Problem 31 - A Complete Resource Book in Chemistry for JEE Main

Question

Which defect causes decrease in the density of a crystal? (a) Schottky (b) F-centre (c) Frenkel (d) Interstitial

Step-by-Step Solution

Answer

Schottky defects cause a decrease in the density of a crystal.

Step 1: Understanding the Defect Types

To solve this problem, we first need to understand what each defect means: a Schottky defect involves the absence of equal numbers of cations and anions, leading to a decrease in density; an F-centre involves electrons trapped in anion vacancies and affects color; a Frenkel defect involves the dislocation of cations, leading to no volume change and thus no density change; and an interstitial defect means additional atoms in crystal gaps, increasing density.

Step 2: Analyzing Density Impact

Now let's analyze each defect with respect to density: Schottky defects remove pairs of ions, thereby decreasing the mass without significantly affecting volume, leading to decreased density. Frenkel and F-centre defects primarily affect color or internal rearrangement without changing mass-to-volume ratio significantly. Interstitial defects increase mass without substantially altering volume, thus increasing density.

Step 3: Drawing Conclusion

From our analysis, the defect associated with decrease in crystal density is the Schottky defect. This is because it involves loss of ionic pairs which explicitly reduces the mass while maintaining the structure's volume, directly resulting in decreased density.

Key Concepts

Schottky Defect

The Schottky defect is a type of vacancy defect found in ionic crystals. It arises when equal numbers of cations and anions are absent from the lattice structure, creating vacancies. These missing ions create tiny holes, leading to disruptions in the crystal's otherwise orderly structure. Because ions are missing, the total mass of the crystal decreases while the volume of the crystal remains largely unchanged. This loss of mass without a change in volume directly leads to a decrease in the density of the material.
Schottky defects are common in ionic compounds like sodium chloride (NaCl) and potassium chloride (KCl), where the sizes of the cations and anions are relatively similar. By understanding these defects, one can better grasp why they decrease crystal density, as they crucially involve losing part of the crystal's mass without compressing its structure. This defect plays a significant role in influencing properties such as ionic conductivity.

Frenkel Defect

The Frenkel defect, unlike the Schottky defect, involves the dislocation of ions within a crystal rather than their complete absence. Typically, a smaller ion, like a cation, vacates its normal spot in the lattice structure and relocates to an interstitial position — a gap between the ions. This migration creates both a vacancy at its original location and an interstitial defect at the new location. Despite these re-positions, the overall number of ions within the crystal remains unchanged.
Because there is no actual loss of material, only a shift from one position to another, the mass-to-volume ratio—and thus the density of the crystal—remains constant with a Frenkel defect. These defects are most common in compounds where there's a noticeable size difference between anions and cations, such as silver chloride (AgCl) or zinc sulfide (ZnS). They primarily affect the crystal's electrical properties as they allow restricted movement of the ions, which can contribute to conductivity.

Density Change in Crystals

Density is defined as mass per unit volume. When analyzing defects in crystals, it's essential to understand their impact on this property. In the context of crystal defects:

• Schottky defects cause a decrease in density due to the removal of ion pairs, reducing total mass while keeping volume largely unchanged.
• Frenkel defects do not alter the density because they involve ions merely shifting positions instead of being lost.
• Other defects such as interstitial defects, where additional atoms are added, can lead to an increase in density due to the increase in mass.

Understanding these changes is crucial for applications where material density is vital, such as in ceramics, semiconductors, and other advanced materials. By modifying the type and concentration of defects, scientists can tailor the physical properties of materials to better suit technological needs.