Sublattice, mobile ion

In recent years, more complex types of transport processes have been investigated and, from the point of view of solid state science, considerable interest is attached to the study of transport in disordered materials. In glasses, for example, a distribution of jump distances and activation energies are expected for ionic transport. In crystalline materials, the best ionic conductors are those that exhibit considerable disorder of the mobile ion sublattice. At interfaces, minority carrier diffusion and discharge (for example electrons and holes) will take place in a random environment of mobile ions. In polycrystalline materials the lattice structure and transport processes are expected to be strongly perturbed near a grain boundary. 

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... 

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. 

Every ionic crystal can formally be regarded as a mutually interconnected composite of two distinct structures cationic sublattice and anionic sublattice, which may or may not have identical symmetry. Silver iodide exhibits two structures thermodynamically stable below 146°C sphalerite (below 137°C) and wurtzite (137-146°C), with a plane-centred I- sublattice. This changes into a body-centred one at 146°C, and it persists up to the melting point of Agl (555°C). On the other hand, the Ag+ sub-lattice is much less stable it collapses at the phase transition temperature (146°C) into a highly disordered, liquid-like system, in which the Ag+ ions are easily mobile over all the 42 theoretically available interstitial sites in the I-sub-lattice. This system shows an Ag+ conductivity of 1.31 S/cm at 146°C (the regular wurtzite modification of Agl has an ionic conductivity of about 10-3 S/cm at this temperature). 

In densely packed solids without obvious open channels, the transport number depends upon the defects present, a feature well illustrated by the mostly ionic halides. Lithium halides are characterized by small mobile Li+ ions that usually migrate via vacancies due to Schottky defects and have tc for Li+ close to 1. Similarly, silver halides with Frenkel defects on the cation sublattice have lc for Ag+ close to 1. Barium and lead halides, with very large cations and that contain... 

We summarize what is special with these prototype fast ion conductors with respect to transport and application. With their quasi-molten, partially filled cation sublattice, they can function similar to ion membranes in that they filter the mobile component ions in an applied electric field. In combination with an electron source (electrode), they can serve as component reservoirs. Considering the accuracy with which one can determine the electrical charge (10 s-10 6 A = 10 7 C 10-12mol (Zj = 1)), fast ionic conductors (solid electrolytes) can serve as very precise analytical tools. Solid state electrochemistry can be performed near room temperature, which is a great experimental advantage (e.g., for the study of the Hall-effect [J. Sohege, K. Funke (1984)] or the electrochemical Knudsen cell [N. Birks, H. Rickert (1963)]). The early volumes of the journal Solid State Ionics offer many pertinent applications. 

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. 

Figure 42 shows the basic elementary ion migration processes in a low defective isotropic ion conductor with a mobility in the A-sublattice. The vacancy mechanism (Fig. 42 top) can be described by a transport process (Zv= effective charge of the A-vacancy) such as... 

Similar valuable information on the structures and dynamics of the mobile sublattice in fast ion conducting silver components have been observed by Vashishta and coworkers in a series of MD studies which have included simulations of Agl and Ag2Se (Vashishta and Rahman, 1978 Vashishta, 1986 Ray et al., 1989). Again the simulations have proved of great value in analysing and interpreting experimental scattering data. 

The rationale for using the number of mobile carriers rather than the total number of ions involved is similar to the one made for Eq. (7.29). Here it can be assumed that one sublattice is the pipe through which the conducting ions are flowing. Referring to Fig. 7.7, the ions or defects enter the solid on one side and leave at the other. In contrast to the case where the crystal as a whole is placed in a chemical potential gradient, here the crystal itself does not move relative to an external frame of reference. 

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