Which of the following shoes both, Frenkel and Schottky defect?

\(AgBr\)

The correct answer is option 3. \(AgBr\).

Let us delve into the details of Frenkel and Schottky defects and examine how they apply to the given compounds.

Types of Defects:

Frenkel Defect:

In a Frenkel defect, an ion (usually a cation) leaves its normal lattice position and occupies an interstitial site, creating a vacancy and an interstitial defect. This defect is common in materials where the cations are significantly smaller than the anions.

Example: In \(AgCl\) (Silver Chloride), Ag\(^+\) ions are much smaller than Cl\(^-\) ions. Due to the size difference, Ag\(^+\) can easily move to an interstitial site, creating Frenkel defects.

Schottky Defect:

In a Schottky defect, an equal number of cations and anions are missing from their lattice positions, creating vacancies. This defect is common in ionic solids where both ions are of similar size.

Example: In \(NaCl\) (Sodium Chloride), both Na\(^+\) and Cl\(^-\) ions are relatively similar in size, and so vacancies can form when both ions are missing from the lattice, leading to Schottky defects.

Analysis of the Given Compounds:

1. \(KCl\) (Potassium Chloride):

Ionic Sizes: Potassium ions (K\(^+\)) and chloride ions (Cl\(^-\)) are relatively similar in size.

Defects: \(KCl\) mainly exhibits Schottky defects due to the similarity in ion sizes. Frenkel defects are not common because the ions are not significantly different in size.

2. \(AgCl\) (Silver Chloride):

Ionic Sizes: Silver ions (Ag\(^+\)) are much smaller than chloride ions (Cl\(^-\)).

Defects: \(AgCl\) primarily exhibits Frenkel defects due to the large size difference between Ag\(^+\) and Cl\(^-\). Schottky defects are less common here because the larger Cl\(^-\) ions don't easily form vacancies in the lattice.

3. \(AgBr\) (Silver Bromide):

Ionic Sizes: Silver ions (Ag\(^+\)) are smaller compared to bromide ions (Br\(^-\)), but not as extreme as in \(AgCl\).

Defects: \(AgBr\) can exhibit both Frenkel and Schottky defects. Frenkel defects occur due to the size difference between Ag\(^+\) and Br\(^-\). Schottky defects can also occur due to the ionic nature of the crystal structure. The balance of these defects makes \(AgBr\) capable of showing both types of defects.

4. \(NaCl\) (Sodium Chloride):

Ionic Sizes: Sodium ions (Na\(^+\)) and chloride ions (Cl\(^-\)) are of similar sizes.

Defects: \(NaCl\) primarily exhibits Schottky defects. Frenkel defects are not common because the ions are not significantly different in size, making it unlikely for a cation to occupy an interstitial site.

Summary:

Frenkel Defects: More common in solids where there is a significant size difference between cations and anions (e.g., \(AgCl\)).

Schottky Defects: More common in solids where the cations and anions are similar in size (e.g., \(NaCl\)).

Thus the correct answer is option 3. \(AgBr\).

Explanation: \(AgBr\) is known to exhibit both Frenkel and Schottky defects. The Frenkel defects arise because Ag\(^+\) ions are smaller than Br\(^-\) ions, which allows Ag\(^+\) to move to interstitial sites. Schottky defects occur because of the overall ionic nature of the crystal, which can result in the formation of vacancies for both ions. Thus, \(AgBr\) is the compound among the options given that shows both types of defects.