The activation energy for conduction

The activation energy for conduction, is the major factor controlling the ionic mobility, u. The Arrhenius expression for conductivity is either 

The prefactor A or At contains many terms, including the number of mobile ions. Of the two equations, Eqn (2.3) is derived from random walk theory and has some theoretical justification Eqn (2.2) is not based on any theory but is simpler to use since data are plotted as log r vs T instead of as log oT vs T, based on Eqn (2.3). Both forms of the conductivity Arrhenius equation are widely used within errors the value of AH that is obtained is approximately the same using either equation in many cases. 

The activation energy represents the ease of ion hopping, as already indicated above and shown in Fig. 2.5. It is related directly to the crystal structure and in particular, to the openness of the conduction pathways. Most ionic solids have densely packed crystal structures with narrow bottlenecks and without obvious well-defined conduction pathways. Consequently, the activation energies for ion hopping are large, usually 1 eV ( 96 kJ mole ) or greater and conductivity values are low. In solid electrolytes, by contrast, open conduction pathways exist and activation energies may be much lower, as low as 0.03 eV in Agl, 0.15 eV in /S-alumina and 0.90 eV in yttria-stabilised zirconia. 

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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. 

In such a compound, a mbced Fe " " valence is only introduced through impurities and/or oxygen vacancies. Upon reduction, the mobile electrons become trapped at oxygen vacancies the activation energies for conduction are 0.48 eV in the ferrimagnetic domain and 0.57 eV in the paramagnetic domain . ... 

When the activation energies for conduction are computed from the log A versus 1/Tplots, it is seen (Table 5.26) that they are a little lower than the activation energies for viscous flow and self-diffusion, i.e.,... 

Grain boundaries offer some impedance to sodium ion conduction (i.e., approximately a factor of five increase for polycrystalline jS -alumina at 300 C) " . They also increase the activation energy for conduction by approximate factors of 1.6-2 depending on the temperature and grain size. Sodium ion grain boundary conduction is dominant in polycrystalline 8"-alumina when the grain size is very small (< 1-2 pm) and when the temperature is below 100°C. 

Two assumptions are implicit in the Wagner derivation (3, 4) of the relationship between conductivity and oxygen pressure for n- or p-type oxide semiconductors. One of these, as Be van and co-workers (1) have pointed out, is that the activation energy for conduction is unchanged as the number of electron defects is changed, and that the specific conductivity, K (in K = is directly proportional to the pre-exponential,... 

In 5 h, the polymer pellet exhibited a maximum in the conductivity and then began to decrease slowly. When film-type polymer was exposed to iodine vapor, it changed from dark violet to blue-black and the electrical conductivity increased from 10 ° Q cm to 10 Q cm . The maximum electrical conductivity of iodine-doped poly(DPDPM) is smaller than that of iodine-doped poly(l,6-heptadiyne), which is reported to have a value of 10 —10 2 Q cm . ° The activation energy for conduction was derived from the temperature, T, dependence of conductivity. For the undoped poly(DPDPM), the activation energies have... 

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