Disorder extrinsic

Defects in mixed phases can be formed by doping or changing the stoichiometry of the mixed phase. An example for this type of disorder is yttria stabilized zirconia (YSZ). 

The tetravaleiit zirconium ion is substituted by the three-valent yttrium ion. As a result twofold charged oxide ion vacancies are formed. 

The highly conducting Zr02 crystalhzes in the fluorite structure, which stabilizes by doping with Y2O3 or CaO. Zr02 is used in several electrochemical developments, e.g., as electrolyte in solid oxide fuel cells (SOFCs) or for an electrochemical oxygen sensor in the car industry (A,-probe). 

Let us imagine immersing the crystal MO in an atmosphere in which the partial pressure of oxygen (P02) i lower than the partial pressure of intrinsic stability (i.e., the partial pressure of oxygen at which crystal MO is perfectly stoichiometric Poj)- We observe two distinct defect processes  

The first process produces doubly ionized positive oxygen vacancies and electrons (el) and the second produces doubly ionized positive cation interstitials and electrons. The equilibrium constants of the two processes are given by 

Because the bulk crystal is electroneutral, we can apply the electroneutrality condition. For process 4.7 we write 

At P02 higher than we observe the formation of doubly ionized cationic vacancies and positive electronic vacancies (usually defined as electron holes by symbol h )  

The defect concentrations in ionic solids can be enhanced by doping with aliovalent ions if, for example, Cd2+ ions replace Ag+ ions in AgCl, additional positive charges are introduced that are compensated by negative silver vacancies (Fig. lb). In terms of a defect chemical reaction the doping can be written as  

The doping of a solid is similar to the enhancement of the H30+ or OH- concentration in water by adding a strong acid or base. However, while in water mobilities of dopant ions are frequently similar to those of the native defects H30+ and OH-[69, 70], dopant ions in solids (e.g. CdXg in AgCl) are almost immobile. This is also why supporting electrolytes (i.e. electrolytes with dissolved dopants that enhance the ionic conductivity, but do not influence electrochemical electrode reactions [71, 72], are unknown in solid state electrochemistry. 

If the intrinsic defect concentration is much lower than the dopant (or impurity) concentration cdop, electroneutrality requires a defect concentration cdef according to 

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We have already noted that the concept of stoichiometric crystal is an extreme idealization of an effectively more complex reality. In the presence of extrinsic disorder, stoichiometry varies as a function of the chemistry of the coexisting phases and of T and P. To clarify this concept better, the procedure developed by Nakamura and Schmalzried (1983) to describe fayalite may be briefly recalled. 

Based on thermogravimetric experiments on the compound Fe2Si04 at various T and conditions, Nakamura and Schmalzried (1983) established that the extrinsic disorder of fayalite is conveniently represented by the equihbrium... 

As shown in figure 4.5B, extrinsic disorder (nonstoichiometry) may vary considerably, as a function of solid paragenesis, between the low Pq stability limit defined by equilibrium... 

Table 4.6 shows the energy of extrinsic disorder calculated for the solid mixture (Fe, Mg)2Si04 at r = 1200 °C, based on the defect scheme of equation 4.68 and on the defect energies of table 4.2. 

We note that the defect energy contribution associated with extrinsic disorder varies considerably as a function of the partial pressure of oxygen of the system. These energy amounts may significantly affect the intracrystalline disorder, with marked consequences on thermobarometric estimates based on intracrystalline distribution. As we will see in detail in chapter 10, most of the apparent complexities affecting trace element distribution may also be solved by accurate evaluation of the defect state of the phases. 

Table 4.6 Energy contributions deriving from extrinsic disorder of mixture (Fe,Mg)2Si04 at T = 1200 °C. Values expressed in J/mole is in bar (from Ottonello et al., 1990).

With decreasing temperature, as we have seen, the intrinsic defect population decreases exponentially and, at low T, extrinsic disorder becomes dominant. Moreover, extrinsic disorder for oxygen-based minerals (such as silicates and oxides) is significantly alfected by the partial pressure of oxygen in the system (see section 4.4) and, in the region of intrinsic pressure, by the concentration of point impurities. In this new region, term Qj does not embody the enthalpy of defect formation, but simply the enthalpy of migration of the defect—i.e.,... 

Based on these four rules, Cameron and Papike (1982) selected 175 analyses out of 405 reported by Deer et al. (1978) and discarded 230 compositions. This selection is extremely rigorous and does not take into account either the possible stabilization of Fe in tetrahedral sites or the existence of extrinsic disorder (cf chapter 4). Robinson (1982) showed that, by accepting a hmited amount of cationic vacancies in M2 sites and assuming possible stabilization of Fe in tetrahedral positions, 117 additional analyses out of the 230 discarded by Cameron and Papike (1982) may be selected. 

If majority point defect concentrations depend on the activities (chemical potentials) of the components, extrinsic disorder prevails. Since the components k are necessarily involved in the defect formation reactions, nonstoichiometry is the result. In crystals with electrically charged regular SE, compensating electronic defects are produced (or annihilated). As an example, consider the equilibrium between oxygen and appropriate SE s of the transition metal oxide CoO. Since all possible kinds of point defects exist in equilibrium, we may choose any convenient reaction between the component oxygen and the appropriate SE s of CoO (e.g., Eqn. (2.64))... 

In many ceramics, intrinsic and extrinsic disorder, as well as the disorder due to nonstoichiometry, have to be considered. Independent of the dopant level, the mass action laws of intrinsic disorder, of the e-h equilibrium and of the reaction with the surrounding phase are valid in thermodynamic equilibrium. Together with the electroneutrality equation... 

It is common practice to divide all high-conductivity electrolytes into two classes, namely those with intrinsic and extrinsic disorder. However, it is suggested that a more detailed classification might include four classes... 

At this point of the discussion it is worthwhile to distinguish between two different kinds of disorder. If the concentrations of the majority defect centers, which constitute the disorder type, are independent of the component activities and are only determined by P and 7, then we speak of thermal disorder or intrinsic disorder (e. g. Frenkel disorder in silver bromide). However, the concentrations of minority defect centers do depend upon the component activities even in the case of a crystal with thermal disorder. This will be discussed more explicitly later. On the other hand, if the concentrations of the majority defects are dependent upon the component activities, then we speak of activity-dependent disorder or extrinsic disorder (e. g. cation vacancies and electron holes in transition metal oxides). 

For the limiting case (Cd g) > we find that (VAg) — (CdAg). That is, the vacancy concentration is completely fixed by the addition of CdBr2. This is called the region of exclusively extrinsic disorder, as opposed to the region of intrinsic disorder. In the extrinsic region, those physical properties of the crystal which depend upon the point defect disorder are functions only of the concentration of dopant. However, in deriving eq. (4-26), it has been tacitly assumed that point defects do not form complexes. This assumption, as shown later, must eventually be modified. 

That means the cation sites result 0.84 + 0.16 = 2. The cation lattice is complete because the Y " ions occupy sites (E and in the Kroger-Vink notation 4)- f o Y ions, a double positively charged oxide ion vacancy Vq is formed, in this case 0.08. The extrinsic disorder is often called as chemical disorder, mixed phase, or nonstoichiometric disorder. 

Point defects fall into two main categories intrinsic defects, which are internal to the crystal in question, and extrinsic defects, which are created when an impurity atom or ion is inserted into the lattice. In, for instance, metal oxides containing transition metal ions, usually a component-dependent extrinsic disorder predominates. 

The concentration of the intrinsic point defects can be influenced by aliovalent impurity doping. Assmning that only ionic point defect concentrations are affected, the following lattice reactions exemplify the formation of extrinsic disorder by substitution in MO, e g., MF2 in MO... 

If aliovalent impurities are present, these have to be included into Equation (5.26) because they influence the point defect concentrations. A great number of studies, including extrinsic disorder in nonstoichiometric compounds, have appeared in the literature, and the concepts have been extended to ternary and multinaiy compounds. Before discussing these compounds, the concepts will be applied to transition metal oxides, because these represent an important technological class of materials. 

While intrinsic disorder of the Schottky, Frenkel, or anti-Frenkel type frequently occurs in binaiy metal oxides and metal halides, i.e., Equations (5.1), (5.3), and (5.5), Schottky disorder is seldomly encountered in temaiy compounds. However, in several studies Schottky disorder has been proposed to occur in perovskite oxides. Cation and anion vacancies or interstitials can occur in ternary compounds, but such defect stractures are usually to be related with deviations from molecularity (viz. Sections II.B.2 and II.B.3), which in fact represent extrinsic disorder and not intrinsic Schottky disorder. From Figures 5.3 and 5.4 it is apparent that deviations from molecularity always influence ionic point defect concentrations, while deviations from stoichiometry always lead to combinations of ionic and electronic point defects, as can be seen from Figures 5.2 and 5.5. 

These authors have reviewed positional disorder in stoichiometric compounds in relation to crystal stmcture, materials exhibiting first-order phase transformations, and diffuse, so-called Faraday, transitions, extrinsic disorder, doping strategies, and solid solutions. 

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