DIAMOND STRUCTURE

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Solid State Physics

Diamond Cubic Structure

An FCC Bravais lattice with a two-atom basis. Each carbon atom is tetrahedrally bonded to four neighbors via sp³ hybridization.

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Space Group
Fd3̄m
Coordination
4 (tetrahedral)
Atoms / Cell
8
Packing Factor
34.01%
Bond Angle
109.5°

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Diamond Crystal Structure – Complete Exam Notes

The diamond crystal structure is one of the most important crystal structures in solid state physics. It is commonly studied in B.Sc Physics, M.Sc Physics, Engineering Physics, and Anna University semesters.

What is Diamond Crystal Structure?

Diamond crystal structure is a special arrangement of atoms where each atom is bonded to four neighboring atoms in a tetrahedral form. The structure is derived from the Face Centered Cubic (FCC) lattice.

In this structure, atoms are connected through strong covalent bonds, making diamond one of the hardest known materials.

Examples of Diamond Structure

  • Diamond (Carbon)
  • Silicon (Si)
  • Germanium (Ge)

Silicon and germanium are widely used in semiconductor industries.

Construction of Diamond Structure

The diamond structure can be understood as:

  • Two interpenetrating FCC lattices
  • One lattice is shifted by:

$$ \left(\frac{1}{4}, \frac{1}{4}, \frac{1}{4}\right) $$

with respect to the other.

This arrangement produces a tetrahedral bonding pattern.

Number of Atoms per Unit Cell

Contribution from FCC lattice

Corner atoms:

$$ 8 \times \frac{1}{8} = 1 $$

Face-centered atoms:

$$ 6 \times \frac{1}{2} = 3 $$

Total FCC atoms:

$$ 1 + 3 = 4 $$

Internal atoms

There are 4 atoms completely inside the unit cell.

Therefore,

$$ \text{Total atoms per unit cell} = 8 $$

Coordination Number

In diamond structure, each atom is surrounded by four nearest neighboring atoms.

Therefore,

$$ \text{Coordination Number} = 4 $$

The atoms form a tetrahedral arrangement.

Atomic Radius Relation

The relation between lattice constant \(a\) and atomic radius \(r\) is:

$$ r = \frac{\sqrt{3}}{8}a $$

This is an important derivation frequently asked in university exams.

Atomic Packing Factor (APF)

The packing efficiency of diamond structure is lower compared to FCC.

$$ \text{APF} \approx 0.34 $$

This means only 34% of the space is occupied by atoms.

Properties of Diamond Crystal Structure

  • Very hard material
  • High melting point
  • Strong covalent bonding
  • Low packing density
  • Excellent thermal conductivity
  • Semiconductor behavior in silicon and germanium

Advantages of Diamond Structure

  • Extremely strong structure
  • High mechanical strength
  • Stable covalent bonding
  • Useful in semiconductor applications

Disadvantages

  • Brittle in nature
  • Difficult to deform
  • Lower packing efficiency

Applications of Diamond

Diamond

  • Cutting tools
  • Drilling machines
  • Abrasive materials
  • Jewelry

Silicon and Germanium

  • Transistors
  • Integrated circuits
  • Semiconductor devices
  • Solar cells

Important Points

  • Diamond structure is derived from FCC lattice
  • Contains 8 atoms per unit cell
  • Coordination number is 4
  • Tetrahedral bonding arrangement
  • Packing factor is 0.34

Atomic radius relation:

$$ r = \frac{\sqrt{3}}{8}a $$

Short 2-Mark Answer

Diamond crystal structure consists of two interpenetrating FCC lattices displaced by $$ \left(\frac{1}{4}, \frac{1}{4}, \frac{1}{4}\right) $$ Each atom is tetrahedrally bonded with four neighboring atoms. The structure contains 8 atoms per unit cell and has coordination number 4.

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