Anthony R. West - Solid State Chemistry and its Applications

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 YBa 2Cu 3O 7and 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), Bi 2Sr 2CaCu 2O 8has rock salt‐like layers, Bi 2O 2, 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

Compound a	a /Å	c/ Å	z (M +ion)	z (anion)
K 2NiF 4	4.006	13.076	0.352	0.151
K 2CuF 4	4.155	12.74	0.356	0.153
Ba 2SnO 4	4.140	13.295	0.355	0.155
Ba 2PbO 4	4.305	13.273	0.355	0.155
Sr 2SnO 4	4.037	12.53	0.353	0.153
Sr 2TiO 4	3.884	12.60	0.355	0.152
La 2NiO 4	3.855	12.652	0.360	0.170
K 2MgF 4	3.955	13.706	0.35	0.15
Other examples b
M 2Y 6+O 4: M = K, Rb, Cs; Y = U, Np
Ln 2YO 4: Ln = La → Nd; Y = Ni, Cu
CaLnAlO 4: Ln = La → Er, Y
SrLnFeO 4: Ln = La → Tb
SrLnCrO 4: Ln = La → Dy
BaLnFeO 4:Ln = La → Eu
A 2BF 4: A = K, Rb, Tl; B = Mg, Ni, Zn, Co, Fe
A 2BCl 4: A = Rb, Cs; B = Cr, Mn, Cd
Sr 2BO 4: 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 Bi 2O 2. The Bi 2O 2layers are formed by a single, 2D square planar net of oxygens in which each square is capped on one side only by Bi 3+to give sheets of pyramids in an alternating ‘up’ and ‘down’ arrangement, Fig. 1.50(b). Bi 3+is a lone pair‐active, heavy p‐ block cation and the spatial disposition of the lone pairs acts to separate the Bi 2O 2layers from the perovskite blocks. This Bi 2O 2structural arrangement is different to the octahedral rock salt arrangement of Bi in the BiSCCO phases.

The general formula of Aurivillius phases is Bi 2O 2[A m−1M mO 3m+1]. Examples include: M=Mo, m = 1 for Bi 2O 2[MoO 4] with a single layer of perovskite‐like octahedra; Bi 2O 2[SrNb 2O 7] with a double perovskite layer of NbO 6octahedra and Sr in 12‐coordinate cages; Bi 2O 2[Bi 2Ti 3O 10] with triple perovskite layers and Bi in the 12‐coordinate perovskite A sites as well as in the Bi 2O 2layers.

The Dion‐Jacobsen phases are related to Aurivillius phases but the Bi 2O 2layers are replaced by layers of alkali cations to give the general formula A′[A m−1M mX 3m+1]. Examples include K[LaNb 2O 7] that has double perovskite layers and Cs[La 2Ti 2NbO 10] with triple layers.

The aluminium diboride family of crystal structures shot to prominence in 2000 when isostructural MgB 2was 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 AlB 2structure, including MB 2: M = Ti, Zr, Nb, Ta, V, Cr, Mo, Mg, U, and MSi 2: M = U, Pu, Th. The crystal structure of some metal hydroxides such as Cd(OH) 2is also closely related.

The AlB 2structure 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 AlB 2. Consequently, the coordination of Ni is octahedral in NiAs instead of 12‐coordinate Al in AlB 2.

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.

Silicates, especially many minerals, often have complex formulae and structures. The purpose of this section is not to give a review of their structures but simply to show that a considerable amount of structural information may be obtained from their chemical formulae. Using certain guidelines, one can appreciate, without the necessity of remembering a large number of complex formulae, whether a particular silicate is a 3D framework structure, sheet‐like, chain‐like, etc.

It is common practice to regard silicate structures as composed of cations and silicate anions. Various silicate anions are possible, ranging from the extremes of isolated tetrahedra in orthosilicates such as olivine (Mg 2SiO 4), to infinite 3D frameworks, as in silica itself (SiO 2). The structures of silicate anions are based on certain principles: