High-pressure reactions between the pnictogens: the rediscovery of BiN

We explore chemical reactions within pnictogens with an example of bismuth and nitrogen under extreme conditions. Understanding chemical reactions between Bi and N, elements representing the first and the last stable elements of the nitrogen group, and the physical properties of their compounds under ambient and high pressure is far from being complete. Here, we report the high-pressure high-temperature synthesis of orthorhombic Pbcn BiN (S.G. #60) from Bi and N2 precursors at pressures above 40 GPa. Using synchrotron single-crystal X-ray diffraction on the polycrystalline sample, we solved and refined the compound’s structure and studied its behavior and compressibility on decompression to ambient pressure. We confirm the stability of Pbcn BiN to pressures as low as 12.5(4) GPa. Below that pressure value, a group–subgroup phase transformation occurs, resulting in the formation of a non-centrosymmetric BiN solid with a space group Pca21 (S.G. #29). We use ab initio calculations to characterize the polymorphs of BiN. They also provide support and explanation for our experimental observations, in particular those corresponding to peculiar Bi–N bond evolution under pressure, resulting in a change in the coordination numbers of Bi and N as a function of pressure within the explored stability field of Pbcn BiN.

At the next pages we provide figures illustrating various steps of analysis process.First, we show specific slices of reciprocal space corresponding to Pbcn and Pca21 phases of BiN collected at 42.5(3) GPa (Figure S 1) and at 1 bar (Figure S 2), respectively.For data collection we used a small beam of 2•2 μm 2 (H•V, fullwidth at half maximum) at the focal spot we could isolate some individual domains corresponding to both phases and solve their structures.The slices represent a typical example of using single crystal methods with polycrystalline samples (overlap with diffraction coming from precursor materials, grains of the same phase but different orientation, etc).

Figure S1
Information on reciprocal space collected from two individual domains (dom1, dom3).The domains belong to the same orthorhombic phase synthesized at 42.5(3) GPa from Bi and N2 precursors.The indicated extinction rules correspond to Pbcn (S.G. 60).We also indicate a*, b* and c* reciprocal space basis vectors of the orthorhombic lattice.Additional signal present at the slices can be attributed to the presence of other domains of the same phase, to the signal of the environment (diamond Bragg or diffuse scattering) or the signal from the precursors.It was important to collect data with a small beam in order to boost the signal to noise ratio and avoid significant signal overlap.

Figure S2
Information on reciprocal space collected from a single domain in different crystallographic basis.Upon decompression from ~10 GPa to 1 bar we saw an appearance of additional reflections contradicting extinction rules for Pbcn space group (lower right panel), we indicate those reflections using light blue circles.The structure quenched to 1 bar was finally indexed and solved as Pca21 (S.G. 29).Considering the choice between Pca21 over Pbc21, we selected the former as the standard setting choice.During decompression pressure was carefully released until we saw nitrogen Raman shift reaching 2330 cm -1 indicating ambient pressure (Ray et al., 2018).

Figure S3
Le Bail profile matching for Pca21 phase quenched to 1 bar.In this case no reliable single crystal data collection was possible as sample got damaged during a Raman measuring attempt using 532 nm laser at ~40 mW power at a focal spot.Pure Bi contributes to the strongest recorded signal, but we also observe peaks which we can attribute to the BiN in Pca21 form.

Figure S4
Group-subgroup relationship between Cmce and Pca21 space groups plotted with help of Bilbao Crystallographic Server (Aroyo et al., 2006b(Aroyo et al., , 2006a)).We observe a close relation between Cmce space group which was attributed to black phosphorus phase of nitrogen: bp-N (Laniel et al., 2020) as well as Pbcn and Pca21 of BiN which may indicate the a yet to be discovered binary or ternary pnictogen compounds may form within the same or expanded group-subgroup space in a contrast to cubic phases of AsN and cubic gauche N (cg-N) which, based on their crystal chemistry, a separate class of compounds (Eremets et al., 2004;Ceppatelli et al., 2022) Calculation of electronic density of state and electron localization function (ELF), phonon dispersion curves, mechanical stability of Bi-N polymorphs.Here we show the full scale of ELF values.Our calculations suggest a pronounced ionic Bi-N bond character.To the right, similar to (Savin et al., 1997;Laniel et al., 2022) we demonstrate electronic density above 0.84 e -/Å 3 .The yellow features likely correspond to lone pairs at nitrogen sites.These shapes are deformed in such a way that they face the center of a tetrahedron formed by nitrogen atoms indicated by dashed lines.Very similar features are visible in our ELF calculations for 49 GPa.
Additionally, we introduce calculations estimating the mechanical stability of the BiN phases (Mouhat & Coudert 2014).The calculated elastic tensors Cij for both polymorphs are shown in Tables 1 and 2 below The mechanical stability criteria for an orthorhombic system are: The values of Cij satisfy all of the criteria for mechanical stability for the corresponding pressure points.

Tables with experimental BiN crystallographic data
Tables are presented below as a function of increasing pressure.In the tables below, we present various information including unit lattice parameters, parameters from structure solution and refinement.The tables provide information from CIF files submitted to the Cambridge Crystallographic Data Centre (CCDC) under deposition numbers 2280721,2280722,2280723,2280724,2280725,2280726,2280727,2280728,2280729.
The limits in H, K, L and θ correspond to CIF file information fields representing minimum and the maximum values of the corresponding Miller indexes (e.g.link) as well as the minimum and maximum θ angles (e.g.link) in degrees for the measured diffraction intensities.Isignal intensity; σ(I)standard deviation of I; R1, wR2crystallographic R-factors; N par /N obsratio between number of parameters to number of observed reflections for I>2σ(I); ρ min , ρ maxminimum and maximum values of residual electronic density; ADPatomic displacement parameters (e.g.* -U equiv ., otherwise -U iso ).

Figure S5
Figure S5 Results of ab-initio calculations on the electronic density of states of the two BiN polymorphs at various pressures.The calculations' details can be found in the main manuscript.Calculations indicate the semiconducting behavior of BiN and a band gap (Eg) reduction as a function of compression.Position E=0 corresponds to the position of the Fermi energy level.(Left) Shows calculations conducted without the inclusion of van der Waals contributions and to the (Right) we show the calculations employing the latter type of interaction.Obviously, although some details differ, both approximations are in good agreement, e.g.band gap values, compression induced suppression of the band gap.

Figure S6
Figure S6Our calculations of phonon dispersion curves conducted for the pressure points of 12.5 and 30 GPa for Pca21 and Pbcn BiN polymorphs, respectively, provide additional support to our enthalpy calculations and experimental data (see Figure3of the manuscript).

Figure S7
Figure S7Results of electron localization function calculation (ELF) for Pbcn BiN at 12 GPa.To the left we show a ELF cross-section parallel to (100) offset close to the indicated Bi and N sites.Here we show the full scale of ELF values.Our calculations suggest a pronounced ionic Bi-N bond character.To the right, similar to(Savin et al., 1997;Laniel et al., 2022) we demonstrate electronic density above 0.84 e -/Å 3 .The yellow features likely correspond to lone pairs at nitrogen sites.These shapes are deformed in such a way that they face the center of a tetrahedron formed by nitrogen atoms indicated by dashed lines.Very similar features are visible in our ELF calculations for 49 GPa.
intensity; σ(I)standard deviation of I; R1, wR2crystallographic R-factors; N par /N obsratio between number of parameters to number of observed reflections for I>2σ(I); ρ min , ρ maxminimum and maximum values of residual electronic density; ADPatomic displacement parameters (e.g.* -U equiv ., otherwise -U iso ).