Silver vacancy concentration

Eq. (19) gives a solution of this integral, and hence the grain boundary conductance for enhanced silver vacancy concentration reads... 

The work of Dick and Styris [75D01] is sufficiently detailed to establish values for vacancy concentrations in silver samples in which resistance measurements were taken. In this work, 15 to 25 yrm-thick silver foils were... 

The hole concentration varies as the square root of bromine pressure. Formation of silver vacancies at interface II results in a concentration gradient in Ag,- across the product layer. The reaction proceeds by migration of Ag " from interface I to interface II and reverse migration of holes. The rate constant for silver bromination is approximately described by... 

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 concentration of normal silver ions and silver vacancies were assumed to be constant and the rate V is related to the equilibrium value C of C by ... 

Fig. 5.89 Concentration of silver vacancies (large shape) and conduction electrons (small shape) as a function of the temperature and the distance from the 7-AI2O3 interface [255].

Therefore, the kinetics of generation of defects in surface-adjacent layers is similar to kinetics of emission of O-atoms. (The estimates indicate that the maximum concentration of vacancies in this case may attain the value of 10 for a sample with area 1 cm ). If one assumes that the emission of oxygen atoms is caused by processes of annihilation of vacancies in the sample, then the coincidence in time dependence of stationary concentration of defects can be indicative that these processes are limited by generation of defects, which, in its turn, is controlled by processes of formation of oxide phase in surface-adjacent silver layers. Oxidation, especially at initial stage, is characterized by intensive formation of defects [54]. 

In terms of formal point defect terminology, it is possible to think of each silver or copper ion creating an instantaneous interstitial defect and a vacancy, Ag and VAg, or Cu and Vcu as it jumps between two tetrahedral sites. This is equivalent to a high and dynamic concentration of cation Frenkel defects that continuously form and are eliminated. For this to occur, the formation energy of these notional defects must be close to zero. 

In this section we are concerned with the properties of intrinsic Schottky and Frenkel disorder in pure ionic conducting crystals and with the same systems doped with aliovalent cations. As already remarked in Section I, the properties of uni-univalent crystals, e.g. sodium choride and silver bromide which contain Schottky and cationic Frenkel disorder respectively, doped with divalent cation impurities are of particular interest. At low concentrations the impurity is incorporated substitutionally together with an additional cation vacancy to preserve electrical neutrality. At sufficiently low temperatures the concentration of intrinsic defects in a doped crystal is negligible compared with the concentration of added defects. We shall first mention briefly the theoretical methods used for such systems and then review the use of the cluster formalism. 

Figure 7 shows the solutions obtained by the more accurate Eq. (39) for both concentrations and conductivities. As soon as the dopant content becomes appreciable, it correspondingly increases the concentration of the oppositely charged defect which depresses the active counter-defect via mass action. In AgCl the mobility of the silver interstitials exceeds that of the vacancies leading to a minimum in the overall ion conductivity approximately at KpUj /uv as can be readily... 

At room temperature the ionic properties of the pure silver halides are primarily determined by Frenkel disorder on the cation sublattice [18,19]. The equilibrium volume concentrations of silver ion interstitials ( ] and vacancies (nv) have the temperature dependence... 

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