Cation interstitials

Taking as an example an ionic oxide MO, this material can be made into a metal-excess nonstoichiometric material by the loss of oxygen. As only neutral oxygen atoms are removed from the crystal, each anion removed will leave two electrons behind, which leads to electronic conductivity. The oxygen loss can be incorporated as oxygen vacancies to give a nonstoichiometric oxide with a formula MOi v, or the structure can assimilate the loss and compensate by the introduction of cation interstitials to give a formula M1+xO. 

Metal-excess oxides can change composition by way of metal interstitials or oxygen vacancies. The formation of cation interstitials in a nonstoichiometric oxide MO can be represented by... 

Following substitution, charge neutrality can be maintained in one of the three ways, as described above, that is, by the introduction of cation interstitials, anion vacancies, or holes. Replacement of some of the La3+ by Sr2+ can be written in terms of La2C>3 alone (Section 1.11.7) ... 

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... 

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

A cation vacancy may be paired with a nearby cation interstitial. This is called a Frenkel pair. An example is the formation of Zn+2 vacancies and Zn+2 interstitials in ZnO. This is illustrated in Figure 5.2B. In principle, paired anion vacancies and interstitials are possible, but this is less likely because of the larger size of the anions. 

Cic is the equilibrium concentration of cation interstitials CVc is the total concentration of cation vacancies... 

Similarly, in thermal equilibrium, some ionic crystals at a temperature above absolute zero enclose a certain number of Frenkel pair defects, that is, anion and cation interstitials in the structure. Since the concentration of Frenkel pair defects at equilibrium at an absolute temperature, T, obeys the mass action law, then [16]... 

Fig. 2. Field-controlled oxide growth, (a) Surface and interfacial charges (b) Cation interstitial (ci) and anion interstitial (ai) currents.

Note in Fig. 4 that there are four primary ionic defect species which we must consider, namely cation interstitials, cation vacancies, anion interstitials, and anion vacancies (denoted by the superscripts ci, cv, ai and av, respectively). In the case of non-simultaneous place exchange, referred to... 

As an example, it is conceivable that in some metal—oxide systems, the cation interstitials entering the oxide at the metal—oxide interface (x = 0) rise to appreciable bulk concentration values C(cl) (0). These defects can then migrate through the oxide layer. Chemical reaction of any such interstitials which happen to reach the oxide—oxygen interface (x = L) will serve to deplete the number at that interface. Thus the bulk concentration C,(d)(L) will be much lower than the number Cparticle current density J(C1). This particle current density proceeding from the source interface (x = 0) to the sink interface (x — L) can be essentially uniform (i.e. J(ci) independent of position x) if there is no build-up or depletion of the bulk density C(ci) between source and sink. On the other hand, any build-up or depletion of the bulk density C(x) at a position x within the layer will require the current to decrease or increase, respectively, at that position x in order to supply or take away, as the case may be, the requisite number of such defects. 

If the particle current J a) of cation interstitials is flowing from the metal—oxide interface to the oxide—oxygen interface at time t, and if the area of the parent metal surface is A, then a number J(d)A At of cation interstitials is transported in the time increment A t. If the volume of new oxide formed per transported cation interstitial is designated as Ria then a total quantity of new oxide Rici) (J(cl) A At) is formed during the time interval At. The increase AL in oxide thickness is given by the ratio of this volume to the area A. Thus... 

In terms of differential calculus, we can write this as a growth rate equation for motion of cation interstitials... 

Fig. 8. Schematic diagrams of concentration profiles and the associated particle currents, (a) Cation interstitials or anion vacancies [(dC/dx)<0] and positively directed particle currents ( 0). (b) Cation vacancies or anion interstitials [(dC/dx) > 0] and negatively directed particle currents (J< 0).

Fig. 9. Electric field polarities produced by the easy diffusion of various charged defect species, (a) Cation interstitials (b) anion interstitials (c) cation vacancies ...

Fig. 13. Possible sign combinations involving the sign of the surface charge at the metal—oxide interface and the sign of the charge of the field-driven mobile species originating at the metal—oxide interface, together with schematic diagrams of the concentration profiles for the mobile species, (a) Field-driven cation interstitial (or anion vacancy) transport (b) Field-driven electron transport.

The reason that our development so far has been restricted to cases of cation interstitial (or anion vacancy) and electron transport, as illustrated in Fig. 13, is that these are the species which have their sources at the metal—oxide interface. To consider the other possibilities of cation... 

THE CASE OF OXIDE GROWTH BY DIFFUSION OF CATION INTERSTITIALS AND ELECTRONS... 

That is, nt cations of Me, each of charge Zte, react with electrons e" and qt molecules of layer i + 1 to form qi+l new molecules for increasing the thickness of layer i. Thus a cation interstitial current through layer i can lead to decomposition of layer i + 1, with the attendant growth of layer i. Layer i therefore grows at the expense of layer i + 1. 

---