#
Novel Functional Materials of Hydrogen Storage B_{20}N_{24}: A First-Principles Calculation

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

_{20}N

_{24}is proposed through first-principles calculations. The stability of the B

_{20}N

_{24}polymorph at ambient conditions is confirmed using the phonon dispersion spectra and the Born stability criteria. Electronic properties calculations show that B

_{20}N

_{24}exhibits a semiconducting feature, with a 0.87 eV direct band gap derived from HSE06 functions, which is much lower than many other B–N polymorphs. Specifically, owing to its cage-like framework, B

_{20}N

_{24}may be used in hydrogen storage at a capacity of ~6.8 wt.%. The B

_{20}N

_{24}polymorph enriches the B–N system theoretically, and this polymorph is promising for use in electronic devices and hydrogen storage.

## 1. Introduction

_{12}N

_{12}and B

_{36}N

_{36}fullerene-like cluster, can be constructed [10,11,12]. Previous studies showed that the stoichiometric BN compound with purely B–N bonds in crystal structures is the generally stable framework and that nonstoichiometric frameworks may lead to energetic, unfavorable B–B and N–N dimers. However, nonstoichiometric BN structures have also been constructed in previous studies. Simone et al. [13] reported the first-principles calculations of the role of stoichiometry in the structure and energy of BN clusters. Results showed that B

_{32}N

_{36}and B

_{60}N

_{64}are more stable than their stoichiometric counterparts in a N-rich environment, even when dimers exist in the framework. Simultaneously, B–B and N–N bonds are unavoidable in these B-rich or N-rich BN polymorphs, and the reality is unclear as to the stability of N-rich B–N compounds which are constructed with purely B–N bonds.

_{1}-B

_{3}N

_{5}was a metastable material that can be recovered under ambient conditions, making it a promising high-energy-density material with an energy density of 3.44 kJ/g. Additionally, stress–strain calculations estimated a Vicker’s hardness of approximately 44 GPa. Structure searching also revealed a new sodalite-like clathrate BN structure that was metastable under ambient conditions. He et al. [27] reported that t-B

_{3}N

_{4}, with structural units composed of sp

^{3}c-BN blocks and sp

^{2}N–N bonds, is metastable at ambient pressure but becomes energetically more stable than layered B

_{3}N

_{4}, h-BN, or N

_{2}under pressure. The electronic structure analysis showed that t-B

_{3}N

_{4}was planar conductive with conduction interrupted by insulated B atomic layers along the c-axis. This unique 2D metallicity in 3D t-B

_{3}N

_{4}has potential applications in electronic devices. The calculated Vickers hardness of t-B

_{3}N

_{4}exceeded 40 GPa, indicating its superhard nature. Moreover, due to the strong N–N bonds along the c-axis, the axial ultra-incompressibility of t-B

_{3}N

_{4}was even greater than that of c-BN and diamond. This type of boron nitride exhibited the combined electrical and mechanical properties of 2D metallicity in a 3D framework, in addition to superhardness and ultra-incompressibility. These findings open a new view of B–N functional materials.

_{1}-B

_{3}N

_{5}, B

_{2}N

_{3}) and metallic t-B

_{3}N

_{4}, have been predicted as novel functional materials, behaving as potential high-energy-density materials, due to the high energy of N–N dimers in their framework. In this work, B

_{20}N

_{24}is constructed with fully B–N bonds, indicating that it is not a potential high-energy-density material. Moreover, hydrogen as a renewable energy has drawn people’s attention for many years, but one limited problem in its widespread application is the storage medium. In terms of advantages in gravimetric density, light element compounds, such as carbon materials, including C

_{60}fullerene and carbon nanotube, are good candidates for hydrogen storage. In recent years, extensive studies showed that porous BN polymorphs and BN cages exhibit promising applications in hydrogen storage [29,30]. For example, studies showed that BN nanotubes can store hydrogen at as much as 2.6 wt.% [29], and the B

_{36}N

_{36}cage can reach to 4 wt.% [30]. Considering the cage-like structural features and low density of B

_{20}N

_{24}, it might be a candidate for hydrogen storage.

_{20}N

_{24}polymorph as a candidate for hydrogen storage is predicted.

## 2. Calculation Methods

_{ij}were derived based on the strain–stress relationship (Hooke’s law), which is within the range of elastic deformation; a finite strain was applied to the optimized structure, and the applied strain and the resulting stress were obtained [30]. The maximum applied strain amplitude was 0.3%, and the number of steps for each strain was set to 9 for this calculation. To verify the accuracy of our calculations, we calculated the lattice parameters and bond length for diamond and cubic BN. The results show that the lattice parameters of diamond and cubic BN are a = 3.528 Å and a = 3.580 Å, and the bond lengths of the C–C and B–N bonds are 1.528 Å and 1.550 Å, respectively, which are close to the results derived from experiments (3.567 Å and 1.545 Å for diamond, 3.615 Å and 1.565 Å for cubic BN). Therefore, we supposed that the calculations in this paper are feasible.

## 3. Results and Discussion

_{8}[40] were obtained. These results confirmed the feasibility of our structural search methodology. Firstly, carbon allotropes with 8~30 atoms in per unit cell were systematically explored based on the first-principles calculations. Secondly, according to the geometries of carbon structures, we have selected some of the special configurations. During this process, these structures with odd rings are thrown away to avoid forming high energy B–B/N–N bonds in the atom’s process of subsequent change. Therefore, some cage-like carbon structures composed of even-membered rings are retained. Finally, carbon atoms are replaced with B and N atoms alternatively to avoid B–B/N–N bonds in the search for stable nonstoichiometric B–N polymorphs. Notably, according to the low energy and structure features, six cubic carbon allotropes, which had 7, 28, 44, 52, and 60 atoms in per unit cell, respectively, are selected among thousands of obtained novel carbon structures. The structural and geometric properties of these selected allotropes are investigated. The results show a mechanical and dynamical stable structure among these obtained structures, which is named as B

_{20}N

_{24}.

_{20}N

_{24}. At ambient pressure, three nonequivalent atoms assemble in a cubic lattice (space group I-43m) with a = b = c = 7.01 Å lattice parameter (Figure 1a). The Wyckoff atom positions of two nonequivalent B atoms, B1 and B2, are occupied 2d (0, 1/2, 1/4), 8c (0.3, 0.7, 0.3), and one N1 atom is occupied 24g (0.126, 0.625, 0.874), respectively. Figure 1a shows the primitive cell of the B

_{20}N

_{24}polymorph. B1-N1-B2 atoms composed the hexagonal rings which can be viewed as puckered hBN layers, and these layers are connected to form a three-dimensional (3D) periodicity structure via sp

^{3}-hybrid B2 atoms. As shown in Figure 1b, the unit cell of the B

_{20}N

_{24}polymorph can be viewed as a cage-like structure, one which the hBN-liked layers connected with B–N single bonds to form a cage with an open boundary. The opened cage-like structure connects with the gap’s overlapping and forms a 3D cage-like network with different cage-size in it (Figure 1c). The B1 atom at the 8c site is a trigonal coordinate with a trigonal N atom added to form B–N bond with length of d

_{1}= 1.43 Å, which is close to that of the sp

^{2}-hybrid B–N bonds in hBN. The B2 atom at the 12d site is a tetragonal coordinate with a trigonal N atom with a B–N distance of d

_{1}= 1.52 Å; when the two combine cages together and construct the 3D N-rich BN allotropes, it is comparable to the sp

^{3}-hybrid B–N bonds in cBN structure.

_{20}N

_{24}polymorph, we calculated the formation energy via alpha-B and alpha-N

_{2}as precursors; the results of the convex hull of B–N compounds are plotted in Figure 2. As shown in Figure 2, the formation energies of some other B–N polymorphs are determined per-atom for comparison. As previous studies show, the layer-like h-B

_{3}N

_{5}and h-B

_{2}N

_{3}structures are stable at ambient pressure, and the bulked C

_{2221}-B

_{3}N

_{5}[26] and t-B

_{2}N

_{3}[28] are metastable, which can derive from the stable phase under high pressure conditions. Additionally, the bulked t-B

_{3}N

_{4}[27] is at a metastable phase at ambient pressure. One can see that the formation energy of B

_{20}N

_{24}is beyond the line at the N-rich part, so we have supposed that the B

_{20}N

_{24}polymorph is at a metastable phase at ambient pressure.

_{20}N

_{24}is validated by elastic constants calculations. The calculated elastic constants are C

_{11}= 427.0 GPa, C

_{44}= 240.4 GPa, and C

_{12}= 184.2 GPa, respectively. The structure of B

_{20}N

_{24}possesses cubic lattice and the known Boron stability criteria for cubic lattice [41], i.e., C

_{11}> 0, C

_{44}> 0, C

_{11}> |C

_{12}|, (C

_{11}+ 2C

_{12}) > 0. Obviously, these elastic constants satisfy the Boron stability criteria, thereby confirming that B

_{20}N

_{24}is mechanically stable. Phonon dispersion curves were used to confirm the dynamic stability of B

_{20}N

_{24}, which is characterized by a lack of imaginary frequencies across the whole spectrum; the results are plotted in Figure 3. No imaginary frequency is observed across the whole Brillion Zone, indicating that B

_{20}N

_{24}is dynamically stable. Therefore, we suppose that the B

_{20}N

_{24}polymorph is at a metastable phase at ambient conditions.

_{20}N

_{24}are studied by calculating the band structures and corresponding partial density of state (PDOS); the results are plotted in Figure 4. As shown in Figure 4a, the B

_{20}N

_{24}structure exhibits a 0.87 eV direct band gap. In order to study the origination of valance band minima (VBM) and conductive band maximum (CBM), we further calculated the PDOS of three nonequivalent atoms PDOS in the framework, and the results are shown in Figure 4b–e. In Figure 4b, the electronic states at the Fermi level originate from the 2p orbits, and Figure 4c–e shows that the CBM and most of the VBM of B

_{20}N

_{24}are contributed from the 2p state of N1 atoms. The contributions of B1 and B2 atoms to the CBM and VBM can be neglected.

_{2}molecule storage in B

_{20}N

_{24}has been studied systematically. For a single H

_{2}molecule, we set it as occupying the center of the B

_{20}N

_{24}cage and ignore other simultaneous sites. In other conditions, ones with more than one H

_{2}molecule, H

_{2}molecules are laid into the B

_{20}N

_{24}cage randomly and kept isolated from each other, keeping the distance between two H

_{2}molecules larger than 0.74 Å (the H–H bond length in a H

_{2}molecule). The calculated formation energies with different n values are plotted in Figure 5. The formation energy of the nH

_{2}@B

_{20}N

_{24}complex is defined as: E

_{f}= E

_{(BN+nH2)}− E

_{BN}− nE

_{H2}, where E

_{(BN+nH2)}is the total energy of nH

_{2}@B

_{20}N

_{24}complex, E

_{BN}and E

_{H2}are the total energy of B

_{20}N

_{24}and H

_{2}molecules, respectively, and n stands for the number of H

_{2}molecules set in the B

_{20}N

_{24}polymorph. Figure 6 shows the atomic configurations of the nH

_{2}@B

_{20}N

_{24}complex. At n = 1, the H

_{2}molecule is set at the center of the framework (Figure 6a). Figure 6b shows the H

_{2}@B

_{20}N

_{24}complex after full geometrical optimization; the formation energy is −0.28 eV/atom. The H

_{2}molecule is isolated in the B

_{20}N

_{24}cage, B-H and N-H bonds are not presented in this complex, and the H

_{2}molecule has a stretched H-H bond length of 0.777 Å. The volume of the complex (348.8 Å

^{3}) is larger than that of B

_{20}N

_{24}(347.5 Å

^{3}), which means that the H

_{2}molecule brings out a structural deformation. As we know, a negative formation energy means an exothermic reaction and energetic-favorable status, indicating that the nH

_{2}@B

_{20}N

_{24}complex is stable relative to decomposition into a B–N compound and H

_{2}molecules. Therefore, we supposed that it was possible to form H

_{2}@B

_{20}N

_{24}complex at ambient conditions with a suitable precursor and method. As H

_{2}molecules increase, the distance between H

_{2}molecules becomes shorter and shorter, resulting in repulsive interactions between H

_{2}molecules; the attractive interactions between H

_{2}molecules and B/N atoms increase correspondingly. This induced a change in the bonding conditions of the complex after the full relaxation of the complex.

_{2}molecules in the B

_{20}N

_{24}cage move away from their initial position where we have set them initially, leading to some of the H

_{2}molecules remaining molecular and some others not. Giving the dangling bonds in the configuration, some H

_{2}molecules dissociate to bind with N/B atoms and form N-H/B-H bonds (Figure 6c). Interestingly, during this process, H atoms bind with N atoms more than with B atoms; this might be caused by fact that the N atom has higher electronegativity difference than does the B atom. The sp

^{3}rehybridization of the formation of N-H/B-H bonds minimizes the total energy of the complex, and as the number of H

_{2}molecules increases, the number of dissociated H

_{2}molecules is decreased. Thus, the formation energy decreases from n = 1 to n = 10, and has a minimum value at n = 10, illustrating that the 10H

_{2}@B

_{20}N

_{24}complex is the most stable state of the nH

_{2}@B

_{20}N

_{24}complex. After that, as the H

_{2}molecule increases, at n = 11–16, the total energy of complex increases and tends to become positive. We supposed that this is because, with the increase of the number of hydrogen molecules in this BN structure, the framework of nH

_{2}@B

_{20}N

_{24}complex acquires more and more deformation. In this, B–N bonds are expanded, thereby inducing the high energy of B–N chemical bonds; also, the repulsion between H atoms is increased as the distance of H atoms grows closer, in order to attain the equilibrium state for the complex. Therefore, the energy levels of the nH

_{2}@B

_{20}N

_{24}complexes are raised. For nH

_{2}@B

_{20}N

_{24}complexes with n = 17, 18, and 19, the formation energies are positive, indicating that the storage is an endoergic reaction. When n = 20, several B–N bonds, such as the bond between the B–N pair (marked with red circles in Figure 6d), are stretched to ~1.75 Å, showing that B–N bonds are destroyed, while the H

_{2}molecules remain in the cage. However, the number of n increases to 21, and the framework of the nH

_{2}@B

_{20}N

_{24}complex is broken, resulting in a number of escaped H

_{2}molecules. Therefore, the maximum H

_{2}molecule storage capacity of H

_{2}@B

_{20}N

_{24}is 19, which corresponds to a gravimetric proportion of 6.8 wt.%.

_{20}N

_{24}structure, its storage ability is excellent. As we know, B–N materials are synthesized compounds. These materials are widely used in industries; most of the B–N compounds are semiconductors with wide band gap, and thus, they are also used in electronics. In recent years, more and more B–N materials have been predicted with the help of computational materials science. The studies of the novel structure of this class not only widen the crystal structure information relevant to it, but can also reveal more possible physical properties within the theoretical space. For one thing, in terms of structural configurations, the results in this work provide a useful method for structural prediction, not only in B–N compounds, but also in many other classes. For another, we provide a new way to design functional material. For example, the cage-like structure can be a candidate in hydrogen storage, and a fully sp

^{3}-hybridzed carbon or BN structure may be a good candidate among superhard materials.

_{20}N

_{24}structure in this study is determined at 0 K. Considering the vibrations of atoms, the periodic boundary condition and some other conditions during the calculations at 0 K and 300 K, we supposed that the hydrogen storage capacity of B

_{20}N

_{24}may not be as high as 6.8 wt.%. The hydrogen storage capacity of these B–N compounds at room temperature or at any other temperature, can be derived via molecular dynamics. Normally, it may be lower than the result at 0 K. Theoretically, determining the actual capacity of B

_{20}N

_{24}at 300 K would require more calculations to reveal. In this work, the B

_{20}N

_{24}structure is proposed as a novel compound of the B–N system, and can be viewed as a candidate for hydrogen storage, given its highly chemical inertness and cage-like structure.

## 4. Conclusions

_{20}N

_{24}is here proposed as a thermodynamically metastable nonstoichiometric N-rich B–N polymorph at ambient pressure. The mechanical and dynamic B

_{20}N

_{24}has stabilities confirmed by the Born criteria and phonon spectra, respectively. B

_{20}N

_{24}displays semiconducting features, with a 0.85 eV direct band gap. On the basis of its structural features, B

_{20}N

_{24}can be seen as a candidate for hydrogen storage. Results show that 19 H

_{2}molecules, corresponding to 6.8 wt.%, can be stored in B

_{20}N

_{24}. B

_{20}N

_{24}enriches the structures of B–N compounds, and its unique properties render it a promising functional material for electronic and hydrogen storage applications.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Structural configurations of B

_{20}N

_{24}: (

**a**) primitive cell, (

**b**,

**c**) unit cell. The pink and blue balls stand for B and N atoms, respectively.

**Figure 2.**Convex hull diagram for the B−N compound at ambient pressure. The formation energies are defined as ΔH = [1/(x + y)]H(BxNy) − [xH(B) +yH(N)]), in which the alpha-B phase and alpha-N

_{2}structures are used in the formula, respectively.

**Figure 4.**Electronic properties of B

_{20}N

_{24}structure: (

**a**) band structure, (

**b**) PDOS, and (

**c**–

**e**) PDOS of N1, B1, and B2 atoms, respectively. The dotted lines reprents Femi level.

**Figure 5.**Formation energies of the nH

_{2}@ B

_{20}N

_{24}complex as a function of the number of H

_{2}molecules stored.

**Figure 6.**Configurations of the nH

_{2}@B

_{20}N

_{24}complex as more and more H

_{2}molecules are stored. The pink, blue and white balls stand for B, N and H atoms, respectively: (

**a**) B

_{20}N

_{24}; (

**b**) H

_{2}@B

_{20}N

_{24}; (

**c**) 19H

_{2}@B

_{20}N

_{24}; (

**d**) 20H

_{2}@B

_{20}N

_{24}.

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## Share and Cite

**MDPI and ACS Style**

Zhao, J.; Huo, Z.; Xu, S.; Xiong, M.; Liu, D.; Wang, Y.; Jia, X.
Novel Functional Materials of Hydrogen Storage B_{20}N_{24}: A First-Principles Calculation. *Crystals* **2023**, *13*, 1029.
https://doi.org/10.3390/cryst13071029

**AMA Style**

Zhao J, Huo Z, Xu S, Xiong M, Liu D, Wang Y, Jia X.
Novel Functional Materials of Hydrogen Storage B_{20}N_{24}: A First-Principles Calculation. *Crystals*. 2023; 13(7):1029.
https://doi.org/10.3390/cryst13071029

**Chicago/Turabian Style**

Zhao, Jing, Zhongtang Huo, Shuailei Xu, Mei Xiong, Dezheng Liu, Yikun Wang, and Xin Jia.
2023. "Novel Functional Materials of Hydrogen Storage B_{20}N_{24}: A First-Principles Calculation" *Crystals* 13, no. 7: 1029.
https://doi.org/10.3390/cryst13071029