3 Most SAQ’s of Solid State Chapter in Inter 2nd Year Chemistry (TS/AP)

4 Marks

SAQ-1 : Derive Bragg’s equation.

Introduction

Bragg’s equation plays a pivotal role in X-ray crystallography, establishing the relationship between the angles at which X-rays are constructively diffracted by a crystal lattice, the lattice spacings, and the wavelength of the X-rays.

Derivation of Bragg’s Equation

1. Setting the Scene: Consider two parallel planes of atoms within a crystal lattice, where X-rays of wavelength λ strike these planes at an angle θ.
2. Points of Diffraction
   • The first X-ray beam is diffracted from point ‘A’ on the first plane.
   • Simultaneously, a second X-ray beam is diffracted from point ‘B’ on the adjacent plane.
3. Path Difference
   • The second X-ray traverses an additional path relative to the first. This additional path comprises the segments CB and BD.
   • The path difference is key to determining the type of interference (constructive or destructive) that will occur.
4. Constructive Interference: For constructive interference to take place, the extra distance covered by the second X-ray (CB + BD) must be an integer multiple of the wavelength λ, expressed as CB + BD = nλ, where n is the diffraction order.
5. Relating Path Difference to Angle of Incidence: Trigonometry reveals that distances CB and BD can be expressed as CB = dsinθ and BD = dsinθ, where d is the spacing between crystal planes.
6. Combining the Equations
   • Adding the distances CB and BD, we obtain CB + BD = 2dsinθ.
   • Integrating this with the equation for constructive interference yields Bragg’s equation: nλ = 2dsinθ

Summary

Bragg’s equation, nλ = 2dsinθ, is fundamental in crystallography, enabling the determination of atomic plane spacings within a crystal by observing how it diffracts X-rays. This equation bridges the physical structure of crystals with the observable patterns of X-ray diffraction, offering profound insights into the atomic scale arrangement of crystalline materials.

---

SAQ-2 : Explain Schottky & Frenkel Defects with structures.

Introduction

In crystalline materials, defects can arise from irregularities in the arrangement of atoms or ions. Schottky and Frenkel defects are two primary types of such point defects, representing deviations from the ideal arrangements in ionic crystals.

Schottky Defect

1. Definition: A Schottky defect occurs when an atom or ion is absent from its normal site in the crystal lattice, creating a vacancy.
2. Characteristics:
   • Electrical neutrality is maintained by the equal absence of cations and anions.
   • The crystal’s overall density decreases due to the missing ions.
   • Predominant in ionic solids with a high coordination number and nearly similar-sized ions.
3. Examples: Commonly found in ionic crystals like Sodium Chloride (NaCl), Cesium Chloride (CsCl), and Silver Bromide (AgBr).
4. Structure: Visualize a grid representing the crystal lattice; Schottky defects would be vacant points where ions should be.

Frenkel Defect

1. Definition: A Frenkel defect arises when an atom or ion is displaced from its regular lattice site to an interstitial site, still within the crystal structure.
2. Characteristics:
   • Involves displacement of usually one type of ion (typically the smaller cation).
   • The crystal’s overall density remains unchanged, as ions are displaced, not removed.
   • More common in ionic crystals with significant size differences between cations and anions.
3. Examples: Frequently observed in ionic crystals like Silver Chloride (AgCl), Silver Bromide (AgBr), and Zinc Sulfide (ZnS).
4. Structure: In the grid analogy, a Frenkel defect shows an ion moved to a position between its correct location and another ion.

Summary

Schottky and Frenkel defects play a significant role in defining the properties of ionic crystals, influencing their conductive and mechanical behavior. Identifying these defects helps elucidate material characteristics under various conditions, enhancing our understanding of crystalline substances.

---

SAQ-3 : Describe the two main types of semiconductors and contrast their conduction mechanism.

Introduction

Semiconductors are materials with conductivity between that of insulators and conductors, pivotal in modern electronics. Their conductivity can be tailored through types and doping, primarily classified into intrinsic and extrinsic semiconductors.

Intrinsic Semiconductors

1. Definition: Pure semiconductors without external impurities.
2. Characteristics:
   • Conductivity increases with temperature.
   • Equal numbers of electrons and holes as charge carriers.
3. Examples: Pure silicon (Si) and germanium (Ge).
4. Conduction Mechanism: Conductivity results from the movement of electrons to the conduction band and the creation of holes in the valence band, especially as temperature increases.

Extrinsic Semiconductors

Definition: Semiconductors doped with impurities to modify their conductivity.

Types of Extrinsic Semiconductors

1. N-type Semiconductor:
   • Majority charge carriers are electrons.
   • Doping with Group VA elements like Phosphorus (P) or Arsenic (As), introducing additional electrons for enhanced conductivity.
2. P-type Semiconductor:
   • Majority charge carriers are holes.
   • Doping with Group IIIA elements like Boron (B) or Aluminum (Al), creating a deficiency in electrons and thus “holes.”
3. Conduction Mechanism
   • N-type: Conductivity is due to the movement of free, delocalized electrons from the doping agent.
   • P-type: Conductivity occurs through the movement of holes, with electrons hopping between holes, giving the illusion of moving holes.

Summary

The distinction between intrinsic and extrinsic semiconductors underlines the versatility of semiconductors in electronics. By adjusting the semiconductor type and its doping, a vast range of electronic devices can be engineered, powering the technological advancements of the modern era.