Attempts to obtain a chemical reaction between pure Bi and N₂ were made to pressures of up to 50 GPa through sample laser heating. The first synthesis attempts at pressures of 12–15 GPa and ∼30 GPa were unsuccessful. Indeed, although at these pressure ranges, laser heating to temperatures of ∼1800 (200) K resulted in bismuth melting, the collected X-ray diffraction data did not reveal any signs of a new phase being produced. However, upon further increasing the pressure to 42.5 (3) GPa and laser heating, new diffraction lines, suggestive of a chemical reaction and the formation of a novel compound, were observed. Although all synthesis attempts were conducted at high temperature, the data discussed here and in the following paragraphs were collected at room temperature. The analysis of the thereafter obtained single-crystal X-ray diffraction data enabled to unambiguously index the produced solid to have lattice parameters of a = 4.8941(5) Å, b = 9.4020(10) Å, and c = 9.176(4) Å, and the Pbcn space group (S.G. #60). The R-factors of the best solution are as follows: R _int = 2.5% and R ₁ = 2.6% for I > 2σ(I), with I and σ being the integrated intensity and its standard deviation value, respectively. More information on the single-crystal data, along with the tables containing the crystallographic parameters for this and other pressure points, is shown in Supplementary Material.

The structure of Pbcn BiN is constituted of four crystallographically independent atoms, two Bi atoms (Bi1 and Bi2) and two N atoms (N1 and N2) (Figure 1). The Bi1, Bi2, N1, and N2 atoms occupy Wyckoff site 8d, and the number of formula units per unit cell is Z = 16. The structure of the compound can be visualized as consisting of edge-sharing octahedra that are distorted to accommodate the Bi–N bonding characteristics.

Considering that N and Bi have similar electronic configurations of the outer electronic shells, it would be natural to draw a comparison of BiN with other pnictogen phases, including the black phosphorous-type phase of nitrogen (Cmce, bp-N) (Laniel et al., 2020), where each N has a direct bond with three other neighbors. As for Pbcn BiN, we can easily imagine that Bi is also bound to three closest neighbors. Then, the structure can be described as polymeric, with weakly interconnected Bi–N layers with an “arm-chair” arrangement along the y-axis of the unit cell. A similar, but more regular, arrangement is seen in bp-N. Nevertheless, within the specified individual layers, we observe a pronounced distinctiveness, as illustrated in Figures 1D, E.

We can also compare Pbcn BiN with cubic gauche polymeric nitrogen (I2₁3, S.G. #199, cg-N) (Eremets et al., 2004) and cubic single-bonded AsN (P2₁3, S.G. #198) (Ceppatelli et al., 2022). The synthesized orthorhombic polymorph of BiN is of lower symmetry and features a fairly specific 3D arrangement. Although the local tetrahedral environment of nitrogen binding to the electrons of nearest As and Bi looks alike, the Bi–N–Bi angles are generally lower than As–N–As angles. From Cepatelli et al., we know that at 38.6 GPa, the As–N–As angles spread from 103.4 (4)° to 112.6 (4)°. At the same time with Pbcn BiN, at a pressure of 42.5 (3) GPa, the Bi–N1–Bi angles have values of 98.8 (6)°, 105.1 (6)°, and 108.3 (4)°, while the values of Bi–N2–Bi angles are 94.2 (6)°, 102.4 (7)°, and 105.6 (4)°. Some of these angles are somewhat smaller than the reference angles of 108.8 (3)° in cg-N (115.4 GPa) (Eremets et al., 2004) and 105.1 (1)° of bp-N (140 GPa) (Laniel et al., 2020). This evidence emphasizes the importance of electronic density contrast between different elements in the nitrogen group, resulting in distinct crystal chemistry and in a strong influence on the properties of synthesized materials. The peculiarity of the Pbcn BiN structural framework is likely related to an increased electronic density featured by our electronic localization function calculations, which could be attributed to the nitrogen lone pair (Supplementary Figure S7).

Our observations indicate that in Pbcn BiN, Bi should have three single bonds with N (sp ³ hybridization), and as we will show in the upcoming section, this should hold true for Bi1 for Pbcn BiN below 50 GPa, but the situation for Bi2 requires an additional discussion and comparison with ab initio calculations. In addition to synthesizing Pbcn BiN at 42.5(3) GPa, we also successfully produced it at pressures of 47.4(2) GPa and 51(1) GPa. In all three syntheses, we could not find any other Bi–N compounds than Pbcn BiN. We also collected the data on decompression and report that upon quenching to 1 bar, Pbcn BiN undergoes a solid–solid phase transition toward a phase with the space group Pca2₁, presumably via a group–subgroup transformation. It is interesting to note that similar behavior is observed for δ-P₃N₅ (Laniel et al., 2022a), spontaneously shifting into α′-P₃N₅ upon decompression below 7 GPa (C2/c → P2₁/c). The crystallographic details of Pca2₁ BiN are provided in the Supplementary Material. We verified the formation of Pca2₁ in two separate different loadings: once by means of powder diffraction (the sample stabilized by an Ar atmosphere after being decompressed in a glovebox) and once by means of single-crystal diffraction and subsequent data analysis (the sample was carefully decompressed until the Raman shift of molecular nitrogen corresponded to ambient pressure). The R-factors of the best Pca2₁ solution are as follows: R _int = 1.4% and R ₁ = 2.9% for I > 2σ(I). Figure 2 shows the structures of Pca2₁ and Pbcn BiN side-by-side.

Comparative analysis of Pca2₁ and Pbcn BiN shows that a loss of a symmetry element on decompression (Pbcn → Pca2₁ = Pbc2₁) resulted in a significant structural reorganization. We obtain twice more independent Bi and N positions (Wyckoff sites 4a) without a change in formula units per unit cell (i.e., Z = 16). Considering the local nitrogen environment of Pca2₁ BiN and the Bi–N–Bi angles, we see a relatively narrow distribution of their values around 111° (a value close to an optimal angle for sp ³ -hybridized N), with the smallest and the largest values being 100.9 (5)° and 114.6 (7)°, respectively. These values are in a closer agreement with the As–N–As angles reported for the cubic AsN (Ceppatelli et al., 2022).

Although our knowledge of pnictogen chemistry is still far from being complete, the comparison of the known structures reveals some interesting observations in relation to their crystal chemistry. As shown in the Supplementary Material, there is a direct group–subgroup path Cmce→ Pbcn →Pca2₁ with the first space group being that adopted by bp-N and the others for Bi–N. If we compare AsN with cg-N, we also see that P2₁3 is also a subgroup of I2₁3. It is conceivable that several yet unexplored high-pressure phases of pnictogens with the 1:1 ratio may reside within the designated crystallographic group–subgroup space. Moreover, it is impossible to make a group–subgroup transformation from I2₁3 or P2₁3 to Pca2₁, suggesting that binary BiN and AsN should belong to different classes, considering the crystal chemistry point of view.

Concerning the stability of the individual Pbcn and Pca2₁ BiN phases, we experimentally confirmed the presence of Pbcn at pressures as low as 12.5(4) GPa. Unfortunately, we do not have experimental datapoints between 12.5(4) GPa and ambient pressure. Here, we performed conventional ab initio calculations investigating the stability of the discovered BiN polymorphs with and without the contribution of van der Waals forces. It was indicated by Ceppatelli et al. (2022) that calculations of pnictogen materials with a larger number of electrons per atom are intrinsically hard and may not capture all the features of the materials at ambient temperature, and indeed, we will see some discrepancies in our discussion of BiN compressibility. At the same time, our ab initio calculations strongly support the experimental observations with respect to the phase stability; Figure 3 shows the plot of relative enthalpy between the compounds and the phonon dispersion plots calculated for Pca2₁ at 1 bar and for Pbcn at 49 GPa. At the same time, the enthalpy calculations, shown in Figure 3, suggest the thermodynamic stability of the Pca2₁ and Pbcn BiN polymorphs at lower and higher pressures, respectively (Figure 3A). The phonon calculations provide additional support for the polymorph dynamic stability (Figures 3B, C), and in the Supplementary Material, we show the results of our calculations, indicating the semiconducting nature of BiN with a band gap decreasing from 1.13 eV (Pca2₁ ^VdW) to 0.45 eV (Pbcn ^VdW) if we consider 0 and 49 GPa, respectively. Both approximations employed in ab initio calculations confirmed the dynamical stability of the phases in their corresponding stability fields. The calculation including van der Waals forces provides better agreement with an experimental unit cell volume for Pca2₁ BiN. We did not see a considerable difference between the results produced by different approximations for the Pbcn phase. In the Supplementary Material, we also demonstrate the results of the structure mechanical stability calculation additionally supporting our conclusion.

The structural complexity of BiN finds a correlation with its peculiar compressibility, as shown in Figure 4 where we compare experimental data with ab initio predictions.

A closer look at experimental data provides the following observations. First, we detect an anomaly in the evolution of the lattice constants of Pbcn BiN at pressures above 35–38 GPa. Indeed, within the pressure range of 40–50 GPa, the volume of the unit cell does not change much. This peculiar behavior correlates with our observation of a strongly reduced compound volume compressibility, as confirmed in three different loadings and syntheses. We note that although nitrogen is far from being a perfect hydrostatic medium, laser heating tends to anneal undesirable deviatoric stress effects and micro-strains (Uts et al., 2013). Thus, we consider that our observations most likely reflect a real process of isostructural crystal chemistry readjustment within the compound at the points of synthesis indicated by star symbols in Figure 4A. Although these observations may look surprising, they are not impossible, as demonstrated in the case of another pnictogen-based compound, CoSb₃ (Kraemer et al., 2007). In a moderate pressure range, CoSb₃ exhibits a phenomenon of ‘self-insertion,’ resulting in an isostructural bond reconstruction under compression, resulting in an apparent strong decrease of compressibility. Although the presence of minor residual deviatoric stress and strain at the synthesis stage cannot be fully dismissed, it is essential to acknowledge that they might not be the sole factors contributing to our observations, and we require a careful analysis of theoretical and experimental results.

If we look at the bulk compressibility, the ab initio equation of state (EoS) seems to overestimate the experimental data at pressures below ∼47 GPa. The overestimation of the lattice parameters and unit cell volume in DFT-relaxed structures is known for other Bi-bearing compounds (Cheng and Ren, 2011; Li et al., 2018; Gao et al., 2021) and attributed to the imperfections in exchange-correlation calculations using the GGA functional. For the Pbcn phase, and for a pressure range of 10–80 GPa, the third-order Birch–Murnagham EoS (Birch, 1952) obtained from the calculated EoS results in parameters of V ₀ = 580(16) Å³, K ₀ = 64(19) GPa, and K’ = 5.6(9), where the parameters correspond to the ambient pressure volume, isothermal bulk modulus at ambient pressure, and its pressure derivative. The theoretical K ₀ value is low, which is expected from a Bi-bearing compound (Akahama et al., 2002). The calculated theoretical volume of Pca2₁ after relaxation at zero pressure is also overestimated and corresponds to 612.8 Å³ and 640.8 Å³ for calculations including van der Waals forces (A2) and those omitting them (A1), respectively. This contrast likely indicates a greater role of the forces for interatomic interactions within the lower pressure Pca2₁ phase. Our calculations for Pbcn propose the suppression of van der Waals forces at higher pressures. Altogether, although our conventional calculations may not be perfect, we will show that they capture essential aspects of Pbcn BiN and the evolution of its crystal chemistry.

As shown in Figure 5 for Pbcn BiN, both the theory and the experiment qualitatively agree with respect to the Bi1-N and Bi2-N distances and to the Bi1 and Bi2 coordination number change under stress. Bi1 has three shortest bonds (e.g., below 2.35 Å), the corresponding coordination number CN_Bi1 = 3, and this situation does not change at different pressures. In contrast, the connectivity of Bi2 is different and does vary as a function of pressure. At ∼12.5(4) GPa, we observe two short Bi2-N bonds with lengths comparable to Bi1-N and two bonds of larger intermediate length (∼2.5–2.6 Å). The latter are illustrated using dashed ellipses in Figure 5 and using dashed lines in Figure 6. At lower pressures, the Bi–N layers are weakly bound through the indicated Bi2–N2 network with CN_Bi2 = 4, but at higher pressures, the network is rearranged with the shortest Bi2–N bonds (below 2.35 Å) being enclosed within the Bi–N layers and resulting in CN_Bi2 = 3 at 51.0(5) GPa. Additional graphical information comparing the unusual Bi near neighbor coordination at pressure points of 12.5(4) and 51.0(5) GPa is presented in the Supplementary Material. Considering Pca2₁, we observe CN = 3 for all atoms.

We emphasize that the observation of CN_Bi2 = 4 in Pbcn BiN is highly peculiar, and it is supported by both our experiment and calculations. It implies the same coordination number CN_N2 = 4 for nitrogen occupying position N2 at 12.5(4) GPa and directs to a general discussion of the nitrogen strength as an electron acceptor in inorganic compounds and bonding type. Calculated Bader charges for BiN at 12.5(4) GPa (Bi: + [1.36–1.37], N: [1.36–1.37]) and electron localization function calculations (Supplementary Figure S7) demonstrate that ionic contribution to the Bi–N bonds is significant. This is in line with the difference in electronegativity between Bi and N atoms (Rahm et al., 2019; Tantardini and Oganov, 2021).

The presence of ionic bond may explain the intermediate coordination number CN_Bi2 = CN_N2 = 4 between Pca2₁ and Pbcn phases if we think of the structures at the pressures of 0 GPa (CN_Bi = 3) and 51.0(5) GPa (CN_Bi = 3), respectively. A review of the literature will show various examples with the coordination number strictly increasing as a function of pressure (Prescher et al., 2017; Pakhomova et al., 2019; Spiekermann et al., 2019), and the case of BiN is a rare exception to this general empirical rule. A change of coordination is typically correlated with a change of electronic properties, and considering the pressure range, it fits well with our observation of unit cell-reduced compressibility and the anisotropic compressibility of the lattice parameters (Figure 4).

To conclude our discussion, the experimental evidence in combination with ab initio calculations demonstrates a peculiar compressibility related to the subtleties of binary BiN crystal chemistry. The polymorphs of this compound should have enhanced electronic properties, which may even stimulate the effect of thermoelectricity. Here, we direct to the similarities between Pbcn BiN and SnS, a compound made from elements belonging to the 14th and the 16th groups of the periodic table. SnS has been exhaustively investigated, and we note that it has a similar atomic arrangement band gap (∼1.3 eV) to Pbcn BiN and also exhibits thermoelectricity (Lanigan-Atkins et al., 2020), among many other fascinating properties (Tian et al., 2017; Ho et al., 2022).

At the same time, if we reflect on the Pca2₁ polymorph of BiN, we find that it can be stabilized at ambient conditions in an inert atmosphere and potentially can be further stabilized by doping. In addition, the Pca2₁ group is non-centrosymmetric, which leads to pyro- and piezo-electric properties. A review of the literature will show many materials attributed to the same space group exhibit piezoelectricity (Li et al., 2019; Silva et al., 2023). Altogether, the Bi–N system is highly interesting and will require further investigations.