Diffusion defect chemistry

The first four chapters introduce basic concepts that are developed to build up a framework for understanding defect chemistry and physics. Thereafter, chapters focus rather more on properties related to applications. Chapter 5 describes diffusion in solids Chapter 6, ionic conductivity Chapters 7 and 8 the important topics of electronic conductivity, both intrinsic (Chapter 7) and extrinsic (Chapter 8). The final chapter gives a selected account of magnetic and optical defects. 

Where R is the growth rate, t the thickness of the diffusion layer and D the diffusion constant. The understanding gleaned from studies such as those of Fig. 6 was used to improve the Q of synthetic quartz from initial Q s of 30,000 to present Q s in excess of 2 x 106. Thus systematic studies of the defect chemistry of quartz lead to procedures for defect control so as to provide device quality material equal and in some cases superior to natural quartz. Fig. 7 shows an early commercial quartz synthesis run in the AT T factory facility in North Andover, Massachusetts. 

Figure 57. Conservative ensembles in the case of complex defect chemistry for various examples discussed in the text.233 234 (Reprinted from J. Claus, I. Denk, M. Leonhardt, and J. Maier, Influence of Internal Reactions on Chemical Diffusion Application to Fe-doped SrTiCV , Ber. Bunsenges. Phys. Chem. 101, 1386-1392. Copyright 1997 with permission from WILEY-VCH Verlag GmbH.)...

The advantage of the kinetic treatment lies in the fact that (i) also solutions far from equilibrium can be handled and (ii) the range of validity of Eq. (169) can be given (similarly as in the diffusion case, cf. Section VI.2./). Since in the above derivations bulk defect chemistry was assumed to be established at x = 0, the index bulk was used in Eq. (169) to allow for more general situations. Note that these explicit formulae predict defined dependencies on the control parameters which can be checked provided defect chemistry is known. For simple situations (see Refs.252,253) a power law relationship results ( is a constant)... 

The limits of integration are the oxygen partial pressures maintained at the gas phase boundaries. Equation (10.10) has general validity for mixed conductors. To carry the derivation further, one needs to consider the defect chemistry of a specific material system. When electronic conductivity prevails, Eqs. (10.9) and (10.10) can be recast through the use of the Nemst-Einstein equation in a form that includes the oxygen self-diffusion coefficient Dg, which is accessible from ionic conductivity measurements. This is further exemplified for perovskite-type oxides in Section 10.6.4, assuming a vacancy diffusion mechcinism to hold in these materials. 

In the second part of Eq. (10.22) the fact has been used that, if correlation effects can be neglected, the tracer diffusion coefficient, D, is equal to the self-diffusion coefficient, It is important to note once again that Eq. (10.18) is valid in the limit of small Po -gradients only. Since both D and kg for a given material are a function of its specific defect chemistry, in general, will be a function of process parameters Pq and temperature. 

The foregoing survey was focused on situations where bnlk diffusion processes were rate determining. Such systems are amenable to analysis using an electrochemical approach. Other factors such as transport down pores or cracks, volatilization or melting of the oxide scale may occur and require different analyses but diffusion controlled processes may be mathematically modeled and correlated with the defect chemistry of the corrosion product. These limiting cases provide a guide to understanding the more complex phenomena frequently encountered. 

If you increase the PO2, then the diffusion coefficient will decrease. This is found for a very wide temperature range and implies that diffusion is a complex process. It is interesting to compare this case to that of ZnO. Both cations exist in the 2+ or 1+ charge state, but the crystal structures and point defect chemistry are very different. 

For more information on defect chemistry of the material in this chapter and introduction to diffusion and conductivity, see ... 

Poulsen, F. W. (2000). Defect chemistry modelling of oxygen stoichiometry, vacancy concentrations, and conductivity of (Lai xSrx)j,Mn03+j. Solid State Ionics 129 143-162. Mizusaki,., Saito, T., and Tagawa, H. (1996). A chemical diffusion-controlled electrode reaction at the compact Lai- Sr MnOa-stabilized zirconia interface in oxygen atmospheres. J. Electrochem. Soc. 143 3063-3073. 

Whereas an additive can alter each of the diffusion coefficients for matter transport (A, Dgb, A, and Dg), historically the major emphasis has been placed on the ability of the additive to alter Di through its effect on the defect chemistry of the host. To determine how an additive will influence A, the defect chemistry of the host must be known. Specifically, we must know the nature of the ratecontrolling species (anion or cation), the type of defect (vacancy or interstitial), and the state of charge of the defect. In practice, this information is known in only a very few cases. To illustrate the approach, let us consider AI2O3, a system that has been widely studied. According to Kroger (62), the intrinsic defect structure consists of cationic Frenkel defects ... 

In 1972 Per Kofstad published his "Non-stoichiometry, diffusion and electrical conductivity in binary metal oxides". It has been a popular textbook in defect chemistry of oxides worldwide, not least because it contained a comprehensive review of defect stmcture and defect-related properties of all binary metal oxides. It followed Kofstad s equally well-recognized book "High temperature oxidation of metals" from 1967, revised and published under the title "High temperature corrosion" in 1987. 

Furthermore, the relationships between the transport coefficients have become evident, enabling an interpretation in the atomistic picture. Rate constants of the hopping process, mobility and the diffusion coefficient of the hopping particle (point defect) are closely related parameters. Equation (6.35) emphasizes the importance of the specific conductivity as a transport parameter, which extends beyond its role as a valuable measurement parameter and an electrical material property. Equation (6.32) demonstrates that (close to equilibrium) it is proportional to the equilibrium concentration of the defect under consideration and its mobility. The proportionality to S was exploited extensively in Chapter 5 for experimental verification of defect chemistry. 

Fig. 6.18 Ttacer diffusion data ( Fe) for various temperatures as a function of the partial pressure of oxygen for Fe3 i04. In agreement with the special defect chemistry (Rrenkel disorder in the Fe-sublattice with high electronic disorder) a dependence of the form aP /3+j8P+2/3 jg fulfilled. lYom Ref. [387].

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