Electronic and mechanical properties of predicted tin nitride stoichiometric compounds under high pressure

Computational Materials Science 169 (2019) 109113

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Electronic and mechanical properties of predicted tin nitride stoichiometric compounds under high pressure

T

Muhammad Aamir Aslam, Z.J. Ding

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Hefei National Laboratory for Physical Sciences at the Microscale and Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China

ARTICLE INFO

ABSTRACT

Keywords: High pressure Tin nitride Phase transition Structure prediction

High pressure has the capacity to produce potential novel structures with exciting physical and chemical properties. Nitrides find diverse usages in industry and captivate much attention in research. We have explored Sn-N system under pressure range 0–300 GPa with an objective to construct the complete phase diagram of Sn-N system. We have revealed two thermodynamically stable compounds; SnN2-Pa-3 and SnN4-P-1. The SnN2-Pa-3 has a wide indirect band gap 4.2 eV and transformed to a tetragonal structure SnN2-I4/mcm at 100.5 GPa. We have also calculated the mechanical properties of the predicted compounds and expect these results are significant to understand the Sn-N system under high pressure.

1. Introduction High pressure has the capacity to change the hybridization modes, valence electron orbits and produces potential novel structures with unusual exciting physical and chemical properties, which cannot be possible at ambient conditions [1–3]. Nitrides find diverse uses in industry and attract much attention in research [4–6]. The physical and chemical properties of the group IV-A nitrides enhance their importance and usages in technological applications. For example, Si and Ge nitrides are chemically inert insulators and used as dielectric layers, diffusion barriers and passivation layers in microelectronic devices [7], while Ge nitrides are also used in Ge-based devices as diffusion mask [8]. The various fields of chemistry, physics and material science are searching for new functional materials and gained lot of success due to prediction of new stable materials [9,10] and their experimental realization [11]. Normally, IV3N4 stoichiometry is taken by group IV nitrides and depicts excellent properties including super hardness and photocurrent generation in carbon nitride C3N4 [12,13], silicon nitride Si3N4 is useful in wear resistance applications [14,15], germanium nitride Ge3N4 is suitable in catalytic activities [16]. Tin nitride Sn3N4 possesses the band gap in the visible range, making it valuable in the solar energy applications [17]. Regardless of the other elements in this group tin nitrides are less explored. There are only few reports on the Sn3N4 compounds [18,19], while there is no reported data about other possible stoichiometric compounds of tin nitrides under high pressure. It is well known that

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there are many similarities between oxides and nitrides compounds and we found SnO2 compound in the literature [20,21]. This motivated us to explore tin nitride system under high pressure to reveal new possible stoichiometric compounds. We have used recently developed state-ofthe-art technique, i.e., Universal Structure Predictor: Evolutionary Xtallograpgy (USPEX) [22–25], to explore all stable compounds of Sn-N system in the pressure range of 0–300 GPa, and, we have revealed two new compounds, SnN2 and SnN4, along with the already existing Sn3N4. The electronic and mechanical properties of predicted compounds are also investigated [26]. 2. Computational details An unbiased search for global energy minimization of free energy surfaces has been employed to explore all potential structures of the SnN system under high pressure, which is based on the evolutionary algorithm as implemented in USPEX code and ab initio energy calculations. This methodology has the capacity to predict the stable compounds with only chemical composition information under any external condition of pressure. We have carried out variable-composition mode of evolutionary algorithm [27] to explore all stable structure at 0, 50, 100, 200, 300 GPa and kept up to 16 atoms in a primitive unit cell. First generation of random structures was produced in a large number and the subsequent generations were produced by applying different operators, i.e. lattice mutation, (20%); atom transmutation, (20%); heredity, (40%); and random structures, (20%) in each generation. The density functional theory (DFT) [28] framework within the

Corresponding author. E-mail address: [email protected] (Z.J. Ding).

https://doi.org/10.1016/j.commatsci.2019.109113 Received 3 April 2019; Received in revised form 24 May 2019; Accepted 2 July 2019 0927-0256/ © 2019 Published by Elsevier B.V.

Computational Materials Science 169 (2019) 109113

M.A. Aslam and Z.J. Ding

Perdew-Burke-Ernzerhof (PBE) parameterization of generalized gradient approximation (GGA) [29], as implemented in Vienna Ab Initio Simulation Package (VASP) [30] code was carried out for structural relaxation and electronic calculations. Furthermore, we have used hybrid functional Heyd-Scuseria-Emzerhof (HSE06) for more accurate estimations of band gap of predicted structures. The ions and the electrons interactions with a cutoff energy of 520 eV were described by the projector-augmented wave (PAW) method [31]. The electronic configurations 5s25p2 and 2s22p3 were treated as valences for Sn and N, respectively. A uniform Γ-centered Monkhorst-Pack grid with higher resolution of 2π × 0.03 Å−1 were employed to ensure the sufficient convergence of energy, stress tensor and forces. The energy convergence test in function of the k-point mesh are plotted in Fig. S-1 in supporting information. The finite displacement methodology, as implemented in the PHONOPY [32] code was used to determine the dynamical stability of the predicted structures. The strain-stress methodology [33] was used to calculate the elastic stiffness constants and the analysis was done with the ELATE code [34]. Bader’s quantum theory was employed for charge transfer analysis [35]. Chemical bonding nature of predicted structures were analyzed with crystal orbital Hamilton papulation method [36,37], as implemented in LOBSTER code [38]. VESTA [39] software was used to visualize and analyze all predicted structures. The theoretical Vickers hardness Hv was estimated by Chen’s model [40] as Hv = 2(k2G)0.585-3, where k = G/B is the Pugh ratio. 3. Results and discussion The energetically most favorable compounds of Sn-N system under high pressure were revealed by exploring the chemical stabilities of SnxNy system in the pressure range of 0–300 GPa, which was calculated by formation enthalpy of a compound relative to its constituents, i.e. Sn and N,

H = [H (Sn x Ny )

xH (Sn)

yH (N )]/(x + y )

where ΔH and H are the formation enthalpy per atom of a compound and chemical unit of a compound, respectively. The convex hull was constructed to quantify the thermodynamics of Sn-N compounds, which described a complete set of stable phases against decomposition and transformation into any other phases. We have constructed convex hull at pressures of 0, 50, 100, 200, 300 GPa by joining all decomposition routes as shown in Fig. 1(a), where open circle represents metastable or unstable structures while the solid circle represents stable structures. At 0 GPa, our variable-evolutionary search reproduced a Sn3N4 (space group 227) structure with lattice parameter, a = 9.14 Å, which is in good agreement with theoretical value, a = 9.13 Å [41], and experimental value, a = 9.01 Å [42]. At pressure of 50 GPa, there emerged a new compound SnN2 (space group 205) on a convex hull. By increasing the pressure up to 100 GPa, another compound SnN4 (space group 2) also emerged on the convex hull, while, there is no more stoichiometric compounds on the convex hull by further increasing pressure up to 300 GPa. To reveal the phase transition and pressure range of all the predicted structures, we have constructed the pressure composition phase diagram as shown in Fig. 1(b), which revealed that the SnN2 transforms from Pa-3 to I4/mcm at 100.5 GPa and SnN4-P-1 remains stable from 55 GPa to 300 GPa. These predicted structures are depicted in the Fig. 2 and their structure details are provided in Table 1. At 100 GPa, SnN2 (Pa-3, space group 205, four formula unit) has the lattice parameters, a = b = c = 4.69 Å, α = β = γ = 90.0° and Wyckoff positions occupied by Sn 4b (0.5, 0.5, 0.5) and N 8c (0.86, 0.86, 0.86). The bond length of Sn and N atom is 2.03 Å. SnN4 (P-1, space group 2, two formula unit) has lattice parameters, a = 4.27 Å, b = 3.76 Å, c = 4.67 Å, α = 95.74°, β = 85.39° and γ = 69.64°. One inequivalent atom of Sn and four

Fig. 1. (a) Convex hull for Sn-N at 0, 50, 100 and 300 GPa; (b) pressure phase transition of SnN2 from Pa-3 to I4/mcm and inset figure represents pressure composition phase diagram of Sn-N.

inequivalent atoms of N occupy Wyckoff positions, 2i (-0.21, 0.41, 0.24), 2i (−0.27, 0.21, −0.35), 2i (−0.03, 0.21, −0.19) and 2i (0.44, 0.15, 0.08), respectively. The shortest bond length of Sn and N atom is 2.08 Å. At 200 GPa, SnN2 (I4/mcm, space group 140, four formula unit) has the following lattice parameters, a = b = 4.10 Å, c = 5.02 Å, α = β = γ = 90.0° and the bond length between Sn and N atoms is 2.05 Å, while the Wyckoff positions for inequivalent atoms of Sn and N are 4a (0.0, 0.0, 0.25) and 8 h (0.11, 0.61, 0.0), respectively. To reveal the thermodynamic stability of these predicted structure we have carefully calculated the phonon dispersion spectra within finite displacement methodology at respective pressures, SnN2-Pa-3 at 100 GPa, SnN2-I4/mcm at 300 GPa and SnN4-P-1 at 100 GPa, as shown in Fig. 3. We found that these structures have positive phonon dispersion spectra which confirmed that these structures are thermodynamically stable. The charge transferred between Sn and N atoms of predicted compounds is analyzed by Bader’s theory, and the calculated charges transferred from Sn to N atoms for SnN2-Pa-3 at 100 GPa, SnN2-I4/mcm at 200 GPa and SnN4-P-1 at 100 GPa are 2.08 e, 2.08 e and 2.10 e, respectively. To reveal the electronic properties of Sn-N system under high pressure, we have calculated the electronic band structure under respective pressures of all the predicted structures with PBE-GGA and HSE06, as shown in Fig. 4. The horizontal dashed line represents the Fermi energy level. The SnN2-Pa-3 structure possesses the lowest

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Computational Materials Science 169 (2019) 109113

M.A. Aslam and Z.J. Ding

Fig. 2. Predicted structures: (a) SnN2-Pa-3 at 100 GPa; (b) SnN2-I4/mcm at 300 GPa; (c) SnN4-P-1 at 100 GPa. Table 1 Structural details of the predicted structures; SnN2-Pa-3, SnN2-I4/mcm, SnN4-P-1 and Sn3N4-Fd-3m. Phases

Pressure (GPa)

Space group

Lattice parameters a, b, c (Å), α, β, γ (deg.)

SnN2

100

205 (Pa-3)

a = b = c = 4.69, α = β = γ = 90.0

SnN2

200

140 (I4/mcm)

a = b = 4.10, c = 5.02, α = β = γ = 90.0

SnN4

100

2 (P-1)

a = 4.27, b = 3.76, c = 4.67 α = 95.74, β = 85.39, γ = 69.64

Sn3N4

0

227 (Fd-3m)

a = b = c = 9.14, α = β = γ = 90.0

Atom

Fractional atomic coordinates

Wyckoff positions

x

y

z

Sn (4b) N (8c) Sn (4a) N (8h) Sn (2i) N1 (2i) N2 (2i) N3 (2i) N4 (2i) Sn (8b) Sn (16c) N2 (32e)

0.50 0.86 0.0 0.11 −0.21 −0.27 −0.03 0.44 0.30 0.37 0.0 −0.24

0.50 0.86 0.0 0.61 0.41 0.21 0.21 0.15 0.13 0.37 0.0 −0.24

0.50 0.86 0.25 0.0 0.24 −0.35 −0.19 0.08 0.35 0.37 0.0 −0.24

Fig. 3. Phonon band structures of predicted structures: (a) SnN2-Pa-m at 100 GPa; (b) SnN2-I4/mcm at 300 GPa; (c) SnN4-P-1 at 100 GPa.

conduction band values from G to R and highest valence band at G. We found that SnN2-Pa-3 structure has indirect band characteristic with a wide band gap of 2.7 eV at 100 GPa as shown in Fig. 4(a). While the band structure of SnN2-I4/mcm at 300 GPa and SnN4-P-1 at 100 GPa exhibit the metallic characteristics because the bands cross the Fermi level as shown in Fig. 4(b)-4(c). Furthermore, we have used hybrid functional Heyd-Scuseria-Emzerhof (HSE06) for more accurate estimations of band gap and found that SnN2-Pa-3 has indirect band gap of 4.2 eV, while SnN2-I4/mcm has small direct band gap 0.68 eV as shown in Fig. 4(d) and (e). We have also calculated the density of states (DOS) of these predicted structure for further insight into the electronic properties as shown in Fig. 5. The structures SnN2-I4/mcm at 200 GPa and SnN4-P-1 at 100 GPa possesses finite states on the Fermi level, which show their metallic character, while SnN2-Pa-3 structure has a gap of 2.7 eV, showing a wide band gap semi-conducting character. We employed crystal orbital Hamilton population (COHP) analysis

to get further insight into the chemical bonding information of the Sn-N compounds under high pressure. This approach also provides the orbital-pair interactions and useful indicator of bonding, antibonding and nonbonding regions. The projected crystal orbital Hamilton population against energy is depicted in Fig. 6. The negative region of the –pCOHP plot represents the antibonding character and positive region indicating bonding character. SnN2-Pa-3 and SnN2-I4/mcm represented the bonding below the Fermi level and antibonding above the Fermi level, while SnN4-P-1 antibonding region is below the Fermi level up to −4 eV as depicted in Fig. 6(c). To investigate the mechanical properties of these compounds, we have calculated the elastic stiffness constants, which determine all the necessary information against any applied stress-strain, and have also confirmed the mechanical stability criteria of these phases. Shear modulus G and bulk modulus B describe materials resistance to shape deformation and volumetric changes. Shear modulus is related to the hardness of a material and those materials possess higher shear

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Computational Materials Science 169 (2019) 109113

M.A. Aslam and Z.J. Ding

Fig. 4. Band structures of predicted structures with PBE-GGA and HSE06: (a) SnN2-Pa-m at 100 GPa; (b) SnN2-I4/mcm at 300 GPa; (c) SnN4-P-1 at 100 GPa; (d) SnN2Pa-m at 100 GPa; (e) SnN2-I4/mcm at 300 GPa; (f) SnN4-P-1 at 100 GPa; where (a)-(c) were estimated with PBE-GGA and (d)-(f) with HSE06.

Fig. 5. Density of states of the predicted structures: (a) SnN2-Pa-m at 100 GPa; (b) SnN2-I4/mcm at 200 GPa; (c) SnN4-P-1 at 100 GPa.

Fig. 6. Crystal orbital Hamilton population of the predicted structures: (a) SnN2-Pa-m at 100 GPa; (b) SnN2-I4/mcm at 200 GPa; (c) SnN4-P-1 at 100 GPa.

modulus can have higher hardness, while bulk modulus value represents the material’s ability to resist against uniform compression. We have calculated the B, G and Hv of these structures under respective pressure as tabulated in Table 2. The brittleness and ductility of a material is described by the bulk modulus-to-shear modulus ratio, i.e.

k = G/B, which is also called Pugh’s ratio. The critical value of this ratio is about 1.75, which classifies the ductile and brittle materials. Those materials having Pugh’s ratio less than 1.75 are classified as brittle material, while the other are ductile material. Our calculated Pugh’s ratio values for SnN2-Pa-3, SnN2-I4/mcm and SnN4-P-1 are 0.41,

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Computational Materials Science 169 (2019) 109113

M.A. Aslam and Z.J. Ding

References

Table 2 Calculated elastic constants; Shear modulus G, bulk modulus B, Young’s modulus E, poison ratio v and Hardness Hv.

Elastic stiffness Cij constants

B (GPa) G (GPa) E (GPa) v Hv (GPa)

C11 C22 C33 C44 C55 C66 C12 C13 C14 C15 C16 C23 C24 C25 C26 C34 C35 C36 C45 C46 C56

SnN2 Cubic

SnN2 Tetragonal

SnN4 Triclinic

877.29

115.80

171.03

147.80 30.85

749.47 826.22 701.84 302.67 263.68 216.28 286.25 402.08 121.99 40.498 64.379 289.25 −43.01 32.79 −11.06 −51.16 −11.26 −20.23 −30.73 41.25 −58.82 468.74 219.39 568.85 0.297 16.27

310.18

75.02 79.39 36.34

499.92 209.67 551.72 0.315 13.53

75.91 37.85 97.25 0.286 4.42

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0.49 and 0.46, respectively, which indicate that these compounds have brittle characteristics. Poisson’s ratio v describes the bonding forces characteristics of a material: covalent materials possess the value 0.1, while ionic materials are 0.25 and a central force solid have the value in between 0.25 and 0.5. Poisson’s ratio for SnN2-Pa-3, SnN2-I4/mcm and SnN4-P-1 are 0.31, 0.28 and 0.29, respectively, indicating that these are central force solids. 4. Conclusion In Summary, we have explored Sn-N system under pressure range of 0–300 GPa with an objective to construct the complete phase diagram of Sn-N system. We have used evolutionary methodology in the recently developed state-of-the-art software, USPEX, to explore all stable compounds of Sn-N system. We have revealed two thermodynamically stable compounds, SnN2-Pa-3 and SnN4-P-1. The SnN2-Pa-3 has a wide indirect band gap, 2.7 eV with PBE-GGA and 4.2 eV with HSE06 functional, and it transforms to a tetragonal structure SnN2-I4/mcm at 100.5 GPa. The SnN4-P-1 has a metallic characteristic and it remains stable from 55 GPa to 300 GPa. We have also calculated the mechanical properties of the predicted compounds and we expect these results are significant to understand the Sn-N system under high pressure. CRediT authorship contribution statement Muhammad Aamir Aslam: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Validation, Visualization, Writing - original draft. Z.J. Ding: Conceptualization, Project administration, Resources, Supervision, Writing - review & editing. Acknowledgments This work was supported by the National Natural Science Foundation of China (No. 11574289). The authors also thank Dr. H.M. Li and acknowledge the supercomputing center of USTC for the support of parallel computing. 5

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