Diffusion in Oxides

G. H. Frishat, Ionic Diffusion in Oxide Glasses Trans Tech Pubbcations, Bay Village, Ohio, 1975. 

Frischat, G.H. (1975) Ionic Diffusion in Oxide Glass, Tans. Teh. Publ., Aedermannsdorf, Schweiz... 

The study of oxygen diffusion in oxides with mixed-valence 3d-ions presents great interest both in theoretical and practical terms. Such systems with Jahn-Teller (JT) 3d-cations are suitable model objects for analysis of the diffusion process in degenerate or pseudo-degenerate condensed systems. The mechanism of multi-well potential formation has been explored well for JT ions [1,2] and it is possible to give a simple microscopic description of the inter-center interactions and different properties of these systems. The practical interest paid to diffusion properties of the... 

Following a phenomenological approach, the driving force for chemical diffusion, in oxides, is the gradient of the electrochemical potential, ri-... 

V.S. Stubican and J.W. Orenbach, Influence of anisotropy and doping on grain-boundary diffusion in oxide systems, Solid State Ionics 12, 375 (1984). 

Freer R (1980) Bibliography Self-diffusion and impurity diffusion in oxides. J Mater Sci 15 803-824 Freer R G981) Diffusion in silicate minerals and glasses A data digest and guide to the literature. Contrib Mineral Petrol 76 440-454... 

G. H. Frischat, in Ionic Diffusion in Oxide Glasses, Trans Tech Publications, Aedermannsdorf, Switzerland, 1975. 

This chapter has, we hope, illustrated the scope of lattice dynamics and molecular dynamics to model the structure, thermodynamics and diffusion in oxides and minerals. Although the techniques are well-established there are many applications to minerals that still need to be addressed. One area that we have touched on is the study of the mineral-... 

More interesting is the commonly encountered situation where an ion diffuses in a majority electronic conductor. Thus, diffusion in metallic and semiconducting alloys or of inserted species in transition metal oxides and chalcogenides fall into this category. Many electrode reactions are of this type. Lithium diffusion in j5-LiAl and other alloys is of interest in negative electrode reactions for advanced hthium batteries hydrogen and lithium diffusion in oxides (e.g. VeOn) and sulfides (e.g. TiSa) are of importance as positive electrode reactions for batteries and elec-trochromic devices. 

Moya, E. G. (1994). Some apects of grain boundary diffusion in oxides. Science of Ceramics Interfaces II, 277-309, Novotny,/., ed., Amsterdam Elsevier Science. 

Diffusion in oxides occurs by means of point defects interstitial ions and vacancies. In stoichiometric oxides one finds two types of point defects, referred to as Frenkel defects and Schottky defects. These are presented schematically, for a divalent oxide of type MO, in Figure 9.6. To describe the chemical reactions of point defects and electronic charges we use the symbols given in Table 9.7. A Frenkel defect in a divalent oxide consists of an interstitial cation M and a cation vacancy A Schottky defect consists of a cation vacancy and an anion vacancy Vq- Because the oxide as a whole is electrically neutral, the concentrations of negative and positive charges associated with the defects are equal (electroneutrality condition). Thus, we find for Frenkel defects. 

Figure 9.11 Cation diffusion in oxide MO by interstitials or vacancies.

The relative contribution of the different types of diffusion in oxides and other inorganic compounds are functions of the temperature, partial pressures or activities of the constituents of the compounds, the microstructure, grain size, porosity etc. Grain boundary and dislocation diffusion generally have smaller activation energies than lattice diffusion and as a result become increasingly important the lower the temperature in solids with a given microstructure. 

Similar considerations may be applied to free transport of protons (cf. Fig.5.11). For dilute solutions of protons in an oxide essentially all nearest neighbour oxygen ions are available, and thus in this case Nd is unity. However, the specification of Z, s and co is not straightforward in this case. The dynamics of free proton diffusion in oxides are complicated by 1) the multistep process (jump+rotation), 2) the dependency on the dynamics of the oxygen ion sublattice, and 3) the quantum mechanical behaviour of a light particle such as the proton. 

Ion conductivity or diffusion in oxides can only take place because of the presence of imperfections or defects in the lattice. A finite concentration of defects is present at all temperatures above 0°K arising from the entropy contribution to the Gibbs free energy as a consequence of the disorder introduced by the presence of the defects. 

The purpose of this chapter has been to draw attention to the possibility of using a network analysis technique for treating diffusion in oxides. Such analyses should be able to articulate possible relationships between individual jumps within a structure and measured values of diffusion coefficients. The determination of the values of individual jump frequencies may then be approached in a number of different ways, and the following have some prospect of being useful ... 

To solve System (II), we consider that and Pi are small (this is justified by the fact that this assuirqition will make it possible to find the law of the pure case of diffusion in oxide as in section 5.6.3). Under these conditions, we can use approximations [5.66] and [5.67]. System (II) is then reduced to equation [16.10] which is the general expression of the two diffusion-mixed modes by taking account of equations [16.5] and [16.7] ... 

In conclusion, if an element of an alloy which constitutes an ideal solid solution is oxidized selectively by a gas, the diffusion in alloy of the oxidized element is compensated by a diffusion of vacancies in opposite direction. The paraboUc law of oxidation can have two different origins a pure mode of diffusion in oxide and a diffusion-mixed mode in both oxide and alloy. If the oxide is a p-type semiconductor with cationic vacancies, the two modes can be distinguished by both influences of gas pressure and initial alloy compositioa... 

To apply the preceding methods of calculation, it is necessary to know the concentration in added element B in A oxide. However, we know oidy the alloy composition and there is no reason, a priori, for the B ftaction in the oxide to be the same one as in alloy. We then look for a relationship between these two quantities. For that we suppose that B ions diffuse in oxide at the same speed as do A ions, that is, the same assuming that their mole fraction in oxide is independent of the distance to the internal interface. We also assume that A and B stable oxides are AO and BO. 

---