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Chemistry: Solid State: Number of Atoms in Cubic Unit Cells and Simple Cubic Unit Cell
Number of Atoms in Cubic Unit Cells
- In the cubic crystal system, the three distances are equal, and all the three angles are right angles.
- The unit cells of three possible lattice types viz. , primitive or simple cubic, body centered cubic and the face centered cubic, belonging to cubic crystal system.
Number of Atoms Per Unit Cell
- In unit cells the atoms are present in the corners, in body center and on face centers.
- All the atoms do not belong to a single unit cell as they are shared between different unit cells.
- It is important to know the number of atoms per unit cell.
Simple Cubic Unit Cell
- The simple or primitive unit cell has the atoms at the corners of the cube.
- A lattice point at the corner of the unit cell is shared by eight-unit cells, Therefore, the contribution of an atom at the corner to the unit cell will be 1β8.
- The number of atoms per unit cell can be calculated as follows:
1. Number of corner atoms = 8
2. Contribution of each corner atom =
3. The number of atoms in a simple cubic unit cell =
Body Centered Cubic Unit Cell
- A body centered cubic (bcc) unit cell has lattice points at the center of the cube.
- The atom in the center of the cube belongs to the unit cell.
- The corner atom in the simple cubic unit cell is shared by eight-unit cells.
The number of atoms per unit cell can be calculated as:
1. Number of corner atoms = 8
2. Contribution of each corner atom =
3. Contribution of all the corner atoms to the unit cell =
4. Number of atoms at the center of the cube = 1
5. Contribution to the unit cell = 1 (as it is not shared)
6. The number of atoms in a body centered cubic unit cell =
Faces Centered Cubic Unit Cell
- A face centered cubic (FCC) unit cell has atoms at the corners and at the center of each face.
- It has eight lattice points at the corners and six at the face centers.
- A face centered lattice point is shared by two-unit cells
1. Number of corner atoms = 8
2. Contribution of each corner atom =
3. Contribution of all the corner atoms to the unit cell =
4. Number of atoms at the face center = 6
5. Contribution of each atom at the face center =
6. Contribution of all the face centered atoms to the unit cell =
7. The number of atoms points in a face centered cubic unit cell =
The number of atoms per unit cell in different types of cubic unit cells is given in the following table: