Solid State Chemistry and its Applications. Anthony R. West

above are two examples of anion‐ordered crystal structures which occur at specific compositions. Other anion ordering arrangements are known both at these and other compositions. In addition, solid solutions form in many systems in which the anion content is variable and can be represented by the general formula ABO_3–δ . In these, the oxygen vacancies may be distributed at random through the perovskite structure or locally ordered structures may form in which small domains of a particular structure type are distributed at random through a disordered perovskite network.

       1.17.7.6 Stoichiometry–property relations

      The perovskite structure, with two different‐sized cations and several possible cation charge combinations, occurs with a very wide range of compositions. In addition, defect perovskites form in which there are either cation or anion vacancies. Defects, solid solutions and various kinds of properties are all considered in later chapters. All we wish to note here is the incredible range of properties found in materials with perovskite‐related structure whose composition has been adjusted to optimise a particular property. Almost every physical property imaginable has been found in materials with the perovskite structure by changing their composition and/or defect structure; for this reason, perovskite is sometimes referred to as an inorganic chameleon! A selection of perovskites and their properties is listed in Table 1.19.

       1.17.7.7 Cation‐ordered perovskites

Oxide perovskites ABO₃ have an overall cation charge of 6+ which allows the possibility of different cation charge combinations. Since the A and B sites are also very different in size, most elements in the periodic table can be found, somewhere, in a perovskite structure. In complex perovskites with more than two cations, many examples are known of cation ordered arrangements on A and/or B sites, such as in double perovskites with general formula A₂(BB′)O₆. In these, two different cations are arranged on the B sites in the same way that the anions and cations are arranged in the rock salt structure. A 2D section through the structure of Ba₂FeMoO₆, Fig. 1.42(e), shows FeO₆ and MoO₆ octahedra that alternate in an fcc arrangement. In ordered, undistorted structures such as this, the structure is still cubic but the unit cell edge, a, is twice the length of the perovskite subcell lattice parameter, a _p .

       Table 1.19 Perovskites: some composition–property correlations

Composition	Property
CaTiO3	Dielectric
BaTiO3	Ferroelectric
Pb(Mg1/3Nb2/3)O3	Relaxor ferroelectric
Pb(Zr1−x Ti x )O3	Piezoelectric
(Ba1−x La x )TiO3	Semiconductor
(Y1/3Ba2/3)CuO3−x	Superconductor
Na x WO3	Mixed conductor (Na^+, e^−); electrochromic
SrCeO3:H	Proton conductor
RE TM O3−x	Mixed conductor (O^2−, e^−)
Li0.5−3x La0.5+x TiO3	Li^+ ion conductor
A MnO3−δ	Giant magnetoresistance

      RE = rare earth; TM = transition metal.

      Whether the B site cation arrangement is ordered, Fig. 1.42(e) or disordered, (d) depends on whether the increased entropy associated with cation disorder would offset the loss in enthalpy on forming a disordered structure containing dis‐similar cations. This is because cations of dissimilar size and charge are more likely to segregate into clusters or to form an ordered arrangement over two sets of lattice sites than to randomise over a single set of lattice sites, leading to a higher lattice energy or more negative enthalpy of formation for an ordered structure than for a disordered one. The reason why partial or complete disorder is observed in many structures, especially at high temperatures, is because of the increasing influence of the TΔS term in the overall free energy, ΔG (from ΔG = ΔH − TΔS), which offsets the increased lattice energy of an ordered structure. One effect of increasing temperature is therefore to introduce structural disorder through the term TΔS. A similar result may arise by compositional change, or doping. For example, Ca₂FeReO₆ has B‐site order of Fe and Re, but partial substitution of La onto the A sites, in the solid solution Ca_2−x La _x FeReO₆, causes (indirectly) the B cations to disorder.

      Two additional complications in seeking to rationalise ordered vs disordered cation arrangements are first, many perovskites become non‐stoichiometric through oxygen loss at high temperatures. In this process, electrons are released by the O²⁻/O₂ reaction but are retained in the perovskite lattice and are associated with transition metal ions that therefore have a reduced valence state, leading to the mixed valence of transition metals on the B sites. Second, synthesis temperature may be important, especially if kinetically stable but thermodynamically metastable structures are obtained at moderate synthesis temperatures. There is no simple way to tell whether a particular structure is thermodynamically stable or metastable until follow‐on experiments are performed to investigate its thermal stability and possible polymorphic transitions, Chapter 7. Many cases are known in which a partially ordered or fully disordered structure may be synthesised as a consequence of the moderate synthesis temperatures or conditions that are used, although the fully ordered structure would be the true, thermodynamically stable, low temperature polymorph.

      The significance of the lattice energy component associated with BB′ order in double perovskite structures is illustrated well by three Ba₂BB′O₆ phases in which the BB′ combinations, and the extra lattice energy calculated to be associated with BB′ order, are: Sc^IIIRe^V, 594 kJ mol⁻¹; Ni^IIRe^VI, 2414 kJ mol⁻¹; Li^IRe^VII, 5381 kJ mol⁻¹ [data taken from Rosenstein and Schor, J. Chem. Phys. 38, 1789 (1963)]. Note, these all contain octahedrally coordinated Re but unusually, in three different valence states. The three structures have similar‐sized unit cells and therefore, charge difference rather than size difference between B and B′ appears to be the main factor that determines their increased lattice energy.

      Many different structural and compositional variations are observed within the family of cation‐ordered double perovskites. The A site is frequently occupied by Ca, Sr or Ba, but the B sites may contain a wide range of, mainly transition metals, in III/V, II/VI and I/VII combinations, as shown by the above examples. The A site may also be occupied by larger, trivalent rare earth cations with II/IV BB′ combinations, as in La₂MgHfO₆ and I/V, as in La₂LiIrO₆. Some compositions, such as Ba₂BiIrO₆, are polymorphic and exhibit both a cation‐disordered cubic structure at a high temperature and a non‐cubic ordered structure(s) at a lower temperature.

In addition to thermodynamic considerations of the enthalpy and entropy of possible ordered or disordered arrangements of dis‐similar cations on the B sites, tolerance factor considerations influence