Pressure modulates the phase stability and physical properties of zinc nitride iodine

Abstract

To explore new stable phases in metal nitride halides, the structural, electronic and optical properties, and chemical bonding characteristics of Zn₂NI under pressure were studied on the basis of crystal structure predicting evolution and density function calculations. Three new high-pressure phases of Zn₂NI were revealed: Pna2₁ and Pnma-II phases with NZn₄ tetrahedrons, and P6₃/mmc phase with NZn₆ polyhedrons above 6, 23, and 94 GPa, respectively. The calculated electronic structures of all the phases of Zn₂NI under pressure indicated that they are all semiconductors except P6₃/mmc phase. Therefore, pressure can simulated Zn₂NI a transition from a semiconductor to a metal. The optical properties (e.g., absorption coefficient, dielectric function) of these high-pressure phases were also discussed.

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1. Introduction

The solid-state chemistry of ternary metal nitrides has rapidly emerged and matured in recent years, driven by their varied physical properties and potential applications.^1–12 Many types of nitrides have been investigated, with most studies having focused on MN-type compounds, such as transition metal nitrides (TiN, CrN),^13–20 alkaline metal nitrides (Li₃N),²¹ layered alkaline-earth metal nitrides (BaN₂, CaN₂),²² and metals with lower electronegativity formed the “nonmetallic” nitrides (Zn₃N₂,²³ Cd₃N₂,²⁴ and others^25–28). These metal nitrides have potential applications in magnetic storage devices, superconductors, or in the semiconductor industry, where they may replace established oxides because of their superior properties. Moreover, changes in the physical properties of these nitrides are accompanied by changes in their crystal structures.

Recently, “double anion” nitrides, which include both nitride and halide compounds (denoted MNX), have attracted attention owing to their superior electronic and optical properties. Two types of layer-structured polymorphs of metal nitride halides have been synthesized: α- and β-MNX (M = Ti, Zr, Hf, X = Cl, Br, I). These materials crystallize in a two-dimensional FeClO structure, with the exception of M (M = Ti, Zr)NF. Moreover, they were found to adopt the three-dimensional structure of TiNF and ZnNF and are band insulators.^29,30 These observations indicate that the structure of metal nitride halides can be tuned by anion substitution or insertion. Recently, alkaline metal nitride halides, A₂ (A = Ca, Sr, Ba)NX (X = Cl, Br, I), have also been synthesized, which exhibit stronger ionic character.^31,32 In these compounds, the halides are inserted in the A₂N lattice and fill the vacancies between the layers, which results in the formation of a filled anti-CdCl₂-type layered structure (i.e., anti-α-NaFeO₂ structure). Moreover, the crystal structure of these compounds can be tuned by the size of the halides. For example, Ca₂NBr_1−yI_y (0.7 ≤ y ≤ 0.8) transformed from an anti-α-NaFeO₂ structure to an anti-β-RbScO₂ structure,^33,34 and M₂NF (M = Ba, Ca, Sr) adopted a rock salt structure.³⁵ Therefore, the crystal structure of metal nitride halides is affected by the dimensions of the halide (X) and the metal element. Moreover, the synthesis conditions and structure strongly affect the electronic and optical properties of these compounds. Zn₂NX (X = Cl, Br, I)³⁶ compounds have been synthesized from solid–liquid reactions of zinc nitrides with the respective zinc halides under vacuum, and their crystal structures have been determined using single-crystal and powder X-ray diffraction; Zn₂NX (X = Cl, Br) adopted an acentric orthorhombic space group Pna2₁, whereas Zn₂NI adopted the centrosymmetric space group Pnma.

Despite the attention Zn₂NI has received as a semiconductor, the nature of its high-pressure phases has barely been studied. Therefore, it is of fundamental interest to investigate the crystal structure of the novel high-pressure phases of Zn₂NI. In this letter, we discovered three new high-pressure phases of Zn₂NI above 5 GPa: Pna2₁ (phase II), Pnma-II (phase III), and P6₃/mmc. These phases were predicted using the ab initio particle swarm optimization (PSO) algorithm for crystal structure prediction,^37,38 which requires only the chemical compositions for a given compound under the specific external conditions. Our findings represent a significant step towards understanding the behavior of A₂MN compounds under extreme conditions.

2. Theoretical method

The crystal structural predications were performed by PSO methodology as implemented in crystal structure analysis by particle swarm optimization (CALYPSO) code.^37,38 The significant feature of this methodology is capable of predicting the stable and metastable structures at given pressure with only the knowledge of the chemical composition. This method has been successful in predicting structures for various systems including lithium,³⁹ polymeric nitrogen,⁴⁰ superhard carbon nitride,⁴¹ and LiN₃,⁴² among which the insulating Aba2-40 (or oC40) structure of Li has been confirmed by independent experiments.⁴³ The underlying ab initio structural relaxations and electronic band structure calculations of Zn₂NI have been carried out by density functional theory within the Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation (GGA) exchange–correlation potential⁴⁴ as implemented in the VASP code.⁴⁵ The projector augmented wave (PAW) pseudopotential⁴⁶ is treated as 3d¹⁰4s², 2s²2p³ and 3s²3p⁵ for Zn, N and I, respectively. The cutoff energy of 600 eV for the expansion of the wave function into plane waves and appropriate Monkhorst–Pack k meshes for all the cases have been measured to ensure that all the enthalpy calculations are well converged to better than 1 meV per atom. The phonon calculations were carried out by a supercell approach as implemented in the PHONOPY code.⁴⁷

3. Results and discussion

Structural predictions of Zn₂NI were performed using the CALYPSO code.^37,38 The simulations comprised 1–4 formula units per primitive cell at 0, 10, 40, 70, 100, and 150 GPa. At ambient pressure, the ground-state phase of Zn₂NI revealed by the ab initio structural prediction corresponded perfectly to the experimentally determined Pnma structure (Fig. 1a, which includes four molecules, and is referred to as Pnma-I), thereby demonstrating the validity of the method. The Pnma-I phase is a three-dimensional framework of corner-linked NZn₄ tetrahedra with nitrogen atoms occupying tetrahedral cavities in the framework. In the NZn₄ tetrahedra, each Zn atom has a nearest N neighbor with a Zn–N bond length of 1.917 Å, which is in good agreement with the experimental result (1.92 Å).³⁶ The lattice parameters of the predicted Pnma structure at ambient pressure are a = 6.440 Å, b = 6.321 Å, and c = 8.042 Å, which are in excellent agreement with the experimental data (a = 6.3590 Å, b = 6.2529 Å, and c = 7.9549 Å). Above 5.2 GPa, an orthorhombic Pna2₁ phase (Z = 4, Fig. 1b) was predicted to be the most stable form of Zn₂NI, which is not surprising because it is the ambient-pressure structure of other zinc nitride halides (e.g., Zn₂NCl, Zn₂NI).³⁶ This structure is characterized by a network of corner-sharing NZn₄ tetrahedra, in which the nearest length of N–Zn at 10 GPa is 1.886 Å. Upon further compression to 23–94 GPa, our simulations revealed a novel structure, Pnma-II (Z = 4 and Fig. 1c), which also consists of NZn₄ tetrahedra. The lattice constants at 50 GPa are a = 5.612 Å, b = 3.552 Å, c = 10.72 Å, and α = β = γ = 90°. At high pressure (up to 95 GPa), a new crystal structure (Z = 2, space group P6₃/mmc) becomes the most stable phase, which comprises alternately stacked ZnINZn along its crystallographic axis. Moreover, this structure includes NZn₆ polyhedra, in which almost all N–Zn bonds have the same bond length (1.959 Å). All crystal structures information and atomic coordinates are shown in Table 1, which are fully optimized at different pressures.

Fig. 1 Structures of the predicted Zn₂NI phases: (a) Pnma-I, (b) Pna2₁, (c) Pnma-II, and (d) P6₃/mmc. Purple (large), gray (middle), and off-white (small) spheres denote I, Zn, and N atoms, respectively.

Table 1 Lattice constants and atomic coordinates of Zn₂NI for the different space groups obtained in the present study: Pnma-I at 0 GPa, Pna2₁ at 10 GPa, Pnma-II at 50 GPa, and P6₃/mmc at 100 GPa

	P (GPa)	Lattice constants (Å)	Atom position
Pnma-I	0.001	a = 6.640	Zn (4a)	0.000	0.000	0.000
		b = 6.321	Zn (4c)	0.652	0.250	0.197
		c = 6.079	N (4c)	0.942	0.250	0.127
			I (4c)	0.917	0.250	0.616
Pna21	10	a = 6.236	Zn (4a)	−0.416	0.040	0.732
		b = 7.542	Zn (4a)	−0.481	0.040	0.732
		c = 8.042	N (4a)	−0.564	0.873	0.518
			I (4a)	−0.079	0.124	0.515
Pnma-II	50	a = 5.612	Zn (4c)	0.373	0.750	−0.443
		b = 3.552	Zn (4c)	0.343	0.750	−0.776
		c = 10.172	N (4c)	0.934	0.250	−0.123
			I (4c)	0.612	0.250	−0.884
P63/mmc	100	a = b = 3.034	Zn (4f)	0.333	0.667	0.581
		c = 10.799	N (2a)	0.000	0.000	0.000
			I (2c)	0.667	0.333	0.750

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The relative differences of enthalpies of selected structures relative to the C₂ phase of Zn₂NI and the volumes of these phases are plotted as a function of pressure in Fig. 2. The results show that the Pnma-I phase remains the most stable structure up to 5.2 GPa, beyond which the Pna2₁ structure is favored. Furthermore, for the first time, our calculations predict a new Pnma-II phase in Zn₂NI that is stable in the pressure range of 22.5–94.6 GPa. Beyond this pressure, the P6₃/mmc phase becomes the most stable crystal structure. Therefore, the successive transition pressures of Pnma-I → Pna2₁, Pna2₁ → Pnma-II, and Pnma-II → P6₃/mmc are 5.2, 22.5, and 94.6 GPa, respectively. Moreover, the calculated P–V curves of these high-pressure structures (see Fig. 2b) suggest that the phase transitions of Pnma-I → Pna2₁, Pna2₁ → Pnma-II, and Pnma-II → P6₃/mmc are first-order with clear volume drops of 0.11%, 10.4%, and 1.5%, respectively. The phase transition originates from volume reduction, which is favorable for denser packing under compression and can be easily detected experimentally.

Fig. 2 (a) Enthalpy of the Pnma-I, Pna2₁, Pnma-II, and P6₃/mmc-Zn₂NI phases relative to the C₂-Zn₂NCl phase as a function of pressure; (b) P–V curves of the Pnma-I, Pna2₁, Pnma-II, and P6₃/mmc Zn₂NI phases.

The stability of the crystal structure cannot be determined exclusively by comparing enthalpies because the structure might be subject to dynamic instabilities. Therefore, we calculated the phonon-dispersion curves for the predicted high-pressure phases, Pna2₁, Pnma-II, and P6₃/mmc using the supercell method. No imaginary phonon frequencies are found in the whole Brillouin zone (see Fig. 3a–c), indicating that the three structures are dynamically stable in the corresponding pressure range. The primitive cells of the Pna2₁, Pnma-II, and P6₃/mmc structures contain 16, 16, and 8 atoms, respectively. The calculated zone-center (Γ) phonon eigenvectors were used to deduce the symmetry labels of the phonon modes. Group theory analysis shows that the Raman modes at the zone center have the irreducible representations: Γ_Pna21 = 12A₂, Γ_Pnma = 8A_g + 4B_1g + 8B_2g + 4B_3g, and Γ_P63/mmc = A_1g + 2E_2g + E_1g. To determine the pressure dependence of the frequencies of the Raman modes of the high-pressure Zn₂NI phases, the Raman frequencies were calculated, as shown in Table 2. We can found that the Raman modes are different from each other, which is due to different space groups of their crystal structures of Zn₂NI. The calculated theoretical frequencies can give some information about the positions of sharp peaks of Raman spectrum. Unfortunately, no experimental data are available for comparison. The calculated frequencies of the Raman modes for the three high-pressure structures may be useful for future experimental confirmation of these predicted phases.

Fig. 3 Phonon-dispersion curves for the different phases of Zn₂NI: (a) Pna2₁ at 10 GPa, (b) Pnma-II at 50 GPa, and (c) P6₃/mmc at 100 GPa.

Table 2 Theoretical frequencies (cm⁻¹) of Raman modes of Zn₂NI for Pna2₁ at 10 GPa, Pnma-II at 50 GPa, and P6₃/mmc at 100 GPa

Pna21 at 10 GPa	Pnma-I at 50 GPa	P63/mmc at 100 GPa
A2 25; 38; 81; 100; 127; 154; 194; 255; 584; 630; 673; 713	Ag 79; 137; 190; 193; 249; 264; 613; 650	E1g 274; 343
	B1g 28; 48; 182; 682	E2g 86; 271
	B2g 74; 147; 189; 254; 276; 313; 546; 712
	B3g 33; 61; 164; 683

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Atomic displacements are always accompanied by striking changes in the physical properties, especially the electronic properties. There is widespread interest in MNX-type nitrides because of their predicted wide band gap, high atomic density, and excellent optical absorption.⁴⁸ The Pnma-I, Pna2₁, and Pnma-II Zn₂NI phases at 0, 10, and 50 GPa have direct energy band gaps at Γ (0, 0, 0) points of 2.63, 2.01, and 0.81 eV, respectively. However, at 100 GPa, the hexagonal phase of Zn₂NI has a metallic character. Therefore, all phases of Zn₂NI except P6₃/mmc exhibited semiconducting behavior. Moreover, we found that the band gap values decrease with pressure, indicating that high pressure induces a transition from semiconductor to metal. The calculated partial density of states projected on Zn, N, and I atoms are shown to the right of the corresponding band gaps in Fig. 4. For the Pnma-I phase nitrides at ambient pressure, the valence band is composed of N 2p and I 5p, 4d orbitals, and the conduction band is composed mainly of N 2p and I 5p orbitals, as shown in Fig. 4a. As the pressure increases to 10 GPa for the Pna2₁ phase nitrides, there is a downshift of the N 2p and I 5p4d orbitals to the valence band maximum, and an upshift of the I 4d orbitals to the conduction band maximum, which decrease the band gap energy (Fig. 4b). As the pressure further increases, the electrons in the I 4d orbitals move to N 2p orbitals, further decreasing the band gap energy (Fig. 4c). At higher pressure, the stronger hybridization between the N 2p and I 5p, 4d orbitals leads to a reduction in the band gap energy, transforming the Zn₂NI from a semiconductor to a metal (Fig. 4d).

Fig. 4 Band structures and corresponding partial density of states (PDOS) of the different phases of Zn₂NI: (a) Pnma-I at 0 GPa, (b) Pna2₁ at 10 GPa, (c) Pnma-II at 50 GPa, and (d) P6₃/mmc at 100 GPa. The Fermi level was set at 0 eV.

The wide band gap of Zn₂NI makes it a promising solar cell absorber. Here, we focused on the optical properties of all high-pressure phases of Zn₂NI; the absorption coefficients along the different planes are shown in Fig. 5. It is clear that the absorption coefficient at lower energies decreases rapidly with increasing energy and the visible range between 0 and 5 eV becomes wider with pressure. Fig. 6a–d shows the real ε₁(ω) and imaginary ε₂(ω) components of the dielectric function of Zn₂NI along the different planes; the solid and dotted lines represent the real and imaginary components, respectively. The maximum peaks of all phases obtained in the absorption spectrum match the peaks of the imaginary component of the dielectric function, which indicates that the origin of absorption is the imaginary component of the dielectric function. The profile of the real component of the dielectric function (Fig. 6) has similar peaks to the absorption spectrum, with the maximum peaks in the range of 2.8–4.0 eV. As the pressure increases, before the Zn₂NI becomes metallic, the peak values of the imaginary component increase. This renders the material more suitable for use in solar cells.

Fig. 5 Absorption coefficients of Zn₂NI along the different planes: (a) Pnma-I at 0 GPa, (b) Pna2₁ at 10 GPa, (c) Pnma-II at 50 GPa, and (d) P6₃/mmc at 100 GPa.

Fig. 6 Real ε₁(ω) and imaginary ε₂(ω) components of the dielectric function of the different Zn₂NI phases along different planes represented as solid and dotted lines, respectively: (a) Pnma-I at 0 GPa (b) Pna2₁ at 10 GPa, (c) Pnma-II at 50 GPa, and (d) P6₃/mmc at 100 GPa.

4. Conclusions

In summary, we investigated the high-pressure phases of Zn₂NI using the CALYPSO method coupled with first-principles, density-functional calculations at zero temperature and in the pressure range of 0–100 GPa. Three new stable phases, Pna2₁, Pnma-II, and P6₃/mmc were predicted. NZn₄ tetrahedra and NZn₆ polyhedra emerged in the new predicted crystal structures with increasing pressure. The calculated phonon-dispersion curves indicated that all three crystal structures are dynamically stable under pressure. Moreover, under high pressure, the sequence of Zn₂NI structural phase transitions was found to be as follows: Pnma-I (5.2 GPa) → Pna2₁ (22.5 GPa) → Pnma-II (94.6 GPa) → P6₃/mmc. The electronic structures indicated that all three phases of Zn₂NI are semiconducting. However, under higher pressure, the band gap of the P6₃/mmc phase narrowed and the P6₃/mmc phase became metallic. Therefore, pressure can induce the transformation of Zn₂NI from a semiconductor to a metal. Analysis of the DOS of Zn₂NI revealed the existence of strong covalent bonding in these phases, which greatly contributes to their stability. Accompanying the structural transformation with increasing pressure, the optical absorption of Zn₂NI increases in the visible region. These findings represent a key step towards understanding the behavior of metal nitride halides under pressure.

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China Grant No. 11304140, 11304141 and 11104127.

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