Primitive Cubic Unit Cell and Coordinate Number

Primitive cubic unit cell is the simplest type of unit cell in which the lattice points are situated only at the corners of the cube. It is also known as a simple cubic unit cell. In this type of unit cell, the lattice points are located at the eight corners of the cube. The edge length of the cube is designated as ‘a’.

The coordinate number or coordination number is the number of atoms or ions that surround an atom or ion in a crystal lattice. In other words, it is the number of nearest neighbors of an atom in a crystal lattice.

Answer and Explanation

The coordinate number for an atom in a primitive cubic unit cell is 6. This means that each atom in a primitive cubic unit cell is surrounded by six nearest neighboring atoms. The following points can explain why the coordinate number is 6 in a primitive cubic unit cell:

- In a primitive cubic unit cell, each corner atom is shared by eight unit cells. Hence, each corner atom contributes only 1/8th to the unit cell.
- Out of the eight atoms at each corner, only one atom belongs to the unit cell. Therefore, each corner atom contributes only 1/8th to the unit cell.
- The atom at the center of the unit cell is not surrounded by any other atom, as there is no other atom in the same unit cell. Therefore, the coordinate number of the central atom is zero.
- The six atoms that are located at the center of the faces of the cube are the nearest neighbors of each corner atom. Hence, the coordinate number of each corner atom is 6.

Therefore, the coordinate number of an atom in a primitive cubic unit cell is 6.