A microscopic approach to ionic transport in glasses

Note that this is equivalent to the expression Tj = Cj Uj used in Chapters 2 and 3 except that Cj and q refer to the individual ions rather than moles of ions. 

Since the relative dielectric constant of inorganic glasses is low, typically between 5 and 15, ionic species are strongly associated. For instance most of the Ag cations will be associated with non-bridging oxygens in AgPOj glass. Nevertheless, thermal vibrations allow a partial 

From a thermodynamic point of view the formation of an interstitial pair obeys the chemical equilibrium (Kittel, 1968) 

Taking into account that every associated pair may accept an interstitial cation and that c+ C it then follows that 

Such a mechanism is not incompatible with a Haven ratio between 0.3 and 0.6 which is usually found for mineral glasses (Haven and Verkerk, 1965 Terai and Hayami, 1975 Lim and Day, 1978). The Haven ratio, that is the ratio of the tracer diffusion coefficient D determined by radioactive tracer methods to D, the diffusion coefficient obtained from conductivity via the Nernst-Einstein relationship (defined in Chapter 3) can be measured with great accuracy. The simultaneous measurement of D and D by analysis of the diffusion profile obtained under an electrical field (Kant, Kaps and Offermann, 1988) allows the Haven ratio to be determined with an accuracy better than 5%. From random walk theory of ion hopping the conductivity diffusion coefficient D = (e / r)vo in an isotropic medium. Hence for an indirect interstitial mechanism, the corresponding mobility is expressed by 

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