Stoichiometric defects in silver bromide

Stoichiometric defects (Schottky and Frenkel defects) in ionic crystals are formed due to irregularities in the ionic arrangement which maintain the stoichiometry and electroneutrality of the solid. It is known that $\ce{AgBr}$ shows both Frenkel and Schottky defects while most other compounds show only one of these defects; for example, $\ce{AgCl}$ shows only Frenkel defects.

The ratio of the sizes of the cation and anion determines which type of defect is shown by the crystal. If the ratio is closer to unity, Schottky defects are more common, and if it deviates significantly from one, Frenkel defects are more common. Intuitively, this is correct since Frenkel defects involve the movement of the cation (or the smaller ion) into interstitial sites, which is indeed easier if the ion is very small as compared to the other ion, making it more mobile. Generally, the activation energy for cationic movement is lower. And if the ionic sizes are comparable, filling the interstitial sites is not feasible, and hence Schottky defects are more likely to be exhibited by the crystal.

The $\ce{Cl-}$ ion is smaller than $\ce{Br-}$ (i.e. the ratio $r_+/r_-$ for $\ce{AgCl}$ is closer to 1 than it is for $\ce{AgBr}$). Yet, $\ce{AgBr}$ displays Schottky defects while $\ce {AgCl}$ does not. Why is that so? (The size and hence the mobility of $\ce{Ag+}$ should be the same in both cases.)

• Usually schottky defect is observed in strongly ionic compounds having ions (cations and anions) of almost similar size. You can see that Ag and Br have comparetively similar size than Ag and Cl, so AgBr shows Schottky defect whereas AgCl won't. – Immortal Player Dec 8 '13 at 21:00

Fundamentally, although ionic radii may offer some guidance as to defect formation, the bottom line is that the silver halides have complex bonding energetics that have to be taken into consideration. I might suggest 'Defect structures in the silver halides', D.J. Wilson et al., Phys. Rev. B77, 064115 (2008) (presuming you have APS journal access). There the authors present DFT calculations on the formation energies of both Frenkel and Schottky defects in AgCl and AgBr.

• What happens if the radius ratio of AgBr is intermediate for the two effects? – Divyansh Verma May 10 '20 at 12:33