First-Principles Study of Three-Dimensional Electrides Containing One-Dimensional [Ba3N]3+ Chains.

Electrides, a unique type of compound where electrons act as anions, have a high electron mobility and a low work function, which makes them promising for applications in electronic devices and high-performance catalysts. The discovery of novel electrides and the expansion of the electride family have great significance for their promising applications. Herein, we reported four three-dimensional (3D) electrides by coupling crystal structure database searches and first-principles electronic structure analysis. Subnitrides (Ba3N, LiBa3N, NaBa3N, and Na5Ba3N) containing one-dimensional (1D) [Ba3N]3+ chains are identified as 3D electrides for the first time. The anionic electrons are confined in the 3D interstitial space of Ba3N, LiBa3N, NaBa3N, and Na5Ba3N. Interestingly, with the increase of Na content, the excess electrons of Na5Ba3N play two roles of metallic bonding and anionic electrons. Therefore, the subnitrides containing 1D [Ba3N]3+ chains can be regarded as a new family of 3D electrides, where anionic electrons reside in the 3D interstitial spaces and provide a conduction path. These materials not only are experimentally synthesizable 3D electrides but also are promising to be exfoliated into advanced 1D nanowire materials. Furthermore, our work suggests a discovery strategy of novel electrides based on one parent framework like [Ba3N]3+ chains, which would accelerate the mining of electrides from the crystal structure database.

Introduction

Electrides are a unique type of compound in which electrons occupy interstitial space and serve as anions.[1,2] Therefore, electrides exhibit a variety of unique properties, such as high electron mobility and low work function, which makes them promising for applications in electronic devices and high-performance catalysts.[3] According to the dimensions of anionic electrons, electrides can be classified into zero-dimensional (0D), one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) electrides.[4] Until now, 167 materials from the Inorganic Crystal Structure Database (ICSD) have been identified as electrides by automated screening, including 77 0D, 52 1D, and 38 2D electrides.[5] However, 3D electrides from the ICSD have not been reported. In this work, we look for 3D electrides in the subnitride system from the ICSD.

The alkali-earth metal subnitrides have gained a lot of curiosity recently because of their special electronic structure.[6,7] Unlike common inorganic compounds, the standard rules of valency are invalid for subnitrides since the number of electrons is more than the expected based on well-established electron counting rules.[8] One typical example of subnitrides is Ca2N, which was determined as a layered structure of the anti-CdCl2 type using single-crystal X-ray diffraction in 1968.[9] Sr2N is isostructural with Ca2N and was identified by Gaudé et al. in 1972.[10] Although both of the subnitrides were reported early but their electronic properties had not been revealed until recent years. In 2000, Gregory et al. confirmed that Ca2N is metallic and paramagnetic at room temperature.[11] In 2013, Lee et al. demonstrated that Ca2N is a 2D electride in which conduction electrons are confined between [Ca2N]+ layers with a concentration in good agreement with the chemical formula [Ca2N]+·e–.[6] The 2D nature of its electronic structure was confirmed by both transport measurements and a band calculation. Ca2N can be exfoliated into 2D nanosheets using liquid exfoliation.[12] Moreover, Ca2N has a very small work function, making it attractive for use as an electron donor.[13−16] Shortly afterward, Walsh and Scanlon calculated the electronic structures of Sr2N and Ba2N and showed that they are also 2D electrides similar to Ca2N.[8]

Another typical example of subnitrides is Ba3N, which was synthesized under harsh reaction conditions by Steinbrenner and Simon in 1998.[17] Ba3N crystallizes in the anti-TiI3 structure type, and represents a hexagonal close packing of ∞1[NBa6/2] chains. Actually, the first subnitride of Ba and Na, NaBa3N, was reported by Rauch and Simon as early as 1992.[18] The thermal decomposition of NaBa3N under high vacuum could form Ba3N.[17] In the hexagonal structure of NaBa3N, the Ba and N atoms form ∞1[NBa6/2] chains, while single Na atoms are arranged between these chains. In 1995, Snyder and Simon reported another subnitride of Ba and Na, Na5Ba3N.[19] Its structure contains ∞1[NBa6/2] chains nearly identical with those found in NaBa3N. In 2007, Smetana et al. reported two subnitrides of Ba and Li, LiBa2N and LiBa3N. LiBa2N has a tetragonal structure (space group, P42/nmc), and its structure contains infinite mutually perpendicular rows of edge-sharing NBa5Li octahedra, and LiBa3N is isostructural with NaBa3N.[20] The subnitrides of alkaline earth metals and alkali metals are still being excavated these years,[21−26] although all subnitrides are both air- and water-sensitive.

There is continuing interest in the electronic properties of the subnitrides.[27−29] Recently, Park et al. reported that Ba3N is identified as a new electride via first-principles calculation and claimed that anionic electrons are aligned in a 1D manner along an interstitial channel.[30] Zhou et al. carried out a first-principles calculation of LiBa2N, identifying it as a new electride, wherein both of Ba and Li provide anionic electrons in different distributions, yielding LiBa2N a unique electride with a coexistence of 1D and 0D anionic electrons.[31] The objective of the present work is to demonstrate that the Ba3N, LiBa3N, NaBa3N, and Na5Ba3N subnitrides containing ∞1[NBa6/2] chains are identified as 3D electrides through detailed electronic structure analysis including the electron localization function (ELF), band structure, density of states (DOS), partial charge density, and work function. Furthermore, our work suggests a discovery strategy of novel electrides based on one parent framework like [Ba3N]3+ chains, which may accelerate the discovery of more novel electride family.

Calculation Methods

Density functional theory (DFT) calculations were implemented using the generalized gradient approximation (GGA) Perdew–Burke–Ernzerhof (PBE) functional,[32] and the projected augmented plane-wave (PAW) method[33] was implemented using the Vienna Ab-initio Simulation Package (VASP) code. We also employed a van der Waals (vdW) scheme corrected on top of the PBE functional (PBE-D2,[34] PBE-D3,[35] and PBE-dDsC[36]). The plane-wave basis-set cutoff was set to 500 eV. Self-consistent solutions of the Kohn–Sham equations were obtained by employing 2 × 2 × 2 Monkhorst-Pack grids of k-points to perform integration over the Brillouin zone.[37] Relaxed atomic positions were obtained by using the total energy and force minimization methods. The convergence criterion of energy and force is 2 × 10–5 eV and 0.02 eV/Å. The full electronic DOS was also calculated with a high k-point sampling of 4 × 4 × 4. The ELF[38] was calculated to determine whether the electrons were confined in the interstitial space.

Results and Discussion

Structures

Ba3N crystallizes in the hexagonal space group P63/mcm.[17] In the asymmetric unit, there are one unique Ba atom and one unique N atom. Figure a shows the crystal structure of Ba3N along the c-axis. The Ba and N atoms form an infinite ∞1[NBa6/2] chain along the c-axis composed of face-sharing NBa6 octahedra. The energetic stability of a material against spinodal decomposition in thermodynamics is determined uniquely by convex hull phase diagrams.[39] The formation energies of the Ba–N system are given in Table S1 and Figure S1 in the Supporting Information, all the chemical formulas correspond to experimentally existing stable crystalline materials in the Materials Project database[40] and ICSD. Ba2N and Ba are the only required reference materials to uniquely determine the thermodynamic stability of Ba3N. The formation energy of Ba3N is negative (−7.25 meV/atom) with respect to Ba2N and Ba, indicating the thermodynamic stability of Ba3N. Actually, Ba3N is an experimentally synthesizable material.[17]

Figure 1

Structure of Ba3N (a) and NaBa3N (b) as viewed along the c-axis and Na5Ba3N (c) as viewed along the b-axis. A side view of an isolated ∞1[NBa6/2] chain is also shown in (a). The green, gray, and orange spheres, respectively, denote Ba, N, and Na atoms.

NaBa3N[18] and LiBa3N[20] crystallize in the hexagonal space group P63/mmc. Because NaBa3N and LiBa3N are isostructural, only the structure of NaBa3N will be discussed in detail. In the asymmetric unit of NaBa3N, there are one unique Na atom, one unique Ba atom, and one unique N atom. Figure b shows the crystal structure of NaBa3N along the c-axis. The Ba and N atoms form an infinite ∞1[NBa6/2] chain along the c-axis composed of face-sharing NBa6 octahedra, with single Na atoms arranged between these parallelly arranged ∞1[NBa6/2] chains. The formation energy of NaBa3N is negative (−17.4 meV/atom) with respect to Ba3N and Na, indicating the thermodynamic stability of NaBa3N. In fact, NaBa3N has been synthesized experimentally.[18] Note that there is a π/6 rotation of the ∞1[NBa6/2] chain of NaBa3N with respect to those of Ba3N. The distance between chains of NaBa3N (8.44 Å) is significantly larger than that of Ba3N (7.64 Å), while the smallest chain-chain bond length of NaBa3N (4.80 Å) is close to that of Ba3N (4.87 Å). However, in the ionic compound Ba3NBi,[41] which is isostructural with NaBa3N, the distance between chains (7.61 Å) is almost the same as that of Ba3N (7.64 Å), while the smallest chain-chain bond length (3.95 Å) is significantly smaller than that of Ba3N (4.87 Å). These results indicate that NaBa3N is not a common ionic compound.

Na5Ba3N crystallizes in the orthorhombic space group Pnma.[19] In the asymmetric structure, there are four unique Na atoms, three unique Ba atoms, and one unique N atom. The crystal structure of Na5Ba3N, projected along the b-axis is shown in Figure c. The infinite ∞1[NBa6/2] chains along the b-axis are very similar to those in NaBa3N, but slightly distorted. The difference is the presence of more Na atoms in the areas between the ∞1[NBa6/2] chains in Na5Ba3N, as compared to NaBa3N, which leads to the distance between chains of Na5Ba3N (10.71 Å) to be much larger than NaBa3N (8.44 Å). The formation energy of Na5Ba3N is negative (−9.11 meV/atom) with respect to Ba3N and Na, indicating the thermodynamic stability of Na5Ba3N. Actually, Snyder and Simon have synthesized Na5Ba3N experimentally.[19]

The nearest Ba–Ba interatomic distance (4.87 Å) between the ∞1[NBa6/2] chains in Ba3N is 0.53 Å greater than that in the elemental metal Ba (4.34 Å), which excludes the possibility of direct Ba–Ba bonding. The bond length is another indication supporting ionic bonding characteristic.[6,39] Within the ∞1[NBa6/2] chain of Ba3N, the bond lengths of Ba–N are extremely close to the sum of the respective ionic radii. The Ba–N bond length is 2.726 Å, which is in close proximity to the sum of the ionic radii of Ba2+ (1.35 Å) and N3– (1.46 Å). The ∞1[NBa6/2] chain of Ba3N can be regarded as a positively charged ionic chain, [(Ba2+)3N3–]3+. To compensate for the positive charge of the [Ba3N]3+ chains, the interstitial space of Ba3N should work as a confinement space for the anionic electrons, resulting in a [Ba3N]3+·3e– configuration. Within the ∞1[NBa6/2] chain of LiBa3N, NaBa3N, and Na5Ba3N, the bond lengths of Ba–N are also close to the sum of the respective ionic radii. The Ba–N bond lengths of LiBa3N, NaBa3N, and Na5Ba3N are, respectively, 2.722, 2.734, and 2.729–2.746 Å. The ∞1[NBa6/2] chain of LiBa3N, NaBa3N, and Na5Ba3N also can be regarded as a positively charged ionic chain, [Ba3N]3+. In addition, the insertion of alkali metals leads to a larger distance between chains. Therefore, it is natural to speculate that LiBa3N, NaBa3N, and NaBa3N formed by intercalating alkali metals (Li or Na) into Ba3N may be also generate electrides.

Because the interaction between [Ba3N]3+ chains of Ba3N, LiBa3N, NaBa3N, and Na5Ba3N involves both electron interaction and vdW interaction, we employed three vdW correction methods (PBE-D2, PBE-D3, and PBE-dDsC) corrected on top of the PBE functional to elucidate the role of vdW interactions in stabilizing structures and to confirm the accuracy of PBE structure optimization. The results are listed in Table S2 in the Supporting Information. Figure shows the plotted linear correlations between the computed lattice constants and corresponding experimental values.[17−20] For Ba3N, LiBa3N, and NaBa3N, the lattice constants computed by using the PBE-D3-corrected PBE functional are closest to the experimental values, and for Na5Ba3N, the lattice constants computed by using the PBE functional are closest to the experimental values. The absence of imaginary frequency in the phonon dispersion diagrams for Ba3N, NaBa3N, and Na5Ba3N confirm the dynamic stability of structures closest to the experimental value as shown in Figure S2 in the Supporting Information. The structure model closest to the experimental value is used for subsequent electronic property calculation.

Figure 2

Computed lattice constants (PBE, PBE-D2, PBE-D3, and PBE-dDsC) versus experimental lattice constants including volume (a), lattice constant a (b), lattice constant b (c), and lattice constant c (d) of Ba3N,[17] LiBa3N,[20] NaBa3N,[18] and Na5Ba3N.[19]

Electronic Structures

Ba3N has been identified as an electride, whereas a detailed analysis of the electronic properties of Ba3N is still scarce.[30] Therefore, we calculated its ELF, band structure, DOS, and partial charge density. The ELF isosurface and map of Ba3N in Figure indicates a pronounced electron localization distributed in the 3D interstitial space between [Ba3N]3+ chains. No electrons are observed between the electron localization space and the [Ba3N]3+ chains, substantiating the ionic bonding nature between the anionic state and the [Ba3N]3+ chains, which is similar to the Ca2N[6] cases. The difference is that in Ba3N, the anionic electrons are distributed in the 3D space between [Ba3N]3+ chains, while in Ca2N, they are distributed in the 2D space between [Ca2N]+ layers. To further confirm the electride nature of Ba3N, we artificially constructed three structures (Ba3N-e–, Ba3N-2e–, and Ba3N-3e–) by removing three electrons from the primitive cell of Ba3N one by one and calculated their ELF (Figure S3 in the Supporting Information).[42,43] It shows that with the removal of electrons, the confined electrons gradually decrease until all disappear.

Figure 3

ELF for Ba3N. The isosurface plot (a) and the corresponding map of the (0001) plane at c = 1 (b), the (0001) plane at c = 3/4 (c), and the (112̅0) plane (d).

The calculated electronic band structures and projected densities of states (PDOSs) of Ba3N are plotted in Figure a,b. The existence of bands crossing the Fermi level in Figure a suggests its metallic characteristics. Figure b shows that the bands between −2.6 and −1.5 eV below the Fermi level are predominantly formed by the N 2p orbitals with the Ba 5p orbitals, and bands above the Fermi level are determined the unoccupied Ba 6s orbitals, while the contributions from the atomic orbitals of Ba and N near the Fermi level (between −1.5 and 0 eV) are smaller.

Figure 4

Calculated band structure (a), PDOS (b), the isosurface and the map of partial charge density of interstitial band 1 (c), band 2 (d), and band 3 (e) of Ba3N. The bands around the Fermi level, mainly contributed by the interstitial electrons, are highlighted in red, blue, and green lines. In (c–e), the green and gray spheres, respectively, denote Ba and N atoms.

The contributions from the interstitial sites are dominant around the Fermi level, which is a typical character of electrides.[44] However, due to the connection with neighboring bands, the band structure around the Fermi level of Ba3N is more complicated than other known electrides. In Ca2N,[6] for example, there is only one band near the Fermi level. Therefore, the existence of the interstitial electrons in Ba3N is confirmed by the decomposed partial charge densities.[45] By plotting the partial charge density of the three bands (Figure c–e) around the Fermi level, we can clearly find that they correspond to interstitial electrons. The results suggest that the electrons of band 1 mainly accumulate around the V1 site, the electrons of band 2 accumulate around both of the V1 site and the V2 site, and the electrons of band 3 mainly accumulate around the V2 site. Because the anionic electrons in Ba3N are confined in the 3D interstitial space, Ba3N can be regarded as a 3D electride according to the classification of inorganic electrides in terms of dimensions of anionic electrons.[4] Ca2N can be exfoliated into 2D nanosheets because layers of atoms are separated by layers of a 2D electron gas.[12] Similarly, Ba3N is promising to be exfoliated into 1D nanowires because chains of atoms are separated by a 3D electron gas.

To further confirm that bands 1, 2, and 3 are contributed by interstitial electrons of Ba3N, we, respectively, inserted six and four H atoms at the V1 and V2 sites and relaxed. We found that unlike the little lattice changes caused by the insertion of anions in 0D and 1D electrides, large lattice change happened in Ba3NH3-V1 and Ba3NH2-V2 after relaxation, and the situation is similar to inserting anions into 2D electrides, such as Ca2N (Table S3 in the Supporting Information). The reason may be that the anionic electrons are confined in the interstitial space formed by the rigid frame in 0D and 1D electrides, only anions matching the interstitial space can be inserted. While 2D and 3D electrides have more flexible frame structures, when anions are inserted, the distance between layers or chains as well as the thickness of layers and the length of chains can be adjusted according to the size of the anion. If the anion is too large or too small, the most stable structure will not retain its original configuration (such as Ca2NH[46] and Ca2NF[47]).

The calculated band structure of the artificial Ba3NH3-V1 shows that the bands 1, 2, and 3 disappeared after the introduction of H atoms at the V1 sites, and hydrogen-related bands appear at the energy range of around −3.5 to −1.5 eV for H– (Figure S4a in the Supporting Information). Ba3NH3-V1 turned to be a semiconductor with the introduction of H atoms at the V1 sites. The calculated band structure of the artificial Ba3NH2-V2 shows that the bands 1–3 disappeared after the introduction of H atoms at the V2 sites, and hydrogen-related bands appear at the energy range of around −4.5 to −2.6 eV for H–. At the same time, a new band contributed by excess electron appears near the Fermi level (Figure S4b in the Supporting Information). Ba3NH2-V2 remains as metal because the excess electrons are still present in Ba3NH2-V2. The above results show that bands 1, 2, and 3 of Ba3N are the contributions of anionic electrons at the V1 and V2 sites.

Because of the interchain electron distribution, Ba3N is expected to have a low work function. We calculated its work functions on the (11̅00) plane and the (0001) plane; the (11̅00) plane is cleaved parallel to [Ba3N]3+ chains, and the (0001) plane is cleaved perpendicular to [Ba3N]3+ chains. As presented in Figure S5a,b in the Supporting Information, the work functions of Ba3N exhibit small surface anisotropy with the value 2.45 eV on the (11̅00) plane and 2.53 eV on the (0001) plane. By contrast, the work function of 2D electrides Ca2N exhibits large surface anisotropy with the value 3.39 eV on the plane parallel to [Ca2N]+ layers and 2.35 eV on the plane perpendicular to [Ca2N]+ layers.[39] The small surface anisotropy of Ba3N relative to that of Ca2N further indicates the 3D feature of anionic electrons in Ba3N. It should be noted that the work function of Ba3N is smaller than the value of metal Ba (2.7 eV). Such a low work function of Ba3N makes it promising in applications such as efficient thermionic emitters, low injection-barrier cathodes for organic light-emitting diodes, and high-performance catalysts.

Since there is a π/6 rotation of [Ba3N]3+ chains of NaBa3N with respect to those of Ba3N, we first studied the effect of the rotation of [Ba3N]3+ chains on electron distribution before studying the electronic properties of NaBa3N. We build the rotation structure by removing the Na atom of the NaBa3N structure and named the rotation structure NaBa3N-Na (Figure S6 in the Supporting Information). The ELF isosurface and map of NaBa3N-Na are shown in Figure . The electron localization of NaBa3N-Na also distributed in the 3D interstitial space between [Ba3N]3+ chains, but the rotation of [Ba3N]3+ chains obviously changes the distribution of localized electrons. Almost no electrons are observed between the electron localization space and the [Ba3N]3+ chains, indicating the ionic bonding nature between the anionic state and the chains, which is the same as the Ba3N cases. The electron localization also gradually decreases until it disappears as the three excess electrons in the structure of NaBa3N-Na are removed one by one (Figure S7 in the Supporting Information).

Figure 5

ELF for NaBa3N-Na. The isosurface plot (a) and the corresponding map of the (0001) plane at c = 1 (b), the (0001) plane at c = 3/4 (c), and the (112̅0) plane (d).

The calculated electronic band structures and PDOSs of NaBa3N-Na are plotted in Figure S8a,b in the Supporting Information. Similar to Ba3N, the bands between −2.8 and −1.5 eV below the Fermi level are predominantly formed by the N 2p orbitals with the Ba 5p orbitals, and bands above the Fermi level are determined the unoccupied Ba 6s orbitals, while the contributions from the atomic orbitals of Ba and N near the Fermi level (between −1.5 and 0 eV) are smaller. The partial charge density of the three bands for NaBa3N-Na around the Fermi level is shown in Figure S8c–e in the Supporting Information, and we can clearly find that they correspond to interstitial electrons. The results suggest that the electrons of band 1 and band 2 mainly accumulate around the V1 site, and the electrons of band 3 mainly accumulate around the V2 site.

When anions (such as Sb3– and Bi3–) are inserted into the rotation structure, Ba3NX (X = Sb and Bi) is converted into common ionic compounds and becomes a semiconductor.[41] However, if alkali metal atoms (such Li and Na) are inserted into the rotation structure, it may still be an electride. Figure shows the ELF isosurface and map of NaBa3N. The electron localization of NaBa3N is also distributed in the 3D interstitial space between [Ba3N]3+ chains and the distribution shape of localized electrons is similar to NaBa3N-Na. To further confirm the electride nature of NaBa3N, we artificially constructed four structures (NaBa3N-e–, NaBa3N-2e–, NaBa3N-3e–, and NaBa3N-4e–) by removing four electrons from the primitive cell of NaBa3N one by one and calculated their ELF (Figure S9 in Supporting Information). It shows that with the removal of electrons, the confined electrons gradually decrease until they almost disappear.

Figure 6

ELF for NaBa3N. The isosurface plot (a) and the corresponding map of the (0001) plane at c = 1 (b), the (0001) plane at c = 3/4 (c), and the (112̅0) plane (d).

The calculated electronic band structures and PDOS of NaBa3N are plotted in Figure a,b. The existence of bands crossing the Fermi level in Figure a suggests that NaBa3N is metallic. Compared with NaBa3N-Na, the Fermi level of NaBa3N moves up. Figure b shows that the bands between −1.5 and −2.7 eV below the Fermi level are predominantly formed by the N 2p orbitals with some mixing with the Ba 5p orbitals, and bands between 0.2 and 1 eV above the Fermi level are determined by the unoccupied Ba 6s orbitals, while the contributions from the atomic orbitals of Ba and N near the Fermi level are smaller. By plotting the decomposed partial charge density of the four bands (band 1, 2, 3, and 4) around the Fermi level, we can clearly find that they correspond to interstitial electrons. The results suggest that the electrons of bands 1 and 2 mainly accumulate in the V1 site (between two Ba atoms from the same [Ba3N]3+ chain and one Na), and the electrons of band 3 and 4 mainly accumulate in the V2 site (between two Ba atoms from different [Ba3N]3+ chains and one Na). The results reveal that the anionic electrons in NaBa3N are confined in the 3D interstitial space. Thus, NaBa3N also can be regarded as a 3D electride.

Figure 7

Calculated band structure (a), PDOS (b), the isosurface and the map of partial charge density of interstitial band 1 (c), band 2 (d), band 3 (e), and band 4 (f) of NaBa3N. The interstitial bands, mainly contributed by the interstitial electrons, are highlighted in bold red, blue, green, and cyan lines. In (c–f), the green, gray, and orange spheres, respectively, denote Ba, N, and Na atoms.

To further confirm that bands 1, 2, 3, and 4 are contributed by interstitial electrons of NaBa3N, we, respectively, inserted six H atoms at the V1 and V2 sites and relaxed. As expected, large lattice change happened in NaBa3NH3-V1 and NaBa3NH3-V2 after relaxation (Table S3 in the Supporting Information). The calculated band structure of the artificial NaBa3NH3-V1 shows that the bands 1, 2, 3, and 4 disappeared after the introduction of H atoms at the V1 sites, and hydrogen-related bands appear at the energy range of around −3.5 to −1.5 eV for H–. At the same time, a new band contributed by excess electron appears near the Fermi level (Figure S10a in the Supporting Information). The calculated band structure of the artificial NaBa3NH3-V2 shows that the band 1, 2, 3, and 4 disappeared after the introduction of H atoms at the V2 sites, and hydrogen-related bands appear at the energy range of around −4.5 to −2.6 eV for H–. At the same time, a new band contributed by excess electron appears near the Fermi level (Figure S10b in the Supporting Information). The NaBa3NH3-V1 and NaBa3NH3-V2 are still metal after the H atoms were introduced at the V1 and V2 sites because the excess electrons are present in NaBa3NH3-V1 and NaBa3NH3-V2. The above results show that bands 1, 2, 3, and 4 of NaBa3N are the contributions of anionic electrons at sites V1 and V2.

We calculated the work functions of NaBa3N on the (11̅00) plane and the (0001) plane; the (11̅00) plane is cleaved parallel to [Ba3N]3+ chains, and the (0001) plane is cleaved perpendicular to [Ba3N]3+ chains. As presented in Figure S11a,b in the Supporting Information, the work functions of NaBa3N exhibit small surface anisotropy with the value 2.62 eV on the (11̅00) plane and 2.58 eV on the (0001) plane. The work function of NaBa3N is smaller than the value of metal Ba (2.7 eV) and Na (2.75 eV). This result further indicates that NaBa3N is a 3D electride.

Next, we studied the electronic properties of Na5Ba3N. The ELF isosurface and map of Na5Ba3N with different charge states are plotted in Figure . Figure e shows that the anionic electrons between the Na atom and the [Ba3N]3+ chain (V sites) disappeared after removing eight extra electrons, and the removal of six extra electrons (Figure d) shows almost the same ELF distribution except the metallic bonding near Na atoms is enhanced. This reveals that the metallic bonding has stronger ability to attract electrons than V sites. Electron localization appears at V sites with the increase of the number of extra electrons (Figure a). The result shows that Na5Ba3N is different from NaBa3N and possess mixed ionic and metallic bonding similar to NaBa2O and Ca5Ga2N4.[42]

Figure 8

Calculated ELF for Na5Ba3N (a), Na5Ba3N-2e– (b), Na5Ba3N-4e– (c), Na5Ba3N-6e– (d), and Na5Ba3N-8e– (e). The isosurface plot (left) and the corresponding map of the (010) plane at c = 3/4 (right). The green, gray, and orange spheres, respectively, denote Ba, N, and Na atoms.

The calculated electronic band structures and PDOSs of Na5Ba3N are plotted in Figure a,b. The existence of bands crossing the Fermi level in Figure a suggests its metallic characteristics. Figure b shows that the bands between −3.0 and −1.4 eV below the Fermi level are predominantly formed by the N 2p orbitals with some mixing with the Ba 5p orbitals, and bands above the Fermi level are determined the unoccupied Ba 6s orbitals, while the contributions from the atomic orbitals of Ba and N near the Fermi level are smaller. The existence of the interstitial electrons in Na5Ba3N is further confirmed by the partial charge densities as shown in Figure c. Electrons near the Fermi level (−1.38 eV < E–EF < 0 eV) mainly accumulate between the Na atoms and the [Ba3N]3+ chains.

Figure 9

(a) Calculated band structure of Na5Ba3N. The Ba-, Na-, and N-related bands are depicted using blue, purple, and red dots. (b) Total and projected DOS of Na5Ba3N. (c) Calculated partial charge density for Na5Ba3N around the Fermi level (−1.38 eV < E–EF < 0 eV). The isosurface plot of the partial charge density is set as 0.003 e/Å3 along the b-axis and the corresponding map of the (010) plane at c = 3/4.

We calculated the work functions of Na5Ba3N on the (001) plane and the (010) plane; the (001) plane is cleaved parallel to [Ba3N]3+ chains, and the (010) plane is cleaved perpendicular to [Ba3N]3+ chains. As presented in Figure S12a,b in the Supporting Information, the work functions of Na5Ba3N exhibit small surface anisotropy with the value 2.63 eV on the (010) plane and 2.56 eV on the (001) plane. The work function of Na5Ba3N is smaller than the value of metal Ba (2.7 eV) and Na (2.75 eV). This result further indicates that Na5Ba3N is a 3D electride.

Conclusions

In summary, we have identified subnitrides (Ba3N, LiBa3N, NaBa3N, and Na5Ba3N) containing 1D [Ba3N]3+ chains as 3D electrides for the first time through ELF, band structure, DOS, partial charge density, and work function calculations. These materials not only are experimentally synthesizable 3D electrides but also are promising to be exfoliated into advanced 1D nanowire materials. Interestingly, LiBa3N, NaBa3N, and Na5Ba3N are obtained by inserting alkali metals (Li or Na) into Ba3N. Therefore, our work also demonstrates that the discovery strategy of novel electrides based on one parent framework like [Ba3N]3+ chains may accelerate the discovery of more novel electrides.