Face-Centred Unit Cell

A face-centred unit cell is a type of crystal lattice where each corner of the cube has an atom, and there is an additional atom in the centre of each face of the cube. This type of unit cell is also known as a cubic close-packed (ccp) or a face-centred cubic (fcc) lattice.

Tetrahedral Voids

A tetrahedral void is a void or empty space in a crystal lattice that is formed by four atoms or ions. In an fcc lattice, the tetrahedral voids are located at the center of each of the six faces of the cube. Each tetrahedral void is surrounded by four atoms or ions, which are located at the corners of a tetrahedron.

Calculation of Total Number of Tetrahedral Voids

To calculate the total number of tetrahedral voids in an fcc unit cell, we use the following formula:

Number of tetrahedral voids = Number of atoms in the unit cell x 1/3

In an fcc unit cell, there are four atoms at the corners of the cube and one atom at the center of each of the six faces of the cube. Therefore, the total number of atoms in an fcc unit cell is:

Number of atoms = 4 (corners) + 6 x 1/2 (face-centers) = 4 + 3 = 8

Using the formula above, we can calculate the total number of tetrahedral voids in an fcc unit cell:

Number of tetrahedral voids = 8 x 1/3 = 2.67

Since the number of tetrahedral voids must be a whole number, we round up to the nearest whole number, which is 3.

Therefore, the correct answer to the question is 8 tetrahedral voids in the face-centred unit cell.