Zinc sulphide exists in two different structural forms as zinc blende (FCC) and Wurtzite (HCP). What will be the coordination number of cation and anion in both the structures ?

Options

A. 6 :6 are both
B. 4 : 4 for both
C. 4 :4 and 6 :6 respectively
D. 6:6 and 4:4 respectively

Answer

To determine the coordination number of cations and anions in the two structural forms of zinc sulfide (ZnS), namely zinc blende (FCC) and wurtzite (HCP), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Structures**:
- Zinc blende has a face-centered cubic (FCC) structure.
- Wurtzite has a hexagonal close-packed (HCP) structure.

2. **Coordination Number in Zinc Blende (FCC)**:
- In the FCC structure, the anions (S²⁻) are located at the corners and face centers of the cube.
- The contribution of corner atoms is \( \frac{1}{8} \) per corner atom, and there are 8 corners, giving a total contribution of \( 8 \times \frac{1}{8} = 1 \).
- The contribution of face-centered atoms is \( \frac{1}{2} \) per face atom, and there are 6 faces, giving a total contribution of \( 6 \times \frac{1}{2} = 3 \).
- Therefore, the total number of anions in the unit cell is \( 1 + 3 = 4 \).
- The tetrahedral voids in FCC are equal to twice the number of atoms in the FCC unit cell, which is \( 2 \times 4 = 8 \).
- The cations (Zn²⁺) occupy half of these tetrahedral voids, which gives us \( \frac{8}{2} = 4 \) cations.
- Thus, the coordination number for both cations and anions in zinc blende is **4**.

3. **Coordination Number in Wurtzite (HCP)**:
- In the HCP structure, the anions (S²⁻) are arranged in a hexagonal close-packed manner.
- The coordination number for the anions in HCP is also **4**.
- The cations (Zn²⁺) occupy half of the tetrahedral voids in the HCP structure, similar to the zinc blende structure.
- Therefore, the coordination number for cations in wurtzite is also **4**.
- Thus, the coordination number for both cations and anions in wurtzite is **4**.

4. **Conclusion**:
- For both zinc blende and wurtzite structures, the coordination numbers are:
- **Zinc Blende (FCC)**: Coordination number of Zn²⁺ = 4, S²⁻ = 4
- **Wurtzite (HCP)**: Coordination number of Zn²⁺ = 4, S²⁻ = 4

### Final Answer:
The coordination number of cation and anion in both structures is **4:4**.