressures are slightly shifted. For example, the P3̅m1 phase transformed into the Cm phase at about 5 GPa for PBE and at about 6 GPa for SCAN. These slight differences cannot change our main results and provide strong support for our previous study. The results are shown as Figure S1 in the Supporting Information.

Figure 1

The relative enthalpy between the different structures of each formula for the Mg3Sb2 compound varies with pressure relative to the P3̅m1 structure.

Figure shows four novel crystal phases of Mg3Sb2, which are predicted in this work. At ambient conditions, the Ia3̅ structure is the ground-state phase for the Mg3Sb2 compound, which has a well-known configuration as shown in Figure a. The Mg–Sb bond length in this interesting configuration is about 2.87–3.94 Å and slightly larger than that of Mg3As2 (about 2.62–2.73 Å).[19] This is mainly caused by the larger ionic core of Sb than that of the As atom. The primitive cell of the Ia3̅ phase contains eight formula units with the Mg atoms located in the 48e Wyckoff position, while the Sb atoms are located in the 8b and 24d positions. The P3̅m1 phase is stable in the pressure range of 0.25 to 5 GPa, and the structure character is shown in Figure b. It is clearly found that Mg atoms and Sb atoms form several diamond surfaces, which are connected with each other and form a spatial three-dimensional network configuration. The Sb atom behaves as a six coordination in this phase, while the Mg atom is connected with four neighboring Sb atoms. There are two kinds of Mg atoms in its primitive cell occupying in 2d and 1a Wyckoff positions. Meanwhile, Mg atoms are only located at the 2d position. The distance between the Mg and Sb atoms is about 2.82–3.06 Å. These results are very consistent with other known informations that are collected by the Materials Project database.[59] The Cm phase has an interesting structural configuration as shown in Figure c with the bond lengths of Mg–Sb being between 2.74 and 2.94 Å at 8 GPa. This structure is formed by several tetrahedrons and rhombuses, which are combined with shared Sb atoms. Figure d shows the C2/m phase of Mg3Sb2, which contains two formula units in its primitive cell. This novel phase is very interesting as its crystal configuration contains several hexagons and rhombuses, which are in the same distorted face and are connected to each other with sharing atoms. The chemical bond between the Mg atom and Sb atom is about 2.65–2.85 Å at the pressure of 20 GPa. The relaxed structural informations of these four phases are listed in Table . Through our calculation, we determined the clear phase transformation of the Mg3Sb2 compound. The clear sequence is shown below: Ia3̅ → P3̅m1 (at 0.25 GPa) → Cm (at 5 GPa) → C2/m (12.7 GPa). By comparing to the other three magnesium compounds, Mg3N2 (Ia3̅ → C2/m (at 20.6 GPa) → P3̅m1 (at 67 GPa)),[10] Mg3P2 (Ia3̅ → P3̅m1 (at 2.5 GPa) → P63/mmc (at 35 GPa) → C2/c (at 65 GPa)),[10] and Mg3As2 (Ia3̅ → (at 1.3 GPa) P3̅m1 → (at 12 GPa) C2/m → P1̅ (at 30 GPa)), we can find that the phase transition pressure point of Mg3Sb2 is earlier than the other three A3B2 compounds and can also make a conclusion that large atomic radii facilitate structural phase transitions for Mg3X2 (X = N, P, As, Sb). Another finding is that the high pressure and ionic radius both influence the structural configuration for different systems. For example, the Mg3N2, Mg3P2, Mg3As2, and Mg3Sb2 systems share the same ground state at ambient conditions, while at high pressure, their stable phases vary from system to system.

Figure 2

Crystal structures of Mg3Sb2 (green, Mg; black, Sb). (a) Ia3̅ phase at ambient pressure. (b) P3̅m1 phase at 2 GPa. (c) Cm phase at 8 GPa. (d) C2/m phase at 30 GPa.

Table 1

Configuration Parameters of Ia3̅, P3̅m1, Cm, and C2/m Phases of the Mg3Sb2 Compound in Different Conditions

pressure (GPa)	space group	lattice parameters	atomic coordinates (fractional)
0	Ia3̅	a = b = c = 13.40 Å	Mg (48e) (0.38321, 0.13949, 0.37748)
		α = β = γ = 90°	Sb (8b) (0.25000, 0.25000, 0.25000)
			Sb (24d) (0.48445, 0.50000, −0.25000)
2	P3̅m1	a = b =4.53 Å	Mg (2d) (0.33333, 0.66667, 0.63137)
		c = 7.15 Å	Mg (1a) (0.00000, 0.00000, 0.00000)
		α = β = 90°, γ = 120°	Sb (2d) (0.33333, 0.66667, 0.22282)
8	Cm	a = 15.04 Å	Mg (2a) (0.29007, 0.50000, 0.37780)
		b = 4.25 Å	Mg (2a) (0.95266, 0.50000, 0.36587)
		c = 7.71 Å	Mg (2a) (0.19930, 0.50000, 0.69622)
		α = γ =90°	Mg (2a) (0.11525, −0.00000, 0.35398)
		β = 117.28°	Mg (2a) (0.20600, −0.00000, 0.03554)
			Mg (2a) (0.95266, −0.00000, 0.86589)
			Sb (2a) (0.08176, −0.50000, 0.10753)
			Sb (2a) (0.82355, −0.50000, 0.62425)
			Sb (2a) (0.84831, −0.00000, 0.08813)
			Sb (2a) (0.05700, −0.00000, 0.64362)
20	C2/m	a = 14.85 Å	Mg (2d) (0.00000, 0.50000, 0.50000)
		b = 4.43 Å	Mg (4i) (0.40103, 0.50000, 0.72099)
		c = 5.70 Å	Mg (4i) (0.29928, −0.00000, 0.32333)
		α = 90°	Mg (2b) (0.00000, 0.50000, −0.00000)
		β = 92.03°	Sb (4i) (0.41490, 0.50000, 0.23575)
		γ = 90°	Sb (4i) (0.31001, −0.00000, 0.81515)

The structure parameters and cell volumes as a function of pressure of the four phases for the Mg3Sb2 compound are calculated, as shown in Figure . The results reveal that all the phase transitions belong to the first-order nature, as the volume collapsed at the phase transition. This phenomenon also occurred in its sister systems, like Mg3P2 and Mg3As2.[11,19] This can regard as a common character of the A3B2 compounds under high pressure.

Figure 3

Lattice constants and volume of the Mg3Sb2 system as a function of pressure.

In order to determine the thermodynamic stability of each phase, the phonon dispersion at its stable pressure point is calculated theoretically as shown in Figure . From the figure, we can conclude that all the phases of Mg3Sb2 are mechanically stable as there is no imaginary phonon frequency in all the Brillouin zone. We also checked the thermodynamic stability of these phases under ambient pressure. The results show that Ia3̅ and P3̅m1 phases of Mg3Sb2 are dynamically stable at ambient conditions, while for Cm and C2/m phases, their phonon dispersions have imaginary values, which reveal that they are unstable at ambient pressure. The results are shown as Figure S2 in the Supporting Information. Figure shows the electronic band structures and the projected density of states for the four structures of Mg3Sb2 in their relative pressure. Note that all of the calculations were carried out in the PBE level, which always underestimates band gap, as we all know. Our calculations show that the Ia3̅ and P3̅m1 phases of Mg3As2 exhibit semiconductor properties with a band gap of 1.42 eV at ambient conditions and 0.86 eV at 0.25 GPa. This also indicates that the band gap is getting smaller and smaller driven by pressure. When the pressure above 5 GPa, the semiconductor phase P3̅m1 transforms into a metallic phase Cm. This unique phenomenon is the first time to occur in Mg3X2 magnesium and may be mainly caused by the larger ionic radius of Sb compared to N, P, and As atoms and high compression.

Figure 4

Phonon dispersions of Mg3Sb2 for (a) the Ia3̅ phase at ambient pressure, (b) the P3̅m1 phase at 2 GPa, (c) the Cm phase at 8 GPa, and (d) the C2/m phase at 20 GPa.

Figure 5

Electronic band structures and densities of state (DOS) of Mg3Sb2 for (a) the Ia3̅ phase at ambient pressure, (b) the P3̅m1 phase at 2 GPa, (c) the Cm phase at 8 GPa, and (d) the C2/m phase at 20 GPa.

Conclusions

In summary, using first-principle swarm-intelligence structure search, we investigate systematically the stability and electronic properties of Mg3Sb2. We identified two hitherto unknown phases stabilized at a wide pressure range that are readily available for experimental synthesis. All the phases of Mg3Sb2 from ambient to high pressure are confirmed, including Ia3̅, P3̅m1, Cm, and C2/m. At low pressures, the stable phases of Mg3Sb2 are Ia3̅ and P3̅m1. There is a novel metallic phase Cm that is stable from about 5 to 12.7 GPa. With the increasing pressure, the Cm phase will transform into another metallic phase C2/m at around 12.7 GPa. The phase transformation sequence of Mg3Sb2 is Ia3̅ → P3̅m1 (at 0.25 GPa) → Cm (at 5 GPa) → C2/m (12.7 GPa). Their mechanical stability is confirmed by the phonon calculations. At lower pressures, the Ia3̅ and P3̅m1 phases are semiconductors with a narrow band gap. However, when the pressure increases, the metallic phases Cm and C2/m are more stable under high pressure ranges. This is the first time that this phenomenon occurred in the Mg–Sb system. These results show a remarkable phase transition of Mg3Sb2 and can serve as an important guide for further experimental studies of this compound.

Methods

We start with structural prediction of the Mg3Sb2 compound by using the CALYPSO method[28,29] with the cells ranging from 2 to 8 formula units (f.u.) at 0, 50, and 100 GPa. Each prediction runs about 40 generations to ensure generating at least 1200 structures. The target structures that we selected from prediction were accuracy optimized by Kohn–Sham density function theory, within the projector augmented wave (PAW[60]) method as implemented in the Vienna ab initio simulation package (VASP code[61]) and with the Perdew–Burke–Ernzerhof (PBE[62]) approximation to the exchange-correlation functional. The cutoff energy of all the calculations was set to 600 eV, and the K meshes used Monkhorst–Pack grids with the density of 0.03 Å–1 to reach the convergence of better than 1 meV per atom. We computed the phonon dispersions of all the novel phases by using a phonopy program.[63]