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The K₂NiF₄ structure is the simplest structure of a large family of related materials that has attracted much attention in recent years because several of them are superconductors. The structure may be regarded as alternating layers of perovskite and rock salt structures, as shown in Fig. 1.50. The formula K₂NiF₄ could be written in expanded form as KNiF₃.KF to indicate the perovskite and rock salt components. The structure is body centred tetragonal with perovskite‐like layers of octahedra centred at c = 0 and . K⁺ ions lie at the interface between rock salt and perovskite blocks and have a coordination number of 9. The coordination number of K in rock salt would be 12 but the rock salt blocks are less than one unit cell thick and the K coordination in rock salt is interrupted by the atomic displacements that generate perovskite blocks. The K₂NiF₄ structure occurs with a range of fluorides and chlorides containing small divalent cations, Table 1.26, and with a range of oxides with different charge combinations such as A₂ ⁺B⁶⁺O₄, A₂ ²⁺B⁴⁺O₄, A₂ ³⁺B²⁺O₄, A²⁺A′³⁺B³⁺O₄ and A₂ ³⁺B_1/2 +B′ _1/2 ³⁺ O ₄ containing large A and small B cations; probably other cation combinations are also possible.

Table 1.25 Examples of A, B, X combinations in garnets

Garnet	A	B	X	O
Grossular	Ca3	Al2	Si3	O12
Uvarovite	Ca3	Cr2	Si3	O12
Andradite	Ca3	Fe2	Si3	O12
Pyrope	Mg3	Al2	Si3	O12
Almandine	Fe3	Al2	Si3	O12
Spessartine	Mn3	Al2	Si3	O12
	Ca3	CaZr	Ge3	O12
	Ca3	Te2	Zn3	O12
	Na2Ca	Ti2	Ge3	O12
	NaCa2	Zn2	V3	O12

A‐site cation ordering occurs in A⁺A′³⁺B⁴⁺O₄: A = Na, A′ = La → Lu, B = Ti; Na and the lanthanides occupy different layers in the c direction. Anion‐deficient and anion‐excess K₂NiF₄ structures exist. For example, in Sr₂XO₃: X = Cu, Pd, one‐quarter of the oxygens are removed, giving square planar coordination for X and seven‐coordinate Sr, whereas in La₂NiO_4+x , interstitial oxygens are present.

The Ruddlesden–Popper series of compounds have the K₂NiF₄ structure as their simplest family member; other family members exist with more layers in the perovskite blocks. Thus, with strontium titanates, a family of phases exists with general formula Sr _{n + 1}Ti _n O_{3n + 1} and consist of nSrTiO₃ perovskite blocks interleaved with SrO rock salt layers. Two members of this family are Sr₃Ti₂O₇ (n = 2) and Sr₄Ti₃O₁₀ (n = 3). The n = ∞ member corresponds to SrTiO₃ perovskite. These phases retain a tetragonal unit cell with similar a dimensions but have much longer c axes. A similar family of phases forms for La _{n + 1}Ni _n O_{3n + 1} : n = 1, 2, 3, ∞. In most cases, only one or two members of the Ruddlesden–Popper series are known, with examples such as

A large and diverse family of Cu‐based perovskite‐rock salt intergrowth phases contains many examples of the high T _c cuprate superconductors. The key element for the superconductivity is Cu and it shows enormous structural diversity in the cuprates with coordination numbers ranging from 2 (linear) to 4 (square planar), 5 (pyramidal) and 6 (octahedral), as discussed in Section 8.3.6. In addition to YBa₂Cu₃O₇ and related materials which are basically oxygen‐deficient perovskites, Bi‐ and Tl‐based cuprates are perovskite–rock salt intergrowth phases with considerable compositional and structural complexity. The BiSCCO superconductors consist of three phases that are labelled according to their Bi:Sr:Ca:Cu ratios: 2201, 2212 and 2223. The 2212 phase (80 K superconductor), Bi₂Sr₂CaCu₂O₈ has rock salt‐like layers, Bi₂O₂, that separate double perovskite layers containing Cu in octahedral sites, whereas the 2223 phase (110 K superconductor) has triple perovskite layers. In these structures, SrO layers form a coherent interface between rock salt and perovskite components.

Figure 1.50 (a) The K2NiF4 structure. (b) The Bi2O2 layers that form part of the intergrowth structure of Aurivillius phases.

Table 1.26 Some compounds with the K2NiF4 structure

Compounda	a/Å	c/Å	z (M+ ion)	z (anion)
K2NiF4	4.006	13.076	0.352	0.151
K2CuF4	4.155	12.74	0.356	0.153
Ba2SnO4	4.140	13.295	0.355	0.155
Ba2PbO4	4.305	13.273	0.355	0.155
Sr2SnO4	4.037	12.53	0.353	0.153
Sr2TiO4	3.884	12.60	0.355	0.152
La2NiO4	3.855	12.652	0.360	0.170
K2MgF4	3.955	13.706	0.35	0.15
Other examples b
M2Y6+O4: M = K, Rb, Cs; Y = U, Np
Ln2YO4: Ln = La → Nd; Y = Ni, Cu
CaLnAlO4: Ln = La → Er, Y
SrLnFeO4: Ln = La → Tb
SrLnCrO4: Ln = La → Dy
BaLnFeO4:Ln = La → Eu
A2BF4: A = K, Rb, Tl; B = Mg, Ni, Zn, Co, Fe
A2BCl4: A = Rb, Cs; B = Cr, Mn, Cd
Sr2BO4: B = Ti, Sn, Zr, Hf, Mo, Tc, Ir, Ru, Rh, Mn

^a R. W. G. Wyckoff, Crystal Structures, Vols 1 to 6, Wiley (1971).

^b O. Muller and R. Roy, The Major Ternary Structural Families, Springer‐Verlag (1974).

The Aurivillius family of phases are ordered intergrowth structures consisting of one or more perovskite layers of corner‐sharing octahedra separated by single layers of formula Bi₂O₂. The Bi₂O₂ layers are formed by a single, 2D square planar net of oxygens in which each square is capped on one side only by Bi³⁺ to give sheets of pyramids in an alternating ‘up’ and ‘down’ arrangement, Fig. 1.50(b). Bi³⁺ is a lone pair‐active, heavy p‐block cation and the spatial disposition of the lone pairs acts to separate the Bi₂O₂ layers from the perovskite blocks. This Bi₂O₂ structural arrangement is different to the octahedral rock salt arrangement of Bi in the BiSCCO phases.

The general formula of Aurivillius phases is Bi₂O₂[A _m−1M _m O_3m+1]. Examples include: M=Mo, m = 1 for Bi₂O₂[MoO₄] with a single layer of perovskite‐like octahedra; Bi₂O₂[SrNb₂O₇] with a double perovskite layer of NbO₆ octahedra and Sr in 12‐coordinate cages; Bi₂O₂[Bi₂Ti₃O₁₀] with triple perovskite layers and Bi in the 12‐coordinate perovskite A sites as well as in the Bi₂O₂ layers.

The Dion‐Jacobsen phases are related to Aurivillius phases but the Bi₂O₂ layers are replaced by layers of alkali cations to give the general formula A′[A _m−1M _m X_3m+1]. Examples include K[LaNb₂O₇] that has double perovskite layers and Cs[La₂Ti₂NbO₁₀] with triple layers.