Stability, Elastic Properties, and Deformation of LiBN2: A Potential

Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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Stability, Elastic Properties, and Deformation of LiBN2: A Potential High-Energy Material Chunye Zhu,* Wenjun Zhu, and Yanqiang Yang National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, Chinese Academy of Engineering Physics, Mianyang 621900, China ABSTRACT: Searching for high-energy-density materials is of great interest in scientific research and for industrial applications. Using an unbiased structure prediction method and first-principles calculations, we investigated the phase stability of LiBN2 from 0 to100 GPa. Two new structures with space groups P42̅ 1m and Pnma were discovered. The theoretical calculations revealed that Pnma LiBN2 is stable with respect to a mixture of 1/3Li3N, BN, and 1/3N2 above 22 GPa. The electronic band structure revealed that Pnma LiBN2 has an indirect band gap of 2.3 eV, which shows a nonmetallic feature. The Pnma phase has a high calculated bulk modulus and shear modulus, indicating its incompressible nature. The microscopic mechanism of the structural deformation was demonstrated by ideal tensile shear strength calculations. It is worth mentioning that Pnma LiBN2 is dynamically stable under ambient conditions. The decomposition of this phase is exothermic, releasing an energy of approximately 1.23 kJ/g at the PBE level. The results provide new thoughts for designing and synthesizing novel high-energy compounds in ternary systems.

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INTRODUCTION The search for high-energy-density materials (HEDMs) has attracted considerable interest because of their important role in energy, national defense, and aerospace.1−4 Compared with conventional energetic materials, HEDMs with high density, good thermal stability, high detonation velocity and pressure, insensitivity, and environmental safety have become the aim people seek.5−7 However, high energy and stability are quite often contradictory to each other, leading to challenging problems for the synthetic chemist to develop new HEDMs.7−9 Recently, high-nitrogen compounds have led to a new surge of interest because these compounds possess high thermal and kinetic stability and energy release capability.5,6,9−11 In 2004, polymeric N24 and CO12 were synthesized at high pressure in succession, which created a new trend of designing new HEDMs at high pressure.13 Even more interestingly, theoretical calculations showed that the polymers of CO−N2 mixtures14,15 are also potential HEDMs, providing a promising new area of synthesis of ternary HEDMs. Most recently, through structural prediction from first-principles, LiN511 and B3N516 can be formed at high pressure, and they have energy densities of about 2.72 and 3.44 kJ/g, respectively. This led to the question of whether there are ternary Li−B−N compounds that have high energy density. Moreover, it is commonly considered that there is a class of potential superhard materials formed by light elements, since these elements can form strong and short three-dimensional (3D) covalent bonds, which are fundamental motifs of superhard materials.17 If the B and N atoms form a 3D framework structure encircling the Li atoms, would the Li−B−N compounds have a superhard character© XXXX American Chemical Society

istic? Therefore, in this work, we selected LiBN2 as the representative compound to investigate the energy density and hardness properties. We here present extensive swarm structure searches on LiBN2 in an effort to attain a stable phase under high pressure. As a result, a novel capsule-shaped Pnma phase has emerged at pressures above 22 GPa. It may be recovered to ambient pressure because of its mechanical and dynamical stability. The energy density of the Pnma LiBN2 structure is around 1.23 kJ/ g. The calculated high bulk and shear moduli indicate the incompressible nature of Pnma LiBN2. The ideal strength (under tensile and shear strains) of Pnma LiBN2 has been investigated to understand the atomistic mechanism of the structural deformation.

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COMPUTATIONAL METHOD

We used the CALYPSO method18,19 with the same-named code to predict candidate stable stuctures. This method has successefully predicted structures of various systems.20−23 The structural relaxation, total energy, and electronic and elastic constant calculations were carried out using density functional theory as implemented in the VASP code.24 The electronic exchange−correlation energy was calculated in the generalized gradient approximation with the PBE functional.25 The ionic potentials were described by the projector augmented wave method26 with 1s22s1, 2s22p1, and 2s22p3 valence electron configurations for Li, B, and N atoms, respectively. The van der Waals (vdW) interactions27 were found to be too minor to affect the energetics of LiBN2, so they were not included in the calculations. Received: February 7, 2018

A

DOI: 10.1021/acs.inorgchem.8b00359 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Figure 1. Crystal structures of the predicted LiBN2 phases. (a, b) Views of the predicted P4̅21m structure along the (a) z and (b) x crystal axes. (c) Polyhedral view of the predicted Pnma structure. (d) Capsule-shaped unit in the Pnma structure. Colors: red, Li; yellow, B; blue, N. The use of an energy cutoff of 900 eV for the expansion of the electronic wave functions and Monkhorst−Pack28 k-point meshes with a grid of 0.03 Å−1 for Brillouin zone sampling were chosen to achieve excellent convergence of the total energy. The direct supercell method was adopted to calculate the phonon spectrum as implemented in the Phonopy code.29 The bulk and shear moduli were derived from the Voigt−Reuss−Hill averaging scheme.30 The previous method was used to estimate the quasistatic ideal strength.31,32 The theoretical Vickers hardness calculations were based on the bulk and shear moduli as proposed by Chen.33

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8.929 Å, b = 2.402 Å, and c = 4.153 Å, as shown in Figure 1c,d. The atomic positions are Li at the Wyckoff 4c (0.9031, 0.25, −0.3795), B at the 4c (1.3074, 0.25, −0.6623), and N at the 4c (0.7170, 0.25, −0.1407) and (0.9798, 0.25, −0.8985) sites. The structure can be seen as capsules stacking along the z axis. The B atoms are tetrahedrally bonded, similar to the P42̅ 1m structure. In addition, this structure has two types of N atoms. Atoms of the first type are shared by BN4 tetrahedra and bond with three boron atoms. Atoms of the other type are bonded to each other as bridges connecting two BN4 tetrahedra. The Li atoms are located in the cages of BN. The calculated N−N bond lengths are 1.585 Å. Three types of B−N bonds in this structure have lengths of 1.469, 1.494, and 1.560 Å, among which the one along the x axis is much longer than the others, indicating a weak interaction along the x axis. The pressure−enthalpy relationships for the predicted P4̅21m and Pnma phases of LiBN2 are presented in Figure 2. Considering that many different decomposition reactions can be defined for this compound, the stabilities were quantified in terms of formation enthalpies with respect to decompositions as follows:

RESULTS AND DISCUSSION

Considering the experimentally accessible pressure, we performed extensive structural searches on LiBN2 with one to four formula units (f.u.) in the pressure range of 0−100 GPa. We generated at least 1500 structures in generations for one CALYPSO prediction. At 0 GPa, the predicted LiBN 2 crystallizes in the tetragonal space group P4̅21m (2 f.u./cell) with lattice parameters a = b = 3.548 Å and c = 4.681 Å, as shown in Figure 1a,b. Li, B, and N occupy the Wyckoff 2c (0.5, 0, 0.4321), 2a (0, 0, 0), and 4e (0.3488, 0.1512, 0.8307) sites, respectively. Each B atom is coordinated by four nitrogen atoms, forming a tetrahedral environment. Each N atom is threefold-coordinated by two boron atoms and one nitrogen atom. BN4 tetrahedra are connected to each other by sharing of single N atoms and form layers in the xy plane. From Figure 1b, the P4̅21m structure can be seen as BN−Li−BN sandwiches stacking along the z axis. The B−N bond lengths are 1.565 Å, and the N−N bond lengths are 1.518 Å, which are close to the C−C bond lengths in diamond (1.545 Å). At higher pressures, a new orthorhombic phase (space group Pnma, 4 f.u./cell) was uncovered. At 50 GPa, the optimized lattice parameters are a =

ΔH = HLiBN2 − (HLi + HB + HN2)

(1)

ΔH = HLiBN2 − (HLiB + HN2)

(2)

⎛ ⎞ 1 ΔH = HLiBN2 − ⎜HLi + HBN + HN2⎟ ⎝ ⎠ 2

(3)

ΔH = HLiBN2 − B

⎛1 ⎞ 1 ⎜ H HN2⎟ Li3N + HBN + ⎝3 ⎠ 3

(4)

DOI: 10.1021/acs.inorgchem.8b00359 Inorg. Chem. XXXX, XXX, XXX−XXX

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in Figure 3a−c, the absence of imaginary frequency modes in the Brillouin zone confirms the dynamic stability of the P4̅21m and Pnma phases. The layered structural characteristics are responsible for the flat phonon dispersions along the highsymmetry A−M, Γ−Z, and R−X directions for P4̅21m, which reflects the weak interaction between the layers along the z axis. From Figure 3b, the flat modes along the Z−T, S−X, and U−R directions for Pnma can also be seen. The weakest B−N bonding direction is along the x axis, as mentioned above (1.560 Å). To get a better understanding of the bonding behavior of the Pnma phase, the Bader charge40 and electron localization function (ELF)41 were calculated. A charge of approximately −0.86 e/atom was transferred from the Li atom to BN cage, which reveals the ionic nature of the bonding between the BN cages and Li atoms. The large ELF values correspond to a high tendency of electron pairing, such as covelant bonds, cores, and lone pairs. Generally, the nature of the bonding is covalent, with a high ELF ≥ 0.8. As shown in Figure 3d, there are electrons that are highly localized to form B−N and N−N bonds, revealing strong covalent bonding. Large electron locations around N atoms but not in the direction of bonding explicate electrons forming localized nonbonding lone pairs. The electronic states of the N atoms are actually 3D tetrahedral-like configuration. Therefore, the N atoms are sp3hybridized and form N−N single bonds. Since there is a large energy difference between the triple and single bonds of nitrogen, substantial energy will be released once the transformation occurs from the polymeric phase back to the molecular phase. The calculated phonon dispersions (Figure 3b) confirm the dynamical stability of Pnma LiBN2 at 0 GPa,

Figure 2. Calculated enthalpies per formula unit for the predicted structures as functions of pressure relative to Li + B + N2.

Body-centered cubic (bcc) Li, I4̅3d Li, Aba2-40 Li, Cmca-24 Li,20,34 α-B12, γ-B28, α-Ga type B,35 cubic gauche N and αN2,4,36 P63/mmc LiB, NaTl-type LiB,37 cubic BN,38 Fm3̅m Li3N, P63/mmc Li3N, and P6/mmm Li3N39 were chosen as the reference phases. Under atmospheric pressure, both P4̅21m and Pnma are thermodynamically unstable toward decomposition into a mixture of Li3N, BN, and N2. Under compression to 22 GPa, the Pnma phase becomes stable toward decomposition with respect to the four reaction paths shown above. As a consequence, it should be possible to stabilize LiBN2 and to synthesize it from the parent phases. Phonon dispersions were calculated to establish the dynamical stabilities of the predicted LiBN2 phases. As shown

Figure 3. (a−c) Phonon dispersion relations of (a) P4̅21m at 0 GPa, (b) Pnma at 0 GPa, and (c) Pnma at 50 GPa. (d) Calculated ELF of Pmna at 0 GPa. The isosurface value is set at 0.8. The red, yellow, and blue balls represent Li, B, and N atoms, respectively. C

DOI: 10.1021/acs.inorgchem.8b00359 Inorg. Chem. XXXX, XXX, XXX−XXX

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Table 1. Calculated Elastic Constants Cij (in GPa), Bulk Moduli B (in GPa), Shear Moduli G (in GPa), and Hardness Values (in GPa) phase

C11

C22

C33

C44

C55

C66

C12

C13

C23

B

G

G/B

HV

P42̅ 1m Pnma bct CN2 diamond

487 304 836 1058

487 455

213 640 1269

32 212 397 569

32 189

277 192 313

26 134 150 129

70 56 120

70 88

169 217 407 439

136 193 386 524

0.81 0.89 0.95 1.19

25 35 77 93

Figure 4. Electronic band structure and partial densities of states of Pnma LiBN2 at 0 GPa. The zero of energy is at the Fermi level.

Figure 5. (left) Tensile stress vs strain for Pnma LiBN2 in various tension deformation directions. (right) Structural snapshots corresponding to key points before and after the large drop of stress in the ⟨100⟩ direction.

criteria for the orthorhombic structure are44 C11, C22, C33, C44, C55, and C66 > 0, C11 + C22 + C33 + 2(C12 + C13 + C23) > 0, (C11 + C22 − 2C12) > 0, (C11 + C33 − 2C13) > 0, and (C22 + C33 − 2C23) > 0. Our calculated Cij for the P42̅ 1m and Pnma phases satisfy the above criteria, confirming that these two phases are mechanically stable. The elastic constant C33 for the Pnma phase is larger than others, indicating that this phase is extremely incompressible along the z direction. The bulk modulus B and shear modulus G can be determined by the Voig−Reuss−Hill approximation method.30 The smaller bulk and shear moduli of P4̅21m are due to its layered stacking along the z axis. Although the calculated moduli of the Pnma phase are also much smaller than those of bct CN2 and diamond, the calculated mechanical properties are very close to those of SiC (B = 225 GPa, G = 192 GPa)45 and

suggesting that it is possible to be quench-recoverable. The energy for decomposition of Pnma LiBN2 into 1/3Li3N, BN, and 1/3N2 at ambient pressure is estimated to be 0.59 eV per unit at the PBE-GGA levelthe equivalent of an energy density of approximately 1.23 kJ/g. The energy density of Pnma LiBN2 is very close to those of modern explosives such as TATB, RDX, and HMX (energy densities in the range of 1−3 kJ/g42). We next characterized the mechanical properties of LiBN2 and obtained the results shown in Table 1. Diamond and bodycentered tetragonal (bct) CN243 are also added in Table 1 for comparison. A stable crystal should meet the criteria of elastic stability. For the tetragonal structure, the necessary stability criteria are44 C11, C33, C44, and C66 > 0, C11 and C12 > 0, C11 + C33 − 2C13 > 0, and 2(C11 + C12) + C33 + 4C13 > 0. The stability D

DOI: 10.1021/acs.inorgchem.8b00359 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 6. (left) Shear stress vs strain for Pnma LiBN2 in the (100) and (101) planes. (right) Structural snapshots corresponding to key points before and after the large drop of stress in the (101)[101̅] direction.

component. Near the peak stress at the tensile strain ε = 0.138, the B4−N6 bond (as same as B2−N8) is stretched from 2.013 Å at T1 to 3.314 Å at T2, which demonstrates the breaking of the B−N bonds. The easiest cleavage planes are generally determined by the weakest tensile directions.51,52 The peak of tensile stresses along the ⟨100⟩ direction are closed to those along the ⟨101⟩ direction, implying that these two planes are viably cleaved. The stress−strain relationships for these two shear planes along various shear directions are displayed in Figure 6. The (101)[101̅] direction is identified to be the weakest shear direction, with a peak shear stress of 20.0 GPa. The right panels of Figure 6 display the deformation and failure process of Pnma LiBN2 for shear along the least-stress slip system (101)[101̅]. As the shear strain reaches 0.187, the B4− N6 bond is stretched from 2.037 Å at S1 to 4.121 Å at S2 and breaks. Similarly, another B2−N8 bond is stretched from 2.037 to 3.856 Å. The failure mechanism of shear strain−stress is the same as the condition of tensile strain−stress, which is the direct deconstruction of the capsule structure from the B−N bond breaking. The calculated results prove that the collapse of the Pnma LiBN2 structure is mainly of the tensile type, which is similar to bct CN2. It is known that ideal strength is widely confirmed and a benchmark quantity in assessing the hardness. The ideal strength (15.0 GPa) is significantly smaller than the calculated hardness (35 GPa). This is mainly due to the fact that the empirical hardness models tend to overestimate the hardness of open-framework structures. The lower ideal strength of Pnma LiBN2 is due to the localized lone-pair nonbonding states around N atoms, compared with covalent bonds, which under large strain are much more flexible.

some transition metal carbides (e.g., B = 242 GPa, G = 188 GPa for TiC;46 B = 223 GPa, G = 170 GPa for ZrC47). Since there is an intrinsic correlation between elasticity and hardness of materials, the Vickers hardness (HV) for polycrystalline materials is derived from the values of G and B,33 leading to HV values of 25 and 35 GPa for the P4̅21m and Pnma phases of LiBN2, respectively. This model predicts a remarkably high hardness for the Pnma phase that is close to those of superhard materials (hardness > 40 GPa), allowing it to be classified as a hard materials (hardness > 20 GPa). The partial densities of states (pDOS) and electronic band structure were calculated to understand the electronic properties of Pnma LiBN2, as shown in Figure 4. Our results show the nonmetallic nature of this phase, with an indirect band gap of 2.3 eV. N 2p states make the main contribution to the DOS around the Fermi level. At around −8 eV, the B 2s states exhibit a strong peak. The pDOS profiles for B 2s (around −8 eV), B 2p (−4 to −7 eV), and N 2p are very similar, reflecting the fact that boron is sp3-hybridized and forms BN4 tetrahedra, thus indicating the covalent characteristics of B−N bonds. To bring out the fundamental connection between the mechanical response of Pnma LiBN2 and the chemical bonding, we applied a quasistatic relaxation method to calculate the deformation modes and ideal strength under various strain conditions. The lowest peak stress under various types of strains defines the corresponding ideal strength at which a perfect crystal becomes mechanically unstable.48−50 In order to identify the easiest cleavage plane of Pnma LiBN2, the ideal tensile strength was calculated along different high-symmetry directions. The ⟨001⟩ direction of Pnma LiBN2 shows peak tensile stress, indicating a strong stress response in this direction, as shown in Figure 5. In fact, ⟨001⟩ is just the direction of the N−N and B−N zigzag chain. The strong covalent bonding makes it have a higher ideal strength under larger strain. At the tensile strain ε = 0.116, N−N bonds along the z axis break, and the B−N bonds along the z axis are the main load-bearing component. The ⟨100⟩ direction is identified to be the weakest tensile direction, with a peak tensile stress of 15.0 GPa. The ⟨100⟩ direction corresponds to the direction of the weakest B−N bonds (corresponding to the largest B−N bond length). The structural deformation modes are shown in the right panel of Figure 5 at corresponding strains in order to unravel the bonding-state mechanism in its weakest tensile deformation direction. Structural snapshots show that the bonding between boron and nitrogen is the main load-bearing

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CONCLUSIONS By the CALYPSO method, a new ternary compound, LiBN2, has been predicted to adopt an orthorhombic Pnma structure and, with reference to the decomposition path, to be thermodynamically stable under hydrostatic pressures above 22 GPa. The dynamical and mechanical stabilities of Pnma LiBN2 have been demonstrated by phonon and elastic constant calculations at ambient pressure, respectively. Pnma LiBN2 is found to be a wide-gap semiconductor with an indirect energy gap of 2.3 eV. Moreover, at ambient pressure LiBN2 is expected to release considerable energy (1.23 kJ/g) under the decomposition into 1/3Li3N, BN, and 1/3N2. The calculated bulk modulus of 217 GPa and shear modulus of 193 GPa are close to those of traditional hard materials (SiC, TiC, ZrC, E

DOI: 10.1021/acs.inorgchem.8b00359 Inorg. Chem. XXXX, XXX, XXX−XXX

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etc.), which show an incompressible nature. The ideal strength calculations demonstrate that Pnma LiBN2 can withstand a great deal of strain, with a tensile strength of 15.0 GPa and a shear strength of 20.0 GPa. Thus, Pnma LiBN2 has good stability under impact and friction as a high-energy material. The current study will advance and develop novel ternary compounds for HEDMs and encourage experimental synthesis.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Chunye Zhu: 0000-0001-8761-6788 Wenjun Zhu: 0000-0002-8001-6605 Yanqiang Yang: 0000-0003-2184-8126 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS C.Z. acknowledges funding from the National Natural Science Foundation of China under Grant 11704355 and a project funded by the China Postdoctoral Science Foundation under Grant 2016M590902, C.Z. and Y.Y. acknowledge the funding from Science Challenge Project TZ2016001. Computational resources were provided by the National Supercomputer Center in Guangzhou.

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DOI: 10.1021/acs.inorgchem.8b00359 Inorg. Chem. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.inorgchem.8b00359 Inorg. Chem. XXXX, XXX, XXX−XXX