Haven ratios

The values of the conductivity due to Na+ ions in a glass are given in the following table, (a) Estimate the activation energy for conductivity. The conductivity at 700 K is 0.00316 S m-1. (b) Estimate the value of the diffusion coefficient Da at this temperature if the concentration of Na+ ions is 7.2 x 1027 m-3. (c) Using the data in Chapter 5, Question 5, calculate the Haven ratio at this temperature. 

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 /isotropic medium. Hence for an indirect interstitial mechanism, the corresponding mobility is expressed by... 

One of the problems associated with the use of heterocycles is that the intrinsic concentration of protonic charge carriers can only be moderately increased through acid doping (also see Section 4.3). This is particularly the case when the dynamics within the hydrogen-bonded domain is highly constrained through immobilization (especially in fully polymeric systems), which is probably the direct consequence of a reduced dielectric constant. This also leads to a further increase of the Haven ratio... 

Nernst-Einstein relation D show subtle differences because ionic motion in tracer experiments is correlated. The Haven ratio, is proportional to the correlation... 

Diffusion coefficients (Dimp) obtained from measurement are calculated via the Nernst-Einstein equation. Furthermore, electrochemical diffusion coefficient measurements are possible which directly measure the diffusion coefficient. The degree of dissociation of a component ion in the IL can be estimated from the relation (DNMR/Amp) between Dimp and the diffusion coefficient measure by PFG-NMR (Dnmr) [132], This parameter is called the Haven ratio and should be unity... 

In alkali hydroxides extended ring mechanism for proton motion can occur leading to a tracer propagation but not to any charge transport. The Haven ratio (H) amounts to several thousand in such cases.216... 

NMR measurements) by D = Here Hr is the Haven ratio, which can give... 

The Haven ratio may deviate from unity when correlation effects and possibly different jump distances and jump frequencies can not be neglected [51]. For a vacancy diffusion mechanism Hr equals the well-known tracer correlation factor /. 

G. E. Murch, The Haven ratio in fast ionic conductors. Solid State Ionics, 7 (1982) 177-198. J. Maier and G. Schwitzgebel, Theoretical treatment of the diffusion coupled with... 

Haven ratio, Hr, first defined by Le Claire (1970)is the ratio, DJD where D, and are the tracer and conduetivity diffusion coefficients respectively. The implieation of // for ion transport has been discussed by Mundy and Jin (1986). 

Fig. 11.1 The Haven ratios, plotted against inverse temperature, for the diffusion of silver ions in three solid ionic conductors Ag2S, Ag2Se, and Ag2Te. (From H. Okazaki, J. Phys. Soc. Jpn, 43, 213 (1977).)...

It should be realized thatand just express the properties ofthe conductivity and mobility from which they are derived, and using them in the Fick s law Jc = —D c is at best a crude approximation. On the other hand they contain information about interparticle correlations that result from carrier-carrier interactions. A useful quantity that gauge the importance of such correlations is the Haven ratio... 

The most obvious experimental manifestations of interionic correlation are found in the Haven ratio (deduced from diffusion and conductivity measurement, see Chapter 4), in the static structure factor S(Q) (deduced from partial occupation factors measured by X-ray or neutron diffraction) and from the dynamical properties (S Q, co), quasi- and inelastic-neutron scattering, frequency dependent conductivity) and e(co) dielectric relaxation. 

Figure 9. Calculated charge carrier concentrations N for crystal data based on the Nemst Einstein equation (eq. 8) with (open symbols) Dc = D = a 2jtVc and (closed symbols) Dc = D = a Odc/Ssi o (using eq. 7), a = average lattice parameter, assuming a Haven Ratio = 1...

The conductivity diffusion coefficient and the tracer diffusion coefficient are related by the Haven ratio ... 

Murch, G.E. (1982) The Haven ratio in fast ionics conductors. Solid State Ionics,... 

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