Ternary oxides

The principles described above apply equally well to oxides with more complex formulas. In these materials, however, there are generally a number of different cations or anions present. Generally, only one of the ionic species will be affected by the defect forming reaction while (ideally) others will remain unaltered. The reactant, on the other hand, can be introduced into any of the suitable ion sites. This leads to a certain amount of complexity in writing the defect equations that apply. The simplest way to bypass this difficulty is to decompose the complex oxide into its major components and treat these separately. Two examples, using the perovskite structure, can illustrate this. 

The perovskite structure, ABO3 (where A represents a large cation and B a medium-size cation) is adopted by many solids and solid solutions between them can readily be prepared. Vacancy-containing systems with the perovskite structure are of interest as electrolytes in solid-state batteries and fuel cells. Typical representatives of this type of material can be made by introducing a higher valence cation into the A sites or a lower valance cation into the B sites. 

The first example is the substitution of La3+ for the alkaline earth Ca2+ cation in CaTi03. In this reaction, the Ti sites are unaffected, and it can be written simply in terms of the reaction between the impurity La203 and a CaO matrix. The site 

One vacancy is generated for every two La3+ substituents. If one wishes to include the T1O2, which is a sleeping partner, it is only necessary to maintain the correct stoichiometry. The creation of three new A cation sites (2La a + V a) requires the inclusion of three Ti sites and the corresponding number of anion sites  

Exactly the same approach can be employed for substitution on the B sites, and this can provide our second example. Assuming ionic compounds, consider the substitution of Cr3+ for Ti4+ in CaTi03. This time the CaO component is the sleeping partner and can be ignored so the reaction can be considered to be between the Cr203 impurity and the Ti02 matrix. The site maintenance rule requires that inclusion of two Cr3+ ions on Ti4+ sites requires the creation of four O2- sites  

---

Among the high-temperature superconductors one finds various cuprates (i.e., ternary oxides of copper and barium) having a layered structure of the perovskite type, as well as more complicated oxides on the basis of copper oxide which also include oxides of yttrium, calcium, strontium, bismuth, thallium, and/or other metals. Today, all these oxide systems are studied closely by a variety of specialists, including physicists, chemists, physical chemists, and theoreticians attempting to elucidate the essence of this phenomenon. Studies of electrochemical aspects contribute markedly to progress in HTSCs. 

This argument with respect to the ionic radii would predict a surface enrichment of Sn4+ (0.083 nm) for the ternary oxide, which is not observed. Hutchings et al. [50]... 

The interest in the synthesis and properties of delafossite structured compounds that have the general formula of ABO2 have grown due to their p-type conductivity and optical transparency. The application of ultrasound for the synthesis of ternary oxide AgMC>2 (M = Fe, Ga) has been investigated by Nagarajan and Tomar [44]. Above materials were obtained in crystalline form within 40-60 min of sonication. 

Nagarajan R, Tomar N (2009) Ultrasound assisted ambient temperature synthesis of ternary oxide AgM02 (M = Fe, Ga). J Solid State Chem 182 1283-1290... 

It is interesting to note that the large difference in covalency parameters for the Mn2+—0 bond in MnO Nathans et al., 1964) vs the Mn2+—O bond in MnCC>3 (Lindgard and Marshall, 1969) agrees well with the spin transfer anticipated from Rv and R. This covalency difference for an M—0 bond in ternary oxides M Y Oz, which is dependent on the nature of the Y—0 bonds [in this case (Mn—O)—Mn for MnO and (Mn—0)-C for MnCOs], was also shown to exist for other oxides (see Table 4). 

In ternary oxides, M.xYyOz, the unit cell volume of compounds in which M = transition metal vs the volume of MgxY j,Oz is a function of the Y—0 group, being smaller as the ratio of x y decreases the coordination of Y decreases and the Y—0 covalence increases. Thus, the... 

Structural Imperfections. In many respects HREM has had a greater impact upon our knowledge of the nature of the atomic reorganization at crystalline imperfections than any other single technique. One of the very first contributions of HREM as a new analytical and structural tool was described in the paper by Iijimia (42) in 1971 on 2 10 29 v -ewe< down to its b - axis. Structural faults, arising from subtle fluctuations in composition, could be clearly seen in the block-structure (based on NbO octahedra) which is a feature of this ternary oxide system. More than a decade later similar materials are yielding to active scrutiny by HREM, and Horiuchi (43), for example, has shown how point defects may be directly viewed... 

ArV is not necessarily positive, and to compare the relative stability of the different modifications of a ternary compound like AGSiOs the volume of formation of the ternary oxide from the binary constituent oxides is considered for convenience. The pressure dependence of the Gibbs energies of formation from the binary constituent oxides of kyanite, sillimanite and andalusite polymorphs of A SiOs are shown in Figure 1.10. Whereas sillimanite and andalusite have positive volumes of formation and are destabilized by pressure relative to the binary oxides, kyanite has a negative volume of formation and becomes the stable high-pressure phase. The thermodynamic data used in the calculations are given in Table 1.7 [3].1... 

A number of theoretical approaches can account for the fact that an enthalpy of formation of such a binary oxide or a ternary oxide is large and negative. The stability of a ternary oxide relative to the binary constituent oxides is, however, often small, as demonstrated in Table 7.1 using Mg2SiC>4 as an example [1], The enthalpy differences between the three different polymorphs of Mg2Si04 - olivine, /3-phase and spinel - are less than 2% of the enthalpy of formation of the polymorphs. These enthalpy differences are comparable in magnitude to the enthalpy... 

Table 7.1 Magnitudes of enthalpies of various reactions of a ternary oxide using Mg2SiC>4 as an example (after Navrotsky [1]).

The relative stabilities of the dioxides, sesquioxides and monoxides for first period transition metals are given in Figure 7.11(c). The stability of the higher oxidation state oxides decreases across the period. As we will discuss later, higher oxidation states can be stabilized in a ternary oxide if the second metal is a basic oxide like an alkaline earth metal. The lines in Figure 7.11(c) can in such cases be used to estimate enthalpies of formation for unstable oxidation states in order to determine the enthalpy stabilization in the acid-base reactions see below. Finally, it should be noted that the relative stability of the oxides in the higher oxidation states increases from the 3d via 4d to the 5d elements, as illustrated for the Cr, Mo and W oxides in Figure 7.11(d). 

Although periodic trends in enthalpies of formation are often striking, these trends can in general not be used to estimate accurate data for compounds where experimental data are not available. Other schemes are frequently used and these estimates are often based on atomic size and electronegativity-related arguments. As an example, the enthalpy of formation of a ternary oxide from the binary constituent oxides, i.e. the enthalpy of a reaction like... 

Figure 7.15 (a) Enthalpy of formation of ternary oxides and nitrides from their binary constituent compounds as a function of the ratio of ionic potential [16]. Reprinted with permission from [16] Copyright (1997) American Chemical Society, (b) Gibbs energy of the oxide-sulfide equilibrium for group 1 and 2 metals at 1773 K as a function of the optical basicity of the metal. 

In ternary oxides AMO3 the second class of structures arises when A and M are the same size and the size is suitable for octahedral co-ordination. These adopt structures in which both ions are 6-coordinate. An example is the lithium nio-bate structure, which contains hexagonally packed anion layers (Figure 11.6(d)). Surprisingly, no known fluoride adopts such a structure. 

Af,ox m standard molar enthalpy of formation (of a ternary oxide) from (binary) oxides... 

---