Theoretical Investigation of the High-Pressure Structure, Phase

Article pubs.acs.org/JPCC

Theoretical Investigation of the High-Pressure Structure, Phase Transition, and Mechanical and Electronic Properties of Mg3N2 Jian Li, Changzeng Fan,* Xu Dong, Ye Jin, and Julong He State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, P.R. China ABSTRACT: The potential structures of magnesium nitride with a chemical composition of Mg3N2 are examined by utilizing a widely adopted evolutionary methodology for crystal structure prediction. In addition to the previously proposed phases (α-, β- and γ-Mg3N2), we find five high-pressure phases for Mg3N2: (1) a Cmc21 symmetric structure (ε-Mg3N2) at 27 GPa, (2) a R3c ̅ symmetric structure (τ-Mg3N2) at 30 GPa, (3) a Cmcm symmetric structure (ω-Mg3N2) at 53 GPa, (4) a Ima2 symmetric structure (λ-Mg3N2) at 68 GPa, and (5) a Ibam symmetric structure (μ-Mg3N2) at 115 GPa. All these phases are mechanically and dynamically stable by checking the elastic constants and phonon dispersion. All phases are direct band gap semiconductors except that the ω-Mg3N2 phase has a nontrivial indirect band gap. Mechanical properties calculations reveal that the γ-Mg3N2 phase has superior ductility than other phases. The Vickers hardness of each phase has been evaluated to be about 15 GPa based on an empirical relation. presented therein. Braun et al.23 has also reported the highpressure behavior of Ca3N2 and Mg3N2. In their work, Mg3N2 shows decomposition starting at very moderate pressures (e.g., in situ 2 GPa and ex situ 12 GPa), thereby acting as a precursor for Mg nanoparticle formation with bcc structure. It is known that the required pressure for the formation of high-pressure phases can significantly be reduced even down to ambient conditions for nanosized particles. The pressure induced elimination of nitrogen from Mg3N2 causes the formation of nanosized Mg-particles because of diffusion-limited crystallite growth, resulting in the surprising low pressures for Mg3N2 decomposition.24 These earlier studies highlight the importance of highpressure behaviors of Mg3N2, however, the lack of systematic investigations hampers our understanding of their properties and further application of Mg3N2. In this work, we extensively explore the potential candidate crystal structures of Mg3N2 under high-pressure by using ab initio evolutionary algorithm USPEX.25−27 Several new high-pressure Mg3N2 phases have been predicted. The stability of these structures is determined by elastic constants and phonon spectra. The transition behaviors under high-pressure among different structures are studied as well. In addition, the mechanical and electronic properties are also discussed.

1. INTRODUCTION In the search for novel functional materials, the multifaceted family of nitride compounds exhibiting diverse properties is widely studied as a model system. Some binary nitrides, such as AlN and Si3N4, have been widely used as high-performance engineering and substrate materials in the semiconductor industry.1 In industry, Mg3N2 possesses various applications, such as nitriding agent in reactions leading to formation of various nitrides,2−5 as catalyst for the synthesis of superhard silicon nitride and cubic boron nitride,6,7 and as additive in the refinement process of steel.8 Beyond that, the related magnesium-containing nitrides are potential high-temperature materials and substrates or other heterostructure components9,10 in the electronic industry. Moreover, they have attracted interests as hydrogen-storage materials.11−13 As early as in 1933, α-Mg3N2 has been confirmed to crystallize in the cubic antibixbyite structure14 of the mineral (Mn, Fe)2O3, which is also known in many sesquioxides15−18 and other group II metal nitrides.9,19 Theoretical calculations have been reported by Römer et al.,20 which predict the existence of two high-pressure phases of Mg3N2 (β- and γMg3N2). Relating to the high-pressure behavior of Mg3N2, there are some experimental and theoretical investigations reported by Hao et al.,21 where the theoretical results are in good agreement with those of Römer et al.20 However, the proposed high-pressure phases are not fully supported by the XRD patterns displayed in ref 21. Gladkaya et al.22 investigated the temperature−pressure phase diagram of Mg3N2 in a range up to 1900 K and 1.5 to 9.0 GPa by in situ differential thermal analysis. They proposed six phases, of which two should be accessible from α-Mg3N2 upon heating at ambient pressure and three can be obtained at temperature exceeding 1000 K at high pressure. Unfortunately, the exact crystal structures were not © 2014 American Chemical Society

2. CALCULATION METHODS Evolutionary simulation method by USPEX with variable cell number (up to 30 atoms) were performed at ambient Received: November 28, 2013 Revised: March 21, 2014 Published: April 22, 2014 10238

dx.doi.org/10.1021/jp411692n | J. Phys. Chem. C 2014, 118, 10238−10247

The Journal of Physical Chemistry C

Article

Table 1. Actual Value of the k-Point Meshes for Various Mg3N2 Phases system

α-Mg3N2

β-Mg3N2

γ-Mg3N2

ττ-Mg3N2

μ-Mg3N2

λ-Mg3N2

ω-Mg3N2

ε-Mg3N2

k-point

4×4×4

4 × 12 × 5

12 × 12 × 7

7×7×3

5×8×8

5×8×8

11 × 3 × 6

12 × 3 × 7

Figure 1. Schematic crystal structure of τ-Mg3N2 (Mg atoms are depicted in light blue, N atoms are rose red). Left side, NMg6 octahedral layer viewed along [001]; right side, MgN4 tetrahedral viewed along [110].

Figure 2. Schematic crystal structure of μ-Mg3N2 (Mg atoms are depicted in light blue, N atoms are rose red). Left side, NMg6 triangular prism viewed along [0 1 2]; right side, MgN4 tetrahedral viewed along [001], green represents Mg1N4; purple represents Mg2N4.

2s22p3 electrons were considered as the valence electrons, respectively. The geometric optimization per unit cell was carried out using the BFGS minimization algorithm.32 The plane-wave kinetic energy cutoff is 540 eV for all of the mentioned structures. During the structural optimization process iterations were continued until the following criteria are satisfied: (1) the maximum force on the atom is below 0.01 eV/Å; (2) the maximum displacement of atoms between cycles is below 5 × 10−4 Å; (3) the maximum energy change is less than 5 × 10−7 eV/atom. Proper Monkhorst−Pack k-point grids were checked to ensure that the results are in accordance with the convergence criteria and listed in Table 1. To avoid the inherent shortcoming of GGA when treating the band gaps for semiconducting materials, the projector augmented wave (PAW) pseudopotential33 using PBE as well as Heyd− Scuseria−Ernzerhof (HSE) hybrid functional34,35 have also been used to calculate the nontrivial band structures of ωMg3N2 phase. The cutoff energy was set to be 500 and 450 eV for PAW−PBE and HSE methods, respectively. The Monkhorst−Pack k-point meshes of 15 × 15 × 15 and 6 × 6 × 6 were used for PAW−PBE and HSE methods, respectively. Both

temperature without any experimental information. The system starts from five atoms, i.e., three Mg atoms and two N atoms. The first generation of structures was created randomly and the number of structures in the population was set to 200. The upper 60% of each generation were used to produce the nextgeneration structures by heredity. The rest are produced by soft mutation (20%), random space group specificity (10%), and lattice mutation (10%). The best structure of previous generation was set to survive and compete in the following generation. Twenty-five generations (maximum) was required in our global optimization. Once a new structure was obtained from USPEX, the geometry optimization and property calculations were performed using first-principles calculations, which were carried out using the plane-wave pseudopotential method within the framework of density functional theory as implemented in the CASTEP code.28 The exchange correlation potentials were treated within the generalized gradient approximation (GGA) of Perdew−Burke−Ernzerhof (PBE).29,30 An ultrasoft pseudopotential (USPP) was employed to describe the atomic electronic configuration.31 For Mg and N, the 2p63s2 and 10239



Article

Figure 3. Schematic crystal structure of λ-Mg3N2 (Mg atoms are depicted in light blue, N atoms are rose red). Left side, NMg6 polyhedron viewed along [−0.5 0 2]; right side, MgN4 tetrahedral viewed along [001], purple represents Mg1N4; orange represents Mg2N4.

Figure 4. Schematic crystal structure of ω-Mg3N2 (Mg atoms are depicted in light blue, N atoms are rose red). Left side, NMg6 polyhedron viewed along [001]; right side, MgN4 tetrahedral viewed along [001].

Figure 5. Schematic crystal structure of ε-Mg3N2 (Mg atoms are depicted in light blue, N atoms are rose red). Left side, NMg7 polyhedron (green) and NMg6 octahedral (yellow) viewed along [1 0 0.5]; right side, MgN4 tetrahedral (green and orange) and MgN5 (purple) pyramid viewed along [−1 0−1].

3. RESULTS AND DISCUSSION 3.1. Optimized Crystal Structures. A wide selection of candidate structures with composition Mg3N2 was calculated. In addition to α-Mg3N2, two more structure types (β- and γMg3N2) have already been proved to be of importance for the high-pressure behavior of Mg3N2 in the previous study. Their detailed crystallographic data was introduced elsewhere (refs 20

methods adopt the same self-consistent energy convergence criteria of 1 × 10−5 eV/atom. To ensure that the obtained structures are dynamically stable, the phonon frequencies were calculated throughout the Brillouin zone using the finitedisplacement approach as implemented in the phonopy code36 as well as the CASTEP code. 10240



Article

Table 2. Optimized Crystallographic Data of τ-Mg3N2 a (Å)

c (Å)

V (Å3)

ρ (g/cm3)

R3c ̅ (no. 167) 5.47 atom position

14.52 x

376.38

2.67

space group

Mg N

18e 12c

0.3666 0.3333

Z 6

y

z

0.3333 0.6667

0.0833 0.3117

Table 3. Optimized Crystallographic Data of μ-Mg3N2 a (Å)

b (Å)

c (Å)

V (Å3)

ρ (g/cm3)

Z

Ibam (no. 72) 9.30 atom position

5.23

5.40

262.83 y

2.55

4

space group

Mg1 Mg2 N

8f 4b 8j

x 0.2022 0.0000 0.3563

0.0000 0.5000 0.1998

z 0.7500 0.2500 0.5000

Table 4. Optimized Crystallographic Data of λ-Mg3N2 a (Å)

b (Å)

Ima2 (no. 46) 8.59 atom position

5.33

space group

Mg1 Mg2 N1 N2

8c 4b 4b 4a

c (Å)

V (Å3)

ρ (g/cm3)

Z

5.50

251.95 y

2.66

4

x 0.0917 0.2500 0.2500 0.0000

0.2317 0.8279 0.4591 0.0000

Figure 6. Volume of the eight phases of Mg3N2 as a function of pressure. The solid squares and the solid lines represent the calculated data and the fitting results, respectively.

z

coordinated by N and N atoms in octahedrally coordinated by Mg. The Mg and N atoms occupy Wyckoff 18e and 12c positions, respectively. The second new structure, termed μMg3N2, has been identified with space group Ibam (No. 72) (Figure 2). In this structure, there are 20 atoms in a unit cell, of which N and two inequivalent Mg (Mg1 and Mg2) atoms occupy Wyckoff 8j, 8f, 4b positions, respectively. Each N atom is coordinated by four Mg1 and two Mg2 atoms, forming a Mg6N triangular prism. The coordination of Mg1 and Mg2 are both tetrahedrons with four N atoms, which are indicated in different color in Figure 2. The third new structure−denoted as λ-Mg3N2−belongs to orthor-hombic crystal system (space group Ima2, No. 46, see Figure 3). Both Mg and N have two inequivalent sites in this structure, of which eight Mg1 and four N2 atoms occupy Wyckoff 8c and 4a position, respectively, while the other Mg and N atoms (Mg2 and N1) take the 4b (0.25, y, z) position. In λ-Mg3N2 the Mg1 and Mg2 atoms are tetrahedrally coordinated by four N atoms (two N3 and two N4 atoms), whereas the N atoms are coordinated by four Mg1 and two Mg2 atoms, forming Mg6N1 triangular prism and distorted Mg6N2 octahedral. This structure is built up by a three-dimensional network of corner- and edge-sharing MgN4tetrahedra and NMg6-polyhedron. The forth new structure− denoted as ω-Mg3N2−belongs to orthorhombic crystal system (space group Cmcm, No. 63, see Figure 4). In this structure, both Mg and N atoms also have two different types. The Wyckoff positions for Mg1 and N1 are 8f and 4b; Mg2 and N3 occupy the 4c position. In ω-Mg3N2, the coordination environment of N atoms is similar to λ-Mg3N2. The N1 atoms are octahedrally coordinated by two Mg1 and four Mg2 atoms, whereas the N2 atoms are coordinated by six Mg1 atoms, developing a triangular prism. The structure comprises

0.5283 0.1596 0.3009 0.2641

Table 5. Optimized Crystallographic Data of ω-Mg3N2 c (Å)

V (Å3)

ρ (g/cm3)

Z

5.99

247.59 y

2.71

4

x 0.5000 0.0000 0.5000 0.0000

0.1642 0.0118 0.0000 0.2141

a (Å)

b (Å)

Cmcm (no. 63) 3.27 atom position

12.61

space group

Mg1 Mg2 N1 N2

8f 4c 4b 4c

z 0.5198 0.2500 0.5000 0.2500

Table 6. Optimized Crystallographic Data of ε-Mg3N2 space group

a (Å)

Cmc21 (no. 36) 3.31 atom position Mg1 Mg2 Mg3 N1 N2

4a 4a 4a 4a 4a

b (Å)

c (Å)

V (Å3)

ρ (g/cm3)

Z

13.59 x

5.42

243.79 y

2.75

4

0.5000 0.5000 0.0000 0.5000 0.0000

0.0343 0.3053 0.1222 0.1798 0.0492

z 0.6855 0.2818 0.3009 0.5118 0.95721

and21). The first new structure belongs to trigonal symmetry system (space group R3c,̅ No.167), having 30 atoms in the conventional cell. For the convenience of further discussion, we denote this polymorph as τ-Mg3N2 hereafter (see Figure 1). This structure exhibits a similar structure which is related to that of β-Ca3N2 (ref 37) and comprises Mg atoms tetrahedrally

Table 7. Calculated Values of Elastic Constants Cij (GPa) of the Newly Discovered Phases systems

C11

C22

C33

C44

C55

C66

C12

C13

C23

C14

τ-Mg3N2 μ-Mg3N2 λ-Mg3N2 ω-Mg3N2 ε-Mg3N2

225.7 145.1 129.1 230.3 226.1

− 229.7 238.0 238.1 173.7

184.0 321.0 267.1 256.4 291.5

69.5 64.0 70.6 59.4 80.9

− 52.0 58.7 54.7 43.4

− 67.3 86.0 82.9 92.1

68.1 60.0 75.3 59.2 56.4

50.9 23.1 35.5 24.4 24.2

− 17.4 38.5 33.5 52.6

13.4 − − − −

10241



Article

Table 8. B0 (GPa), B0′, V0 (Å3/f.u.), Bulk Modulus B (GPa), Shear Modulus G (GPa), Young’s Modulus E (GPa), Poisson’s Ratio σ, B/G Ratio and Vicker’s Hardness Hv (GPa) for the Whole Structure Types of Mg3N2 at 0 GPa and 0 K B0 V0 B0′ B G E σ B/G Hv

α-Mg3N2

β-Mg3N2

γ-Mg3N2

τ-Mg3N2

μ-Mg3N2

λ-Mg3N2

ω-Mg3N2

ε-Mg3N2

106.9 64.2 3.8 104.8 71.5 174.7 0.22 1.47 12.5

109.9 60.5 3.6 108.0 65.8 164.0 0.25 1.64 10.0

100.6 60.2 3.9 102.1 47.8 124.1 0.30 2.14 4.9

110.3 62.7 3.6 107.5 73.4 179.3 0.22 1.47 12.8

87.8 65.7 3.7 96.7 71.8 172.7 0.20 1.35 14.2

98.8 62.9 3.8 99.5 71.8 173.5 0.21 1.39 13.6

107.4 61.9 3.9 106.5 77.1 186.3 0.21 1.38 14.4

101.3 61.0 4.0 105.3 76.0 183.8 0.21 1.39 14.2

three-dimensional network of corner- and edge-sharing MgN4 tetrahedra (Figure 5, right), which can also be composed of the three-dimensional network of corner- and edge-sharing NMg6 octahedral and NMg7 polyhedron (Figure 5, left). The detailed optimized crystallographic data of the above Mg3N2 polymorphs can be found in Tables 2−6. Referring to our GGA calculations at zero pressure, μ-Mg3N2 has the lowest density, ρ = 2.55 g/cm3, which is 2.4% lower than that of α-Mg3N2 (ρ = 2.61 g/cm3). τ-Mg3N2 (ρ = 2.67 g/ cm3) and λ-Mg3N2 (ρ = 2.66 g/cm3) is larger (by 2.3% and 2.0%, respectively) than that of α-Mg3N2, whereas the density of ω-Mg3N2 (ρ = 2.71 g/cm3) and ε-Mg3N2 (ρ = 2.75 g/cm3) is about 3.8% and 5.4%, respectively, larger than that of αMg3N2. The γ-Mg3N2 (ρ = 2.78 g/cm3) polymorph has the highest density, follows by β-Mg3N2 with ρ = 2.77 g/cm3 among all these structures. 3.2. Mechanical Properties. The elastic constants are calculated as the second-order coefficient in the polynomial function of distortion parameter δ used to fit their total energies according to Hooke’s law. In the view of their differences in crystal symmetries, different groups of deformations are adopted in our calculation. The calculated elastic constants are summarized in Table 7. Because of these new structures belong to trigonal or orthorhombic crystal system, so there are six or nine independent elastic constants for them, respectively. For the trigonal structure, the mechanical stability under ambient pressure can be judged by

Figure 7. Calculated enthalpy curves (relative to α-Mg3N2) as a function of pressure for various Mg3N2 phases. Inset: enthalpy for μMg3N2 (relative to α-Mg3N2).

repeated layers of corner-sharing NMg6 octahedral and triangular prism layers, which are stacked along [001] (Figure 4). Each Mg1 atom is still tetrahedrally coordinated by one N1 and three N2 atoms, while each Mg2 atom is bonded to four N1 atoms in the same plane. All these four structures comprise Mg atoms tetrahedrally coordinated by N atoms and N atoms exhibits a 6-fold coordination (prismatically and octahedrally) by Mg, giving a coordination description of Mg[4]N[6]]. Finally, an orthorhombic Cmc21 (No. 36) structure (termed as εMg3N2) is showed in Figure 5. In this structure, there are three Mg and two N sites in a unit cell, where both Mg and N atoms take Wyckoff 4a position. For ε-Mg3N2, the coordination environments are quite different: each N1 atom is bonded to one Mg1 atom, three Mg2 atoms and two Mg3 atoms, forming a distorted octahedral, while each N2 atom exhibits a 7-fold by different types of Mg atoms. Mg2 and Mg3 atoms exhibits a 4fold coordination (tetrahedrally) and Mg1 a 5-fold coordination (pyramidally) by N atoms, the coordination description [4] [4] [6] [7] being [Mg[5] 1/3Mg1/3Mg1/3N3/8N5/8]. The average coordination number, which is defined by the coordination of one atom to its nearest neighbors averaged over all atoms belonging to the same species, may give us some assumption on the effect of high-pressure on the packing of the studied phases. Compared to the four new structures mentioned above, the average coordination numbers for Mg are increased from 4 to 4.3, the coordination of N increases from 6 to an average 6.6. This structure is built up by a three-dimensional network of edgesharing MgN5 pyramids which is interpenetrated by an equally

(C11 + C12)C33 − 2C132 > 0; (C11 − C12)C44 − 2C14 2 > 0

(1)

For the orthorhombic crystal, the corresponding mechanical stability criterion is as follows: Cii > 0 (i = 1, 2, 3, 4, 5, 6); C11 + C22 + C33 + 2(C12 + C13 + C23) > 0 C11 + C22 − 2C12 > 0; C11 + C33 − 2C13 > 0; C22 + C33 − 2C23 > 0 (2)

From Table 7, these calculated elastic constants satisfy the mechanical stability criteria, suggesting that all these structures are mechanically stable. The calculated pressure−volume data for the different phases of Mg3N2 are fitted to a third-order Birch−Murnaghan equation of state (EOS)38 10242



Article

Figure 8. Phonon dispersion curves for the newly discovered Mg3N2 phases.

It is known that the shear modulus and bulk modulus can reflect the hardness of a solid. The bulk modulus is a measure of resistance to volume change by applied pressure, whereas the shear modulus is a measure of resistance to reversible deformations upon shear stress.40 The calculated shear modulus for ω-Mg3N2 is higher than the others, which indicates it can withstand higher shear stress than other structures. On the contrary, γ-Mg3N2 has the lowest shear modulus. Younǵs modulus is a measure of the stiffness of the solid, the higher the value of Younǵs modulus, the stiffer the material. From Table 8, the ω-Mg3N2 is also the stiffest structure. According to ref 41, a material is ductile if the value of B/G is higher than 1.75; otherwise, it is brittle. In terms of the calculated values, all of the Mg3N2 phases behave in a brittle manner except for γMg3N2. Consider the existence of nitrogen, we further analyzed the hardness of different phases by adopting the empirical scheme which correlates the Vicker hardness and the Pugh modulus ratio through the formula42

P(V ) = 1.5B0 [(V /V0)−7/3 − (V /V0)−5/3 ] {1 + 0.75(B0 ′ − 4)[(V /V0)−2/3 − 1]}

(3)

where V0 is the volume per formula unit at ambient pressure, with V being the volume per formula unit at pressure P given in GPa, B0 is the isothermal bulk modulus, and B0′ is the first pressure derivative of the bulk modulus. The fitting results are presented in Figure 6 and the values of B0, B0′, V0, which are obtained from the equation, are listed in Table 8. It can be seen that, at zero temperature, the value of the volume decreases with increasing pressure for all structures. However, the volume decreasing extent when pressure increasing is different depends on different structure type. Comparatively, the rate of the volume reduction for μ-Mg3N2 (32.4% from zero to 70 GPa) is larger than those for the other structures, suggesting its poorer compressibility. In the same way, there is only about 28.7% volume shrinkage for ω-Mg3N2 during the pressure changes, indicating its compressibility is somewhat higher than other structures. On the basis of the Voigt−Reuss−Hill approximation,39 the corresponding bulk and shear modulus (B and G) are obtained from the calculated elastic constants. The Younǵs modulus (E) and the Poissońs ratio (σ) are then calculated from B and G as follows: E=

9BG , 3B + G

σ=

3B − 2G 2(3B + G)

Hv = 2(κ 2G)0.585 − 3,

κ = G/B

(5)

According to eq 5, the obtained values of Vicker’s hardness are also illustrated in Table 8. The results indicate that the hardness of all the newly discovered phases is comparable to that of αMg3N2, which is much higher than that of β- or γ-Mg3N2. 3.3. Phase Transition Diagram. According to our firstprinciples calculation results, the enthalpy curves relative to αMg3N2 as a function of pressure up to 70 GPa for the chosen structures are presented in Figure 7. From the Figure, we can find that α-Mg3N2 should be the most stable phase due to the

(4)

The values of B, G, E, σ, and B/G are illustrated in Table 8. 10243



Article

Figure 9. Calculated band structure (left panel) and electronic DOS plots (right panel) for various Mg3N2 phases at ambient pressure.

its enthalpy is still higher than α-Mg3N2 even the pressure increases to 70 GPa. It is found that the μ-Mg3N2 gets lower enthalpy than that of α-Mg3N2 until the pressure up to 115 GPa, as plotted in the inset of Figure 7. These phase transition behavior of Mg3N2 under high-pressure suggest that all these novel structures are metastable and can only show up under high-pressure conditions and maybe preserved if quickly quenched to ambient conditions. To study the dynamical stability of these new high-pressure phases of Mg3N2, their phonon properties are investigated by

lowest enthalpy under ambient pressure. It is clearly seen that the α-Mg3N2 transforms to β-Mg3N2 at about 20 GPa and then to γ-Mg3N2 at 65 GPa, in good agreement with the previous studies.20,21 When the pressure exceeds 27 and 30 GPa, respectively, both ε-Mg3N2 and τ-Mg3N2 have lower enthalpy than that of α-Mg3N2, implying that ε-Mg3N2 and τ-Mg3N2 are more stable than α-Mg3N2 and are metastable in comparison to β and γ-Mg3N2. When the pressure further increases to above 53 GPa, ω-Mg3N2 becomes stable than α-Mg3N2. Above 68 GPa, λ-Mg3N2 also becomes lower in enthalpy. For μ-Mg3N2, 10244



Article

Figure 13. Calculated band structure for the ω-Mg3N2 phase by the PAW−PBE and HSEmethods at ambient pressure.

of the first Brillouin zone at ambient pressure. It can be seen that all phases are direct semiconductors owing to the existence of direct band gaps at the Γ point, except for ω-Mg3N2. The calculated band gap of α-Mg3N2 (Figure 9a) is 1.45 eV, in agreement with the earlier theoretical results (1.63 eV),44 whereas it is only about 52% of the experimental value (2.8 eV).10 It is well-known that the DFT-GGA calculations generally underestimate the energy gap for semiconductors and insulators (in most cases just 50% ∼ 80% of the experimentally obtained band gap). As shown in Figure 9b− e, they are all semiconductors with the direct band gaps of 1.27 eV (β-Mg3N2), 1.41 eV (γ-Mg3N2), 1.05 eV (τ-Mg3N2), and 1.22 eV (μ-Mg3N2). ε-Mg3N2 and λ-Mg3N2 are predicted to have a narrow band gap of 0.75 and 0.91 eV, respectively, the band structures are illustrated in Figure 9, parts f and g. As for ω-Mg3N2, there is no energy gap around the Fermi level and there exists electronic states at EF, implying weak metallic character with the applied USPP-PBE approachsee Figure 9h. The pressure has a significant effect on the band gaps. In Figure 10, the values of band gaps as a function of pressure are plotted in the pressure ranges of 0−50 GPa. Results from the figure indicate that the band gaps all increase with the increase of pressure, suggesting the potential optical application of Mg3N2 at high pressures. The most remarkable thing is that the ω-Mg3N2 undergoes a transition from metallic state to semiconductor at approximately at 20 GPa. In Figure 11, we show the band structure of ω-Mg3N2 at 50 GPa. We can see that it is an indirect-band gap semiconductor, the valence band maximum (VBM) and conduction band minimum (CBM) locate at Y-point (−0.5, 0.0, 0.0) and Γ-point (0.0, 0.0, 0.0), respectively, separated by a forbidden band with a gap of 0.27 eV. We also note that the conduction band is separated in two regions by a 0.94 eV band gap, the upper bandwidth is 3.58 eV, while the lower bandwidth is 2.83 eV. On the basis of the calculated DOS as shown in Figure 9, we observe that the whole valence bands are mainly contributed by the N atoms and the whole conduction bands are mainly contributed by the Mg atoms. For ω-Mg3N2 at 50 GPa, the remarkable feature is that the valence DOS show a downward trend compared to that of ambient pressure as shown in Figure 11. To examine the validity of the USPP-PBE when treating the band structures of the ω-Mg3N2 phase, the PAW pseudopotential using PBE as well as HSE hybrid functional have been carried out. Figure 12 shows the calculated DOS with the above-mentioned methods at 0 and 50 GPa. One can see that the results from PAW−PBE approach agree well with previous

Figure 10. Calculated band gaps as a function of pressure for various Mg3N2 phases.

Figure 11. Calculated band structure (left panel) and electronic DOS plots (right panel) for ω-Mg3N2 at 50 GPa.

Figure 12. Density of states (DOS) of the ω-Mg3N2 phase is calculated with HSE as well as PAW−PBE approach for comparison, (a) 0 and (b) 50 GPa.

phonon package31 with the forces calculated from VASP.43 The calculated phonon dispersion curves are shown in Figure 8a−e, respectively. We can see that there are no imaginary frequencies for them, indicating that they are all dynamically stable. 3.4. Electronic Properties. Figure 9 shows the USPP-PBE calculated band structures and density of states (DOS) of eight phases of Mg3N2 along the selected high symmetry directions 10245



■

USPP-PBE results. However, the HSE results indicate that the ω-phase is a narrow band gap semiconductor (Eg is about 0.86 eV) at 0 GPa, and the band gap value becomes wider (Eg is about 1.52 eV) when an external high-pressure of 50 GPa is applied. Hybrid functionals are known to produce much more accurate band gaps than standard semilocal density functionals. Therefore, the ω-Mg3N2 phase, like all other phases, is a semiconductor at ambient pressure. Figure 13 shows the calculated band structure for the ω-phase by the PAW−PBE and HSE methods at ambient pressure. The result from PAW− PBE approach still implies this phase is metallic by evidence of the energy bands crossing the Fermi level. Considering the time-consuming computation, the band structure from the HSE function is restricted to a path between the high symmetry points Γ(0.0, 0.0, 0.0) and S(0.0, 0.5, 0.0). It is clear that there exists an indirect band gap. Therefore, the ω-Mg3N2 phase, contrary to other phases, is an indirect-band gap semiconductor.

REFERENCES

(1) Niewa, R.; DiSalvo, F. J. Recent Developments in Nitride Chemistry. Chem. Mater. 1998, 10, 2733−2752. (2) Bruls, R. J.; Hintzen, H. T.; Metselaar, R. Preparation and Characterization of MgSiN2 Powders. J. Mater. Sci. 1999, 34, 4519− 4531. (3) Parkin, I. P.; Nartowski, A. M. Solid State Metathesis Routes to Group IIIa Nitrides: Comparison of Li3N, NaN3, Ca3N2 and Mg3N2 as Nitriding Agents. Polyhedron 1998, 17, 2617−2622. (4) Groen, W. A.; Kraan, M. J.; De With, G. Preparation, Microstructure and Properties of MgSiN2 Ceramics. J. Eur. Ceram. Soc. 1993, 12, 413−420. (5) Kobashi, M.; Okayama, N.; Choh, T. Synthesis of AlN/Al Alloy Composites by In-situ Reaction Between Mg3N2 and Aluminum. Mater. Trans., JIM 1997, 38, 260−265. (6) Lorenz, H.; Kühne, U.; Hohlfeld, C.; Flegel, K. Influence of MgO on the Growth of Cubic Boron Nitride Using the Catalyst Mg3N2. J. Mater. Sci. Lett. 1988, 7, 23−24. (7) Lorenz, H.; Peun, T.; Orgzall, I. Kinetic and Thermodynamic Investigation of c-BN Formation in the System BN-Mg3N2. Appl. Phys. A: Mater. Sci. Process. 1997, 65, 487−495. (8) Schneider, S. B.; Frankovsky, R.; Schnick, W. Synthesis of Alkaline Earth Diazenides MAEN2 (MAE = Ca, Sr, Ba) by Controlled Thermal Decomposition of Azides under High Pressure. Inorg. Chem. 2012, 51, 2366−2373. (9) Paszkowics, W.; Knapp, M.; Domagala, J. Z.; Kamler, G.; Podsiadlo, S. Low-temperature Thermal Expansion of Mg3N2. J. Alloys Compd. 2001, 328, 272−275. (10) Fang, C. M.; de Groot, R. A.; Bruls, R. J.; Hintzen, H. T.; De With, G. Ab Initio Band Structure Calculations of Mg3N2 and MgSiN2. J. Phys.: Condens. Matter 1999, 11, 4833−4842. (11) Lu, J.; Fang, Z. Z.; Choi, Y. J.; Sohn, H. Y. Potential of Binary Lithium Magnesium Nitride for Hydrogen Storage Applications. J. Phys. Chem. C 2007, 111, 12129−12134. (12) Leng, H.; Ichikawa, T.; Hino, S.; Nakagawa, T.; Fujili, H. Mechanism of Hydrogenation Reaction in the Li−Mg−N−H System. J. Phys. Chem. C 2005, 109, 10744−10748. (13) Lange, B.; Freysoldt, C.; Neugebauer, J. Native and HydrogenContaining Point Defects in Mg3N2: A Density Functional Theory Study. Phys. Rev. B 2010, 81, 224109-1−224109-10. (14) Von Stackelberg, M.; Paulus, R. The Crystal Structure of Nitrides and Phosphides. Z. Phys. Chem. B 1933, 22, 305−322. (15) Yusa, H.; Tsuchiya, T.; Sata, N.; Ohishi, Y. Rh2O3 (II)-type Structures in Ga2O3 and In2O3 under High Pressure: Experiment and Theory. Phys. Rev. B 2008, 77, 064107-1−064107-9. (16) Guo, Q.; Zhao, Y.; Jiang, C.; Mao, W. L.; Wang, Z.; Zhang, J.; Wang, Y. Pressure-Induced Cubic to Monoclinic Phase Transformation in Erbium Sesquioxide Er2O3. Inorg. Chem. 2007, 46, 6164−6169. (17) Zhang, F. X.; Lang, M.; Wang, J. W.; Becker, U.; Ewing, R. C. Structural Phase Transitions of Cubic Gd2O3 at High Pressures. Phys. Rev. B 2008, 78, 064114-1−064114-9. (18) Schleid, T.; Meyer, G. Single Crystals of Rare Earth Oxides from Reducing Halide Melts. J. Less-Common Met. 1989, 149, 73−80. (19) Partin, D. E.; Williams, D. J.; O’Keeffe, M. The Crystal Structures of Mg3N2 and Zn3N2. J. Solid State Chem. 1997, 132, 56− 59. (20) Römer, S. R.; Dörfler, T.; Kroll, P.; Schnick, W. Group II Element Nitrides Mg3N2 under Pressure: A Comparative Density Functional Study. Phys. Status Solidi B 2009, 246, 1604−1613. (21) Hao, J.; Li, Y.; Zhou, Q.; Liu, D.; Li, M.; Li, F.; Lei, W.; Chen, X.; Ma, Y.; Cui, Q.; et al. Structural Phase Transformations of Mg3N2 at High Pressure Experimental and Theoretical Studies. Inorg. Chem. 2009, 48, 9737−9741. (22) Gladkaya, I. S.; Kremkova, G. N.; Bendeliani, N. A. Phase Diagram of Magnesium Nitride at High Pressures and Temperatures. J. Mater. Sci. Lett. 1993, 12, 1547−1548. (23) Braun, C.; Börger, S. L.; Boyko, T. D.; Miehe, G.; Ehrenberg, H.; Hö h n, P.; Moewes, A.; Schnick, W. Ca 3 N 2 and Mg 3 N 2

4. CONCLUSIONS In summary, besides three previously reported phases, five novel high-pressure phases of Mg3N2 have been first uncovered by using an evolutionary methodology to elucidate the pressure-dependent phase diagram of Mg3N2. On the basis of first-principles calculations, it is found that the enthalpy of all these five new structures, ε-, ω-, λ-, τ-, and μ-Mg3N2 will be lower than that of α-Mg3N2 under certain value of external pressure. In addition, the α-Mg3N2 first transforms into βMg3N2 at 20 GPa and then to γ-Mg3N2 at 65 GPa. The calculated elastic constants and phonon dispersion curves suggest that all these phases are mechanical and dynamical stable. What’s more, these new phases of Mg3N2 are slightly harder than α-, β-, and γ-Mg3N2 as suggested by the Vickers hardness calculation by an empirical relation. Electronic band structure calculations show that all the phases of Mg3N2 are direct band gap semiconductors and the band gap increases with increasing pressure except ω-Mg3N2. Interestingly, the ωMg3N2 is an indirect band gap semiconductor with a band gap of only about 0.86 eV at ambient pressure. The superior mechanical properties and tunable band gap under pressure of these phases indicate that these metastable phases of Mg3N2 may find some potential mechanical and optical applications in future.

■

Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Telephone: +86 13315399519 (C.F.). Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the Research Foundation of Education Bureau of Hebei Province (ZD20131039) and the NSFC (Grant No. 51121061/51131002/51271160), which is gratefully acknowledged. We also acknowledge two anonymous referees for fruitful remarks especially on the inherent shortcoming of GGA comparing to the HSE when treating the band gaps for semiconductors and Prof. Yugui Yao at Beijing Institute of Technology and Dr. Feng Liu at Institute of Mechanics, Chinese Academic of Sciences for insightful discussions on the calculations by the HSE approach. 10246



Article

Unpredicted High-Pressure Behavior of Binary Nitrides. J. Am. Chem. Soc. 2011, 133, 4307−4315. (24) Guo, B.; Harvey, A. S.; Neil, J.; Kennedy, I. M.; Navrotsky, A.; Risbud, S. H. Atmospheric Pressure Synthesis of Heavy Rare Earth Sesquioxides Nanoparticles of the Uncommon Monoclinic Phase. J. Am. Ceram. Soc. 2007, 90, 3683−3686. (25) Oganov, A. R.; Glass, C. W. Crystal Structure Prediction Using Evolutionary Algorithms: Principles and Applications. J. Chem. Phys. 2006, 124, 244704−244715. (26) Oganov, A. R.; Lyakhov, A. O.; Valle, M. How Evolutionary Crystal Structure Prediction Works - and Why. Acc. Chem. Res. 2011, 44, 227−237. (27) Lyakhov, A. O.; Oganov, A. R.; Stokes, H. T.; Zhu, Q. New Developments in Evolutionary Structure Prediction Algorithm USPEX. Comput. Phys. Commun. 2013, 184, 1172−1182. (28) Segall, M. D.; Lindan, P. J. D.; Probert, M. J.; Pickard, C. J.; Hasnip, P. J.; Clark, S. J.; Payne, M. C. First-Principles Simulation: Ideas, Illustrations and the CASTEP Code. J. Phys.: Condens. Matter 2002, 14, 2717−2744. (29) Kohn, W.; Sham, L. J. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 1965, 140, A1133− A1138. (30) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (31) Vanderbilt, D. Soft Self-Consistent Pseudopotentials in a Generalized Formalism. Phys. Rev. B 1990, 41, 7892−7895. (32) Dai, Y. H. Vonvergence Properties of the BFGS Algoritm. SIAM J. Optim. 2002, 13, 693−701. (33) Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B 1994, 50, 17953−17979. (34) Heyd, J.; Scuseria, G. E.; Ernzerhof, M. Hybrid Functionals Based on a Screened Coulomb Potential. J. Chem. Phys. 2003, 118, 8207−8215. (35) Heyd, J.; Scuseria, G. E.; Ernzerhof, M. Erratum: “Hybrid Functionals Based on a Screened Coulomb Potential. J. Chem. Phys. 2006, 124, 219906-1−. (36) Togo, A.; Oba, F.; Tanaka, I. First-Principles Calculations of the Ferroelastic Transition between Rutile-type and CaCl2-type SiO2 at High Pressures. Phys. Rev. B 2008, 78, 134106-1−134106-9. (37) Römer, S. R.; Schnick, W.; Kroll, P. Density Functional Study of Calcium Nitride: Refined Geometries and Prediction of High-Pressure Phases. J. Phys. Chem. C 2009, 113, 2943−2949. (38) Birch, F. The Effect of Pressure Upon the Elastic Parameters of Isotropic Solids According to Murnaghan’s Theory of Finite Strain. J. Appl. Phys. 1938, 9, 279−288. (39) Hill, R. The Elastic Behavior of a Crystalline Aggregate. Proc. Phys. Soc. A 1952, 65, 349−354. (40) Ozisik, H. B.; Colakoglu, K.; Deligoz, E.; Ozisik, H. Structural, Electronic, and Elastic Properties of K-As Compounds: A First Principles Study. J. Mol. Model 2012, 18, 3101−3112. (41) Pugh, S. F. Relations Between the Elastic Moduli and the Plastic Properties of Polycrystalline Pure Metals. Philos. Mag. 1954, 7, 823− 843. (42) Niu, H.; Wei, P.; Sun, Y.; Chen, X. Q.; Franchini, C.; Li, D.; Li, Y. Electronic, Optical, and Mechanical Properties of Superhard ColdCompressed Phases of Carbon. Appl. Phys. Lett. 2011, 99, 031901-1− 031901−3. (43) Kresee, G.; Furthmüller, J. Efficiency of ab Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15−50. (44) Orhan, E.; Jobic, S.; Brec, R.; Marchand, R.; Saillard, J. Y. Binary Nitrides α-M3N2 (M = Be, Mg, Ca): A Theoretical Study. J. Mater. Chem. 2002, 12, 2475−2479.

10247


Theoretical Investigation of the High-Pressure Structure, Phase

Recommend Documents