# What is the structure of N₅P₃?

What is the structure of the molecule $\ce{N5P3}$? $\ce{N5P3}$ is not documented online, so could anyone please comment on the structure of the molecule:

• How many ligands does each phosphorous atom have?
• How many ligands does each nitrogen atom have?

I'm not sure why previous answer cited only the first paper on phosphorus(V) nitride $$\ce{P3N5}$$. A couple of years later the same team reported three polymorphs $$\ce{α,β,γ-P3N5}$$ with three-dimensional network. For $$\ce{α-P3N5}$$ and $$\ce{γ-P3N5}$$ crystal structures have been refined. Both modifications demonstrate vastly different structural types and coordination of pnictogens.

### Low-pressure phase $$\ce{α-P3N5}$$

Data obtained via powder neutron diffraction with higher resolution by using synchrotron radiation. The crystal structure was determined by direct methods and refined by the Rietveld method. [1, 2]

Structure description from [1]:

In $$\ce{α-P3N5}$$ zweier single chains occur parallel to $$[110]$$ and $$[1\bar{1}0]$$, in which the $$\ce{PN4}$$ tetrahedra are connected alternately through edge- and corner-sharing. These zweier single chains are linked together through additional vertex-sharing $$\ce{PN4}$$ tetrahedra. [...] The network structure of connected $$\ce{PN4}$$ tetrahedra in $$\ce{α-P3N5}$$ could be characterized by analogy to condensed silicates by the specific distribution of the occurring $$\ce{P_nN_n}$$ ring sizes.

Liebau formula: $$_\infty^3\ce{[P_3^{[4]} N_3^{[2]} N_2^{[3]}]}$$ *

Figure 1. Crystal structure of $$\ce{α-P3N5}$$, view along $$[010]$$. Purple coordination tetrahedra correspond to $$\ce{[PN4]}$$.

### Low-pressure phase $$\ce{β-P3N5}$$

$$\ce{β-P3N5}$$ was reported in a polymorphic mixture with $$\ce{α-P3N5}$$ and is it's stacking modification (no further crystallographic investigation has been published) [1]:

On the basis of the solved crystal structure of $$\ce{α-P3N5}$$, we are now working on the determination of structural models for $$\ce{β-P3N5}$$, and disordered $$\ce{P3N5}$$. The HRTEM results show that similar to the situation in the polytypes of the different stacking variants are based on the same structural modules, which are linked in different ways.

### High-pressure phase $$\ce{γ-P3N5}$$

Data obtained via powder X-ray diffraction. The crystal structure of $$\ce{γ-P3N5}$$ was determined by direct methods and refined using the Rietveld method. [3]

Structure description from [3]:

The novel high-pressure modification consists of a polymeric three- dimensional network structure of linked $$\ce{PN4}$$ tetrahedra and tetragonal-pyramidal $$\ce{PN5}$$ units. [...] Rods from trans-edge-sharing $$\ce{PN5}$$ units running along $$[010]$$ are linked by vertices, leading to the formation of layers perpendicular to $$[100]$$. [...] In accordance with the pressure–coordination rule a partial increase of the coordination number of the phosphorus atoms from four in $$\ce{α-P3N5}$$ to five in $$\ce{γ-P3N5}$$ is observed. [...] The density of $$\ce{γ-P3N5}$$ is $$32\%$$ higher than the density of $$\ce{α-P3N5}$$. [...] Therefore the high-pressure phase could show interesting materials properties (e.g. great hardness or low compressibility).

Liebau formula: $$\ce{P_5^{[5]}[ P^{[4]} N_3]N_2}$$ *

Figure 2. Crystal structure of $$\ce{γ-P3N5}$$, view along $$[010]$$. Purple coordination tetrahedra correspond to $$\ce{[PN4]}$$; yellow coordination pyramids — to $$\ce{[PN5]}$$.

* using Liebau's nomenclature for silicates, where the superscripted number in square brackets after the element symbol denotes the coordination number.

### References

1. Horstmann, S.; Irran, E.; Schnick, W. Synthesis and Crystal Structure of Phosphorus(V) Nitride α-P3N5. Angewandte Chemie International Edition in English 1997, 36 (17), 1873–1875. https://doi.org/10.1002/anie.199718731.
2. Horstmann, S.; Irran, E.; Schnick, W. Phosphor(V)-nitrid $$\ce{α-P3N5}$$: Synthese ausgehend von Tetraaminophosphoniumiodid und Kristallstrukturaufklärung mittels Synchrotron-Pulver-Röntgenbeugung. Zeitschrift für anorganische und allgemeine Chemie 1998, 624 (4), 620–628. https://doi.org/10.1002/(SICI)1521-3749(199804)624:4<620::AID-ZAAC620>3.0.CO;2-K.
3. Landskron, K.; Huppertz, H.; Senker, J.; Schnick, W. High-Pressure Synthesis of $$\ce{γ-P3N5}$$ at 11 GPa and 1500 °C in a Multianvil Assembly: A Binary Phosphorus(V) Nitride with a Three-Dimensional Network Structure from $$\ce{PN4}$$ Tetrahedra and Tetragonal $$\ce{PN5}$$ Pyramids. Angewandte Chemie International Edition 2001, 40 (14), 2643–2645. https://doi.org/10.1002/1521-3773(20010716)40:14<2643::AID-ANIE2643>3.0.CO;2-T.

$\ce{N5P3}$ is more commonly written as $\ce{P3N5}$, and known as triphosphorus pentanitride. It's a crystalline solid at ambient conditions and not a molecular compound. From the first publication that reported the pure compound and its structure [1]:

In the solid a three-dimensional cross-linked network structure of corner sharing $\ce{PN4}$ tetrahedra has been identified with 2/5 of the nitrogen atoms bonded to three P atoms and 3/5 of the nitrogen atoms bonded to two P atoms.

Only the combination of spectroscopical and diffraction methods, especially electron microscopy for structural analysis, enables a detailed structural and crystallographic characterization of $\ce{P3N5}$ as no conventional single-crystal data for structure determination have been available for this compound.

A representative for an unique binary structure type was found for the first time which combines a tetrahedral structure with the very rare molar ratio of 3:5 for the constituent elements.

### References

1. Schnick, W.; Lücke, J.; Krumeich, F. Chem. Mater. 1996, 8 (1), 281–286 DOI: 10.1021/cm950385y.