Kroger-Vink diagram

Approximated solution of eqns (I.204)-(1.216) (Kroger-Vink diagram, see Figs 1.63 and 1.64)... 

Fig. 1.63 Kroger-Vink diagram of semiconductive compound MX for the case Kg < (see Table 1.6).

Fig. 1.67 Kroger-Vink diagrams of (a) Bi-doped PbS, (b) pure PbS, and (c) Ag-doped PbS. Log[ ] denotes log of defect concentration. Thick curves show the Ps. dependence of carrier concentrations (measured). Thin lines are calculated ones.

Figure 18 shows a simplified Kroger-Vink diagram for typical oxidic cathode materials (LSM, LSF, LSC, i.e., Sr-doped La-manganates, ferrates, cobaltates) the high Pq2 regions being... 

Figure 18. Kroger-Vink diagrams of a Schottky disordered negatively doped oxide (trivalent cations assumed). The ordinate refers to a logarithmic concentration axis, the abscissa to a logarithmic partial pressure axis.110 Reprinted from J. Fleig, K.D. Kreuer and J. Maier, in Handbook of Advanced Ceramics. Volume II Processing and Their Applications, S. Somiya, F. Aldinger, N. Claussen, R. M. Spriggs, K. Uchino, K. Koumoto and M. Kaneno (eds.), Elsevier Academic Press (2003) p. 59. Copyright 2003 with permission from Elsevier.

For not too extended T-ranges ArH° is constant and straight lines are observed in the In c vs. 1/T representation. Also straight lines are observed if we plot In Cj vs. In P defining Kroger-Vink diagrams with the characteristic slopes... 

Figure 6. Three experimental examples of Kroger-Vink diagrams in a pure oxide MO with ideal defect chemistry SnOj as n-type conductor, PbO as mixed conductor and La2Cu04 as p-type conductor.45 (Reprinted from J. Maier, Ionic and Mixed Conductors for Electrochemical Devices, Radiat. Eff. Defects Solids, 158, 1-10. Copyright 2003 with permission from Taylor Francis.)...

Figure 35. Kroger-Vink diagram of boundary layers for our model substance MX when 5(v m) > 0. The broken lines refer to the ionic defect concentrations at (two) different distances from the interface. The behavior of the electrons in boundary regions is not shown.The approach to the bulk values (printed boldface) for extreme abscissa values is attributable to the disappearing Debye length. The mirror symmetry on compa-rison of v m with Mi follows from Eq. (6S).94 (Reprinted from J. Maier, Ionic Conduction in Space Charge Regions. Prog. Solid St. Chem. 23, 171-263. Copyright 1995 with permission from Elsevier.)...

J. Maier, Kroger-Vink diagrams for boundary regions. Solid State Ionics, 32/33 (1989) 727-733. 

By combining the three regimes, the functional dependence of the defect concentrations over a wide range of oxygen partial pressures can be succinctly graphed in what is known as a Kroger-Vink diagram, shown in Fig. 6.6a. 

To relate the concentrations of point and electronic defects to temperature and externally imposed thermodynamic conditions such as oxygen partial pressures, the defects are treated as chemical species and their equilibrium concentrations are calculated from mass action expressions. If the free-energy changes associated with all defect reactions were known, then in principle diagrams, known as Kroger-Vink diagrams, relating the defect concentrations to the externally imposed thermodynamic parameters, impurity levels, etc., can be constructed. 

The starting point for understanding the behavior of nonstoichiometric oxides involves constructing their Kroger-Vink diagram, as discussed in Sec. 6.2.5. To illustrate, consider the following examples ... 

TjxOi- The Kroger-Vink diagram for yttria-doped zirconia is shown in Fig. 7.16a, the construction of which is left as an exercise to the reader. In pure zirconia, the concentration of oxygen vacancies is simply y/Ks-However, as noted earlier, that value can be dramatically increased by doping with aliovalent cations such as Ca or. Based on this diagram. 

The data shown in Fig. 6 represent values of the conductivities of CuCl coexisting with copper. However, the electronic and ionic conductivities may both depend on the stoichiometry fixed by the chemical potentials of the constituents. Shown in Fig. 7 are two schematic graphs [18] for the behavior of CaF2 The upper graph shows the isothermal variation of the defect concentration with partial pressure of fluorine (a Brouwer or Kroger-Vink diagram) and the lower one shows the corresponding behavior of the conductivities. 

The effect of the dopant is only apparent in region 1. Figure 4.4(a) shows the Kroger-Vink diagram as a function of the lithium concentration at a given oxygen pressure. 

Figure 4.4. Kroger-Vink diagrams for iithium-doped zinc oxide...

FIGURE 5.2. Kroger-Vink diagram of the model material MX with Frenkel disorder. 

Schematic Kroger-Vink diagrams of metal oxides have been reported, and these resemble the defect diagram in Figure 5.2 as expected.

The Kroger-Vink diagrams of compounds ABX4, in which A, B, and X are ions with charge +1, +3, and -1 are presented in Figures 5.4 and 5.5. It is assumed that the model material exhibits anti-Frenkel disorder. 

For a doped oxide M2O3 exhibiting anti-Frenkel disorder, Colomban and Novak present a sehematie Kroger-Vink diagram of the extrinsic and intrinsic point defects as a function of the partial water pressure. With regard to electrical properties, the proton conductivity in the binary metal oxides is usually much lower than in the perovskite-type oxides. ... 

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