Solids with interstitial cations

We have here defect annihilation and a decrease in electrical conductivity as a result. 

---

Ionic binary solids with interstitial cations B... 

Ionic binary solids with interstitial cations B are characterized by the following conditions on concentrations [Bj 0 and [Vg] = [V ] = [A,] = 0 thus, the simplified expression for the distance from stoichiometry for B becomes, according to equation [2.12],... 

Note that the zone furthest to the left in Figure 3.3 corresponds to the case of the Wagner solid with an interstitial cation A and free electrons, while the zone furthest to the right corresponds to the case of a Wagner solid with a cationic vacancy and free electron holes. Thus, we can show the possibility, with the same solid, of moving from a semiconductor to a semiconductor p merely under the influence of the gas pressure. 

We will examine, as example, the reaction between oxygen gas and barium oxide in the approximation of Wagner. As we saw before, this oxide is with interstitial cations and includes free electrons and thus a cation excess. This distance in excess from stoichiometiy is, at the chemical equilibriiun, more or less important according to the fixed oxygen pressure above the solid. That is due to a reaction that we can write with the usual chemical symbolic system in the form ... 

If the formed solid is, for example, a n-type compound with interstitial cation A, the reaction still proceeds by the jnmp of an ion A from the oxide into an interstitial position of ABO2 and after diffusion causes the deconqxrsition of carbonate ion and... 

At that date, palladium hydride was regarded as a special case. Lacher s approach was subsequently developed by the author (1946) (I) and by Rees (1954) (34) into attempts to frame a general theory of the nature and existence of solid compounds. The one model starts with the idea of the crystal of a binary compound, of perfect stoichiometric composition, but with intrinsic lattice disorder —e.g., of Frenkel type. As the stoichiometry adjusts itself to higher or lower partial pressures of one or other component, by incorporating cation vacancies or interstitial cations, the relevant feature is the interaction of point defects located on adjacent sites. These interactions contribute to the partition function of the crystal and set a maximum attainable concentration of each type of defect. Conjugate with the maximum concentration of, for example, cation vacancies, Nh 9 and fixed by the intrinsic lattice disorder, is a minimum concentration of interstitials, N. The difference, Nh — Ni, measures the nonstoichiometry at the nonmetal-rich phase limit. The metal-rich limit is similarly determined by the maximum attainable concentration of interstitials. With the maximum concentrations of defects, so defined, may be compared the intrinsic disorder in the stoichiometric crystals, and from the several energies concerned there can be specified the conditions under which the stoichiometric crystal lies outside the stability limits. 

The defects which disrupt the regular patterns of crystals, can be classified into point defects (zero-dimensional), line defects (1-dimensional), planar (2-dimensional) and bulk defects (3-dimensional). Point defects are imperfections of the crystal lattice having dimensions of the order of the atomic size. The formation of point defects in solids was predicted by Frenkel [40], At high temperatures, the thermal motion of atoms becomes more intensive and some of atoms obtain energies sufficient to leave their lattice sites and occupy interstitial positions. In this case, a vacancy and an interstitial atom, the so-called Frenkel pair, appear simultaneously. A way to create only vacancies has been shown later by Wagner and Schottky [41] atoms leave their lattice sites and occupy free positions on the surface or at internal imperfections of the crystal (voids, grain boundaries, dislocations). Such vacancies are often called Schottky defects (Fig. 6.3). This mechanism dominates in solids with close-packed lattices where the formation of vacancies requires considerably smaller energies than that of interstitials. In ionic compounds also there are defects of two types, Frenkel and Schottky disorder. In the first case there are equal numbers of cation vacancies... 

As an example, we will examine the reaction between gaseous oxygen and bariiun oxide. This oxide has interstitial cations and contains free electrons and therefore an excess of cations. At equilibrixun, this overstoichiometry is greater or lesser depending on the oxygen pressure, which reigns over the solid. This is due to a reaction which it is tempting to write with the usual chemical symbols in the form ... 

Extrinsic Defects Extrinsic defects occur when an impurity atom or ion is incorporated into the lattice either by substitution onto the normal lattice site or by insertion into interstitial positions. Where the impurity is aliovalent with the host sublattice, a compensating charge must be found within the lattice to pre-serve elec-troneutality. For example, inclusion of Ca in the NaCl crystal lattice results in the creation of an equal number of cation vacancies. These defects therefore alter the composition of the solid. In many systems the concentration of the dopant ion can vary enormously and can be used to tailor specific properties. These systems are termed solid solutions and are discussed in more detail in Section 25.1.2. 

Anion Interstitials The other mechanism by which a cation of higher charge may substitute for one of lower charge creates interstitial anions. This mechanism appears to be favored by the fluorite structure in certain cases. For example, calcium fluoride can dissolve small amounts of yttrium fluoride. The total number of cations remains constant with Ca +, ions disordered over the calcium sites. To retain electroneutrality, fluoride interstitials are created to give the solid solution formula... 

Powder XR diffraction spectra confirm that all materials are single phase solid solutions with a cubic fluorite structure. Even when 10 mol% of the cations is substituted with dopant the original structure is retained. We used Kim s formula (28) and the corresponding ion radii (29) to estimate the concentration of dopant in the cerium oxide lattice. The calculated lattice parameters show that less dopant is present in the bulk than expected. As no other phases are present in the spectrum, we expect dopant-enriched crystal surfaces, and possibly some interstitial dopant cations. However, this kind of surface enrichment cannot be determined by XR diffraction owing to the lower ordering at the surface. 

The crystal structures of the end-members with x = 0 are so-called y-tetrahedral structures , with distorted hexagonal close packed oxide arrays and cations distributed over various tetrahedral sites. In the solid solutions, Li ions are found, by powder neutron diffraction, to occupy partially various tetrahedral and octahedral interstitial sites, which link up to form an essentially three-dimensional conduction pathway. 

Non-stoichiometry is a very important property of actinide dioxides. Small departures from stoichiometric compositions, are due to point-defects in anion sublattice (vacancies for AnOa-x and interstitials for An02+x )- A lattice defect is a point perturbation of the periodicity of the perfect solid and, in an ionic picture, it constitutes a point charge with respect to the lattice, since it is a point of accumulation of electrons or electron holes. This point charge must be compensated, in order to preserve electroneutrality of the total lattice. Actinide ions having usually two or more oxidation states within a narrow range of stability, the neutralization of the point charges is achieved through a Redox process, i.e. oxidation or reduction of the cation. This is in fact the main reason for the existence of non-stoichiometry. In this respect, actinide compounds are similar to transition metals oxides and to some lanthanide dioxides. 

---