Solid State Chemistry and its Applications. Anthony R. West

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.

      1.17.15 The aluminium diboride structure (AlB₂)

      The aluminium diboride family of crystal structures shot to prominence in 2000 when isostructural MgB₂ was discovered to be a superconductor with T _c = 39 K. It has a relatively simple crystal structure, shown in Fig. 1.51, in which Mg atoms form close packed layers stacked in an AAA sequence, which may be referred to as primitive hexagonal packing, hp. The cp Mg layers are separated by B layers arranged as in graphite; hence Mg is 12‐coordinate with hexagonal rings of B atoms above and below. Each B has three B nearest neighbours in a trigonal planar arrangement and six Mg next nearest neighbours arranged in a trigonal prism.

      Numerous borides and silicides have the AlB₂ structure, including MB₂: M = Ti, Zr, Nb, Ta, V, Cr, Mo, Mg, U, and MSi₂: M = U, Pu, Th. The crystal structure of some metal hydroxides such as Cd(OH)₂ is also closely related.

      The AlB₂ structure is closely related to the NiAs structure. In both structures, the metal atoms form a primitive hexagonal array but only half the trigonal prismatic sites are occupied by As in NiAs whereas all trigonal prismatic sites are occupied by B in AlB₂. Consequently, the coordination of Ni is octahedral in NiAs instead of 12‐coordinate Al in AlB₂.

       Figure 1.51 The crystal structure of MgB2 as (a) an oblique projection showing hexagonal rings of B atoms with 12‐coordinate Mg situated between pairs of rings and (b) [001] projection of the crystal structure.

      1.17.16 Silicate structures – some tips to understanding them

      Silicates,