Problem 67 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following statements is correct in context of point defects in a crystal? (a) \(\mathrm{AgCl}\) as well as \(\mathrm{CaF}_{2}\) has Schottky defects (b) \(\mathrm{AgCl}\) as well as \(\mathrm{CaF}_{2}\) have anion Frenkel defects (c) \(\mathrm{AgCl}\) has cation Frenkel defects and \(\mathrm{CaF}_{2}\) has Schottky defects (d) \(\mathrm{AgCl}\) has cation Frenkel defects and \(\mathrm{CaF}_{2}\) has anion Frenkel defects

Step-by-Step Solution

Answer

The correct statement is (c): AgCl has cation Frenkel defects and CaF2 has Schottky defects.

Step 1: Understanding Schottky Defect

Schottky defect is a type of point defect in crystals where an equal number of cations and anions are missing from the lattice, maintaining the electrical neutrality. Typically, this defect occurs in highly ionic compounds with high coordination numbers, such as alkali metal halides (e.g., NaCl).

Step 2: Understanding Frenkel Defect

Frenkel defect occurs when an ion, typically a cation, is displaced from its normal site to an interstitial site within the crystal. This defect is prevalent in compounds where there is a vast difference in size between the cations and anions. It is less common in purely ionic crystals like AgCl but occurs more frequently when one type of ion is much smaller than the other.

Step 3: Analyzing Defects in AgCl

AgCl typically exhibits Frenkel defects. This is because the Ag+ ion is small enough to displace into an interstitial site without disturbing the crystal structure significantly. Therefore, AgCl generally shows cation Frenkel defects rather than Schottky defects.

Step 4: Analyzing Defects in CaF2

CaF2 typically exhibits Schottky defects rather than Frenkel defects. In its structure, pairwise missing Ca2+ and F- ions to maintain electroneutrality is a common phenomenon leading to Schottky defects. The size and ionic nature of the particles involved in CaF2 lead to this defect type.

Step 5: Conclusion - Identifying the Correct Statement

Based on the analysis, AgCl exhibits cation Frenkel defects, and CaF2 exhibits Schottky defects. Hence, the statement that matches this description is (c) "AgCl has cation Frenkel defects and CaF2 has Schottky defects."

Key Concepts

Schottky Defect

Schottky defects represent a type of point defect in crystalline solids where equal numbers of anions and cations are missing from their lattice positions. This absence of ions does not disrupt the overall charge neutrality of the crystal, as the number of missing positively charged ions equals the number of missing negatively charged ions. Uniquely suited to ionic compounds with a high degree of symmetry and high coordination numbers, these defects prominently occur in alkali halides, like NaCl.

The Schottky defect is essentially a paired vacancy defect, as it involves both types of ions leaving their positions. This defect reduces the density of the crystal because mass is lost without a decrease in volume. Schottky defects enhance the ionic conductivity of materials by providing vacancies that can be "hopped" into by charge-carrying ions. In CaF 2, Schottky defects are prevalent due to the compound’s structural tendency to easily accommodate missing Ca^{2+} and F^{-} ions.

Frenkel Defect

The Frenkel defect occurs when an ion in a crystalline lattice is displaced from its original position to an interstitial site, that is, a space within the lattice that is not usually occupied by an ion. Typically, this defect involves a cation because cations are often smaller than anions and thus can more easily fit into interstitial spaces.

One of the key characteristics of the Frenkel defect is that it does not affect the overall charge neutrality of the crystal. These defects are common in crystals where there is a significant difference in size between the ions involved, with smaller cations like the silver ion in AgCl moving into interstitial positions.

While Frenkel defects are less common in purely ionic crystals, they can still occur under certain conditions, especially when the cation is sufficiently small to move around within the lattice. AgCl is a classic example where Frenkel defects are observed, as the small size of the Ag+ ion allows it to occupy an interstitial site without significantly disturbing the overall structure of the crystal.

Crystal Lattice Defects

Crystal lattice defects, sometimes known as point defects due to their localized nature, encompass a range of imperfections found within a crystalline solid. These imperfections occur at distinct points in the lattice, hence the name. There are several types of lattice defects, with Schottky and Frenkel defects being two of the most prominent.

Point defects can significantly influence the physical properties of a material, including its electrical, optical, and mechanical behaviors. By altering atom positions, lattice defects can introduce stress and strain in the crystal, modify its electrical conductivity, and even impact its optical properties under certain conditions.

The presence of these defects is an essential consideration in materials science for tailoring the characteristics of semiconductors, compounds like AgCl and CaF2, and many other ionic crystals. Understanding and controlling these defects allow scientists to enhance material performance for various applications, such as in electronics and optics. Each defect type, whether it's a missing ion or a mispositioned atom, plays a crucial role in the complex puzzle of material behavior.