Valence defect

Fig. 1. Logarithmic scale of the electrical conductivities of materials categorized by magnitude and carrier type, ie, ionic and electronic, conductors. The various categories and applications ate given. The wide conductivity range for the different valence/defect states of Ti oxide is highlighted. MHD is...

Isolated, random point defects and valence defects Defect pair association Rearrangement of coordination environment in isolated defect clusters or microdomains 1- or 2-dimensional assays of ordered defects or reorganized defect complexes Fully defined superstructures or shear structures... 

By rotation of a whole molecule about one of the four bonds linking it to its nearest neighbors, a pair of valence defects is created The L defect is a bond between adjacent oxygen atoms not containing any proton the D defect is a bond with two protons. The rotating molecule remains electrically neutral, except that a displacement of electron clouds takes place during the rotation. 

Once created, the valence defects or ions of each pair may migrate independently, that is, the defects are completely dissociated from the sites at which they originated. 

Granicher and his coworkers first formulated a detailed theory, based on careful experimental measurements (60, 61, 77, 80,140,141), According to this theory, valence defects and ion defects are completely independent from and can not recombine with each other. 

Onsager and Dupuis (II9, 120), on the other hand, proposed that the ionic charge is partly compensated by one or two associated valence defects and is surrounded by a cloud of valence defects in a manner reminiscent of the Debye-Hiickel ion atmospheres in aqueous solutions. Conclusions from Onsager s theory are qualitatively similar to those of Granicher et al,... 

Zaromb (I6J) suggested that the formation or motion of ions by proton displacements may be coupled to rotations of neighboring molecules leading to the formation of valence defects. 

Several investigators (28, 29, 45, 94) criticized as energetically unfavorable the Bjerrum concept of a valence defect pair formed by rotation of a rigid molecule in an otherwise undisturbed lattice. Alternative mechanisms were proposed. 

Based on the experimental observation that self-diffusion of water molecules in ice has an activation energy similar to that of the dielectric and mechanical relaxations ( — 13.5 kcal./mole), some investigators (I2J) see a connection between the formation and migration of valence defects... 

The relaxation time, the d.c. and a.c. conductivities, the equilibrium constants of ions and valence defects, and the mobility of valence defects show a temperature dependence with characteristic activation energies (Table III). The mobility of ions is held to be temperature independent (tunnel eflFect). Magnan and Kahane 112), however, determined mobilities at very low temperatures (—80°C. to —120°C.) which show a pronounced temperature dependence (1.4 X lO" to 1.2 X 10" cm. volts" sec." ). 

HF molecules are held to occupy oxygen sites in the ice lattice. Since only one proton is associated with the fiuoride ion, each acid molecule introduces into the lattice one L type valence defect. In addition, HF is held to ionize according to the mass-action law, so that at a given temperature the number of ions increases with the square root of the concentration. Thus, in ice doped with HF there are hydronium ions from the dissociation of both the water molecules and the HF impurities. The negative ions, OH and F", are believed to have a very much lower mobility and are therefore neglected. Table III gives the relations obtained... 

Na = Avogadro s number V = valence defects in general w = ions from H2O molecules... 

Figure 19. Valence defect, ion, and total conductivity at —3 C. as a function of HF concentration (computed from formulae and data in Table III of this paper)...

Camp (18) discussed further work with single crystals grown from dilute solutions (6.7 X 10" M to 1.1 X 10 W). He found evidence that at temperatures above about —30°C., thermally produced (intrinsic) valence defects provide the major contribution to the dielectric polarization (activation energy 13.2 kcal./mole) while at lower temperatures. 

Figure 21, Static dielectric constant as a function of HF concentration at —3°C. after Steinemann (140). According to Jaccard (77), in Regions I and III valence defects (L defects in Region III) are the majority carriers in Region...

Electrical measurements of ice are diflBcult to interpret because of polarization effects, surface conductivity, injection of defects and/or impurity atoms from sandwich electrodes, diffusion effects, differential ion incorporation, and concentration gradients due to nonsteady state impurity distribution. Theories formulated for pure ice and for ice doped with HF (KF and CsF) in terms of ion states and valence defects, qualitatively account for experimental data, although the problem of the majority and minority carriers in doped ice, as a function of concentration and temperature, requires further examination. The measurements on ice prepared from ionic solutes other than HF, KF, and CsF are largely unexplained. An alternative approach that treats ice as a protonic semiconductor accounts for results obtained for both the before-named impurities as well as ammonia and ammonium fluoride. 

Although the treatment given in the previous section was for pure ice, there is nothing in the derivation of the results (9-3o)-(9.35) restricting them to this case except for the carrier concentrations tif, which are related to the partial conductivities cr by (9.31). Those results may therefore be applied to ice crystals containing known amounts of particular impurities simply by making the necessary adjustments to the concentrations n. Any impurities which leave the concentrations of ion states and valence defects unaltered will have negligible effect on the electrical properties. 

Now in an ice crystal each proton jump over a distance 2/ as in fig. 9.12 effectively moves the defect concerned through some larger distance, say r. From fig. 9.6 these two distances can be related to characteristic spacings in the lattice for either the direct jumps associated with ion states or the oblique jumps characteristic of valence defects. More than this, however, not all jump directions make the same angle with the field, though in the unpolarized ice structure there is always a possible jump with a component in the field direction. This average is simply performed and leads to an average defect displacement parallel to the field which we can write as . From (9.61) the classical mobility is then... 

Defects in ceramics can be charged, which are different from those in metais. For a simple pure ionic oxide, with a stoichiometric formula of MO, consisting of a metal (M) with valence of +2 and an oxygen (O) with valence of -2, the types of point defects could be vacancies and interstitials of both the M and O, which can be either charged or neutral. Besides the single defects, it is also possible for the defects to associate with one another to form defect clusters. Electronic defects or valence defects, consisting of quasi-free electrons or holes, are also observed in crystalline solids. If there are impurities, e.g., solute atoms Mf, substitutional or interstitial defects of Mf could be formed, which can also be either charged or neutral. 

Yamazoe N, Teraoka Y (1990) Oxidation catalysis of poovskites — relationships to bulk structure and composition (valency, defect, etc.). Catal Today 8 175... 

In addition to the structural defects, crystals also contain electronic defects, i.e. electrons and electron holes that are relatively free to move in the crystal. The electronic defects may either be formed through internal excitation of valence electrons or they may be formed in association with point defects. If these electronic defects are localised (trapped) at regular sites in the structure, the electronic defects are termed polarons or - from a chemical point of view - valence defects. Defect electrons or electron holes trapped at point defects often make otherwise transparent materials coloured, and composite defects involving point defects and trapped electronic defects are termed colour centres. 

Similarly, cation vacancies may be neutral or have negative effective charges. To illustrate this let us remove a metal atom from the oxide MO and create a vacant metal ion site. The M + ion picks up two electrons to leave as an atom, leaving behind two positive charges in the form of holes or valence defects. If these are localised at... 

Defect electrons and electron holes that are free to move in the oxide have effective negative and positive charges, respectively. They are written e and h . If the electron, for instance, is associated with a cation on a regular site - and may as such be considered a valence defect - the defect may be written. ... 

As mentioned earlier, the electronic defects may be localized (valence defects). In these cases the reactions are connected with individual atomic sites. For instance the intrinsic ionization (disproprtionation) of Fe " ions into Fe " and Fe" " ions would be written... 

The formation of electron holes may alternatively be expressed in terms of valence defects ... 

For many oxides, and particularly when considering defect stmcture situations close to stoichiometry, it is essential to take into account the intrinsic ionisation of electrons. This can include localised defects (valence defects) or delocalised defects (valence band and conduction band). 

In the case of valence defects, the ionisation of a pure binary metal oxide MOa may typically be assigned to mixed valency of the metal and thus be written as... 

In oxides with oxygen deficit, the predominant defects are oxygen vacancies. If these are fully ionised (doubly charged), and if the electronic defects are localised as valency defects, their formation reaction and the corresponding equilibrium can be written ... 

---