Structural Classification of Quasi-One-Dimensional Ternary Nitrides

This review focuses on the crystal structural features of ternary (mixed-metal) quasi-one-dimensional nitrides i.e., nitrides containing (cation-N3−) coordination polyhedra sharing either corners, edges, or faces, arranged in linear chains, and intercalated by a counter ion. The current relevance of these nitrides, and of quasi-one-dimensional compounds in general, lies in the fact that they are closely related to the pure one-dimensional systems (i.e., nanowires), which are vastly researched for their amazing properties closely related to their low dimensionality. A number of these properties were firstly discovered in quasi-one-dimensional compounds, highlighting the importance of expanding knowledge and research in this area. Furthermore, unlike oxides, nitrides and other non-oxide compounds are less developed, hence more difficult to categorise into structural classes that can then be related to other classes of compounds, leading to a fuller picture of structure–properties relationship. Within this context, this review aims to categorise and describe a number of ternary (mixed-metal) quasi-one-dimensional nitrides according to their structural features, specifically, the polyhedra forming the one-dimensional chains.


Introduction
Traditionally, inorganic solid-state chemistry has focused on oxides.The chemistry of oxides has brought to attention a number of technologically exploitable phenomenon, such as high T c superconductivity and colossal magnetoresistance [1][2][3].The first example of a high-temperature superconductor (HTSC), La 1.8 Ba 0.2 CuO 4 , found by Georg Bednorz and Alex Müller in 1986 [3], followed by YBa 2 Cu 3 O 7-x , the first compound to show superconductivity above the boiling point of liquid nitrogen and all HTSCs, which consist of copper oxide planes and show perovskite-like structures [4][5][6].
Research on non-oxide compounds has been slower in comparison, hence fewer examples are known.A significant factor in the slower development of non-oxide compounds (single and mixed-anion) has been the experimental challenge of synthesis and characterisation, as non-oxide materials need to be prepared in atmospheres different from air/oxygen and may, in some cases, be air/moisture-sensitive, necessitating air-free environments and additional experimental skills.The scarcity of non-oxide compounds, in comparison to their oxide counterparts, is an obstacle for understanding these solids, because we cannot describe, organise, and categorise structures geometrically to the extent we do with oxides, and we are therefore at a disadvantage in appreciating their physical properties.Consequentially, the discovery of new materials with potentially novel properties can be hindered.
The following review article aims to give an overview of quasi-one-dimensional ternary (mixed-metal) nitrides.The most widely known nitrides are binary nitrides-compounds formed by one metal and the nitride anion, N 3− .These have been covered extensively in many papers and reviews, one of the most recent being published by R. S. Ningthoujam [7].Simple binary nitrides have already offered up a number of interesting and useful properties to date.Many nitrides are exploited for their strength and hardness.Examples include AlN, HfN, and TiN, which can be used as scratch-resistant surfaces [8].BN is commonly used as a refractory material, forming a lining in high-temperature devices, as a crucible material, or as an abrasive in the grinding of metals and alloys [8].Simple binary nitrides like GaN and InN show extraordinary semiconducting properties.In fact, the 2014 Nobel Prize in physics was awarded to I. Akasaki, H. Amano, and S. Nakamura for their development of the GaN-AlN-InN family used for lighting technology; there is also a large and growing industry in power electronics based upon these binary nitrides [9].The presence of another metal in ternary nitrides creates new and different materials and adds more flexibility for chemical tailoring, hence property/application targeting.
Quasi-one-dimensional and, in general, low-dimensional (1 and 2) solids are compounds with highly anisotropic bonds.Chains (quasi-one-dimensionality) or planes (quasi-two-dimensionality) of coordination polyhedra held together by strong ionic/covalent bonds are at a large distance from one another and held together by weaker bonds within the solid.Often, in ternary quasi-low-dimensional solids, the second metal lies within the separations between the chains/planes.This leads to electronic interactions between metals to be by far the strongest within the chains/planes, causing a high degree of anisotropy and unique properties [10].For example, quasi-one-dimensional materials may show energetically discrete molecular states extending over large linear distances, and spin-charge separation predicted for a Luttinger liquid [11].
Nevertheless, interchain or plane interactions, albeit weak, cannot be completely discarded, hence the use of the prefix "quasi".
Pure one-and two-dimensional materials have come to have a great deal of attention more recently, particularly nanotubes or nanowires (one-dimensional systems) and nanosheets (two-dimensional sheets) [12][13][14][15].Consequently, the long history of studies on quasi-low-dimensional systems is now becoming of enormous importance for understanding and comparing the properties of these new forms of materials.
In this review, following a brief summary of selected synthesis routes, a number of quasi-one-dimensional ternary (mixed-metal) nitrides is classified on the basis of coordination polyhedra forming one-dimensional chains within the crystal structure.It is the authors' hope that such a review will spark interest in these nitrides, with some of them to be considered as models or precursors for novel pure one-dimensional materials.

Synthesis Routes for Nitrides
A great deal of focus in solid-state chemistry has been placed on oxide materials because these compounds are easily prepared, generally in air or oxygen-rich atmospheres.Similar synthetic routes are not as successful when applied to nitrides.There are several reasons for this.In order to prepare nitrides from nitrogen gas, it is necessary to break the strong triple bond of N 2 , a process that is thermodynamically unfavourable.In fact, the N 2 triple bond has a bond energy of 941 kJ•mol −1 , which is far stronger than the corresponding double bond of O 2 at 500 kJ•mol −1 [16].The necessity to input large amounts of energy into breaking the triple bond increases the energies of formation of nitrides over oxides and results in a low standard free energy of formation.The high temperatures required to form the nitrides tend to favour decomposition due to the entropy gain in forming N 2 gas.The energy of formation of N 3− from N, 2300 kJ•mol −1 , is also particularly high when compared to other anions.The energy of formation of O 2− and S 2− is 700 and 331 kJ•mol −1 , respectively [16].This reduces the effect of ionic bonding on the stability of nitrides.In fact, for ternary nitrides, it is common for a large amount of an electropositive metal to be required to stabilise the system via inductive effects.A further problem for many of the ternary nitrides is oxygen or moisture.
Decomposition to yield hydroxides/oxides and ammonia has meant that ternary nitrides often require inert atmospheres for handling and synthesis, which has slowed their development.
Despite difficulties in nitride preparation, there has been a great deal of progress in the synthetic approaches to nitrides in the last century.In the last few decades there have been a number of excellent reviews on nitrides and their synthesis [8,9,[16][17][18][19][20][21].Several of the more common preparative techniques are summarised here.
In spite of the difficulties in breaking the N≡N bond, it is still possible to synthesise a number of binary and ternary nitrides using nitrogen gas, at elevated temperatures, through traditional solid-state ceramic approaches.Ternary nitrides can be prepared by either the reaction of two metal powders under a nitrogen atmosphere or via reaction of metal nitrides with metals/metal nitrides [17].Such approaches are simple, but limited by the number of metals which readily form binary (and higher) nitrides in nitrogen.
Lithium is the only alkali metal to readily form a nitride, Li 3 N, from the reaction of lithium metal with nitrogen gas at 400 • C [18].Li 3 N can then react with other metals and/or metal nitrides to form ternary nitrides, as it can act as both the nitrogen source and reaction medium.In fact, Li 3 N fluxes have been a common synthetic approach to lithium metal nitrides, as the low melting point of Li 3 N (840-850 • C in N 2 ) facilitates intimate mixing of the reagents and favours crystal growth [17,22,23].A vast majority of ternary nitrides contain lithium, due to their relatively simple synthesis.Juza et al. were the first group to investigate these lithium metal nitrides in 1940 [23].
Although the other alkali metals fail to react directly with nitrogen gas, their use in nitride synthesis has still been valuable.Sodium, for example, has found use as a solvent in nitride preparation [9].Metals are dissolved/dispersed in the molten sodium and nitrogen gas absorbed into the mixture.By dissolving the metals, an increased surface area is generated, favouring a higher and more homogeneous diffusion of nitrogen into the solid.The nonreactivity of sodium towards nitrogen and its low boiling point are exploited, as the unreacted sodium can be removed by vacuum distillation or by washing with liquid ammonia to yield the metal nitride.
The preparation of alkaline-earth nitrides, from reactions with nitrogen gas and in sodium fluxes, have also proven effective, making up the second largest group of ternary nitrides [17,24].
However, nitrogen gas tends to favour the formation of subnitrides when reacting with certain metals, with only partial absorption of nitrogen, resulting in nonstoichiometric products [9,16].For example, two alkaline-earth metals, strontium and barium, tend to produce the subnitrides Sr 2 N and Ba 2 N when reacted directly with N 2 gas [25,26].These subnitrides exhibit interesting bonding, structural, and metallic properties.However, they present disadvantages when used as reagents to prepare ternary or more complex nitrides, via solid-state reaction, due to their low nitrogen stoichiometry.More reactive sources of nitrogen have been employed to prepare a range of nitrides in recent years.
One alternative to nitrogen is the solid nitrogen source sodium azide, which, when coupled with sodium fluxes, produce crystalline nitrides with sodium as a byproduct [9].
The most common alternative to nitrogen, however, is ammonia.This has been known to interact with metals for some time [27].Firstly, ammoniation reactions take place at a lower temperature than reactions in nitrogen and can be performed on a wider range of starting materials, such as oxides, carbides, halides, and sulphides [9].
Organic molecules, such as urea and melamine, were also used as an ammonia/nitrogen source [28,29].Heating pellets of ternary metal oxide and urea, for example, has resulted in M 3 Mo 3 N (M = Fe, Co) [28].Unfortunately, these methods can result in samples of poor crystallinity or unwanted secondary compounds [9].
Another method, which has been used to synthesis ternary nitrides, containing two transition metals, is the reduction-nitridation of oxides under dilute hydrogen in nitrogen.This procedure can be performed on ternary oxides, as in the synthesis of Ni 2-x M x Mo 3 N (M = Co, 0 ≤ x ≤ 1; M = Pd, 0 ≤ x ≤ 1.5), Fe 2-x M x Mo 3 N (M = Ni, Pd, Pt), and Fe 3-x Co x Mo 3 N from binary oxides [32][33][34][35].The advantage of this procedure is a relatively quick synthesis of high-purity phases from simple oxide precursors.
More complex methods have also been explored in order to improve the reactivity of nitrogen.These include plasma synthesis and high-pressure techniques.Plasma nitridation has been used to extend the use of dilute hydrogen in nitrogen to less reactive oxides.In this approach, metal oxides are reacted under a stream of microwave-induced H 2 /N 2 plasma [36].
Through the use of high-temperature and high-pressure synthetic approaches, reagents that are unreactive under normal conditions can be forced together to give novel compounds.In addition, the application of pressure to known samples can induce structural transformation to yield new structural feature.Preparative methods range from simple autoclave synthesis to the use of more complex diamond anvil cells, which can apply up to 500 GPa of pressure [37].This method is, however, limited by the availability of suitable equipment.

Crystal Structures of One-Dimensional Nitrides
The ternary nitrides, of interest in this review, contain an electropositive atom that stabilises the system via inductive effects.This electropositive element is usually an alkali, alkaline earth, or lanthanide metal.The second metal is commonly a transition metal, which has a tendency to form nitridometalate anions, MN x n− [38].The coordination and connectivity of the nitridometalate anions dictates the main structural characteristics of the nitrides and influences the physical properties.
In general, the early transition metals, in ternary nitrides, tend to favour relatively high oxidation states and high coordination numbers (4-6), while the late transition metals show lower oxidation states (0-2), and lower coordination [38].Below are several of the better-known nitride systems, addressed in terms of their coordination of the metal nitrides.Although every effort has been made not to exclude any structurally significant compounds, some may have been unintentionally omitted.

Nitrides Containing Infinite Chains of Octahedra
In general, the ternary nitrides in which the transition metal (TM) shows high coordination numbers (5 or 6) with nitrogen tend to form rocksalt, perovskite, or layered structures and are commonly considered to contain TM-N polyhedra [38].However, many subnitrides, containing a high metal-to-nitrogen ratio, contain chains of octahedra and are commonly described in terms of the nitrogen coordination.This will also be seen for the mixed-anion compounds in Section 3. The following are examples of ternary, s-block nitrides.NaBa 3 N (P6 3 /mmc, a = 8.4414(6) Å, c = 6.9817(8)Å) and Na 5 Ba These chains are hexagonally stacked and separated by sodium atoms at the centre of the triangular channels that the chains form, (Figure 1).As a result, the sodium atoms are coordinated to 12 barium atoms from the 3 nearest chains.

Nitrides Containing Infinite Chains of Tetrahedra
Tetrahedral coordination of the metal in nitrides is particularly common.Compounds with a full range of structural features, from isolated tetrahedra to complex three-dimensional networks, are known to occur [38].The following structures show chains of metal-centred nitrogen tetrahedra, showing either edge or corner connectivity.
The first-row transition metal lithium nitrides tend to fall into either of two structural groups: one based on superstructures of the fluorite structure and the other based on solid solutions of the Li3N type [42].In general, the transition metal elements adopting higher oxidation states have a preference for the fluorite-type structure, while the elements of lower oxidation state tend towards a Li3N-related structure.The ratio between the cation sizes also plays a role, with anti-fluorite-related structures prevalent when the ratio is r(Li + )/r(M n+ ) ≥ 1 [43].Several of the transition metal compounds form structures in both these groups.In the Li-Fe-N system, solid solutions of the compositions Li1 Li3FeN2, however, belongs to the anti-fluorite-like superstructural group of compounds with r(Li + )/r(Fe 3+ ) ≈ 1.2 [42,44,45].
The Li3FeN2 (Ibam, a = 4.872(1) Å, b = 9.641(3) Å, c = 4.792(1) Å) structure consists of a distorted cubic close-packed array of nitrogen atoms with the tetrahedral holes occupied by lithium and iron in a 3:1 ratio, respectively [42].The FeN4 tetrahedra are ordered in such a way as to result in chains of edge-sharing [FeN ⁄ ] tetrahedra connected along [001].These tetrahedral chains are in a similar arrangement to those found in SiS2 [46].In SiS2, edge-sharing [SiS ⁄ ] units are hexagonally packed and held together by van der Waals interactions [46,47].The chains in Li3FeN2 are also arranged with hexagonal rod-packing, but are separated by lithium-centred tetrahedra (Figure 2).

Nitrides Containing Infinite Chains of Tetrahedra
Tetrahedral coordination of the metal in nitrides is particularly common.Compounds with a full range of structural features, from isolated tetrahedra to complex three-dimensional networks, are known to occur [38].The following structures show chains of metal-centred nitrogen tetrahedra, showing either edge or corner connectivity.
The first-row transition metal lithium nitrides tend to fall into either of two structural groups: one based on superstructures of the fluorite structure and the other based on solid solutions of the Li 3 N type [42].In general, the transition metal elements adopting higher oxidation states have a preference for the fluorite-type structure, while the elements of lower oxidation state tend towards a Li 3 N-related structure.The ratio between the cation sizes also plays a role, with anti-fluorite-related structures prevalent when the ratio is r(Li + )/r(M n+ ) ≥ 1 [43].Several of the transition metal compounds form structures in both these groups.In the Li-Fe-N system, solid solutions of the compositions Li .These tetrahedral chains are in a similar arrangement to those found in SiS 2 [46].In SiS 2 , edge-sharing 1 ∞ [SiS 4/2 ] units are hexagonally packed and held together by van der Waals interactions [46,47].The chains in Li 3 FeN 2 are also arranged with hexagonal rod-packing, but are separated by lithium-centred tetrahedra (Figure 2).In this case, the nitrogen atoms are eight coordinate, surrounded by six lithium atoms and two iron atoms to give a distorted cube.
A3M2N4 (A = Sr, Ba; M = Al, Ga), space group Pnna, also show SiS2-like chains of tetrahedra [48-51].In A3M2N4, the nitrogen atoms are in a distorted-cubic close-packed arrangement, with a quarter of the tetrahedral holes occupied by Ga 3+ /Al 3+ , generating the [GaN ⁄ ] [AlN ⁄ ] chains in a similar way to Li3FeN2.Due in part to the larger size of Ba 2+ and Sr 2+ over Li + , barium and strontium cations rest in three-quarters of the octahedral holes, rather than the smaller tetrahedral holes.The result is that the chains have a slight undulation of four tetrahedra, which run along [010] (Figure 3).Table 1 gives the unit cell parameters for A3M2N4 (A = Sr, Ba; M = Al, Ga).As expected, the incorporation of a larger alkaline-earth cation into the structure results in increased unit cell dimensions.In this case, the nitrogen atoms are eight coordinate, surrounded by six lithium atoms and two iron atoms to give a distorted cube.
A 3 M 2 N 4 (A = Sr, Ba; M = Al, Ga), space group Pnna, also show SiS 2 -like chains of tetrahedra [48][49][50][51].In A 3 M 2 N 4 , the nitrogen atoms are in a distorted-cubic close-packed arrangement, with a quarter of the tetrahedral holes occupied by Ga 3+ /Al 3+ , generating the 1 ] chains in a similar way to Li 3 FeN 2 .Due in part to the larger size of Ba 2+ and Sr 2+ over Li + , barium and strontium cations rest in three-quarters of the octahedral holes, rather than the smaller tetrahedral holes.The result is that the chains have a slight undulation of four tetrahedra, which run along [010] (Figure 3).In this case, the nitrogen atoms are eight coordinate, surrounded by six lithium atoms and two iron atoms to give a distorted cube.
A3M2N4 (A = Sr, Ba; M = Al, Ga), space group Pnna, also show SiS2-like chains of tetrahedra [48][49][50][51].In A3M2N4, the nitrogen atoms are in a distorted-cubic close-packed arrangement, with a quarter of the tetrahedral holes occupied by Ga 3+ /Al 3+ , generating the [GaN ⁄ ] [AlN ⁄ ] chains in a similar way to Li3FeN2.Due in part to the larger size of Ba 2+ and Sr 2+ over Li + , barium and strontium cations rest in three-quarters of the octahedral holes, rather than the smaller tetrahedral holes.The result is that the chains have a slight undulation of four tetrahedra, which run along [010] (Figure 3).Table 1 gives the unit cell parameters for A3M2N4 (A = Sr, Ba; M = Al, Ga).As expected, the incorporation of a larger alkaline-earth cation into the structure results in increased unit cell dimensions.Table 1 gives the unit cell parameters for A 3 M 2 N 4 (A = Sr, Ba; M = Al, Ga).As expected, the incorporation of a larger alkaline-earth cation into the structure results in increased unit cell dimensions.Another lithium compound showing an anti-fluorite-like structure with an r(Li + )/r(Ta 5+ ) ≈ 1. ∞ [MN 2 N 3− 2/2 ] chains.These chains run between the a-and c-axes in a sinusoidal manner, with a repeat unit of four tetrahedra (Figure 4).The chains show hexagonal rod-packing, with sodium sitting within the void between the chains [54].
The introduction of a larger electropositive metal onto the sodium site has the effect of altering the orientation of the WN4 tetrahedra and, thus, the overall appearance of the chains.The chains show hexagonal rod-packing, with sodium sitting within the void between the chains [54].
The introduction of a larger electropositive metal onto the sodium site has the effect of altering the orientation of the WN 4 tetrahedra and, thus, the overall appearance of the chains.As stated above, a contributing factor to the structural variation is the larger size of the alkali metal cations.In Na 2 K[WN 3 ] there are two crystallographically independent potassium positions.The first potassium is coordinated to four nitrogen atoms in a distorted tetrahedral manner, in a similar way to Na   In these examples, the chains oscillate in the (010) plane with far less "twisting" when compared to Na 3 WN 3 (Figure 6).The larger alkali metal (Rb or Cs) rests in distorted prismatic coordination, bound to nitrogen, forming layers parallel to the (010) plane.In compensation for the cation size, the chains are diverted around these sites.The sodium rests within the loops of the chains, and also to the sides, separating them along [010].Hence, the sodium remains either in an approximately tetrahedral coordination.This can be extended to include an additional atom, described as 4 + 1 coordination.
The family of A2MN3 nitrides (A = Sr, Ba; M = V, Nb, Ta) all show chains of edge-sharing MN4 tetrahedra.The unit cell parameters are given in Table 2. A2MN3 (A = Sr, Ba; M = Nb, Ta), Sr2VN3, and Ca2VN3 are isostructural with Ba2ZnO3 [57,58].These are examples of zweier single-chain compounds (i.e., containing a repeat unit of two tetrahedra).These chains run parallel to [100].The Ba 2+ , Sr 2+ , and Ca 2+ cations lie on two crystallographically independent sites, both seven coordinate, A(1) is in distorted pentagonal bipyramidal coordination and A(2) shows monocapped trigonal prismatic coordination [59].Increasing the size of the A cation results in straighter chains, and therefore, a reduction in the monoclinic distortion, similar to the Na-Rb-Cs-W-N systems mentioned previously.
A2MN3 (A = Th, U, Ce; M = Cr, Mn) are isostructural to Sr2CuO3 showing an orthorhombic anion deficient T-type structure.In 1970, Benz et al. reported the crystal structure of A2MN3 (A = Th, U; M = Cr, Mn) with space group Immm (unit cell parameters are given in Table 3), as consisting of cornerlinked chains of MN4, which are in approximately square-planar geometry [60].These [MN N ⁄ ] The larger alkali metal (Rb or Cs) rests in distorted prismatic coordination, bound to nitrogen, forming layers parallel to the (010) plane.In compensation for the cation size, the chains are diverted around these sites.The sodium rests within the loops of the chains, and also to the sides, separating them along [010].Hence, the sodium remains either in an approximately tetrahedral coordination.This can be extended to include an additional atom, described as 4 + 1 coordination.
The family of A 2 MN 3 nitrides (A = Sr, Ba; M = V, Nb, Ta) all show chains of edge-sharing MN 4 tetrahedra.The unit cell parameters are given in Table 2.A 2 MN 3 (A = Sr, Ba; M = Nb, Ta), Sr 2 VN 3 , and Ca 2 VN 3 are isostructural with Ba 2 ZnO 3 [57,58].These are examples of zweier single-chain compounds (i.e., containing a repeat unit of two tetrahedra).These chains run parallel to [100].The Ba 2+ , Sr 2+ , and Ca 2+ cations lie on two crystallographically independent sites, both seven coordinate, A(1) is in distorted pentagonal bipyramidal coordination and A(2) shows monocapped trigonal prismatic coordination [59].Increasing the size of the A cation results in straighter chains, and therefore, a reduction in the monoclinic distortion, similar to the Na-Rb-Cs-W-N systems mentioned previously.

Nitrides Containing Infinite Chains of Square Planar Units
Ternary nitrides containing transition metal centres in low oxidation states show some unusual coordination.A 2 MN 3 (A = Th, U, Ce; M = Cr, Mn) contain M + cation, which form one-dimensional chains of planar MN 4 [60][61][62][63][64].  3), as consisting of corner-linked chains of MN 4 , which are in approximately square-planar geometry [60].These 1 ∞ [MN 2 N 8− 2/2 ] chains are linked along the a-axis and show hexagonal rod-packing.The square planar units are all orientated to lie parallel to the (010) plane, and each MN 4 unit sits within a cuboid of A 4+ cations.The nitrogen atoms show two crystallographically independent positions and a near octahedral coordination.N(1) bridges two transition metal centres and is surrounded by four A atoms, while N(2) is the terminal nitrogen position and, therefore, is bound to a single transition metal and five A atoms.Each A is located roughly at the centre of a monocapped trigonal prism of nitrogen anions.The structure may also be thought of as an anion-deficient K 2 NiF 4 -type structure.K 2 NiF 4 is an n = 1 Ruddlesden-Popper, A n+1 TM n O 3n+1 , compound.K 2 NiF 4 consists of two-dimensional layers of corner-sharing NiF 6 octahedra.Each octahedron is surrounded by eight K + cations in an analogous way to the perovskite structure.These perovskite layers are interleaved by a NaCl-type spacer unit of alkali metal and fluoride ions.Removal of half the equatorial anions in an ordered way generates the MN 4 chains seen in A 2 MN 3 .

Nitrides Containing Infinite Chains of Triangular Units
LiCaN (Pnma, a = 8.471(3) Å, b = 3.676(2) Å, c = 5.537(3) Å) is another example of a lithium compound adopting the anti-fluorite-type structure [21,43].In this case, calcium occupies half the tetrahedral holes and lithium occupies the other half, distorted from the centre.These are ordered in such a way as to give planes of edge-sharing LiN 3 triangular units, as shown in Figure 7.
Inorganics 2016, 4, 37 10 of 17 chains are linked along the a-axis and show hexagonal rod-packing.The square planar units are all orientated to lie parallel to the (010) plane, and each MN4 unit sits within a cuboid of A 4+ cations.The nitrogen atoms show two crystallographically independent positions and a near octahedral coordination.N(1) bridges two transition metal centres and is surrounded by four A atoms, while N( 2) is the terminal nitrogen position and, therefore, is bound to a single transition metal and five A atoms.Each A is located roughly at the centre of a monocapped trigonal prism of nitrogen anions.The structure may also be thought of as an anion-deficient K2NiF4-type structure.K2NiF4 is an n = 1 Ruddlesden-Popper, An+1TMnO3n+1, compound.K2NiF4 consists of two-dimensional layers of corner-sharing NiF6 octahedra.Each octahedron is surrounded by eight K + cations in an analogous way to the perovskite structure.These perovskite layers are interleaved by a NaCl-type spacer unit of alkali metal and fluoride ions.Removal of half the equatorial anions in an ordered way generates the MN4 chains seen in A2MN3.

Nitrides Containing Infinite Chains of Triangular Units
LiCaN (Pnma, a = 8.471(3) Å, b = 3.676(2) Å, c = 5.537(3) Å) is another example of a lithium compound adopting the anti-fluorite-type structure [21,43].In this case, calcium occupies half the tetrahedral holes and lithium occupies the other half, distorted from the centre.These are ordered in such a way as to give planes of edge-sharing LiN3 triangular units, as shown in Figure 7.

Nitrides Containing Infinite Linear Chains
Coordination two, of the transition metal, is a less common coordination in ternary nitrides.Linear coordination occurs for several of the late transition metals in low oxidation states, +1 and +2 [66].Those nitrides with transition metals in +1 oxidation state tend to form infinite linear metal nitride chains.These chains can take several orientations: straight, zigzagged, or helical.
Cationic substitution of the lithium in LiCaN can yield Ca[(Ni1−xLix)N] (0 ≤ x ≤ 0.58).This solid solution has a different structure from the parent compound, with [Ni Li N ⁄ ] linear chains, and the CaNiN-type structure [67].

Nitrides Containing Infinite Linear Chains
Coordination two, of the transition metal, is a less common coordination in ternary nitrides.Linear coordination occurs for several of the late transition metals in low oxidation states, +1 and +2 [66].Those nitrides with transition metals in +1 oxidation state tend to form infinite linear metal nitride chains.These chains can take several orientations: straight, zigzagged, or helical.

Nitrides Containing Infinite Linear Chains
Coordination two, of the transition metal, is a less common coordination in ternary nitrides.Linear coordination occurs for several of the late transition metals in low oxidation states, +1 and +2 [66].Those nitrides with transition metals in +1 oxidation state tend to form infinite linear metal nitride chains.These chains can take several orientations: straight, zigzagged, or helical.
Cationic substitution of the lithium in LiCaN can yield Ca[(Ni1−xLix)N] (0 ≤ x ≤ 0.58).This solid solution has a different structure from the parent compound, with [Ni Li N ⁄ ] linear chains, and the CaNiN-type structure [67].
CaNiN (P42/mmc, a = 3.5809(2) Å, c = 7.0096(3) Å) was discovered in 1990 by DiSalvo and found to contain [NiN ⁄ ] linear chains [68].These form planes of parallel chains, which are stacked along the c-axis.The chains alternate between running along [100] and [010] moving along [001] (Figure 9).The calcium sits in tetrahedral coordination with four nitrogen atoms.Introduction of strontium onto the calcium site, Ca Sr x NiN 3 , up to x ≈ 0.5 acts to increase the unit cell dimensions of CaNiN, but the overall structure remains the same [69,70].The increase in unit cell dimensions is more significant in the c-axis, as it is easier for the structure to accommodate the larger cations by increasing the perpendicular interchain separation along c, while the criss-crossing of the chains along a and b restricts expansion due to the limiting Ni-N bond distances.
The LiSrN (I4 2 /mmc, a = 3.924(3) Å, c = 7.085(4) Å), unlike LiCaN, also adopts the CaNiN structure [71].Substitution of the lithium cation with nickel gives SrLi x Ni 1−x N (0 ≤ x ≤ 0.52) and induces a structural transformation [21]  The two strontium positions are four coordinate, surrounded by nitrogen atoms in distorted tetrahedral coordination.Yamamoto et al. proposed that the strontium-centred tetrahedra play an important role in determining the overall structure of the system in Ca1−xSrxNiN [69].As stated previously, as the strontium content increases from x = 0 to x = 0.5 the c-axis expands more than the other two axes.The result is a greater increase in two of the Sr-N distances along c compared to the Sr-N distances within a or b, and hence a greater deviation from the ideal tetrahedron.At x = 1, SrNiN adopts an alternate structure with a more favourable structural environment for strontium [69].
Increasing the size of the alkaline earth metal further (i.e., considering the Ba-Ni-N system) also results in a SrNiN-like structure [72].BaNiN (Pnma, a The two strontium positions are four coordinate, surrounded by nitrogen atoms in distorted tetrahedral coordination.Yamamoto et al. proposed that the strontium-centred tetrahedra play an important role in determining the overall structure of the system in Ca 1−x Sr x NiN [69].As stated previously, as the strontium content increases from x = 0 to x = 0.5 the c-axis expands more than the other two axes.The result is a greater increase in two of the Sr-N distances along c compared to the Sr-N distances within a or b, and hence a greater deviation from the ideal tetrahedron.At x = 1, SrNiN adopts an alternate structure with a more favourable structural environment for strontium [69].
Increasing the size of the alkaline earth metal further (i.e., considering the Ba-Ni-N system) also results in a SrNiN-like structure [72].BaNiN (Pnma, a ∞ [MN 2− 2/2 ] chains, but these chains differ from SrNiN, showing a more complex alternating pattern, as shown in Figure 11 [66,74].
As Figure 11a shows, the pattern of the chains in BaCoN can be described as altering direction after one nitrogen, followed by a section bent on the second nitrogen, which is followed by a bend on the second nitrogen atom.BaCuN has chains that are bent at every first and second nitrogen atom [66,74].As Figure 11a shows, the pattern of the chains in BaCoN can be described as altering direction after one nitrogen, followed by a section bent on the second nitrogen, which is followed by a bend on the second nitrogen atom.BaCuN has chains that are bent at every first and second nitrogen atom [66,74].
Reducing the transition metal content gives rise to Ba8[(NiN

Conclusions
Recent developments in the preparation and characterisation of materials have led to the discovery of a large number of new compounds with novel structural features.Despite this, the number of non-oxide materials discovered to date is low in comparison with their oxide counterparts, due to experimental challenges in synthesis and characterisation.The relatively low number of nonoxide compounds acts as an obstacle for understanding these solids, as we cannot categorise these structures to the same extent as we do with oxides and, importantly, the roles of anions other than oxides within crystal structures cannot be investigated in depth.This review aims to outline the structural features of a number of ternary (mixed-metal) nitrides showing quasi-one-dimensional crystal structure.This low-dimensionality of the crystal structure gives rise to high anisotropy in their chemical bonding, which, in turn, is the cause of anisotropy in their physical properties.Selected ternary (mixed-metal) quasi-one-dimensional nitrides have been described and categorised according to the polyhedra forming the one-dimensional chains.The ionic model, often used to describe and discuss crystal structures of oxides, appears to be applicable to a number of nitrides as well, as shown by the linear increase of the unit cell parameters as Ca 2+ cations are substituted gradually by the larger Sr 2+ and Ba 2+ cations in the A2VN3 family (A = Ca, Sr, Ba).Where possible, similarities between crystal structures of nitrides with different chemical composition were highlighted and, in some cases, similarities could be highlighted with compounds of a different nature, as in the case of Li3FeN2, in which the chains of [FeN ⁄ ] tetrahedra are arranged similarly to the chains of [SiS ⁄ ] units found in SiS2.Finally, this study highlights that the investigation of novel quasi-one-dimensional mixed-metal nitrides would accompany and support the topical research currently carried out on nanowires and nanotubes.

Conclusions
Recent developments in the preparation and characterisation of materials have led to the discovery of a large number of new compounds with novel structural features.Despite this, the number of non-oxide materials discovered to date is low in comparison with their oxide counterparts, due to experimental challenges in synthesis and characterisation.The relatively low number of non-oxide compounds acts as an obstacle for understanding these solids, as we cannot categorise these structures to the same extent as we do with oxides and, importantly, the roles of anions other than oxides within crystal structures cannot be investigated in depth.This review aims to outline the structural features of a number of ternary (mixed-metal) nitrides showing quasi-one-dimensional crystal structure.This low-dimensionality of the crystal structure gives rise to high anisotropy in their chemical bonding, which, in turn, is the cause of anisotropy in their physical properties.Selected ternary (mixed-metal) quasi-one-dimensional nitrides have been described and categorised according to the polyhedra forming the one-dimensional chains.The ionic model, often used to describe and discuss crystal structures of oxides, appears to be applicable to a number of nitrides as well, as shown by the linear increase of the unit cell parameters as Ca 2+ cations are substituted gradually by the larger Sr 2+ and Ba 2+ cations in the A 2 VN 3 family (A = Ca, Sr, Ba).Where possible, similarities between crystal structures of nitrides with different chemical composition were highlighted and, in some cases, similarities could be highlighted with compounds of a different nature, as in the case of Li 3 FeN 2 , in which the chains of 1 ∞ [FeN 3− 4/2 ] tetrahedra are arranged similarly to the chains of 1 ∞ [SiS 4/2 ] units found in SiS 2 .Finally, this study highlights that the investigation of novel quasi-one-dimensional mixed-metal nitrides would accompany and support the topical research currently carried out on nanowires and nanotubes.

Na 5
Ba 3 N is very similar to NaBa 3 N. Na 5 Ba 3 N has the same face-sharing Ba 6 N octahedra.These chains show the same, if slightly distorted, hexagonal stacking arrangement, in this case running along [010].The additional sodium increases the chain separation from 8.44 Å in NaBa 3 N to 10.70 Å in Na 5 Ba 3 N [40].

Figure 1 .
Figure 1.Representation of NaBa3N viewed along [001].The red and black spheres are sodium and barium, respectively.The grey polyhedra are Ba6N.

Figure 1 .
Figure 1.Representation of NaBa 3 N viewed along [001].The red and black spheres are sodium and barium, respectively.The grey polyhedra are Ba 6 N.

Figure 2 .
Figure 2. Representation of Li3FeN2.The red and blue spheres represent lithium and nitrogen, respectively.The chains of grey polyhedra represent the [FeN ⁄ ] chains.

Figure 3 .
Figure 3. Representation of Ba3Ga2N4.The red and blue spheres represent barium and nitrogen, respectively.The chains of grey polyhedra represent the [GaN ⁄ ] chains.

Figure 2 .
Figure 2. Representation of Li3FeN2.The red and blue spheres represent lithium and nitrogen, respectively.The chains of grey polyhedra represent the [FeN ⁄ ] chains.

Figure 3 .
Figure 3. Representation of Ba3Ga2N4.The red and blue spheres represent barium and nitrogen, respectively.The chains of grey polyhedra represent the [GaN ⁄ ] chains.

Figure 4 .
Figure 4. Representation of Na3MN3, M = W, Mo.The red and blue spheres represent sodium and nitrogen, respectively.The chains of grey polyhedra represent the [MN ⁄ ] chains.
3 [WN 3 ], in which the sodium predominantly shows tetrahedral coordination.The second potassium rests in a larger hole, surrounded by 12 nitrogen atoms.It is this larger hole that is partially occupied by rubidium in the Na 11 Rb[(WN 3 ) 4 ] structure.The site is shared between rubidium and sodium in an ordered way, which is the cause of the increased unit cell volume when compared to Na 3 [WN 3 ].The WN 4 tetrahedra are then twisted around towards the sodium positions and away from the larger potassium and rubidium positions to give the winding chains shown in Figure 5 [55,56].These broader chains show tetragonal rod-packing.Inorganics 2016, 4, 37 8 of 17As stated above, a contributing factor to the structural variation is the larger size of the alkali metal cations.In Na2K[WN3] there are two crystallographically independent potassium positions.The first potassium is coordinated to four nitrogen atoms in a distorted tetrahedral manner, in a similar way to Na3[WN3], in which the sodium predominantly shows tetrahedral coordination.The second potassium rests in a larger hole, surrounded by 12 nitrogen atoms.It is this larger hole that is partially occupied by rubidium in the Na11Rb[(WN3)4] structure.The site is shared between rubidium and sodium in an ordered way, which is the cause of the increased unit cell volume when compared to Na3[WN3].The WN4 tetrahedra are then twisted around towards the sodium positions and away from the larger potassium and rubidium positions to give the winding chains shown in Figure 5 [55,56].These broader chains show tetragonal rod-packing.Increasing the rubidium content further gives Na5Rb[(WN3)2] (P21/c, a = 9.355(2) Å, b = 10.277(3)Å, c = 19.165(3)Å, β = 90.12(2)°)[55].Na5Rb[(WN3)2] is isostructural to Na5Cs[(WN3)2] (P21/c, a = 9.403(3) Å, b = 10.236(2)Å, c = 19.501(4)Å, β = 90.01(2)°),and both show vierer chains, four repeating tetrahedra, of [WN N ⁄ ] running along [100][55].In these examples, the chains oscillate in the (010) plane with far less "twisting" when compared to Na3WN3 (Figure6).

A 2
MN 3 (A = Th, U, Ce; M = Cr, Mn) are isostructural to Sr 2 CuO 3 showing an orthorhombic anion deficient T-type structure.In 1970, Benz et al. reported the crystal structure of A 2 MN 3 (A = Th, U; M = Cr, Mn) with space group Immm (unit cell parameters are given in Table

Figure 9 .
Figure 9. Representation of CaNiN.The red, black, and blue spheres represent calcium, nickel, and nitrogen, respectively.

Figure 9 .
Figure 9. Representation of CaNiN.The red, black, and blue spheres represent calcium, nickel, and nitrogen, respectively.

Figure 9 .
Figure 9. Representation of CaNiN.The red, black, and blue spheres represent calcium, nickel, and nitrogen, respectively.

Figure 11 .
Figure 11.Representations of the chains in (a) BaCoN and (b) BaCuN.The red, black, and blue spheres represent barium, cobalt/copper, and nitrogen, respectively.Figure 11.Representations of the chains in (a) BaCoN and (b) BaCuN.The red, black, and blue spheres represent barium, cobalt/copper, and nitrogen, respectively.

Figure 11 .
Figure 11.Representations of the chains in (a) BaCoN and (b) BaCuN.The red, black, and blue spheres represent barium, cobalt/copper, and nitrogen, respectively.Figure 11.Representations of the chains in (a) BaCoN and (b) BaCuN.The red, black, and blue spheres represent barium, cobalt/copper, and nitrogen, respectively.