Problem 117 - A Complete Resource Book in Chemistry for JEE Main

Question

The correct statements regarding defects in solids are, (a) Schottky defects affect the density of solid. (b) Trapping of an electron in the lattice leads to the formation of \(\mathrm{F}\) - center. (c) Frenkel defect is a dislocation effect. (d) Frenkel defect is usually favoured by a very small difference in the sizes of cation and anion.

Step-by-Step Solution

Answer

Correct statements: (a), (b), and (c).

Step 1: Analyze Schottky Defects

Schottky defects occur when an equal number of cations and anions are missing from the lattice, maintaining the stoichiometry but reducing the density of the solid due to the vacant sites. Therefore, statement (a) is correct.

Step 2: Understand F-center Formation

An F-center or Farbzentrum is created when an anion vacancy in the lattice traps an electron, leading to a color center. This matches the description in statement (b), making it correct.

Step 3: Examine Frenkel Defect

A Frenkel defect involves a cation leaving its normal position and occupying an interstitial site, creating a dislocation effect. This is accurately described in statement (c), confirming its correctness.

Step 4: Consider Size Requirement for Frenkel Defect

Frenkel defects usually occur when there is a significant difference in the size of cations and anions, rather than a small difference as suggested in statement (d). Therefore, statement (d) is incorrect.

Key Concepts

Schottky defects

Schottky defects are a fascinating type of imperfection that occur in crystalline solids. These defects are named after the German physicist Walter H. Schottky, who studied them extensively. In a solid with Schottky defects, pairs of neighboring cations and anions leave their lattice sites, creating vacancies. Despite these missing ions, the compound maintains its stoichiometric balance, meaning that the chemical formula of the compound stays the same. However, because ions carry mass, the creation of vacancies results in a decrease in the density of the solid. This is why Schottky defects are known to affect the density of solids.

Schottky defects are commonly observed in ionic compounds with high coordination numbers, such as sodium chloride (NaCl) and potassium chloride (KCl). Such defects are more likely to occur when the size of the cation and anion are similar, allowing them to leave the lattice without causing structural upheaval.

• They involve equal numbers of cation and anion vacancies.
• The overall charge balance remains unchanged.
• The density of the crystal decreases while maintaining stoichiometry.

Frenkel defects

Frenkel defects occur when an ion, typically a cation, is displaced from its normal lattice position and moves to an interstitial site. Despite the displacement, the ion remains within the solid, which differs from Schottky defects where ions completely leave the structure. This movement creates a "hole" or vacancy where the ion used to be, as well as an additional presence at the site it moves to, known as an interstitial defect. Frenkel defects are also sometimes referred to as dislocation defects.

These defects are more common in ionic solids where there is a considerable difference in size between the cation and anion. Typically, they involve smaller cations that can easily shift from their lattice sites to fit into the spaces between other ions. A classic example is silver chloride (AgCl), where silver ions move into interstitial positions.

• Involve shifting of cations to interstitial sites.
• Maintain stoichiometry and electrical neutrality.
• Typically occur in materials with a significant size difference between ions.

F-center formation

The F-center, short for "Farbzentrum" (German for color center), is an intriguing defect primarily responsible for colors observed in certain ionic crystals. It is formed when an electron gets trapped in an anion vacancy, replacing the missing negative ion and maintaining charge neutrality. The presence of this electron in a normally neutral site can absorb visible light, often resulting in vivid colors. This is why F-centers are sometimes referred to as "optical defects."

In essence, the electron acts like a tiny antenna for light, especially in the visible spectrum. For example, crystals of sodium chloride may appear yellow due to F-center formation. The process is influenced by factors such as radiation exposure, which can knock electrons out of their usual places, creating vacancies and subsequent F-centers.

• Occurs when electrons occupy anion vacancies.
• Often gives crystals their characteristic colors.
• Induced by factors like radiation exposure.