Defects, non-stoichiometry and phase transitions

Protonic conduction can be considered as a particular case of ionic conduction however, there are some similarities with electronic conduction because of the proton size. In both cases, defects can play an important role. 

P -aluminas, structures derived from quartz or cristobalite, e.g. LiAlSi04 and structures based on silver iodide. Before discussion of the specific behaviour of protonic conductors, the role of defects in the ionic and electronic conductivity of solids will be reviewed. 

The presence of mobile species in a particular medium can give rise to a macroscopic concentration gradient obeying Pick s law . The flux of matter in a given x direction is given by J = —D dC/dx, where C is the concentration of mobile species and D the diffusion coefficient. The conductivity is given by cr = CBe, where B is the mobility and e the charge of the mobile ions. The Nernst-Einstein law which connects diffusion coefScient and conductivity is a = DCe /kT, where k is Boltzmann s constant and T temperature. Furthermore, the thermal activation of C and D must be taken into account, as follows  

Ef corresponds to the enthalpy of formation of a defect pair Frenkel or Schottky, cf. Chapter 3). In an alkali halide, E( is typically about 3 eV implying a very low defect concentration, of the order of 10 at room temperature. E is the enthalpy of defect migration, usually several eV in dense structures, and / is the correlation or Haven factor. Its value varies between 0 and 1 and takes into account unfruitful attempts at transport in a given direction, caused by random jumps of mobile species and the particular geometry of each site. In other words, this factor takes into account the correlation effects (/ = 1 when correlations are absent). Usually / is of the order of 0.5-0.8 and plays a role in determining the transport mechanism. 

The tracer or self-diffusion coefficient represents only a random walk diffusion process, i.e. in the absence of chemical potential gradients. The true chemical diffusion coefficient refers to diffusion in a chemical-potential gradient and its expression is more complicated .  

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P. Colomban and A. Novak, Defect, Non-stoichiometry and Phase Transitions, in Proton Conductors-Solids, Membranes and Gels-Materials and Devices , ed. P. Colomban, Cambridge University Press, Cambridge, MA, 1992, Chap. 4. 

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