Enthalpy migration

Table 4.7 fists the migration enthalpies of some haUdes and simple oxides... 

Table 4.7 Migration enthalpy in alkali halides and simple oxides. Values in eV. Data from Barr and Liliard (1971) (1) and Greenwood (1970) (2).

Vm = migration enthalpy of cationic vacancy = migration enthalpy of anionic vacancy /7m = migration enthalpy of cationic interstitial //xj = migration enthalpy of anionic interstitial... 

An Arrhenius plot of the cation self-diffusivity will then possess two linear regions. In the high-temperature intrinsic regime, the slope will be — Hg/3 + Hm)/k in the low-temperature extrinsic regime, the slope will be simply Hm/k, where Hm is the migration enthalpy of a cation vacancy. 

The 2.2 eV in equation 57 may represent the migration enthalpy of the phosphorus-self-interstitial pair (56) with the excess self-interstitials produced by damage annealing. 

When moving in a crystal, an atom has to surmount an energy barrier, which is called the migration enthalpy AHm. The mobility of a diffusing species is, therefore, thermally activated and diffusion is described by the... 

In most examples we will refer to the conductivity q as a convenient measure of Cj. Since oj °c Cj with the proportionality factor containing the mobility Uj(T), the temperature dependence (see Eq. 34) of oj will also include the migration enthalpy (cf. Section VI.3.m), while the P-(and later the C-) dependence (Eqs. 35 and 43) is the same. 

Calculate the migration enthalpy for Na ion migration and the enthalpy of Schottky defect formation from the data shown in Fig. 7.3. Discuss all assumptions. 

For diffusion by a vacancy mechanism, the temperature dependence of dilfusivity will depend on both the migration enthalpy A// and the energy required to form the vacancies if the latter are thermally activated i.e., the concentration of intrinsic defects is much greater than the concentration of extrinsic defects. If, however, A is fixed by doping, it becomes a constant independent of temperature. The activation energy for diffusion in the latter case will only depend on A/f, . 

The temperature dependence of the kinetics at constant oxygen pressure is often plotted as log kp or log k-p versus 1/T. In addition to the migration enthalpy of the mobile species, the slope of such an Arrhenius plot may reflect an enthalpy for the change in composition of the oxide with temperature. 

The ionic conductivity a depends on both the migration enthalpy and the formation enthalpy of vacancies. The electric mobility here is not the same as the mechanical mobility B used above. The relation is = Bq = B z e. Here q is the charge per charge carrier, e the elementary charge, and z the number of elementary charges per charge carrier. 

A misprint in the corresponding Eq. (21) in Kim et has been corrected here (ln(a T) rather than In (ct , )), and the activation energy of the electronic conductivity in the bulk has been substituted by the partial molar enthalpy of oxidation and the migration enthalpy, using the relation in Eq. (12.34),... 

As for pure GeOg-, electronic conductivity is introduced in doped ceria by increasing temperature and decreasing pOg, due to the reduction of Ge to Ge and the formation of electronic defects. The n-type conductivity takes place via a small polaron mechanism. According to Eqs (12.30), (12.31), and (12.32), the electronic conductivity of doped ceria is a function of the degree of reduction x, the electronic migration enthalpy and the preexponential term of the electron mobility l . 

According to Eq. (12.31), the pre-exponential factor is expected to decrease with increasing dopant content due to the decreasing number of sites where the small polaron may jump. This was demonstrated to be the case in Cei yGdy02 y/2 x and Cei yCay02 y x by Mogensen et As with the concentration of electronic defects and the electronic migration enthalpy, the pre-exponential factor of the electronic mobility is also found to be rather insensitive to dopant type in 20 mol% REOi 5 doped ceria. 

---