Problem 137 - A Complete Resource Book in Chemistry for JEE Main

Question

What type of crystal defect is indicated in the diagram below? \(\mathrm{Na}^{+}, \mathrm{Cl}^{-}, \mathrm{Na}^{+}, \mathrm{Cl}^{-}, \mathrm{Na}^{+}, \mathrm{Cl}^{-}\) \(\mathrm{Cl}^{-} \square \mathrm{Cl}^{-} \mathrm{Na}^{+} \square \mathrm{Na}^{+}\) \(\mathrm{Na}^{-} \mathrm{Cl}^{-} \square \mathrm{Cl}^{-} \mathrm{Na}^{+} \mathrm{Cl}^{-}\) \(\mathrm{Cl}^{-} \mathrm{Na}^{+} \mathrm{Cl}^{-} \mathrm{Na}^{+} \square \mathrm{Na}^{+}\) (a) Frenkel defect (b) Interstitial defect (c) Schottky defect (d) Frenkel and Schottky defects

Step-by-Step Solution

Answer

The crystal defect shown in the diagram is a Schottky defect.

Step 1: Understand the Defect Types

Frenkel defect occurs when an ion leaves its position in the lattice creating a vacancy and becomes an interstitial. Schottky defect involves missing ions from the lattice, requiring equal numbers of cation and anion vacancies to preserve electrical neutrality.

Step 2: Analyze the Diagram

Look for any missing ions or displacements in the provided lattice diagram. Here, we observe the presence of squares indicating missing ions. Ensure these missing spots are equal in count for both cations and anions to imply a specific defect type.

Step 3: Count the Vacancies

Identify and count the missing ions in the second, third, and fourth rows of the diagram where squares are present. Confirm that the number of missing Na\(^+\) (cations) equals the number of missing Cl\(^-\) (anions).

Step 4: Match with Defect Type

Since there are equal cation and anion vacancies, the representation refers to a Schottky defect according to the defect types studied. As there are no displaced ions occupying interstitial sites, it cannot be a Frenkel defect.

Key Concepts

Schottky defect

A Schottky defect is one of the simplest types of crystal defects you can come across. It happens in ionic crystals, where atoms are arranged in a repeating pattern called a lattice. When a Schottky defect occurs, some atoms or ions go missing entirely, leaving holes, or vacancies, behind.
These vacancies are seen on the lattice where both cations (positively charged ions) and anions (negatively charged ions) are missing. This is important because the removal of these ions must be balanced to preserve the crystal's overall neutrality. So, you'd find an equal number of missing positive and negative ions.

• This defect is common in materials like sodium chloride ( ext{NaCl}) and other alkali halides.
• It reduces the density of the material since some mass is missing but the volume stays the same.
• The missing ions create vacancies, leading to increased ion mobility and a change in the crystal's properties.

This type of defect does not involve any other structural changes beyond the vacancies, making it relatively easy to identify with its signature equal voids for both types of ions.

Frenkel defect

The Frenkel defect is a type of imperfection you would find in a crystal structure where some of the ions, instead of disappearing, just change their spots in the crystal lattice. What happens here is that an ion leaves its regular place and occupies a nearby empty site known as an interstitial site.
This type of defect doesn't affect the electrical neutrality of the crystal, but it does create a hole or vacancy in the spot where the ion originally was and an extra ion now sitting in an interstitial site.

• Frenkel defects are common in crystals with a large size difference between ions, like silver chloride ( ext{AgCl}).
• They don't change the density of the crystal because the total number of ions remains the same.
• The defect creates interesting electrical properties since ions can move more freely, allowing for better conductivity.

There's no disappearance of ions in a Frenkel defect— they are just displaced. Therefore, it's common to see changes in how the crystal interacts with electricity and heat due to these displacements.

Lattice vacancies

Lattice vacancies are among the most fundamental imperfections in a crystal lattice. A vacancy occurs when an atom or ion is missing from one of the spots in the lattice structure, which disrupts the regular repeating pattern of the crystal.
These missing positions are significant because they can affect the properties of the material in several ways. By creating free space, vacancies allow atoms to move around more freely and can facilitate the diffusion of particles through the crystal.

• The presence of vacancies tends to increase with temperature as atoms gain energy and become more mobile.
• Vacancies can lead to changes in mechanical strength, conductivity, and diffusion rates.
• The count of vacancies can directly impact the physical properties of a material, including its electrical and thermal conductivity.

Understanding and controlling vacancies is crucial in material science and engineering, as engineers can leverage these properties to improve the performance of various materials.