Calculation of Schottky Defects in a Face-Centred Cubic Unit Cell

To calculate the percentage of Schottky defects in a face-centred cubic (FCC) unit cell of calcium, we need to first understand what Schottky defects are and how they are related to the crystal structure and density of the material.

Schottky Defects:
- Schottky defects are point defects that occur in ionic crystals.
- They involve the simultaneous absence of an equal number of cations and anions from their lattice sites.
- These defects result in the formation of vacancies in the crystal lattice.

Face-Centred Cubic (FCC) Unit Cell:
- The FCC unit cell is a type of crystal structure where atoms are arranged in a lattice with cubic symmetry.
- In an FCC unit cell, there are atoms at the corners of the cube and one atom at the center of each face of the cube.
- This arrangement gives a total of 4 atoms per unit cell.

Calculation:
1. Calculate the volume of the unit cell:
- The lattice parameter 'a' of the FCC unit cell of calcium is given as 0.556 nm.
- The volume (V) of the unit cell can be calculated using the formula: V = a^3.
- Substituting the given value, V = (0.556 nm)^3.

2. Calculate the mass of the unit cell:
- The density of calcium is given as 1.4848 g/cm^3.
- Since the density is given in g/cm^3, we need to convert the volume from nm^3 to cm^3.
- 1 nm = 10^-7 cm, so (0.556 nm)^3 = (0.556 x 10^-7 cm)^3.
- The mass (m) of the unit cell can be calculated using the formula: m = V x density.
- Substituting the values, m = (0.556 x 10^-7 cm)^3 x 1.4848 g/cm^3.

3. Calculate the number of formula units in the unit cell:
- Since calcium has a face-centered cubic structure, there are 4 atoms per unit cell.
- The number of formula units in the unit cell is equal to the number of atoms divided by the number of atoms per formula unit.
- For calcium, the number of formula units is 4/1 = 4.

4. Calculate the number of Schottky defects:
- Schottky defects involve the absence of an equal number of cations and anions.
- In a unit cell of calcium, there are 4 cations and 4 anions in a perfectly ordered crystal structure.
- The number of Schottky defects can be calculated using the formula: (Number of cations + Number of anions) - Number of formula units.
- Substituting the values, (4 + 4) - 4 = 4.

5. Calculate the percentage of Schottky defects:
- The percentage of Schottky defects is given by the formula: (Number of Schottky defects / Number of formula units) x 100.
- Substituting the values, (4/4) x 100 = 100%.

Conclusion:
The percentage of Schottky defects