Structures of phospho­nitrides in light of the extended Zintl–Klemm concept

The extended Zintl–Klemm concept (EZKC) is applied to explain the crystalline structures of phospho­nitrides (also known as nitridophosphates in the chemical literature). The examples of (AE)₂AlP₈N₁₅(NH) (AE = Ca, Sr, Ba), Ge^IVPN₃ and MP₂N₄ (M = Be, Ca, Sr, Ba, Ge^II) are mainly discussed, although the examples of LiGaGe and LiGaGeO₄ have been also commented on due to their relation with BeP₂N₄. It is shown that the EZKC provides a better understanding of the structures of these compounds than in previous descriptions. In most of these nitrides, P atoms behave as pseudo-Si atoms and N atoms behave as pseudo-O atoms, so providing a good explanation for the four-connectivity of P atoms forming PN₄ units, which behave as pseudo-SiO₄ units like the SiO₄ units in many polymorphs of SiO₂. In addition, the EZKC shows that the notation of these compounds as phospho­nitrides is more appropriate than as nitridophosphates because N atoms act as the anions in these compounds.

1. Introduction

In recent decades, there has been a notable increase in interest in metal phospho­nitrides, largely due to their significant physical properties and potential applications. A significant proportion of these materials are ultra hard, and in addition, exhibit luminescent properties when doped with Eu²⁺. For illustrative purposes, it is worth including the series of ternary compounds MP₂N₄ (M = Be, Ca, Sr, Ba, Mn, Cd) (Karau & Schnick, 2005; Karau et al., 2007; Pucher et al., 2015) and the recently reported Ge^IIP₂N₄ (de Boer et al., 2023) and Ge^IVPN₃ (Ambach et al., 2024) compounds. In addition to the mentioned compounds, the recently reported and promising quaternary phospho­nitrides (AE)₂AlP₈N₁₅(NH) (AE = Ca, Sr, Ba) can be included in the list (Pointner et al., 2024).

Many articles concerning metal phospho­nitrides emphasize the synthesis methods, which are predominantly conducted under high-pressure (HP) conditions. Additionally, the physical properties of these compounds and the theoretical calculations designed to elucidate their luminescent properties are frequently discussed. However, the crystal structures, described with the classical cation-centered anionic polyhedra, have provided only limited insight into explaining the varying coordination numbers (CNs) of each atom species. For instance, the structures of (AE)₂AlP₈N₁₅(NH) (AE = Ca, Sr, Ba) compounds have been described as comprising three structural motifs (Pointner et al., 2024). First, there are three-dimensional tetrahedral PN₄ networks. Second, there are irregular AE-centered N polyhedra. Third, there are non-condensed (isolated) AlN₆ octahedra. In this context, an elucidation of the factors responsible for this diversity of structural elements would have been desirable; however, it has not been addressed to our knowledge. In particular, it has not been explained why the Al atoms are hexacoordinated (isolated AlN₆ octahedra) in (AE)₂AlP₈N₁₅(NH) (Pointner et al., 2024), whereas the P atoms are tetrahedrally coordinated in MP₂N₄ (M = Be, Ca, Sr, Ba) (Karau & Schnick, 2005; Karau et al., 2007; Pucher et al., 2015) as well as in Ge^IIP₂N₄ (de Boer et al., 2023) and Ge^IVPN₃ (Ambach et al., 2024). The cation/anion ratios (P/N ratio for example) cannot account for such different behaviors.

Challenging features also appear in the series of metal phospho­nitrides MP₂N₄ (M = Be, Ca, Sr, Ba, Mn, Cd) (de Boer et al., 2023). For example, BeP₂N₄ is phenakite-like at ambient conditions of temperature and pressure (Pucher et al., 2010); a structure containing a three-dimensional four-connected network of PN₄ tetrahedra, which transforms into an ultra-incompressible material of the spinel type at high-temperature and high-pressure conditions with P atoms in octahedral coordination (Vogel et al., 2020). Curiously, the remaining compounds in the series have more open, four-connected P skeletons, analogous to those found in oxo-aluminates and aluminosilicates (Santamaría-Pérez & Vegas, 2003).

In the same way, there are remarkable and still unexplained differences between the P skeletons of the related compounds Ge^IIP₂N₄ (de Boer et al., 2023) and Ge^IVPN₃ (Ambach et al., 2024). In Ge^IIP₂N₄, the P skeleton is revealed as a four-connected network, analogous to the Si skeletons of the phases of SiO₂ at room pressure. Conversely, in Ge^IVPN₃, the P skeleton forms zigzag chains of corner-connected PN₄ tetrahedra in which the P substructure is formed by planar chains of two-connected P atoms.

We consider that these seemingly strange connectivities between the P atoms are not capricious and must obey a law that accounts for such structural diversity. An example of how such unexpected behavior can be rationalized can be found in the works of Vegas and coworkers (Santamaría-Pérez & Vegas, 2003; Santamaría-Pérez et al., 2005), in which all aluminates and silicates with Al and Si skeletons were put on a common basis by applying the extended Zintl–Klemm concept (hereafter EZKC) to the cation subarrays of these two families of compounds. This concept was extended to many other compounds in subsequent works (Vegas et al., 2009; Vegas, 2018).

Here, we analyze the structures of several phospho­nitrides in the context of the EZKC to provide a rational explanation for their tetrahedral P skeletons, as well as for the unexpected octahedral coordination adopted by the P atoms in some of them. The main purpose of this work is to show that the EZKC concept, successfully applied to rationalize the structures of aluminates (Santamaría-Pérez & Vegas, 2003), silicates (Santamaría-Pérez et al., 2005), and the germanate (NH₄)₂Ge^[6][Ge^[4]₆O₁₅] (Vegas & Jenkins, 2017), allows us to account for the topology and connectivity of the P skeletons in phospho­nitrides, a feature that cannot be explained with the traditional ionic model. We will show that these compounds obey a unique principle that explains all their diverse atomic connectivity.

In Table 1 we have summarized the compounds that are discussed in this work, along with their formulae, the topological name of their structures, the pseudo-formulae obtained by applying the EZKC, and the corresponding references.

Table 1
Phosphonitrides fitting the extended Zintl–Klemm concept

Phospho­nitride section	Pseudo-formula	Topology of anion network†	ICSD reference code	Reference
(AE)2AlP8N15(NH) (AE = Ca, Sr, Ba) (Section 2.1)	(Ψ-Kr)2(Ψ-Ne)[Ψ-Si8O16]	4^4T170	–	Pointner et al. (2024)
Ge^IVPN3 (Section 2.2)	(Ψ-Ar)[Ψ-SO3]	2C1	176671	Ambach et al. (2024)
Ge^IIP2N4 (Section 2.3)	(Ψ-Zn)[Ψ-Si2O4]	sra	176669	Ambach et al. (2024)
CaP2N4, SrP2N4 (Section 2.4)	(Ψ-Kr)[Ψ-Si2O4]	tpd	416930	Karau et al. (2007)
BaP2N4 (Section 2.5)	(Ψ-Xe)[Ψ-Si2O4]	cbo	651183	Karau & Schnick (2005)
phe-BeP2N4 (R3) (Sections 2.6, 2.7)	(Ψ-He)[Ψ-Si2O4]	lcs	40797	Vogel et al. (2020)
sp-BeP2N4 (Fd3m) (Sections 2.7, 2.9)	(Ψ-He)[Ψ-Si2O4]	spn	40805	Vogel et al. (2020)
LiGaGe (Section 2.8)	(Ψ-He)[Ψ-Si]Si	lon	25310	Bockelmann & Schuster (1974)
LiGaGeO4 (Section 2.8)	(Ψ-He)[Ψ-Si2O4]	lcs	67239	Hartman (1989)
LiPN2 (Section 2.10.1)	(Ψ-He)[Ψ-SiO2]	dia	66007	Schnick & Lücke (1990)
Mn4P6N12S (Section 2.10.2)	[Ψ-V][Ψ-SiO2]6[Ψ-Ar]	sod	138799	Griesemer et al. (2021)
LiNdP4N8 (Section 2.10.3)	[Ψ-He][Ψ-La][Ψ-SiO2]4	pcl	429542	Kloß & Schnick (2015)
TiP4N8 (Section 2.10.4)	[Ψ-Ar][Ψ-SiO2]4	crb BCT	46202	Eisenburger et al. (2022)
SrH4P6N12 (Section 2.10.5)	[Ψ-Kr][H^+4][Ψ-SiO2]6	4^2L137	434261	Wendl & Schnick (2018)
SrP3N5(NH) (Section 3)	[Ψ-Kr][Ψ-SiO2]3	4^3T281	434532	Vogel & Schnick (2018)
Sr3P5N10Cl	[Ψ-Kr][Ψ-SiO2]5[Ψ-Ar]	JOZ	143745	Wendl et al. (2021)
Sr3P5N10Br			143746	Wendl et al. (2021)
Ba3P5N10Cl			238968	Marchuk et al. (2015)
Ba3P5N10Br			428381	Marchuk & Schnick (2015)
Ba3P5N10I (Section 3)			238969	Marchuk et al. (2015)

†Topology names are given according to the Reticular Chemistry Structure Resource (RCSR) nomenclature (lowercase bold three-letter symbols) (O'Keeffe et al., 2008), International Zeolite Association (IZA) nomenclature (uppercase three-letter symbols) and ToposPro NDn nomenclature (Blatov et al., 2021). In the NDn nomenclature, N designates the sequence of CNs of all inequivalent nodes of the net, D denotes the net periodicity (C, L or T for one-, two- or three-periodic nets) and n enumerates different topologies with the same ND symbol.

2. Description of the crystal structures

2.1. (AE)₂AlP₈N₁₅(NH) (AE = Ca, Sr, Ba) (orthorhombic, Pnma, No. 62)

This series of phospho­nitrides (also known as imido­nitridophosphates) was reported by Pointner et al. (2024). In that paper, the authors emphasize three matters relative to their structures: (i) concerns the existence of a tetrahedra network, formed by condensed PN₄ tetrahedra; (ii) refers to the presence of (AE)-centered coordination polyhedra; (ii) notes the existence of isolated, non-condensed AlN₆ octahedra. We have not found, however, any discussion regarding the correlation between the three structural moieties.

Fig. 1 shows the orthorhombic Pnma (No. 62) structure of these phospho­nitrides projected on the ac plane. It is formed by a very complicated arrangement of PN₄ tetrahedra leaving very elongated tunnels, in which groups of four (AE) atoms are located (see yellow spheres in Fig. 1). The P atoms forming the elongated spaces, in turn form an elongated P₁₂ ring. The pairs of AlN₆ octahedra are also visible in Fig. 1 at the corners and at the central part of the unit cell. Two of them are indicated with arrows. Even if they seem to be close to each other in projection, there is no connection between them. Further, these pairs of AlN₆ octahedra are surrounded by six-membered rings of PN₄ tetrahedra. Finally, three-membered (PN₄)₃ rings are also visible. One of them is marked by a blue circle in Fig. 1.

Figure 1 Orthorhombic structure of Ca2AlP8N15(NH) viewed in the ac plane. Ca: yellow, P: violet, N: blue, Al: light gray. The pairs of AlN6 octahedra, marked with arrows, close in projection, do not share any edges, but all PN4 tetrahedra are connected by sharing vertices, forming a three-dimensional network. A blue circle is drawn at the center of three tetrahedra sharing vertices (upper-right side).

After this description in terms of classical cation-centered anionic polyhedra, we will tackle the description of Ca₂AlP₈N₁₅(NH) in terms of the EZKC, followed by topological analysis of its P skeleton.

The EZKC involves the electron transfer between atoms, typically from the more electropositive to the more electronegative atoms. It can be considered that, in Ca₂AlP₈N₁₅(NH), the N atoms receive four electrons from the two Ca atoms, three from the Al atom, and eight electrons from the eight P atoms. Thus, there are 15 electrons donated to 15 N atoms, so that N atoms behave as pseudo-O (Ψ-O) atoms, P atoms behave as pseudo-Si (Ψ-Si) atoms, Al atoms behave as pseudo-Ne (Ψ-Ne) atoms, and Ca atoms behave as pseudo-Ar (Ψ-Ar) atoms. As in other networks consistent with the EZKC, and according to the 8-N rule, the P(Ψ-Si) skeleton is four-connected in Ca₂AlP₈N₁₅(NH), whereas Al³⁺ cations (Ψ-Ne) adopt an octahedral coordination, according to their donor character (see Santamaría-Pérez et al., 2005), and Ca²⁺ cations (Ψ-Ar) adopt a variable CN, as already pointed out by Pointner et al. (2024). According to the EZKC, the compound can then be reformulated as (Ψ-Ar)₂(Ψ-Ne)[Ψ-SiO₂]₈.

The P skeleton in Ca₂AlP₈N₁₅(NH) forms a 4⁴-coordinated net with the point symbol {3.4.5.6².7}₂{3.6⁵}{6⁶}; we have deposited it into the TopCryst database (Shevchenko et al., 2022) under the name 4⁴T170. Two views of this P skeleton are depicted in Fig. 2. They show the different rings existing in the P skeleton, i.e. three-, four-, six-, eight- and 12-membered rings. Some ring's connections, like the extended sequence of 4-8-4 rings, running parallel to the b axis [see Fig. 2(a)], resemble the same motif existing in the structures of CrB₄, AlPO₄·2H₂O (metavariscite), CaB₂C₂, CaAl₂Si₂O₈ (anortite), HP-CuCl and Ba[Al₂Si₂O₈] (paracelsian); the latter being a variant of the same skeleton (Vegas, 2018; chapters 8, 12–14; Shevchenko et al., 2022).

Figure 2 (a) Part of the P(Ψ-Si) skeleton in Ca2AlP8N15(NH) showing the four-connectivity of the Ψ-Si atoms. Note the sequence of 4-8-4 rings parallel to the b axis as well as the series of six-membered rings in boat conformation that are parallel to the a axis. (b) Another view of the same skeleton showing the 12-membered ring formed by the 3-4-1-2-4-3-3-4-1-3-3-2 P atoms. The elongated 12-membered ring is that embedding the four Ca atoms, also drawn in Fig. 1.

The partial skeleton depicted in Fig. 3 can help us to understand better the amazing structure of Ca₂AlP₈N₁₅(NH). It is composed of layers of puckered three-, six- and 12-membered rings. Within one sheet, each P atom is connected to three neighboring P atoms. The fourfold P-atom connectivity is achieved when each P atom also connects with one P atom from an adjacent layer. The interlayer contacts yield new six-membered boat-conformed vertical rings. Therefore, the N (Ψ-O) atoms are located near the middle point of each P–P contact, thus forming the three-dimensional network of PN₄ (Ψ-SiO₄) tetrahedra. In summary, we want to highlight that the structure of these phospho­nitrides with the tetrahedral coordination of P atoms can be explained in terms of the EZKC.

Figure 3 Two-connected layers of P (Ψ-Si) atoms in Ca2AlP8N15(NH) that are perpendicular to the b axis. They are projected on the ab plane. Each layer is formed by three-, six- and 12-membered rings in which P atoms are three-connected, but they become four-connected by forming one additional contact with P atoms in adjacent layers. The new rings between layers are of two types: hexagonal boat-conformation and squares. In one of the P6 rings with boat conformation (upper-right side), we have drawn the PN4 (Ψ-SiO4) tetrahedra. P: violet; N: blue.

This point is important because to explain any structure one must be able to account for the connectivity of the atoms forming the main skeleton (in this case, the P skeleton). If the P atoms are four-connected, that means that the P atoms behave as if they were Si atoms and this character is only explained by assuming that the P atoms convert into Ψ-Si atoms by transferring one electron each to the N atoms which, in turn, become Ψ-O, as indeed is proposed by the EZKC.

2.2. Ge^IVPN₃ (monoclinic, C2/c, No. 15)

Ge^IVPN₃ was synthesized at 44.4 GPa (Ambach et al., 2024) and its structure shows a quite different scenario. The structure was described as formed by alternating layers of GeN₆ octahedra and PN₄ tetrahedra along [100] [see Figs. 4(a) and 4(b)]. Each layer of GeN₆ octahedra consists of double zigzag chains of edge-sharing GeN₆ octahedra with no interconnection between the chains. In turn, the tetrahedral layers are built up of chains of condensed PN₄ tetrahedra (zweier single chains). Each tetrahedron shares two vertices with the two contiguous ones forming a [PN₃]⁴⁻ polyanion. Within the tetrahedral chains, the P atoms form planar two-connected zigzag chains as depicted in Figs. 4(c) and 4(d).

Figure 4 (a) Structure of Ge^IVPN3, projected on the ac plane, representing the chains of GeN6 octahedra that alternate with the zigzag tetrahedral chains (zweier), which are drawn solely in (b), intercalated with the Ge atoms. (c) The same structure projected onto the bc plane. The drawing represents only the chains of PN4 tetrahedra (Ψ-SO4). The P atoms are connected by black lines to show that the P(Ψ-S) atoms form chains similar to those of the real S atoms. (d) One isolated chain of PN4 tetrahedra shows its similarity with the chains represented in Fig. 5.

Interestingly, the structure permits an alternative description in terms of the EZKC. If we consider that the Ge atom acts as a donor and transfers one electron to the P atom, the latter transforms into Ψ-S. If in addition, the remaining three valence electrons of the Ge atom are transferred to the three N atoms, they transform into Ψ-O atoms. All in all, this results in the stoichiometry (Ψ-Zn²⁺)[Ψ-SO₃], whose crystal structure, projected on the ac plane in Fig. 4, will be analyzed next.

The zweier single chains of corner-sharing PN₄ tetrahedra, alternating with chains of edge-sharing GeN₆ octahedra are depicted in Fig. 4(a). Both motifs form blocks parallel to the (001) plane. The planes of Ge atoms become visible, alternating with the PN₄ chains when the N₆ octahedra are omitted [see Fig. 4(b)]. If the Ge atoms are neglected, the PN₄ chains appear isolated, projected onto the bc plane, as depicted in Fig. 4(c). One of the PN₄ chains is shown isolated in Fig. 4(d).

Since the P atoms are converted into Ψ-S, they are two-connected as characteristic of sextels, forming extended planar chains of P atoms separated at distances of 2.77 Å, with P—P—P angles of 115.68°. This motif is quite frequent in the extended polyanions in the structures of aluminates, silicates and phosphates, some of which are represented in Fig. 5. They correspond to: (a) fragment of a planar zigzag chain in real SO₃; (b) the structure of the polyanion [Si₂O₆]⁴⁻ ≡ (Ψ-SO₃) as an unbranched single chain in the silicate Na₄{uB,2,1¹_∞}[Si₂O₆] (Santamaría-Pérez et al., 2005); (c) The structure of SeO₂(E) ≡ SeO₃ (Vegas, 2018), where the presence of the LEP (E) on the Se atoms means that SeO₂(E) can be formulated as Ψ-SeO₃; (d) the fragment of the B33 structure of the Zintl phase BaSi in which the Si atoms (Ψ-S) form similar chains with the Si substructure in [Si₂O₆]⁴⁻ (Ψ-SO₃) and in SeO₂(E) in Figs. 5(b) and 5(c), respectively; (e) the structure of BaSiO₃ in which the [BaSi] partial structure is the same as that of BaSi (Rieger & Parthé, 1964) [Fig. 5(d)], even though in BaSiO₃ the Si atoms are tetrahedrally coordinated by four O atoms, forming the extended SiO₃ chains similar to those of Na₄Si₂O₆, drawn in Fig. 5(b).

Figure 5 (a) Fragment of the planar chain of fibrous SO3 formed by SO4 corner-sharing tetrahedra. The S atoms show the twofold connectivity characteristic of sextels. S: green, O: red. (b) Structure of the polyanion [Si2O6]^4− (Ψ-SO3) in the silicate Na4[Si2O6]. Si: dark gray, O: red. (c) Fragment of the planar chain of SeO2(E) ≡ SeO3. Se: light-purple; O: red. (d) Perspective view of a fragment of the structure of the Zintl phase BaSi (B33 type; Cmcm, No. 63), which shows the same zigzag chains of the Si (Ψ-S) atoms. Ba: dark blue; Si: light gray. (e) The structure of BaSiO3 (P212121, No. 19), where the [BaSi] substructure adopts the same topology as the Zintl phase BaSi (d) despite being embedded in an O-atom matrix. Views (a), (b), (c) and (d) are reproduced from Vegas (2018) with permission.

2.3. Ge^IIP₂N₄ (orthorhombic, Pna2₁, No. 33)

The synthesis and crystal structures of Ge^IIP₂N₄ and Ge^IVPN₃ have been reported by Vogel et al. (2020), de Boer et al. (2023) and Ambach et al. (2024). The peculiarity of Ge^IIP₂N₄ resides in the presence of divalent Ge^II cations, which must preserve a nonbonding lone electron pair (LEP) that is localized on the 4s orbital (Ambach et al., 2023). The orthorhombic (Pna2₁, No. 33) structure of Ge^IIP₂N₄ is represented in Fig. 6 and can be rationalized by applying the EZKC: the Ge atom transfers two electrons to two of the four N atoms, and each P atom transfers one electron (two in total) to the other two N atoms, resulting in the pseudo-formula Ge²⁺(P⁺)₂(N⁻)₄ ≡ [Ψ-Zn][Ψ-SiO₂]₂.

Figure 6 (a) View of the tetrahedral PN4 network of Ge^IIP2N4 along the c axis showing the octagonal tunnels lodging the Ge^II atoms. (b) The four-connected P skeleton (sra type) formed by the accordion-like ladders interconnected yo each other to build the octagonal tunnels.

In Ge^IIP₂N₄, like in other phospho­nitrides described in this article, the P atoms act as tetrels (Ψ-Si) so that the underlying P net is four-connected whose topology is of the sra type. The P atoms are coordinated tetrahedrally by four N atoms [see Fig. 6(a)]. When the N (Ψ-O) atoms are omitted, we obtain the skeleton drawn in Fig. 6(b) in which the four-connected P(Ψ-Si) skeleton is unveiled. It is formed by four- and eight-membered rings and shows strong similarities with the structure of the Zintl phase SrAl₂ drawn in Fig. 7(a). It is worth noting that the four d(P–P) distances (2.84, 2.85, 2.92 and 2.95 Å; mean value of 2.89 Å) are in good agreement with the sum of the nonbonding radii for P atoms (2R_P = 2.92 Å) reported by O'Keeffe & Hyde (1981).

Figure 7 (a) Structure of the Zintl phase SrAl2 (sra type). Al atoms, converted into Ψ-Si, form a four-connected skeleton, in accordance with the 8-N rule. (b) One of the accordion-like moieties that are condensed in the structure of the Zintl polyanion Ψ-Si2. The same skeleton is formed by the [AlSi]^− ≡ Ψ-[Si2] subarray in isostructural RbAlSiO4.

Curiously, the different structure of Ge^IIP₂N₄, when compared with those of the other MP₂N₄ (M = AE) compounds, has been interpreted as due to the location of LEPs on the Ge^II atoms (Vogel et al., 2020). However, we consider that it can be interpreted otherwise. As we have mentioned above, the [Ψ-SiO₂]₂ framework is similar to that of the Al skeleton (Ψ-Si atoms) in the Zintl phase SrAl₂ [Fig. 7(a)]. Since the Sr²⁺ cations (Ψ-Kr) do not have LEPs, this type of skeleton, found in Ge^IIP₂N₄, cannot be correlated with the presence of LEPs in Ge^II atoms. Instead, it should be regarded as a new example of the Ψ-Si skeleton that, in this case, results from the transfer of electrons from the less electronegative Ge and P atoms to the more electronegative N atoms, thus converting Ge and P atoms into Ψ-Zn and Ψ-Si atoms, respectively, and yielding the pseudo-formula [Ψ-Zn⁰][Ψ-SiO₂]₂.

Alternatively, the structure can be rationalized as a condensation of the accordion-like ladders, like that represented as a separated moiety in Fig. 7(b). In these ladders, each atom (P atoms in Ge^IIP₂N₄ and Ψ-Si atoms in SrAl₂) is three-connected [see Figs. 6(b) and 7(b)] and becomes four-connected when the ladders condense in the 3D skeletons [see Figs. 6(a) and 7(a)]. The ladder, separated from the Ψ-Si skeleton of SrAl₂ [Fig. 7(b)], has its analog extracted from the Ge^IIP₂N₄ structure in Fig. 6(a) and is separated in Fig. 8(a).

Figure 8 (a) One three-connected ladder-like fragment of PN4 tetrahedra extracted from Ge^2+(P^+)2(N^−)4 ≡ Ψ-Zn^0Si2O4 structure represented in Fig. 6(a). On the right-hand side, we have maintained two additional tetrahedra to illustrate its provenance from a four-connected network. P: violet; N: blue. (b) The partial structure of the [AlSiO5]^3− ≡ Ψ-P2O5 in Al2SiO5 (sillimanite). Al: yellow; Si: dark gray; O: red.

According to the 8-N rule, the three-connected motif, characteristic of pentels, is also finely tuned in sillimanite, one of the polymorphs of Al₂SiO₅, whose structure is represented in Fig. 8(b). The sillimanite structure has already been rationalized in terms of the EZKC (Santamaría-Pérez et al., 2005). In particular, the three-connected Al and Si atoms in this structure can be understood if one of the two Al atoms, in this case Al1, acts as a donor and transfers two electrons to Al2 and the third valence electron to the Si atom. Consequently, both species, Al2 and Si, convert into Ψ-P yielding the pseudo-formula Al³⁺[Ψ-P₂O₅][Ψ-Ne][Ψ-P₂O₅].

As reported by Santamaría-Pérez & Vegas (2003) and Vegas (2018), and according to both the EZKC and the 8-N rule, the Ψ-P atoms should be three-connected. In the skeleton of the pseudo-formula [Ψ-Ne][Ψ-P₂O₅], the five O atoms are located near the Ψ-(P—P) bonds and on the LEP associated with each P atom, as it is clearly seen in the two structures shown in Fig. 8. It should be added that these two ladder-like substructures, P₂O₅ and [AlSiO₅]³⁻, differ in that the one in sillimanite is almost planar [Fig. 8(b)], in contrast to the accordion-like configuration of the same motif in Ge²⁺(P⁺)₂(N⁻)₄ ≡ Ψ-Zn⁰Si₂O₄ [Fig. 8(a)].

The above explanation of the structure of GeP₂N₄ in terms of the EZKC can be extended to the isostructural compounds KAlSiO₄ and KZnPO₄. In the former, the transfer of one electron from K → Al, converts the Al atom into Ψ-Si which, with the real Si atom, forms a four-connected network of stoichiometry Si₂O₄ in the pseudo-formula [Ψ-Ar][Ψ-SiO₂]₂. In KZnPO₄, the transfer of one electron from K → Zn, results in the pseudo-formula [Ψ-Ar][Ψ-AlPO₄], whose AlP substructure forms a four-connected network as it does the binary AlP compound itself. Note also that AlPO₄ is a SiO₂ homeotype. In particular, the mineral berlinite, α-AlPO₄ (P3₁21, No. 152), is related to the α-quartz structure (with AlO₄ and PO₄ units replacing two SiO₄ units), with its c axis being double that of quartz.

The structural significance of these Ge-containing compounds (Ge^IVPN₃ and Ge^IIP₂N₄) resides in that both structures are explained in the frame of the EZKC despite the different valence states of the Ge atoms. It is also worth mentioning that the donor Ge^IV atoms are octahedrally coordinated, a feature coincident with the Al^[6] and Si^[6] atoms that also act as donors in some aluminates and silicates, e.g. the octahedral coordination of the donor Al1 atom in sillimanite (Al₂SiO₅) (Vegas, 2018) and the Si^[6] atoms that coexist with Si^[4] atoms in the oxonitridosilicate Ce₁₆Si₁₅O₆N₃₂ (Köllisch & Schnick, 1999). This structure was reinterpreted by Liebau (1999). The double coordination of Si atoms was later interpreted by Santamaría-Pérez et al. (2005) in the context of the EZKC. The octahedral coordination of the Si^[6] atoms was attributed to their donor character (Si⁴⁺) whilst the tetrahedral coordination was assigned to the acceptor Si atoms (Siⁿ⁻). It should be remarked that both Ge^[4]O₄ tetrahedra and Ge^[6]O₆ octahedra also coexist in the germanate (NH₄)₂Ge^[6][Ge^[4]₆O₁₅] (Cascales et al., 1998). This feature, earlier considered a rarity, was further rationalized by Vegas & Jenkins (2017) in terms of the EZKC. Because Ce₁₆Si₁₅O₆N₃₂ and (NH₄)₂Ge^[6][Ge^[4]₆O₁₅] were obtained at ambient pressure, they break the idea that octahedral coordination for silicon and germanium can only occur under HP conditions, as in stishovite, the HP-SiO₂ polymorph.

Thus, an important feature unnoticed by Ambach et al. (2024) is that the extended Zintl ion [Ge²⁻]_∞ chains existing in the nitride Sr₃Ge₂N₂, as well as the zigzag chains of P atoms underlying in the [PN₃]⁴⁻ tetrahedral chains in Ge^IVPN₃, are the result of a similar electron transfer predicted by the EZKC. In both cases, the Ge and P atoms are converted into Ψ-Se and Ψ-S, respectively. The example of Sr₃Ge₂N₂ is shown in Fig. 9.

Figure 9 Stereopair of the unit cell of Sr3Ge2N4 showing the zigzag chains formed by the Ge^2− anions in the form of an extended Ψ-Se Zintl polyanion. The second Ge atom (gray spheres) also converted into Ψ-Se together with the N atoms (blue spheres), converted into Ψ-O, form molecules of Ψ-SeO2, similar with those occurring in real SO2. The Sr atoms have been omitted.

2.4. CaP₂N₄ and SrP₂N₄ (hexagonal, P6₃, No. 173)

The syntheses and crystal structures of isostructural CaP₂N₄ and SrP₂N₄ were reported by Karau et al. (2007) and Pucher et al. (2015), respectively. The structure is hexagonal and is represented in Fig. 10. Both KAlSiO₄ (megakalsilite) and KZnPO₄ also belong to this structure type. Like the Be- and Ba-containing compounds, the P skeleton, drawn with red lines in Fig. 10, is four-connected, building a network of PN₄ corner-sharing tetrahedra. The underlying P net is of the tpd type, adopted by the [AlGeO₄] ≡ [Ψ-SiGeO₄] partial structure in KAlGeO₄. It is also reported as a hypothetical zeolite (PCOD8128676) in TopCryst. Sr atoms are located inside the hexagonal tunnels which run parallel to the c axis.

Figure 10 The four-connected P skeleton, connected with red lines, in compounds CaP2N4 and SrP2N4. It contains four-, six-, eight- and ten-membered rings. Some of them are drawn with their PN4 tetrahedra.

The four-connected P skeleton is represented in Fig. 10, projected near the ab plane, manifesting the puckered hexagonal 6³ layers, characteristic of the diamond and Si structures. However, these layers connect each other differently to those of Si. The diamond-like structure of Si only contains six-membered rings, while in CaP₂N₄ and SrP₂N₄, the interlayer connections yield four-, six-, eight- and ten-membered rings (see Fig. 10). Nevertheless, the important point is that each P atom is connected to four alike atoms. According to previous experience in the interpretation of the structures of aluminates and silicates in the context of the EZKC (Santamaría-Pérez & Vegas, 2003; Santamaría-Pérez et al., 2005), this four-connectivity indicates that the P atom behaves as a tetrel (Ψ-Si).

This four-connectivity of P atoms can be explained with the EZKC if we admit that the Ca (Sr) atom transfers its two valence electrons to two N atoms and each P atom transfers one electron to the other two N atoms. This implies that Ca (Sr) becomes a Ψ-Ar (Ψ-Kr), P becomes a Ψ-Si, and N becomes a Ψ-O, so the pseudo-formula of CaP₂N₄ is [Ψ-Ar][Ψ-SiO₂]₂ and of SrP₂N₄ is [Ψ-Kr][Ψ-SiO₂]₂. Like in the structures of silica and in the skeletons of silicates as well, the N atoms (Ψ-O) situate near the midpoint of each (Ψ-Si)–(Ψ-Si) contact, so forming the tetrahedral P₂N₄ (Ψ-Si₂O₄) network represented in Fig. 10.

2.5. BaP₂N₄ (cubic, Pa3, No. 205)

The cubic structure of BaP₂N₄ consists of Ba²⁺ cations embedded in a three-dimensional framework of corner-sharing PN₄ tetrahedra, as already recognized by Karau & Schnick (2005). They stated that `from a formula point of view, the [P₂N₄]²⁻ substructure is isoelectronic with SiO₂. However, its topology is quite different from any known SiO₂ polymorph'. In this regard, we consider that this assertion, being correct, falls short in identifying the structural similarity of BaP₂N₄ with one of the HP phases of CaB₂O₄(VI) reported by Marezio et al. (1969) and the implications of this similarity.

The underlying net in BaP₂N₄ is cbo (from CaB₂O₄), also classified as hypothetical zeolite (PCOD8330894) in TopCryst. The structure contains a 3D network of PN₄ tetrahedra sharing corners [Fig. 11(a)]. This network forms hexagonal tunnels where the Ba atoms are lodged. When the Ba and N atoms are neglected, the underlying four-connected P skeleton (Ψ-Si) is unveiled. This distorted P skeleton is drawn in Fig. 11(b) showing that each P atom is connected to four alike atoms, a feature that is characteristic of tetrels but not expected for pentels, i.e. the P atoms existing in BaP₂N₄. The fourfold connectivity is also not expected for triels (elements of Group 13) either. However, it is formed by the B atoms in CaB₂O₄. Next, we will show that the four-connected networks of both P and B atoms in BaP₂N₄ and CaB₂O₄(VI), respectively, can be rationalized with the EKZC.

Figure 11 (a) Structure of BaP2N4 projected on the ab plane. The PN4 network forms hexagonal tunnels where the Ba atoms are lodged. (b) The P skeleton of BaP2N4 (cbo) shows a four-connectivity characteristic of tetrels. This can be understood with the EZKC if we consider that P atoms act structurally as Ψ-Si atoms.

The structure of CaB₂O₄(VI) can be understood if the two valence electrons of the Ca atom are transferred to the two B atoms to form Ψ-C atoms, so the compound can be formulated as Ca²⁺(B⁻)₂O₄ ≡ Ca²⁺[Ψ-CO₂]₂ ≡ [Ψ-Ar][Ψ-CO₂]₂. Similarly, considering that in BaP₂N₄ each Ba atom transfers its two valence electrons to two N atoms and that each P atom transfers one electron to the remaining two N atoms, we obtain the pseudo-formula unit Ba²⁺(P⁺)₂(N⁻)₄ ≡ Ba²⁺[Ψ-Si₂O₄] ≡ [Ψ-Xe][Ψ-SiO₂]₂. Both pseudo-formula units in CaB₂O₄(IV) and BaP₂N₄ are consistent with the four-connectivity observed for P in BaP₂N₄ and for B in CaB₂O₄(IV), as it occurs in the SiO₂ polymorphs (Marezio et al., 1969), since P and B atoms behave as pseudo atoms in Group 14.

2.6. BeP₂N₄ (rhombohedral, R3, No. 148 and cubic, Fd3m, No. 227)

The phe-BeP₂N₄ phase (R3, No. 148) is of the lcs topological type. It was synthesized according to

at high-pressure and high-temperature conditions (Vogel et al., 2020).

phe-BeP₂N₄ is isostructural to mineral phenakite (Be₂SiO₄) although Be plays the role of Si and P the role of Be. phe-BeP₂N₄ transforms into a spinel-type structure (hereafter sp-BeP₂N₄) at 47 GPa and 1800 K. Both phenakite and spinel structures are drawn in Fig. 12. The spinel phase is quenchable to room pressure yielding an ultra-incompressible material (Vogel et al., 2019). Vogel and coworkers stated that this new phase was predicted from theoretical calculations. However, they focused on the spinel-type structure and did not discuss other possible intermediate phases, like the olivine-type structure, in the reported phenakite → spinel transition. It should be recalled that the olivine structure is typically a phase observed at lower pressures than the spinel phase in many M₂XO₄ compounds and that the olivine → spinel transition at HP is undergone by several M₂XO₄ compounds (Vegas et al., 2009; Vegas, 2018). The paradigmatic example is the olivine → spinel transition undergone by mineral forsterite (Mg₂SiO₄) at 22 GPa and 1273 K (Sasaki et al., 1982). This point is important because, unlike phenakite (Be₂SiO₄) in which both Be and Si atoms are tetrahedrally coordinated (P and Be atoms in BeP₂N₄), in both the olivine and spinel structures, the Mg atoms are octahedrally coordinated and Si atoms center the SiO₄ tetrahedra [see Fig. 12(b)].

Figure 12 Structures of (a) phe-BeP2N4 and (b) sp-BeP2N4. In (a) both Be and P atoms are tetrahedrally coordinated. In (b) the P atoms center PN6 octahedra whilst the Be atoms center BeN4 tetrahedra.

The description of the phenakite-like structure of BeP₂N₄ [see Fig. 12(a)] is not an easy task even applying the EZKC that has allowed us to describe the previous phospho­nitrides. Our first approach was to investigate whether the BeP₂ substructure in BeP₂N₄ (the Be₂Si substructure in Be₂SiO₄) had any structural similarity with any of the binary alloy structures, according to the idea of O'Keeffe & Hyde (1985) of describing the structures of oxides as oxygen-stuffed alloys. A topological analysis carried out with the ToposPro (Blatov et al., 2014) package revealed that no binary alloy structure matched those of the BeP₂ or Be₂Si subarrays in BeP₂N₄ and Be₂SiO₄, respectively. This issue confers a great singularity to the phenakite-type structure which could be an indication of a very narrow range of stability for this unusual skeleton. Only ten isostructural compounds have been collected in the ICSD: Be₂SiO₄, Li₂BeF₄, Li₂SeO₄, Zn₂SiO₄, Li₂WO₄, LiAlSiO₄, LiAlGeO₄, β-Si₃N₄, LiGaSiO₄ and LiGaGeO₄.

The phenakite structure of BeP₂N₄ will be described based on the partial structure of the P atoms. Its singularity resides in that the P atoms form a three-dimensional four-connected skeleton which has been drawn, in projection, in Fig. 13(a). When drawn in perspective [Fig. 13(b)], one can see that the P skeleton contains extended hexagonal tunnels running parallel to the c axis and centered at (x, y) positions (0, 0), (⅓, ⅔) and (⅔, ⅓) in the ab plane [see also Fig. 12(a)]. These tunnels are blocks of a lonsdaleite-type structure (also wurtzite type), containing both chair and boat conformation six-membered rings. A fragment of such a tunnel is drawn in Fig. 13(c) to show the chair-conformed rings forming the layers perpendicular to the c axis. These layers are stacked in an …ABABAB… sequence which gives rise to additional boat-conformed rings, running parallel to the c axis [see also Fig. 14(c)].

Figure 13 (a) The P substructure (violet spheres) in phe-BeP2N4 projected on the ab plane. (b) Perspective view of two connected hexagonal tunnels formed by the P atoms in BeP2N4, where some Be atoms (gray spheres) have been inserted for reference. The fourfold connectivity of the P skeleton is clearly evident. (c) A fragment of the lonsdaleite-type tunnel formed by the P atoms in phe-BeP2N4 which shows the tetrahedral coordination of the P atoms. PN4 tetrahedra are drawn in one of the rings of boat conformation. The linear -P-Be-P-Be-P- chains, parallel to the c axis, are clearly evident. (d) A fragment with the diamond structure which connects the tunnels with the lonsdaleite structure. P: violet; Be: gray.

Figure 14 (a) Perspective view of the tetrahedral diamond structure (dia) showing the chair conformation rings. (b) The structure of hexagonal diamond (lon) showing the horizontal layers of rings in chair conformation and the vertical layers of hexagons in boat conformation. (c) Stereopair in perspective of the BeP2 substructure in phe-BeP2N4 showing two interconnected lonsdaleite-type tunnels yielding the irregular four-connected P skeleton. The two conformations (boat and chair) of the six-membered rings are visible. Be: gray; P: violet.

The relative positions of these tunnels are such that, when they connect to each other, new six-membered rings are formed, all of them having a chair conformation like in the diamond-type structure. The result is the irregular tetrahedral skeleton represented in Fig. 14(c). Thus, the P skeleton in BeP₂ is formed by lonsdaleite-type blocks interconnected by diamond-type fragments like that represented in Fig. 13(d). Both fragments, lon type [Fig. 13(c)] and dia type [Fig. 13(d)] can be compared with the respective structures of silicon in Figs. 14(a) and 14(b). The Be atoms, located midway between the two opposite P atoms of the rings in boat conformation, give rise to extended linear chains -P-Be-P-Be-, parallel to the c axis, which can be seen in Figs. 13(c) and 14(c). In the former, the PN₄ tetrahedra have been highlighted in a boat-conformed hexagon.

The four-connected skeleton formed by the P atoms in phe-BeP₂N₄ is unexpected. According to the 8-N rule, that connectivity is characteristic of tetrels (C, Si, Ge) but not for pentels. However, such P skeletons can be rationalized with the EZKC as follows. If we assume that the Be atom transfers its two valence electrons to two N atoms and that the two P atoms each transfer one electron to the two remaining N atoms, then the Be atom becomes Ψ-He, the two P atoms become Ψ-Si and the four N atoms become Ψ-O, so that BeP₂N₄ can be rewritten as Be²⁺(P⁺)₂(N⁻)₄ ≡ Be²⁺[Ψ-Si₂O₄] ≡ [Ψ-He][Ψ-SiO₂]₂, i.e. a new He-filled [Ψ-SiO₂] structure intermediate between those of cristobalite and tridymite. Recall that the Si skeleton in SiO₂ (tridymite) is of the lonsdaleite type.

This interpretation, based on the four-connected skeleton [Figs. 13(b) and 14(c)], provides a new example of the general trend of binary/ternary alloys to form four-connected skeletons (Vegas & García-Baonza, 2007). Since the N atoms are transformed into Ψ-O atoms, they are located near each (Ψ-Si)—(Ψ-Si) bond thus resulting in the tetrahedral coordination shown for the P atoms, as explained for other oxides such as aluminates and silicates (Santamaría-Pérez et al., 2005). It should be added that if we allow only the electron transfer from Be → N and not that from P → N, then, the resulting pseudo-formula would be [Ψ-He][Ψ-PON]₂ which corresponds to that of the real PON compound, isoelectronic with SiO₂, obtained as quartz, cristobalite and moganite types of SiO₂ (Léger et al., 1999).

2.7. Alternative electron transfers for BeP₂N₄ compatible with the EZKC

In addition to the already proposed application of the EZKC to explain the structure of phe-BeP₂N₄ as [Ψ-He][Ψ-SiO₂]₂, three alternative pseudo-formulae can be obtained, which could potentially help us to understand the phe-BeP₂N₄ structure. Note that all four different pseudo-formulae according to the EZKC result from the different possible distributions of the valence electrons between the three types of atoms. The difference between the pseudo-formula explained in Section 2.6 and the three interpretations quoted below is that the three new pseudo-formulae correspond to olivine-type pseudo-oxides.

The additional EZKC pseudo-formulae for phe-BeP₂N₄ are:

(i) Ψ-Al₂BeO₄ (chrysoberyl, olivine-type). If the P atoms transfer four electrons to the four N atoms, then the P atoms become Ψ-Al and the N atoms transform into Ψ-O.

(ii) Ψ-AlMg(Ψ-BO₄) (pseudo-sinhalite, olivine-type). The two P atoms transfer a total of five electrons (one to Be and one each to four N atoms). Of the two P atoms, the one that transfers two electrons becomes Ψ-Al and the other that transfers one electron transforms into Ψ-Mg. On the other hand, the Be and N atoms become Ψ-B and (Ψ-O), respectively, yielding the Ψ-BO₄ group.

(iii) Ψ-Mg₂(CO₄) (non-existing; analogous to the olivine-type Mg₂SiO₄). The P atoms can transfer six electrons (two to Be and one each to four N atoms). Thus, the two P atoms become Ψ-Mg, Be transforms into Ψ-C and the N atoms into Ψ-O, so that BeN₄ can be reformulated as Ψ-CO₄.

Note that Al₂BeO₄ also has its analog in the spinel Al₂MgO₄ (spn) and that the non-existing Mg₂CO₄ has its analog in forsterite Mg₂SiO₄.

To prove whether these additional EZKC pseudo-formulae leading to olivine-like phases could be observed in BeP₂N₄ under any pressure range, for example, as an intermediate stage between the phenakite-like and spinel-like phases, we have performed ab initio calculations of the olivine structure in BeP₂N₄. We found that this phase is not thermodynamically stable between the phenakite-like and spinel-like structures. In addition, we have simulated a distorted olivine (Cmcm, No. 63) phase and found that it is not competitive with the phenakite and spinel phases (see Fig. 15). Therefore, BeP₂N₄ is a rather curious AB₂X₄ compound since it does not show an olivine-like phase at lower pressures than those found for the spinel-like phase. This means that the EZKC explanation we gave in Section 2.6 seems to be the most likely possibility to explain the phenakite structure in BeP₂N₄.

Figure 15 Energy as a function of volume for the phenakite-like (P3, No. 148), olivine-like (Pnma, No. 62), distorted-olivine-like (Cmcm, No. 63) and spinel-like (Fd3m, No. 227) structures in BeP2N4.

An alternative way of checking which of the three alternative pseudo-formulae of BeP₂N₄, compatible with the EZKC, is the most probable to explain the structure of phe-BeP₂N₄ is to make first-principles simulations of phe-BeP₂N₄ to obtain the atomic (B, P and N) charges with density-based and orbital-based methods. In this way, the Bader atomic charges have been calculated according to the density-based Quantum Theory of Atoms in Molecules (QTAIM) (Bader, 1985) using the CRITIC2 software (Otero-de-la Roza et al., 2009; Otero-de-la Roza et al., 2014). In addition, Löwdin and Mulliken charges have been calculated using the orbital-based LOBSTER software (Nelson et al., 2020).

For phe-BeP₂N₄, the average Bader charges are Be^+1.10, P^+2.40 and N^−1.48. The average Löwdin charges are Be^+1.50, P^+1.85 and N^−1.30. The average Mulliken charges are Be^+1.70, P^+2.05 and N^−1.45. These results clearly demonstrate that Be and P atoms donate charge to N atoms; a result that agrees with the donor character of Ge and P atoms in Ge^IVPN₃. It can be observed that QTAIM calculations provide the most ionic picture as already discussed in the literature (Kaupp, 2014). In conclusion, the last three EZKC pseudo-formulae, which assume that Be does not donate charge or even that it accepts charge, can be ruled out to explain the structure of phe-BeP₂N₄. This result is consistent with the lack of observation of the olivine structure in BeP₂N₄ as a possible structure in the pressure range explored (see Fig. 15).

2.8. LiGaGe and LiGaGeO₄

We discussed in Section 2.6 that the cation subarray (BeP₂) in phe-BeP₂N₄ does not match the structure of any other binary (ternary) alloy. This lack of reference has led us to search for possible relationships between the cation substructures of the isostructural phenakite-type compounds and the structures of their corresponding alloys. The analyzed compounds were those mentioned in Section 2.6 and for only one of them, LiGaGeO₄, we have found the existence of a Zintl phase (LiGaGe) (lon type) with the same composition as the cation array of the oxide. The structure of LiGaGeO₄ (lcs type) is represented in Fig. 16(a) and that of the Zintl phase LiGaGe is drawn in Fig. 16(b).

Figure 16 (a) Perspective view of the [GaGe]^− subarray [(Ψ-Ge)(Ge)] in phe-LiGaGeO4 (lcs type), which can be compared with the BeP2 substructure in phe-BeP2N4 represented in Fig. 13(c). The drawing shows the connected lon-type tunnels yielding the four-connected P skeleton. The two conformations (boat and chair) of the six-membered rings are visible. Be: gray; P: violet. (b) The filled wurtzite-type structure of the Zintl phase LiGaGe. The four-connected skeleton is built from the subarray [GaGe]^− ≡ Ψ-Ge. The Li atoms center the hexagonal tunnels running parallel to the c axis. Compare with Fig. 13(b). Li: ochre; Ga: green; Ge: dark blue. (c) The stuffed diamond-like structure of the half Heusler phases such as LiAlSi and LiGaSi.

Both structures can be interpreted as if the Li atoms would donate their valence electron to the Ga atoms, converting them into Ψ-Ge, so that LiGaGe can be reformulated as Li⁺[GaGe]⁻ ≡ [Ψ-He][Ψ-Ge₂] which is equivalent to an He-filled structure identical to the lonsdaleite (wurtzite) type structure of Si(Ge), represented in Fig. 14(b). In the same manner, the phenakite-type structure of LiGaGeO₄ can be formulated as a [Ge₂O₄] skeleton, filled with Li⁺ cations [Fig. 16(a)].

The important point is that the LiGaGe alloy has a filled wurtzite-type structure that corresponds with one of the fragments (hexagonal tunnels) building the partial structure of phe-LiGaGeO₄. According to the Zintl concept, LiGaGe can be reformulated as Li⁺[Ga⁻Ge] ≡ [Ψ-He][Ψ-Ge]Ge ≡ Ψ-(He)Ge₂, i.e. a He-filled lonsdaleite-type structure of Ge atoms. It is worth noting that a tetrahedral skeleton characteristic of tetrels (C, Si, Ge) is here adopted by the P atoms (pentels), whose skeleton, containing fragments (columns) of a lonsdaleite-type structure, is again drawn in perspective in Fig. 16(a) for comparison with Fig. 14(b).

It is now appropriate to compare the structures of LiGaGe and phe-BeP₂N₄. The wurtzite-type tunnels formed by the P atoms in Fig. 13(b) show their similarity to the wurtzite structure of Fig. 14(a) but, at the same time, the differences become apparent. They can be summarized in two features: (i) As discussed above, in BeP₂N₄ the Be atoms no longer center the wurtzite tunnels. (ii) The periodicity of the tunnels in the ab plane [Fig. 14(a)] is broken in BeP₂N₄ and the connection between the tunnels is now achieved by rings in chair-conformation [see Fig. 13(b)].

The structural relationship between phe-BeP₂N₄ and LiGaGe has allowed the structure of phe-BeP₂N₄ to be interpreted not only in terms of the EZKC but also of the oxidation pressure concept. Such an explanation can be attained if we consider the oxide LiGaGeO₄ (lcs type), one of the ten compounds having the phenakite structure, as mentioned in Section 2.6. In the structure of LiGaGeO₄ represented in Fig. 16, the Ga and Ge atoms are not distinguished because they could not be differentiated in the crystal structure determination.

2.9. sp-BeP₂N₄ (spn type)

We would also like to comment on the spinel-type phase of BeP₂N₄ [Fig. 12(b)]. It has been observed that the structure of phe-BeP₂N₄ contains slightly distorted octahedra of Be atoms (i.e. Si atoms in the mineral phenakite, Be₂SiO₄). The octahedra [Fig. 17(a)] are contained into an extremely distorted Be₈ cube that contains not only the Be₆ octahedron but also eight P atoms, drawn as purple spheres in Fig. 17(a). Despite its irregularity, the image in Fig. 17(a) is reminiscent of a fluorite-type structure, so that phe-BeP₂N₄ can be considered as a frustrated fluorite-type structure. This makes sense if we compare this structure with that of monoclinic β-Li₂SO₄ (P2₁/c) (Alcock et al., 1973), shown in Fig. 17(b). The relationship between the structure of β-Li₂SO₄ and the antifluorite (anti-CaF₂) structure was first noticed by Parfitt et al. (2005) and is much closer to the antifluorite-type than it is to phe-BeP₂N₄.

Figure 17 (a) Fragment of the hexagonal structure of phe-BeP2N4, isostructural to the mineral phenakite Be2SiO4. Be: green; P: violet (N atoms omitted). The fragment has similarities with the Li2S substructure of β-Li2SO4 (P21/c) at ambient conditions. S: yellow; Li: blue (O atoms have omitted). The stereopair of the room-temperature structure of β-Li2SO4 is shown in (b). The Li2S substructure forms a distorted antifluorite structure in which the S atoms form a distorted fcc array, with the 2n tetrahedral voids occupied by Li atoms. Note the irregularity of both the Li8 and S8 cubes, in contrast with the rather regular S6 octahedron. Reproduced from Vegas (2018) with permission.

The similarity between both structures is only apparent because in the partial motif of phe-BeP₂N₄, represented in Fig. 17(a). The Be₆ octahedra share faces, a feature that cannot exist in Li₂SO₄ which has a distorted fcc array of S atoms as it corresponds to its cubic fluorite-type structure.

Since the binary Li₂S sulfide is fluorite type, the distortion of that cubic structure in the oxide Li₂SiO₄ has been explained by Vegas & Jenkins (2017) in the frame of the oxidation pressure concept. Thus, the insertion of four O atoms per Li₂S unit provokes a strong distortion of the antifluorite (anti-CaF₂) substructure of Li₂S in Li₂SO₄, but when β-Li₂SO₄ is heated, the pressure exerted by the O atoms is released and a cubic phase with antifluorite structure is obtained. However, the pressure exerted by the O atoms is not high enough to cause the stabilization of any of the two possible HP phases of Li₂S, i.e. anticotunnite or anti-Ni₂In, as a substructure in Li₂SO₄. Nonetheless, when extra pressure is applied to β-Li₂SO₄, the olivine-type structure is obtained. For a complete analysis of the phase transitions observed in Li₂S and Li₂SO₄, see Vegas (2018).

The inclusion of the Li₂S/Li₂SO₄ structures pair into the discussion is appropriate, considering that one of the ten phenakite-type compounds is the closely related Li₂SeO₄ (Hartman, 1989). This is consistent with the rule that within a group of the Periodic Table of the Elements, the structure of a heavier analog (the selenate) can occur for the lighter one (the sulfate) at HP. Since the HP polymorph of Li₂SO₄ has an olivine-type structure, the existence of a phenakite structure, at lower pressures, should not be discarded. In the same way, the stabilization of an olivine-type structure for the selenate could also be expected.

This reasoning can be also applied to the description of the sp-BeP₂N₄ structure. It is worth recalling that the connection of the structures of Li₂S with those of the antifluorite and olivine types conveys with the transition path anti-CaF₂ → anti-PbCl₂ → anti-Ni₂In → anti-MgCu₂. This transition pathway, observed in several AB₂ compounds (Vegas, 2011), also covers the phe → sp transition in BeP₂N₄ (Vogel et al., 2020) because this transition involves the BeP₂ → MgCu₂ transition undergone by the cation substructures. Notice the partial antifluorite structure in Fig. 17(a) and the regular MgCu₂-type of the BeP₂ array drawn in Fig. 18.

Figure 18 Stereopair of the MgCu2-type substructure formed by the BeP2 subarray in the HP spinel-type phase of BeP2N4. P: purple; Be: green (N atoms are omitted). The Be atoms center the P12 truncated tetrahedra. When the Be atoms are connected, they form a diamond-like network.

It is important to note that both the alloy Be₂C (the lighter analog of Be₂Si) and Mg₂Si exhibit an antifluorite-type structure, and that Mg₂Si also adopts the MgCu₂-type structure when the Si atoms are partially replaced by small amounts of Sn atoms (Boudemagh et al., 2011). This agrees with the view of Vogel et al. (2020), who noticed that the Be atoms are at the center of BeN₄ tetrahedra, whereas the P atoms are octahedrally coordinated (PN₆ octahedra), like in the β-BP₃N₆ structure obtained at 47 GPa (Vogel et al., 2019).

In summary, the phe-BeP₂N₄ and sp-BeP₂N₄ structures isolated at different pressures can be understood using the EZKC. The BeP₂ substructure of phe-BeP₂N₄ [Fig. 12(a)] can be considered as an intergrowth of fragments of the cristobalite and the tridymite structures while in sp-BeP₂N₄ [Fig. 12(b)], the BeP₂ substructure is MgCu₂ type, characteristic of both the AB₂ cubic Laves phases and the cation arrays in the spinel-type structures (Fig. 19).

Figure 19 Structure of the cubic Laves phase MgCu2, identical to the cation subarray of the spinel structures and, hence, to the BeP2 substructure of sp-BeP2N4 (spn type) drawn in Fig. 18.

2.10. Additional four-connected phospho­nitrides

To conclude this work, we want to mention that four-connected P skeletons also occur in many other compounds. Some of them will be described briefly next. In all of them, the P atoms are tetrahedrally coordinated by four N atoms, yielding networks with PN₂ stoichiometry. These networks and hence the three-dimensional substructure obey the EZKC. The donor atoms are not only the cations (counterions) but also the P atoms which donate one electron each to the N atoms. The result is that the P atoms convert into Ψ-Si and the N atoms into Ψ-O, producing structures characteristic of tetrels, like in SiO₂.

Compounds LiPN₂, NaPN₂ and CuPN₂ (I42d, No. 122) are of the γ-LiBO₂ type (ICSD database). Thus, the structure of LiPN₂ (Schnick & Lücke, 1990) is an Li-filled cristobalite-like structure in which both the Li and the P atoms donate one electron each to the two N atoms, converting LiPN₂ into Ψ-He[Ψ-SiO₂]. The tetrahedral PN₂ substructure has a dia-type P skeleton (Fig. 20).

Figure 20 The structure of LiPN2. P atoms are four-connected in a diamond-like network like Si atoms in β-cristobalite. The tetrahedral coordination of the PN4 units is highlighted in one of the rings in chair conformation.

Compounds Zn₇(P₁₂N₂₄)Cl₂, Zn₄(P₂N₄)₃S, Sn₆(P₁₂N₂₄), Mg₄P₆N₁₂S, Mn₄P₆N₁₂S and Fe₄P₆SN₁₂ are of the sod type (I43m, No. 217) forming a tetrahedral PN₂ skeleton in which the P atoms are four-connected. In Mn₄P₆N₁₂S (Griesemer et al., 2021), represented in Fig. 21, the Mn and the P atoms transfer a total of (eight + six = 14 electrons). Two of them are accepted by the S atom and the remaining 12 electrons are transferred to the 12 N atoms. The formula becomes [Ψ-V][Ψ-SiO₂][Ψ-Ar].

Figure 21 Mn-filled structure of the sod type formed by the P atoms in Mn4P6N12S, showing the four-connectivity of P atoms (Ψ-Si) and the tetrahedral coordination of Ψ-SiO4 units (highlighted on upper right). S atoms are located at the center of Mn4 tetrahedra.

LiNdP₄N₈ is orthorhombic (Pnma, No. 62) (Kloß & Schnick, 2015). The P₄N₈ substructure is similar to that of [Al₂Si₂O₈] in paracelsian Ba[Al₂Si₂O₈] as mentioned by the authors. Both structures are drawn in Fig. 22.

Figure 22 (a) Perspective view of the structure of LiNdP4N8 showing the four-connectivity of the P skeleton. Nd atoms occupy positions in the octagonal tunnels. Li atoms locate in the square tunnels (small ochre spheres). (b) Structure of paracelsian Ba[Al2Si2O8] projected onto the ab plane. The octagonal tunnels contain the Ba atoms.

The P skeleton is again four-connected [see Fig. 22(a)] and the P atoms center the PN₄ tetrahedra. The Nd atoms locate at the octagonal tunnels (Ba atoms in paracelsian), whereas the Li atoms occupy positions in the square tunnels. Similar tunnels are empty in paracelsian.

The four-connectivity of the P skeleton fits the EZKC. A total of eight electrons are transferred to the eight N atoms. The Li and Nd atoms donate four electrons and the four P atoms transfer four additional charges that convert LiNdP₄N₈ into [Ψ-He][Ψ-La][Ψ-Si₄O₈]. An in-depth discussion of this skeleton can be found in the book by Vegas (2018).

TiP₄N₈ (Pmn2₁, No. 31) was reported by Eisenburger et al. (2022), who described the skeleton simply as formed by four-, six- and eight-membered rings. The structure analysis with ToposPro (Blatov et al., 2014) reveals that the [P₄N₈] skeleton corresponds with the zeolite BCT motif (crb), which is also found in CrB₄, β-BeO as well as in the [AlP] skeleton of metavariscite AlPO₄·2H₂O (see Fig. 23). The four-connected skeleton of the P atoms fits the EZKC. Thus, eight electrons (four electrons from Ti and one electron from each of the four P atoms) transferred to eight N atoms convert N → Ψ-O, yielding the Ψ-formula Ψ-Ar[Ψ-Si₄O₈].

Figure 23 (a) The four-connected P skeleton in TiP4N4 in which P atoms center PN4 tetrahedra, highlighted in the upper part. Ti atoms are located in the octagonal tunnels. (b) The structure of CrB4 (crb). The charge transfer from Cr to B atoms makes B atoms adopt a Ψ-C skeleton.

In SrH₄P₆N₁₂ (Fmm2, No. 42) (Wendl & Schnick, 2018), the P₆N₁₂ moiety presents a layered structure in which the PN₂ blocks are intercalated with monoatomic 3⁶ sheets of Sr atoms. The layer net is 4²L137 and is represented in Fig. 24. Again, the P skeleton is four-connected with the P atoms at the center of the PN₄ tetrahedra. The EZKC is accomplished since the Sr atoms and the six P atoms provide eight electrons which transferred to the eight N atoms converting them into Ψ-O atoms. The four H atoms are bonded to four N atoms producing NH groups (equivalent to O atoms). SrH₄P₆N₁₂ can be reformulated as [Ψ-Kr][Ψ-SiO₂]₆.

Figure 24 The layered structure of SrH4P6N12 showing the four-connected network of P atoms (violet) forming 4^2L137 layers and their tetrahedral coordination by N(Ψ-O) atoms. Some NH groups are shown (H atoms as small yellow spheres).

3. Concluding remarks

In this work, we have analyzed the structures of a series of phospho­nitrides (also known as nitridophosphates) and shown that, like in the aluminates, silicates, and many other oxides, the extended Zintl–Klemm concept (EZKC) also applies to these compounds, i.e. their crystal structures can be rationalized and better understood in light of this concept.

This study complements a previous one (Santamaría-Pérez et al., 2005) in which the EZKC was applied to the structure of the oxonitride Ce₁₆Si₁₅O₆N₃₂. In this compound, reported by Köllisch & Schnick (1999), the Si atoms present two types of coordination, i.e. tetrahedral Si^[4] and octahedral Si^[6], the latter being unexpected in a compound obtained at standard pressure. The application of the EZKC as well as the assumption of an amphoteric character of the Si atoms, allowed us to explain the double coordination sphere of the Si atoms. Thus, if Si^[6] atoms are considered as donors and tetrahedral Si^[4] atoms are considered as acceptors, then, the structure is fully explained. The EZKC has also been successfully applied by Vegas & Lobato (2023) to explain the structures of other closed-packed nitrides (Mg₂PN₃, Zn₂PN₃ and Ca₂PN₃).

The application of the EZKC to phospho­nitrides finds that the P atoms typically act as donors and N atoms as acceptors, allowing us to conclude that the name of phospho­nitrides given to these compounds is correct. A similar conclusion was reached by Contreras-García et al. (2020) when they studied the boron phosphate, BPO₄, which should now be called phospho­rus borate, PBO₄. The fact that the P atoms donate one electron to the N atoms in most structures described here, makes the P atoms convert into Ψ-Si, so explaining the tetrahedral skeletons of the P atoms within P₂N₄ networks. The conversion of N atoms into Ψ-O also justifies the tetrahedral coordination of P atoms (Ψ-Si), just as Si atoms do in many of the polymorphs of SiO₂ at room pressure. As found in previous studies (Santamaría-Perez & Vegas, 2003; Santamaría-Pérez et al., 2005), either O or Ψ-O atoms locate near the midpoint between Al—Al, Si—Si, or P—P bonds to capture each bonding electron pair, i.e. the P skeletons are converted into skeletons of the p-block elements obeying the 8-N rule and forming single covalent 2c—2e bonds. These explanations represent a good example of the superiority of the EZKC over the classical ionic model.

As an example, we can recall the structure of Ge^IIP₂N₄ whose P₂N₄ substructure is formed by a four-connected skeleton of P atoms, with the N atoms located close to every P⋯P contact. The four-connected skeleton, characteristic of tetrels, should not be expected for a pentel, so that the structure is better explained as due to the transfer of two electrons from Ge → two N, followed by the transfer of two more electrons from two P → two N, giving the pseudo-formula Ψ-Zn⁰Si₂O₄. The four connectivity of the P atoms is then justified. Moreover, the similarity of the P(Ψ-Si) skeleton (Fig. 6) with that of Al atoms (Ψ-Si) in the Zintl phase SrAl₂ (Fig. 7) is eloquent and says that the Zintl–Klemm concept applies not only to the Zintl phases but also to both oxides and nitrides. Numerous examples have been given previously (Vegas & Jansen, 2002; Vegas, 2018) which illustrate how the nominal cations in oxides fulfill the Zintl–Klemm concept despite being embedded in an anionic matrix (either oxides or nitrides). The surprising example of the pair of compounds, BaSi and BaSiO₃, shown in Figs. 5(c) and 5(d), is paradigmatic.

The model can be extended to other compounds containing skeletons with P_xN_2x stoichiometry. We can mention the series Sr₃P₅N₁₀Cl, Sr₃P₅N₁₀Br, Ba₃P₅N₁₀Cl, Ba₃P₅N₁₀Br and Ba₃P₅N₁₀I, with orthorhombic symmetry (Pnma, No. 62). Analysis using the ToposPro package (Blatov et al., 2014) indicates that they are isostructural to the zeolite JOZ whose PN₂ tetrahedral substructure contains four-connected P atoms (Ψ-Si), according to the EZKC. Similarly, in SrP₃N₅(NH) (P2₁/c, No. 14), the P atoms are four-connected and the P₃N₅(NH) substructure, equivalent to P₃N₅O, is similar to other silica structures of the topological type 4³T281. After the EZKC, the transfer of two electrons from Sr → two N atoms and three electrons from three P → three N, gives the pseudo-formula Ψ-Kr[Ψ-SiO₂]. The reader may visualize the skeletons of these compounds for further examples of how the EZKC can account for the connectivity of the P skeletons, an aspect of the crystal structures that is not considered when the structures are regarded as the result of interactions between nominal anions and cations as done by the traditional ionic model.