UNIT 1: SOLID STATE (XII CHEMISTRY KEY NOTES) PART VI CBSE

 

1. Defects in Solids

• Defects (or imperfections) are irregularities in the arrangement of constituent particles (atoms, ions, or molecules) in a crystal.
• Types of Defects

• Point Defects – Irregularities at single lattice points.

• Line Defects – Irregularities along a line (dislocations).

Point Defects

These occur due to the absence or displacement of atoms/ions at lattice points.
They are of two main types:

• 1. Stoichiometric Defects
• Do not change the stoichiometry (chemical composition) of the compound.
• Common in ionic crystals.
• (a) Schottky Defect

• Definition: A pair of vacancies (one cation and one anion missing) from the lattice.

• Condition: Maintains electrical neutrality.

• Example: NaCl, KCl, CsCl, AgBr

• Characteristics:

  • Decreases density of the crystal.

  • Common in ionic compounds with high coordination numbers and similar cation & anion sizes.

  • Number of defects ∝ exp(–E/2kT) (increases with temperature).

Normal lattice:   + - + - + -

With defect:      + -   - + -    (missing + and - ions)

(b) Frenkel Defect

• Definition: An ion (usually a smaller cation) leaves its regular site and occupies an interstitial site.

• Condition: No ions are missing from the crystal → stoichiometry remains unchanged.

• Example: ZnS, AgCl, AgBr, AgI

• Characteristics:

  • Density remains unchanged (no ions lost).

  • Common in ionic crystals with large size difference between cation and anion.

  • Produces both a vacancy and an interstitial defect.

Normal lattice:   + - + - + -

With defect:      +   + - + -   (one + ion moved to interstitial site)

2. Non-Stoichiometric Defects

     Change the ideal ratio of cations to anions.
→ Often due to metal excess or metal deficiency.

(Examples: F-centres, variable valency ions, etc., but not required here if only Schottky & Frenkel are asked.)

Property	Schottky Defect	Frenkel Defect
Nature	Vacancy defect	Displacement defect
Density	Decreases	Unchanged
Electrical Neutrality	Maintained	Maintained
Ionic Size	Similar sizes	Large size difference
Common in	NaCl, KCl, CsCl, AgBr	ZnS, AgCl, AgBr, AgI

Key Formula

Number of Schottky defects (Ns) at temperature T:

$$N_s = N \, e^{-E_s / (2kT)}$$

where

• $\mathrm{<span\; class="katex"><span\; style="font-size:\; medium;"><span\; aria-hidden="true"\; class="katex-html"><span\; class="base"><span\; class="mord\; mathnormal">N</span></span></span>=\; total\; number\; of\; lattice\; sites</span></span>}$

• ${}_{}$Es​ = energy required to form a defect

• $\mathrm{<span\; style="font-size:\; medium;">k\; =\; Boltzmann\; constant</span>}$

• $\mathrm{<span\; style="font-size:\; medium;">T\; =\; absolute\; temperature</span>}$