Stability of Sulfur Nitrides: A First-Principles Study - ACS Publications

Subscriber access provided by UNIV OF REGINA

Article

Stability of Sulfur Nitrides: A First-Principles Study Da Li, Fubo Tian, Yunzhou Lv, Shuli Wei, Defang Duan, Bingbing Liu, and Tian Cui J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b11563 • Publication Date (Web): 04 Jan 2017 Downloaded from http://pubs.acs.org on January 5, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Stability of Sulfur Nitrides: A First-Principles Study Da Li, Fubo Tian, YunZhou Lv, Shuli Wei, Defang Duan, Bingbing Liu, Tian Cui*

State Key Lab of Superhard Materials, College of Physics, Jilin University, Changchun 130012, P. R. China. *Email: [email protected]

ABSTRACT A systematic computational study on the structural, electronic, and bonding properties of binary sulfur nitrides has been performed using the projector augmented wave method based on density functional theory. The pressure-composition phase diagram of S-N system has been established. The simulated pressure-temperature phase diagram and X-ray diffraction pattern of (SN)x explains the experimentally observed two phase coexistence. The crystal structure of experimentally observed orthorhombic (SN)x is predicted. The high-pressure phase transition of (SN)x has been studied. Sulfur-sulfur interactions induced by localized sulfur 3pz electrons are found in the high-pressure phase of (SN)x. With increasing nitrogen composition, the coordination number of sulfur atoms increases from two to six in the S-N system. Furthermore, two nitrogen-rich sulfur nitrides SN2 and SN4 have been found at high pressure. SN4 exhibits a high energy density (2.66 kJ·g-1), which makes it potentially interesting for industrial applications as a high energy density material.

ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

I. INTRODUCTION

Binary sulfur nitrides are scientiﬁcally interesting materials and have a broader technological impact as explosive powder, solar cells, light emitting diodes, or as electrodes. Many important sulfur-nitrogen molecules are reported in previous experiments.1 Most of them can only exist under low temperature condition. The thiazyl monomer radical (NS) with one unpaired electron has only a transient existence in the gas phase. Dinitrogen sulfide (N2S) decomposes into N2 and diatomic sulfur S2 at temperatures above 160 K. Tetrasulfur dinitride (S4N2) sublimes easily at room temperature and can be saved only at temperatures below -20 ºC.2-4 Pentasulfur hexanitride (S5N6) is an explosive, hazardous, air-sensitive orange solid and decomposes in warm solvents with the byproduct of S4N4. The unstable nitrogen disulfide (NS2) molecule can be produced in an argon/nitrogen/chalcogen microwave discharge and trapped in the solid argon at low temperature (12 K).1 The key compound of sulfur nitrides is the best known tetrasulfur tetranitride (S4N4) which is a potential explosive powder and was discovered in 1835.5-6 S4N4 is also the starting material for various synthetic fields in sulfur-nitrogen chemistry. The high symmetry of the cage-like S4N4 molecule (D2d) induces a peculiar electronic structure. Short intramolecular S…S interactions are found in S4N4.7-9 Most experimental investigations of S4N4 were performed at low temperature (< 120 K).10 At temperatures close to 393 K, there is a high-temperature orthorhombic phase with Pbcn space group.11 Due to the potential explosion hazard of S4N4, its structural investigations at higher pressures or temperatures are missing up to now.12 By thermal


Page 2 of 29

Page 3 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


cracking the gaseous S4N4 on silver wool,13 more challenging disulfur dinitride (S2N2) was obtained. The S2N2 molecule is closed shell and aromatic.11-12 Crystallized S2N2 is a monoclinic molecular crystal with space group P21/c. Due to its aromaticity, S2N2 is the most widely studied prototype of tetraatomic square planar 6π-electron ring molecule.13 Ab initio calculations indicate that the molecular crystal of S2N2 is an insulator with a band gap of 2.7 eV.14 Solid S2N2 undergoes thermally or photolytically induced polymerization at low temperature to form metallic polysulfur nitride (SN)x (space group: P21/c). At the here the SN units are linked head-to-tail and form planar quasi-one-dimensional chains.15 It is the first example of polymeric metal.15 It is rather unstable and explodes in air at about 240 °C. It can be used as explosive powder, solar cells, light emitting diodes, or as electrodes.16 In 1975, it was found to be a superconductor with critical temperature Tc of 0.26 K.17-18 The 3p electronic states of sulfur at fermi level provide the metallic and superconducting properties of (SN)x.16, 19 Pressure-induced band-structure changes induce the increase of Tc with enhancing pressure (0.33 K @ P = 0 to 0.54 K @ P = 9 kbar).18 However, higher pressures cannot remarkably improve its Tc values. The Tc values of (SN)x are only in the range of 2 and 3 K with the pressures increasing from 130 to 400 kbar.20 Although (SN)x is not a good superconductor at lower pressure conditions, the electronic structure and polymerization mechanism of (SN)x have important application values.21-25 For instance, a very interesting application of its polymerization progress is the rapid imaging of latent fingerprints.26-27 Furthermore, an additional orthorhombic phase of (SN)x with possible P222 space group was found



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

in in-situ time-resolved X-ray diffraction (XRD). The coexistence of monoclinic and orthorhombic phases of (SN)x has been found.28 However, the detailed crystal structure of the orthorhombic phase of (SN)x is still not clear. Other sulfur nitrides were also studied in the past decades. Very recently, Xiao et al.29 predicted a novel two-dimensional material S3N2 composed solely of covalent S-N σ bonds, with a direct band-gap (3.17 eV) and good hole mobility. Zhang et al. did a computational investigation of the thermochemical stability of kinetic persistence of binary SxNy compounds, such as SN2, S2N2, S3N2, S4N2, SN4, S2N4, S3N4 and S4N4.30 Although many molecular compounds had been found in sulfur nitrides, only crystal S4N4, S2N2 and (SN)x were reported to have good stability. Mei et al.31 studied the intrinsic conductivity of polysulphur-nitride and suggested that the detailed crystal geometry can profoundly influence electronic properties of sulfur nitrides. Over the past several decades, a number of studies have been devoted to the structural properties, electronic properties, and polymerization mechanism of sulfur nitrides. However, many fundamental aspects of sulfur nitrides are still not well understood, particularly their high-pressure behaviors, because of well-known explosion hazards. The ground-state crystal structures of (SN)x, are the subject of continuing debate. Detailed knowledge about the crystal structures of sulfur nitrides is very important for understanding their stability and polymerization. The high-pressure structural phase transitions of (SN)x are revealed in this work. We also construct the pressure-temperature diagram of (SN)x which is useful for understanding the experimentally observed two phase coexistence. Furthermore, two nitrogen-rich sulfur


Page 4 of 29

Page 5 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


nitrides SN2 and SN4 have been predicted. SN4 is expected to be a high energy material with energy density of 2.66 kJ·g-1.

II. COMPUTATIONAL METHOD

The calculations in this paper are performed within the density functional theory (DFT), carried out within the Vienna ab initio simulation package (VASP), with the projector augmented wave method.32-34 The S 3s23p4 electrons and N 2s22p3 electrons are treated as valence electrons. For all calculations, the Perdew-Burke-Ernzerhof generalized gradient approximation (GGA) exchange and correlation functional is used. Convergence tests give a kinetic energy cutoff 800 eV, with a grid of spacing 2π×0.03 Å-1 for the electronic Brillouin zone (BZ) integration in all phases. The geometries are regarded as optimized when the remanent Hellmann-Feynman forces on the ions are less than 0.01 eV/Å. The phonon frequencies are calculated by using a supercell approach as implemented in the PHONOPY code, with the forces calculated from VASP.35 The heat of formation (∆Hf) for various SxNy compositions are calculated by the equation36-39 of ∆Hf = Etotal(SxNy) – (xEtotal(S) + yEtotal(N)), in which the respective solid phase of S and N at different pressure are adopted.40-41 The pressure-temperature diagram has been calculated by using the quasi-harmonic approximation, performed by PHASEGO package.42 The Helmholtz free energies F at different volumes V and fixed temperature T were obtained for three phases of (SN)x. The pressure P is obtained by P = −(

∂F )T . The 4th-order Birch-Murnaghan equation ∂V

of state was used in our calculations. Then the Gibbs free energy G as a function of



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

temperature and pressure was obtained by G(T, P)=F(V, T)+PV.

III. RESULTS AND DISSCUTION

Figure 1. (a) Convex hull of the S-N system at high pressures and 0 K. Dotted lines are used to connect the phases. (b) Pressure-phase diagram of the stable S-N compounds (SN)x, SN2, and SN4 at 0 K.

Energetic stabilities of S-N Compounds at high pressure. In order to uncover the ground-state crystal structures of sulfur nitrides, we used the ab initio particle swarm optimization algorithm, implemented in the CALYPSO code which has been shown to provide reliable predictions of crystalline phases.43-44 Extensive structural searches of S-N compounds for various stoichiometries of SxNy (x, y = 0-1) at ambient temperature and selected pressures of 0, 30, 80, 150, and 200 GPa are performed. The local optimizations of the possible structures are performed using the VASP code. In our prediction, random structures with certain symmetry are chose as candidate


Page 6 of 29

Page 7 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


structures in the first generation. 60% of them with lower energies are selected to construct the next generation structures by particle swarm optimization algorithm. In the next step, 40% of the structures in the new generation are randomly generated. The structure search is considered converged when ~1000 structures are generated after a lowest energy structure is found. The candidate structure for each composition is then used to evaluate the heat of formation (∆Hf) relative to elementary S and N solids. By evaluating the averaged ∆Hf for each composition at 0 K and different pressures, the convex hull data for the S-N system at different pressures are obtained and shown in Figure 1a. It is well known that any structure whose formation enthalpy lies on the convex hull is deemed thermodynamically stable and experimentally synthesizable in principle. At 40 GPa, only the best known 1:1 stoichiometry appears in our prediction. With the pressure increasing, the nitrogen-rich stoichiometric SN2 and SN4 appear at 60 GPa. It is found that previously reported unstable dinitrogen sulfide (N2S), tetrasulfur dinitride (S4N2), nitrogen disulfide (NS2) and pentasulfur hexanitride (S5N6) are also unstable in our calculations. This is in good agreement with previous studies.30 Other sulfur nitrides stabilized at temperatures above 0 K are not found in our calculations because our structural searches are performed at the temperature of 0 K. The crystal structures of our predicted S-N phases are presented in Figure 2. In the following part, we mainly analyze the S-N phases with composition 1:1, 1:2, and 1:4. The high-pressure behaviors, bonding properties, and potential energy storage applications of sulfur nitrides will be discussed.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 2. The crystal structures of sulfur nitrides (a) Pnma-(SN)x (b) Immm-(SN)x (c) SN2 (d) SN4. The yellow circles represent sulfur atoms; the blue circles represent nitrogen atoms.

Ground-state structures of (SN)x phases. Among the sulfur nitrides, (SN)x has attracted much attention due to its unique physical and chemical properties in fundamental science and technological applications, such as explosive powder, solar cells, light emitting diodes, or as electrodes etc. However, the ground-state crystal structure of (SN)x is the subject of continuing debate. Previous in situ time-resolved X-ray diffraction already identified an orthorhombic phase of (SN)x with a possible P222 space group. It coexists with the monoclinic P21/c-(SN)x phase in experiments.28 However, no detailed crystal structure about the orthorhombic phase is reported because it is difficult to obtain the pure phase in experiments and the difference of X-ray diffraction between monoclinic and orthorhombic phases is too small. In our study, a new polymeric phase (SN)x with orthorhombic Pnma space group (hereafter denoted as Pnma-(SN)x) is found as depicted in Figure 2a. There are


Page 8 of 29

Page 9 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


eight atoms in the unit cell. At 40 GPa, the equilibrium lattice parameters are a = 4.076 Å, b = 2.554 Å, c = 7.302 Å. Within this structure, two inequivalent atoms occupy the crystallographic 4c sites in the unit cell, which are the (N: -0.092, 0.25, -0.843) and (S: -0.206, 0.25, -0.63) positions. This structure is composed of quasi-linear armchair chains which can be clearly observed along the crystallographic b axis. The S-N-S bond angles are 113.56° and the S-N bond lengths are 1.584 Å and 1.621 Å. Actually, the consensus has been reached on the basic building block of (SN)x, which is the well-known quasi-linear armchair chains.

Figure 3. (a) The enthalpy difference curves of (SN)x, S2N2, S4N4. (b) The pressure-temperature diagram of (SN)x. Detailed enthalpy vs pressure curves indicate that although the formation enthalpy of Pnma-(SN)x is very close to that of previously reported S4N4, S2N2, and P21/c-(SN)x phases at low pressure and 0 K, the P21/c-(SN)x phase still has the best stability in energy (Figure 3a). The Pnma-(SN)x is more energetically favorable than the P21/c-(SN)x phase at pressure above 5 GPa. The Pnma-(SN)x phase is closely



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

related to the P21/c-(SN)x phase. Only the latter adopts a monoclinic lattice, the former adopts an orthorhombic lattice (see Figure S1). The pressure-temperature diagram of (SN)x indicates that the P21/c-(SN)x phase exists at lower temperatures and pressures (0-300 K and 0~5 GPa) as shown in Figure 3b. Meanwhile, the Pnma-(SN)x phase can exist at above 300 K and 0 GPa. So the Pnma-(SN)x phase should be the experimentally observed orthorhombic phase which can coexist with the monoclinic P21/c-(SN)x phase in experiments.

Figure 4. The simulated XRD patterns of Pnma-(SN)x, S2N2, P21/c-(SN)x, and the experimental XRD pattern (from Ref. 28). To confirm the consistency of Pnma-(SN)x with the experimentally observed orthorhombic phase, we simulate the XRD pattern of Pnma-(SN)x and compare with the experimental results (Figure 4). Five characteristic peaks of P21/c-(SN)x can be easily indexed in the range of 4° and 7°. The peak of Pnma-(SN)x at 4° can explain the experimentally observed individual peak of the orthorhombic phase at 4°. The peaks of Pnma-(SN)x at ~6° contribute to the peak broadening of P21/c-(SN)x at ~6°. The


Page 10 of 29

Page 11 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


peak of S2N2 at ~4.5° can explain the experimentally observed weak peak at ~4.5°. Other peaks of S2N2 in the range of 5°-7° also contribute to the peak broadening of P21/c-(SN)x. So our simulated XRD patterns for Pnma-(SN)x, S2N2, and P21/c-(SN)x are consistent with experimental XRD patterns. The experimentally observed two phase coexistence of (SN)x can be explained by Pnma-(SN)x and P21/c-(SN)x. Previous reports also demonstrate that (SN)x is a superconductor with critical temperature Tc of 0.26 K.17-18 Our calculated electronic band structure and density of states (DOS) for the Pnma-(SN)x phase at 40 GPa reveal that the Pnma-(SN)x phase is metallic because of the finite density of states (DOS) at the Fermi level (see Figure S2). The strong hybridization between N-p and S-p orbitals especially around the Fermi level is found. The electronic DOS near the Fermi level is dominated by the 3pz states of sulfur and 2pz states of nitrogen which are responsible for metallic and superconducting properties (Figure S3). At 52 GPa, (SN)x predictably undergoes an orthorhombic Pnma Immm phase (denoted as Immm-(SN)x) transition (Figure 1b and Figure 3). Immm-(SN)x crystallizes with the orthorhombic Immm space group. The high-pressure Immm-(SN)x is a metallic material, composed of planar sheets. The stacking order of sheets along the crystallographic c axis is AA’AA’... It has eight atoms in the unit cell with equilibrium lattice parameters a = 5.658 Å, b = 2.517 Å, c = 4.295 Å, occupying the 4f (N: 0.304, 0.5, 0.0), 2b (S: 0.5, 0.0, 0.0), and 2d (S: 0.0, 0.5, 0.0) positions at 60 GPa. Under the application of pressure, the quasi-linear armchair chains transform into the planar sheets in Immm-(SN)x, in which partial sulfur atoms form six bonds



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

with the neighboring nitrogen and sulfur atoms. Other sulfur atoms form four planar bonds with the neighboring nitrogen and sulfur atoms. There are two types of S-N bonds in Immm-(SN)x with bond lengths of 1.723 and 1.676 Å at 60 GPa (Figure 2b). The longer bonds are located between nitrogen and fourfold coordinated sulfur. The shorter bonds are located between nitrogen and sixfold coordinated sulfur. Shorter bond lengths indicate strong interatomic interactions between nitrogen and sixfold coordinated sulfur atoms. The nearest distance of sulfur atoms between two neighboring sheets is 2.148 Å which is larger than the S-S bond length in elementary sulfur (2.025 Å) at the same pressure.

Figure 5. Projected density of states of sulfur atoms (fourfold coordinated and sixfold coordinated sulfur atoms) and its neighboring nitrogen atoms in Immm-(SN)x at 60 GPa.


Page 12 of 29

Page 13 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Electronic structure and binding properties of Immm-(SN)x. It is well known that pressure-induced changes in the coordination are accompanied by changes in the electronic structure. The projected density of states of the Immm-(SN)x phase at 60 GPa suggests that it is a metal (Figure 5). The density of states at the fermi level are mainly originated from N_2p, S_3s, and S_3p orbitals. Similar to Pnma-(SN)x, obvious strong orbital hybridization between N-p and S-p orbitals are found. It is also found that obvious sp2 hybridization appears in the nitrogen atoms. And there are unhybridized pz orbitals of nitrogen in the energy range of -6 and 0 eV. For fourfold coordinated sulfur atoms, the S_px orbital has strong hybridization with the N_px orbital in the range of -14 to -6 eV. The py orbitals of fourfold sulfur atoms are localized in the range of -12 to 0 eV. For six-fold coordinated sulfur atoms, S_px and S_py orbitals have strong hybridization with N_px and N_py orbitals in the range of -18 and -6 eV. So the sulfur and nitrogen atoms have a strong covalent interaction in Immm-(SN)x. Furthermore, one may clearly see some other secondary resonating electron system at a higher energy level (in the range of -12 to 0 eV) between S_pz orbitals of fourfold coordinated and sixfold coordinated sulfur atoms. Obvious S_pz and S_pz orbital hybridization indicates the potential covalent interaction between sulfur atoms in neighboring sheets. These results also indicate that with increasing pressure, the metallicity of (SN)x is weakened, accompanied by the Pmmm to Immm structural transition, because more free electrons are present to form covalent σ bonds in Immm-(SN)x.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 6 (a,b,c) The 2D electron localization function slice of Immm-(SN)x in the (001), (100) and (010) planes, respectively. (d) The isosurface of the electron localization function with isovalue of 0.8. In order to understand the stability and bonding mechanisms of the S-S interaction, the electron localization function (ELF) of Immm-(SN)x in speciﬁc planes has been calculated. Figure 6a shows large areas with big ELF values (approximately 0.85) between S and N atoms, which are typical of strong covalent bonding. The ELF maps also clearly illustrate the presence of localized electrons in fourfold and sixfold coordinated sulfur atoms along the crystallographic c axis in Immm-(SN)x (Figure 6b and 6c). It is found that there is one attractor between two neighboring sulfur atoms along the crystallographic c axis (Figure 6d). These attractors are composed of localized 3pz electrons of sulfur. There is weaker covalent bonding induced by localized 3pz electrons between two neighboring sulfur atoms along the crystallographic c axis. The ELF value between two nearest neighboring sulfur atoms along the c axis is about 0.85 which is a typical covalent bonding feature.


Page 14 of 29

Page 15 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


This is consistent with the DOS calculation. The primary strong bonds in Immm-(SN)x are the covalent S-N σ bonds, which form the planar covalent sheets in the ab plane. The formation of the weaker covalent S-S interaction between the adjacent sheets plays an important role in stabilizing the structures.

Figure 7. The electronic band structure and density of states of SN2 and SN4 at 60 GPa. The s state of nitrogen is denoted by the red circles. The p state of nitrogen is denoted by the blue circles.

Nitrogen-rich S-N compounds at high pressure. Materials that contain much nitrogen are considered to be promising candidates for high energy density materials (HEDMs) because their decomposition reactions release large energy. Recently, it has been proposed that the search for high-pressure nitrogen-rich compounds might be a good strategy for search of HEDMs.45-46 With the pressure increasing, the two nitrogen-rich compositions of SN2 and SN4 appear to be stable in our calculations. The enthalpy difference curves indicate that SN2 and SN4 are more energetically favorable than elementary S and N solids at 44 GPa and 49 GPa, respectively.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Previous reports suggested that dinitrogen sulfide (SN2) is unstable at ambient condition. However, pressure makes SN2 stable at high pressure. We find that high-pressure SN2 has the orthorhombic Pnnm space group. The equilibrium lattice parameters are a = 3.822 Å, b = 4.036 Å, c = 2.509 Å at 60 GPa. Within this structure, two inequivalent atoms occupy the crystallographic 4g and 2d sites in the unit cell, which are the (N: -0.276, 0.835, -0.5) and (S: -0.5, 0.0, 0.0) positions. With the nitrogen composition increasing, the coordination number of sulfur atoms increases from two in (SN)x to six in SN2. The sulfur atoms are enclosed by N atoms in SN2 as shown in Figure 2c and the structure is entirely composed of covalent S-N σ bonds. All the valence electrons of S form σ bonds with nitrogen atoms in SN2, remanent lone pair electrons of nitrogen atoms are highly localized. These signal the semiconducting properties of SN2. The partial density of states calculations indicate that SN2 is a semiconducting material with a direct band gap of 0.66 eV at 60 GPa (Figure 7a). For SN4, it is the most nitrogen-rich phase of the sulfur nitrides. It is predicted to take the monoclinic C2/c space group. It has equilibrium lattice parameters of a = 8.160 Å, b = 3.603 Å, c = 10.661 Å, β = 152.05° at 60 GPa. Three inequivalent atoms occupy the crystallographic 8f (N: 0.173, -0.834, 0.008), 8f (N: 0.461, -0.380, 0.351) and 4b (S: 0.5, 0.0, 0.5) positions. The basic building blocks of SN4 are four membered zigzag nitrogen chains and sulfur atoms (Figure 2d). The DOS calculations suggest that SN4 is a metal. The DOS near the Fermi level is dominated by the 2p states of nitrogen (Figure 7b). The N-N bonds in the four membered zigzag nitrogen


Page 16 of 29

Page 17 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


chains are the single bonds because the bond lengths (1.319 and 1.546 Å) are much larger than the N-N double bond length (1.107 Å) at the same pressure. It is well known that N-N single bonds are critical for the high energy density of nitrogen-rich compounds. The calculated energy density of SN4 (relative to products N2 and S solids) is 2.66 kJ·g-1 which is larger than the 2.2 kJ·g-1 of the CO/N2 mixture47 and is comparable with typical high-energy materials TATB, RDX, and HMX (energy densities: 1 to 3 kJ·g-1).48 SN4 can thus be regarded as a possible candidate for a high energy density material.

IV. CONCLUSIONS

In conclusion, the ground-state structures of stoichiometric binary sulfur nitrides are extensively explored. The ground-state crystal structure of (SN)x has been confirmed. The high-pressure phase transition of (SN)x has been studied. (SN)x is predicted to undergo a structural phase transition to the orthorhombic Pnma structure at ~5 GPa, with further transitions to Immm structures at 52 GPa. Meanwhile, the quasi-linear armchair chains of the Pnma structure transform into two-dimensional sheets in the Immm structure. And weaker covalent S-S interactions composed of localized sulfur pz electrons have been found between two neighboring sheets of Immm structure. The presences of the S-S covalent interactions play an important role in stabilizing the structures. The simulated pressure-temperature diagram and XRD of (SN)x explain the experimentally observed two phase coexistence. The old controversy about the crystal structure of orthorhombic (SN)x is resolved. Moreover,



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

two high-pressure nitrogen-rich compounds SN2 and SN4 are predicted. SN4 can be expected to be a potential high energy density material with simulated energy density of 2.66 kJ·g-1. The established enthalpy vs composition phase diagram of the S-N system is of fundamental interest and important for future experiments.

ASSOCIATED CONTENT

Supporting Information The crystal structure of (SN)x, electronic properties, and phonon dispersion curves.

AUTHOR INFORMATION

Corresponding Author *E-mail: [email protected] Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Nos. 51632002, 51572108, 11404134, 11634004, 11574109), Program for Changjiang Scholars and Innovative Research Team in University (No. IRT_15R23), National Found for Fostering Talents of basic Science (No. J1103202), and China Postdoctoral Science Foundation (2014M561279, 2016T90246). Parts of calculations were performed in the High Performance Computing Center (HPCC) of Jilin University.

REFERENCES (1)

Chivers, T. A Guide to Chalcogen-Nitrogen Chemistry. World Scientific: 2005; p 334.

(2)

Chivers, T.; Codding, P. W.; Oakley, R. T. The X-ray crystal and molecular structure of


Page 18 of 29

Page 19 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


tetrasulphur dinitride. J. Chem. Soc., Chem. Commun. 1981, 584-585. (3)

Chivers, T.; Codding, P. W.; Laidlaw, W. G.; Liblong, S. W.; Oakley, R. T.; Trsic, M. Crystal,

molecular, and electronic structure of tetrasulfur dinitride, S4N2. J. Am. Chem. Soc. 1983, 105, 1186-1192. (4)

Chandler, G. S.; Jayatilaka, D.; Wajrak, M. Radiation-Molecule and Molecule-Molecule

Interactions Ab initio study of the cyclic isomers of N2S4. Chem. Phys. 1995, 198, 169-181. (5)

Boeré, R. T.; Chivers, T.; Roemmele, T. L.; Tuononen, H. M. Electrochemical and Electronic

Structure Investigations of the [S3N3]• Radical and Kinetic Modeling of the [S4N4]n/[S3N3]n (n = 0, −1) Interconversion. Inorg. Chem. 2009, 48, 7294-7306. (6)

Pritchina, E. A.; Gritsan, N. P.; Zibarev, A. V.; Bally, T. Photochemical Study on the Reactivity of

Tetrasulfur Tetranitride, S4N4. Inorg. Chem. 2009, 48, 4075-4082. (7)

Sharma, B. D.; Donohue, J. The crystal and molecular structure of sulfur nitride, S4N4. Acta

Crystallogr. 1963, 16, 891-897. (8) Clarke, R. X-ray determination of the linear compressibilities of (SN)x. Solid State Commun. 1978,

25, 333-336. (9)

Clark, D. The structure of sulphur nitride. J. Chem. Soc. (Resumed) 1952, 1615.

(10) DeLucia, M. L.; Coppens, P. Crystal structure of tetrasulfur tetranitride (S4N4) at 120 K. Inorg.

Chem. 1978, 17, 2336-2338. (11) Irsen, S. H.; Jacobs, P.; Dronskowski, R. Tetrasulphur Tetranitride: Phase Transition and Crystal

Structure at Elevated Temperature. Z. anorg. allg. Chem. 2001, 627, 321-325. (12) Springborg, M. Density-functional studies of electronic properties of polymers. Int. Rev. Phys.

Chem. 1993, 12, 241-303. (13) Mikulski, C. M.; Russo, P. J.; Saran, M. S.; MacDiarmid, A. G.; Garito, A. F.; Heeger, A. J.

Synthesis and structure of metallic polymeric sulfur nitride, (SN)x, and its precursor, disulfur dinitride, S2N2. J. Am. Chem. Soc. 1975, 97, 6358-6363. (14) Kurmaev, E. Z.; Poteryaev, A. I.; Anisimov, V. I.; Karla, I.; Moewes, A.; Schneider, B.; Neumann,

M.; Ederer, D. L.; Lyubovskaya, R. N. Electronic structure of superconducting inorganic polymer (SN)x. Physica C: Superconductivity 1999, 321, 191-198. (15) Greene, R. L.; Grant, P. M.; Street, G. B. Low-Temperature Specific Heat of Polysulfur Nitride,

(SN)x. Phys. Rev. Lett. 1975, 34, 89-92. (16) Banister, A. J.; Gorrell, I. B. Poly(sulfur nitride): The First Polymeric Metal. Adv. Mater. 1998, 10,

1415-1429. (17) Greene, R. L.; Street, G. B.; Suter, L. J. Superconductivity in Polysulfur Nitride (SN)x. Phys. Rev.

Lett. 1975, 34, 577-579. (18) Gill, W. D.; Greene, R. L.; Street, G. B.; Little, W. A. Pressure Dependence of Superconductivity

and Normal Conductivity in Polymeric Sulfur Nitride, (SN)x Phys. Rev. Lett. 1975, 35, 1732-1735. (19) Cohen, M. J.; Garito, A. F.; Heeger, A. J.; MacDiarmid, A. G.; Mikulski, C. M.; Saran, M. S.;

Kleppinger, J. Solid state polymerization of sulfur nitride (S2N2) to (SN)x. J. Am. Chem. Soc. 1976, 98, 3844-3848. (20) Dunn, K. J.; Bundy, F. P.; Interrante, L. V. Superconductivity in polymeric sulfur nitride at

ultrahigh pressure. Phys. Rev. B 1981, 23, 106-111. (21) MacDiarmid, A. G.; Mikulski, C. M.; Russo, P. J.; Saran, M. S.; Garito, A. F.; Heeger, A. J.

Synthesis and structure of the polymeric metal, (SN)x, and its precursor, S2N2. J. Chem. Soc., Chem. Commun. 1975, 476-477.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(22) Bright, A. A.; Soven, P. Band structure of polymeric sulfur nitride. Solid State Commun. 1976, 18,

317-320. (23) Takaluoma, T. T.; Laasonen, K.; Laitinen, R. S. Molecular Dynamics Simulation of the

Solid-State Topochemical Polymerization of S2N2. Inorg. Chem. 2013, 52, 4648-4657. (24) Mawhinney, R. C.; Goddard, J. D. A theoretical study of H(S2N2)YH (Y = 1, 2, 3, 4, 5): Modeling

the superconducting polymer (SN)X. J. Mol. Struct. (THEOCHEM) 2008, 856, 16-29. (25) Tuononen, H. M.; Suontamo, R.; Valkonen, J.; Laitinen, R. S.; Chivers, T. Electronic Structures

and Molecular Properties of Chalcogen Nitrides Se2N2 and SeSN2. J. Phys. Chem. A 2005, 109, 6309-6317. (26) Kelly, P. F.; King, R. S. P.; Mortimer, R. J. Fingerprint and inkjet-trace imaging using disulfur

dinitride. Chem. Commun. 2008, 6111-6113. (27) Bleay, S. M.; Kelly, P. F.; King, R. S. P. Polymerisation of S2N2 to (SN)x as a tool for the rapid

imaging of fingerprints removed from metal surfaces. J. Mater. Chem. 2010, 20, 10100-10102. (28) Müller, H.; Svensson, S. O.; Birch, J.; Kvick, Å. In Situ, Time-Resolved X-ray Diffraction Study

of the Solid-State Polymerization of Disulfur Dinitride to Poly(sulfur nitride). Inorg. Chem. 1997, 36, 1488-1494. (29) Xiao, H.; Shi, X.; Hao, F.; Liao, X.; Zhang, Y.; Chen, X. Prediction of a Two-dimensional Sulfur

Nitride (S3N2) Solid for Nanoscale Optoelectronic Applications. arXiv:1606.01597 [cond-mat] 2016. (30) Zhang, G.-H.; Zhao, Y.-F.; Wu, J. I.; Schleyer, P. v. R. Why Are SnN4 (n =1–4) Species “Missing”?

Answers in a Broader Theoretical Context of Binary S–N Compounds. Inorg. Chem. 2012, 51, 13321-13327. (31) Mei, C. J.; Monkhorst, H. J.; Bartlett, R. J. On the intrinsic conductivity of polysulphur-nitride. Z.

Phys. B - Condensed Matter 2014, 101, 73-78. (32) Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using

a plane-wave basis set. Phys. Rev. B 1996, 54, 11169-11186. (33) Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method.

Phys. Rev. B 1999, 59, 1758-1775. (34) Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 1994, 50, 17953-17979. (35) 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. (36) Santos, A. V. d. Stability of Ir–Fe alloys and nitrides Ir–Fe–N through first principles models.

Comp. Mater. Sci. 2012, 56, 108-115. (37) Vanderlei dos Santos, A.; Padilha, G.; Monçalves, M. Determination of the stability and magnetic

properties of Fe–Pd nitride using the generalised gradient approximation (GGA). Solid State Sci. 2012, 14, 269-275. (38) dos Santos, A. V.; Samudio Pérez, C. A.; Muenchen, D.; Anibele, T. P. First principles calculations

of the magnetic and hyperfine properties of Fe/N/Fe and Fe/O/Fe multilayers in the ground state of cohesive energy. Solid State Commun. 2015, 201, 120-124. (39) dos Santos, A. V.; Samudio Pérez, C. A. Ab initio investigation of the substitution effects of 2p

elements on the electronic structure of γ-Fe4X (X = B, C, N, and O) in the ground state. J. Mater. Res. 2016, 31, 202-212. (40) Degtyareva, O.; Gregoryanz, E.; Somayazulu, M.; Mao, H.-k.; Hemley, R. J. Crystal structure of

the superconducting phases of S and Se. Phys. Rev. B 2005, 71, 214104. (41) Wang, X.; Wang, Y.; Miao, M.; Zhong, X.; Lv, J.; Cui, T.; Li, J.; Chen, L.; Pickard, C. J.; Ma, Y.


Page 20 of 29

Page 21 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Cagelike Diamondoid Nitrogen at High Pressures. Phys. Rev. Lett. 2012, 109, 175502. (42) Liu, Z.-L. Phasego: A toolkit for automatic calculation and plot of phase diagram. Comp. Phys.

Commun. 2015, 191, 150-158. (43) Wang, Y.; Lv, J.; Zhu, L.; Ma, Y. Crystal structure prediction via particle-swarm optimization.

Phys. Rev. B 2010, 82, 094116. (44) Wang, Y.; Lv, J.; Zhu, L.; Ma, Y. CALYPSO: A method for crystal structure prediction. Comp.

Phys. Commun. 2012, 183, 2063-2070. (45) Peng, F.; Yao, Y.; Liu, H.; Ma, Y. Crystalline LiN5 Predicted from First-Principles as a Possible

High-Energy Material. J. Phys. Chem. Lett. 2015, 2363-2366. (46) Yin, K.; Wang, Y.; Liu, H.; Peng, F.; Zhang, L. N2H: a novel polymeric hydronitrogen as a high

energy density material. J. Mater. Chem. A 2015, 3, 4188-4194. (47) Raza, Z.; Pickard, C. J.; Pinilla, C.; Saitta, A. M. High Energy Density Mixed Polymeric Phase

from Carbon Monoxide and Nitrogen. Phys. Rev. Lett. 2013, 111, 235501. (48) Evans, W. J.; Lipp, M. J.; Yoo, C. S.; Cynn, H.; Herberg, J. L.; Maxwell, R. S.; Nicol, M. F.

Pressure-Induced Polymerization of Carbon Monoxide: Disproportionation and Synthesis of an Energetic Lactonic Polymer. Chem. Mater. 2006, 18, 2520-2531.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table of Contents graphic


Page 22 of 29

Page 23 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 1. (a) Convex hull of the S-N system at high pressures and 0 K. Dotted lines are used to connect the phases. (b) Pressure-phase diagram of the stable S-N compounds (SN)x, SN2, and SN4 at 0 K. 66x54mm (600 x 600 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 2. The crystal structures of sulfur nitrides (a) Pnma-(SN)x (b) Immm-(SN)x (c) SN2 (d) SN4. The yellow circles represent sulfur atoms; the blue circles represent nitrogen atoms. 45x25mm (300 x 300 DPI)


Page 24 of 29

Page 25 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 3. (a) The enthalpy difference curves of (SN)x, S2N2, S4N4. (b) The pressure-temperature diagram of (SN)x. 45x25mm (300 x 300 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 4. The simulated XRD patterns of Pnma-(SN)x, S2N2, P21/c-(SN)x, and the experimental XRD pattern (from Ref. 28). 58x42mm (300 x 300 DPI)


Page 26 of 29

Page 27 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 5. Projected density of states of sulfur atoms (fourfold coordinated and sixfold coordinated sulfur atoms) and its neighboring nitrogen atoms in Immm-(SN)x at 60 GPa. 66x55mm (300 x 300 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 6 (a,b,c) The 2D electron localization function slice of Immm-(SN)x in the (001), (100) and (010) planes, respectively. (d) The isosurface of the electron localization function with isovalue of 0.8. 52x34mm (300 x 300 DPI)


Page 28 of 29

Page 29 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 7. The electronic band structure and density of states of SN2 and SN4 at 60 GPa. The s state of nitrogen is denoted by the red circles. The p state of nitrogen is denoted by the blue circles. 50x32mm (300 x 300 DPI)


Stability of Sulfur Nitrides: A First-Principles Study - ACS Publications

Recommend Documents