Animated Solution for Chemistry - States of Matter: Which of the following compounds is likely to show both Frenkel and Schottky defects in its crystalline form?

The study of solid-state chemistry often reveals that perfection is an illusion. Even the most beautifully structured crystals harbor microscopic flaws. These imperfections, rather than ruining the crystal, often give it fascinating new properties.

Today, we are diving into a classic and highly tested concept in JEE: identifying a compound that exhibits both Schottky and Frenkel defects simultaneously.

To understand why a specific compound behaves this way, we must first understand the nature of these two fundamental point defects.

Schottky Defect

Imagine a perfectly ordered classroom where every student has an assigned seat. Now, imagine two best friends—one boy and one girl—deciding to skip class together. They leave their desks empty, but the overall ratio of boys to girls in the school remains balanced.

This is exactly what happens in a Schottky defect. It arises when an equal number of cations and anions are completely missing from their designated lattice sites.

Because they leave in pairs, the electrical neutrality of the crystal is perfectly maintained. However, since mass is physically removed from the crystal while the volume remains roughly the same, the density of the crystal decreases.

This defect is typically observed in highly ionic compounds where the cation and anion are of similar sizes, such as $NaCl$ or $CsCl$. The similar sizes mean that if one goes missing, it's relatively easy for the other to also be missing without causing the entire structure to collapse.

Frenkel Defect

Now, let's picture a different scenario. A restless student decides they don't want to sit at their desk anymore. Instead of leaving the classroom, they simply move and sit in the aisle between the desks.

This perfectly describes the Frenkel defect. In this case, an ion—usually the smaller cation—leaves its normal lattice site and squeezes into an empty space between the other ions, known as an interstitial site.

This creates a vacancy defect at its original position and an interstitial defect at its new location. Because no ions have actually left the crystal, the density remains completely unchanged.

Frenkel defects are common in crystals where there is a large difference in ionic sizes, such as $ZnS$ or $AgCl$. The large anions form the rigid lattice, while the much smaller cations have the freedom to slip into the interstitial voids.

Silver Bromide

So, what happens when a crystal is caught right in the middle of these two extremes? Enter Silver Bromide ($AgBr$).

The behavior of a crystal is heavily dictated by its radius ratio, mathematically expressed as $\frac{r_{+}}{r_{-}}$. For $AgBr$, this ratio is intermediate.

The silver cation ($A{g}^{+}$) is highly polarizable and just small enough to squeeze into the interstitial sites, which perfectly sets the stage for Frenkel defects.

At the same time, the sizes of $A{g}^{+}$ and $B{r}^{-}$ are close enough, and the lattice energy is such that pairs of ions can go missing entirely, allowing for Schottky defects to form as well.

$AgBr$ is the quintessential "Goldilocks" compound. It strikes the perfect balance, making it the classic textbook example of a solid that exhibits both types of point defects simultaneously.

When faced with this question on an exam, the logic is straightforward but requires memorization of this unique exception.

While $CsCl$ and $KBr$ show only Schottky defects, and $ZnS$ shows only Frenkel defects, Silver Bromide ($AgBr$) proudly displays both.

Therefore, the correct answer is Option (a). Keep this unique property of $AgBr$ locked in your memory, as it is a favorite among examiners!