The correct option for the number of body centred unit cells in all $14$ types of Bravais lattice unit cells is :
- 7
- 5
- 2
- 3
The Correct Option is D
Solution and Explanation
The question asks about the number of body-centered unit cells in the 14 types of Bravais lattices. To find the correct answer, let's briefly review what Bravais lattices are and identify which of them are body-centered:
Bravais lattices are distinct lattice systems in crystallography that describe the geometric arrangement of points in space. There are 14 such lattices, which can be categorized based on their centering:
- Simple (or Primitive)
- Body-Centered (also known as I-Centered)
- Face-Centered
- Base-Centered (or End-Centered)
Specifically, the body-centered Bravais lattices are:
- Body-Centered Cubic (BCC)
- Body-Centered Tetragonal
- Body-Centered Orthorhombic
Conclusion: There are exactly 3 body-centered unit cells within the 14 Bravais lattices.
Thus, the correct option is:
This option is correct based on the definition and classification of body-centered unit cell types within the Bravais lattices.
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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.