Sublattice rigid

As a first approximation, let us consider the X atoms as rigid spheres arranged in an ideal hexagonal close-packed (hep) sublattice. On transforming the usual hexagonal unit cell (a, 6, c ) to an ortho-hexagonal cell, defined by a0 = c, bo = b —a, and Co = + b, and introducing... 

In other cases, however, and in particular when sublattices are occupied by rather immobile components, the point defect concentrations may not be in local equilibrium during transport and reaction. For example, in ternary oxide solutions, component transport (at high temperatures) occurs almost exclusively in the cation sublattices. It is mediated by the predominant point defects, which are cation vacancies. The nearly perfect oxygen sublattice, by contrast, serves as a rigid matrix. These oxides can thus be regarded as models for closed or partially closed systems. These characteristic features make an AO-BO (or rather A, O-B, a 0) interdiffusion experiment a critical test for possible deviations from local point defect equilibrium. We therefore develop the concept and quantitative analysis using this inhomogeneous model solid solution. 

From Eqn. (9.16), we see that the metal A is precipitated within the rigid, dense-packed oxygen ion sublattice of the oxide matrix. The local volume at the reaction front is thus increased by the molar volume per mole of vacancies. Large strains and stresses are the immediate result. In contrast, if (A,B)304 is internally reduced to yield (A, B)0, the oxygen ion sublattice remains essentially undistorted, except for... 

Under usual conditions at least one sublattice is very rigid and—in the case of interest (in particular when dealing with solid ion conductors)—one sublattice exhibits a significant atomic mobility. The selectivity of the conductivity (cf. also the selective solubility of foreign species) is indeed a characteristic feature of solids. 

The three optic types modes (vtz Aig and vixEg) the latter mode vtx Eg is doubly degenerate, only involve distortions to the O—O bonding interactions i.e. the sublattices move as rigid units. The frequencies of these modes are in effect the spring-constants of the O—0 interactions involved which can be related to the bond stiffness Xi /Xs. 

We caimot assume that all the ions have found their ideal sites in sintered material, e.g., some AP" ions in MgAl204 may be on tetrahedral sites. The structure predicted by computer modeling for the [112 lateral twin interface in NiO contains a rigid-body translation. Such a translation is not observed experimentally for the same type of interface in spinel, which has the same oxygen sublattice. It may be that the reason for this difference is that the translation-free configuration is what is present on a migrating GB and this becomes frozen in when the sample is cooled. The structure predicted by minimum energy calculations is a stationary structure. 

LSE, the classical electrochemistry, is concerned with electrochemical cells (ECs) based on liquid ionic-conductors (liquid electrolytes (LEs)). Solid-state electrochemistry is concerned with ECs in which the ionic conductor (electrolyte) is a solid. Both fields are based on common thermodynamic principles. Yet, the finer characteristics of ECs in the two fields are different because of differences in the materials properties, conduction mechanisms, morphology and cell geometry. Differences that come immediately to mind are (1) The lack of electronic (electron/hole) conduction in most LEs, while electronic conduction exists to some extent in all solid electrolytes (SEs). (2) In LEs both cations and anions are mobile, while in SEs only one kind of ions is usually mobile while the other forms a rigid sublattice serving as a frame for the motion of the mobile ion. An... 

The discovery of the various ionic conductors has elicited strong interest, as they can be used in batteries and other devices. It could be shown after numerous studies that the high ionic mobility in these compounds are the result of particular lattice structures. In such lattices, the immobile ions of one kind (most often the anions) are fixed at their lattice sites and form a rather rigid, nondeformable sublattice. The sublattice of the other ions (most often the cations), to the contrary, is disordered the cations are not bound to particular sites but can occupy any of a large number of equally probable sites. As at any particular time an ion physically occupies just... 

Finally, the occurrence of different types of defects can serve as a guide in the identification of the H migration mechanism. The defects can be (or H502 ) defects that occur either as (a) thermally activated (Frenkel) excess sites, such as are present in ionic cpd materials, (b) voids in a quasi-liquid sublattiee , (e) proton defeets in the same sense as oxonium defects in a rigid sublattice or (d) proton voids occurring in a quasi-liquid proton sublattice. 

Solid electrolytes have also been variously described as Fast Ionic Conductors or Superionic conductors and may cover ionic conductivities within the range of 10 to 1 S/cm with activation energies of 0.1 to 2eV/atom. The levels of ionic conductivity achieved in many of these solid electrolytes are well below their melting points and the values are more typical of liquids than solids. In contrast to liquid electrolytes such as the aqueous electrolytic solutions or molten salts, the mobile ions in a solid are limited to one sublattice such that one ionic component can move through a rigid framework provided by the other components. 

The angle between the moment direction and the tetragonal c-axis, assuming both iron and rare-earth sublattices are completely rigid, at OK, is given by ... 

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