Diffusion kinetics of stoichiometry change

At this stage we are going to treat explicitly the important example of diffusion-controlled alteration of oxygen stoichiometry as an example (Fig. 6.17c). In other words The rate of dissolution of oxygen in the oxide M20i+ Ada chemical diffusion is considered, presupposing that the smface reaction is comparatively rapid. 

We assume that a conductance measurement is used to monitor the stoichiometric change. We consider a thin rectangular sheet of isotropic material, which has been equilibrated under a partial pressure of oxygen Pi (=M20n-6j). We suddenly alter the partial pressure to the value P2 and follow the relaxation process to the final state (=M20i+i2) (Fig. 6.27). The initial homogeneous profile is described by Ci, (here c denotes the concentration of the charge carrier measured in the conductance 

27 The partied pressure of oxygen over an equilibrated sample is suddenly changed and the conductance is measured as described. 

The profiles set up are illustrated in Fig. 6.28 (see also Fig. 6.23d) they exhibit the weighted cosine-shaped spatial dependence predicted by Eq. (6.71). 

We will see below that these profiles can be experimentally verified as a function of space and time using an optical in-situ technique. (Compare Fig. 6.28 with Fig. 6.33 on page 318.) If one would like to carry out such a time and space resolved analysis by conductivity measmements, a great number of microelectrodes would have to be positioned along the diffusion direction. 

---