Diffusion in ionic materials

Diffusion in ionic materials occurs primarily by the movement of charged species. Therefore, the application of an electric field can provide a very powerful driving force for mass transport. There have been numerous studies on the effects of electric fields on transport phenomena. Several studies have been performed on the evaporation of alkali halides in the presence of an external field. These investigations showed that the application of an electric field enhanced the evaporation of the crystal species. Similar studies have been performed on oxide ionic conductors, including ZrOi and p-aluminas. However, only a few experiments have been performed on classical insulating oxides such as a-A Os and MgO (perhaps because they are insulators). 

Diffusion in ionic materials normally occurs by a vacancy mechanism localized charge neutrality is maintained by the coupled diffusive motion of a charged vacancy and some other charged entity. 

The aim of this chapter is to review the current state of knowledge in ionic materials with crystallite dimensions less than 100 nm, systems which sometimes are referred to as nanoionics. The chapter will detail the preparation, characterization and the important applications of these materials, especially in sensors, solid-state batteries, and fuel cells. Particular focus will be placed on ionic transport in these materials, as this is a topic of considerable contemporary interest, and where conflicting reports exist of enhanced diffusion in nanocrystals. 

The moments ratio, Pa (equation (26)) is unity, which is obeyed reasonably well for non-diffusing species in ionic materials and for ionic melts. 

We often think that only cations move in ionic materials because so much work has been carried out on oxides or halides where the anion is much larger than the cation, for example, MgO, AI2O3, and NaCl. Ceramics that are being used for electronic applications often contain heavier (hence larger) cations so that the assumption is not necessarily valid. In solid-oxide fuel cells, it is the oxygen ion that diffuses. 

The nature of H diffusion in this material was investigated by using ionic conductivity, nuclear magnetic resonance, and infra-red optical methods. It was found that the diffusivities of OH" interstitial ions and of H during annealing in molten carbonic acid could both be described by the expression ... 

Funke K, Cramer C, Wihner D (2005) Concept of mismatch and relaxation for self-diffusion and conduction in ionic materials with disordered structures. In Karger J, Heitjans P (eds) Diffusion in condensed matter. Springer, Berlin, pp 857-893... 

Both cations and anions in ionic materials possess an electric charge and, as a consequence, are capable of migration or diffusion when an electric field is present. Thus, an electric current results from the net movement of these charged ions, which are present in addition to current due to any electron motion. Anion and cation migrations are in opposite directions. The total conductivity of an ionic material o-totai is thus equal to the sum of electronic and ionic contributions, as follows ... 

In polycrystalline materials, ion transport within the grain boundary must also be considered. For oxides with close-packed oxygens, the O-ion almost always diffuses much faster in the boundary region than in the bulk. In general, second phases at grain boundaries are less close packed and provide a pathway for more rapid diffusion of ionic species. Thus the simplified picture of bulk ionic conduction is made more complex by these additional effects. 

Other refractory oxides that can be deposited by CVD have excellent thermal stability and oxidation resistance. Some, like alumina and yttria, are also good barriers to oxygen diffusion providing that they are free of pores and cracks. Many however are not, such as zirconia, hafnia, thoria, and ceria. These oxides have a fluorite structure, which is a simple open cubic structure and is particularly susceptible to oxygen diffusion through ionic conductivity. The diffusion rate of oxygen in these materials can be considerable. 

The coalescence of atoms into clusters may also be restricted by generating the atoms inside confined volumes of microorganized systems [87] or in porous materials [88]. The ionic precursors are included prior to irradiation. The penetration in depth of ionizing radiation permits the ion reduction in situ, even for opaque materials. The surface of solid supports, adsorbing metal ions, is a strong limit to the diffusion of the nascent atoms formed by irradiation at room temperature, so that quite small clusters can survive. 

The drug may be incorporated in a slowly eroding matrix of waxy materials, embedded in a plastic matrix, complexed with anion exchange resins or incorporated in a water-insoluble hydrophilic matrix. Drug release from these systems occurs by several mechanisms diffusion, dissolution, ionic exchange or osmotic pressure [1,2], depending on the type of polymeric excipient present and the formulation used. 

Consider an ionic material that contains a dilute concentration of positively charged ions that diffuse interstitially (interstitial diffusion is described in Section 8.1.4). D is the interdiffusivity of these ions in the absence of any field. As shown in Sections 2.2.2 and 2.2.3, if an electric field, E = —V, is applied, the diffusion potential will be the electrochemical potential given by Eq. 2.41. According to Eq. 2.21, the flux of charged interstitials is... 

Intrinsic Crystal Self-Diffusion. A simple example of intrinsic self-diffusion in an ionic material is pure stoichiometric KC1, illustrated in Fig. 8.11a. As in many alkali halides, the predominant point defects are cation and anion vacancy complexes (Schottky defects), and therefore self-diffusion takes place by a vacancy mechanism. For stoichiometric KC1, the anion and cation vacancies are created in equal numbers because of the electroneutrality condition. These vacancies can be created... 

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