Right option for the number of tetrahedral and octahedral voids in hexagonal primitive unit cell are:
- 8,4
- 6,12
- 2,1
- 12,6
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.
- 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.
- In an hcp arrangement, each atom is surrounded by 12 others, which creates the possibility of voids being formed.
- 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.
- 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.
- Primitive Unit Cells: In a primitive unit cell constituent particles are present only on the corner positions of a unit cell.
- Centred Unit Cells: A centred unit cell contains one or more constituent particles which are present at positions besides the corners.
- 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.
- Face Centered Unit Cell: Such a unit cell contains one constituent particle present at the centre of each face, as well as its corners.
- 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.