Question:

Right option for the number of tetrahedral and octahedral voids in hexagonal primitive unit cell are:

Updated On: Nov 13, 2025
  • 8,4
  • 6,12
  • 2,1
  • 12,6
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The Correct Option is D

Solution and Explanation

To determine the correct number of tetrahedral and octahedral voids in a hexagonal primitive unit cell, we need to understand the structure of the hexagonal close-packed (hcp) arrangement. 

  1. The hexagonal close-packed (hcp) structure consists of two layers: the top and a bottom layer representing hexagonal packing, with an additional layer that fits into the spaces of these two layers.
  2. In an hcp arrangement, each atom is surrounded by 12 others, which creates the possibility of voids being formed.
  3. There are two types of voids based on their geometrical configuration:
    • Tetrahedral Voids: Formed when an atom in one layer fits into the triangular void formed by three atoms in the adjacent layer. In a unit cell, the number of tetrahedral voids is twice the number of atoms. Since there are 6 atoms in an hcp unit cell, there are \(2 \times 6 = 12\) tetrahedral voids.
    • Octahedral Voids: Occur when an atom sits in the space formed by touching three top-layer atoms and three bottom-layer atoms. For an hcp unit cell, the number of octahedral voids is equal to the number of atoms. Therefore, in an hcp unit cell, there are 6 octahedral voids.
  4. Considering the above points, the number of tetrahedral and octahedral voids in a hexagonal primitive unit cell is 12 and 6 respectively.

Thus, the correct option is 12,6.

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Concepts Used:

Unit Cells

The smallest portion of a crystal lattice which repeats in different directions to form the entire lattice is known as Unit cell.

The characteristics of a unit cell are:

  • The dimensions are measured along the three edges, a, b and c. These edges can form different angles, they may be mutually perpendicular or may not.
  • The angles held by the edges are α (between b and c) β (between a and c) and γ (between a and b).

Therefore, a unit cell is characterised by six parameters such as a, b, c and α, β, γ.

Types of Unit Cell:

Numerous unit cells together make a crystal lattice. Constituent particles like atoms, molecules are also present. Each lattice point is occupied by one such particle.

  1. Primitive Unit Cells: In a primitive unit cell constituent particles are present only on the corner positions of a unit cell.
  2. Centred Unit Cells: A centred unit cell contains one or more constituent particles which are present at positions besides the corners.
    1. Body-Centered Unit Cell: Such a unit cell contains one constituent particle (atom, molecule or ion) at its body-centre as well as its every corners.
    2. Face Centered Unit Cell: Such a unit cell contains one constituent particle present at the centre of each face, as well as its corners.
    3. End-Centred Unit Cells: In such a unit cell, one constituent particle is present at the centre of any two opposite faces, as well as its corners.