The compound AB crystallizes in a cubic lattice in which both A and B atoms have coordination number of 8. To what crystal class does that unit cell belong?

Options

A. CsCl structure
B. NaCl structure
C. ZnS structure
D. `Al_(2)O_(3)` strucuture

Answer

To determine the crystal class of the compound AB that crystallizes in a cubic lattice with both A and B atoms having a coordination number of 8, we can analyze the given options based on their structures and coordination numbers.

### Step-by-Step Solution:

1. **Understanding Coordination Number**:
- The coordination number refers to the number of nearest neighbors surrounding an atom in a crystal structure. A coordination number of 8 indicates that each atom is surrounded by 8 other atoms.

2. **Identifying the Crystal Structures**:
- We have four options: Cesium chloride (CsCl), Sodium chloride (NaCl), Zinc sulfide (ZnS), and Aluminium trioxide (Al2O3).

3. **Analyzing Each Option**:
- **Cesium Chloride (CsCl)**:
- In CsCl, the cesium ion (Cs⁺) is located at the body center of the cubic unit cell, while the chloride ions (Cl⁻) occupy the corners. This structure has a coordination number of 8 for both Cs⁺ and Cl⁻ ions.
- **Sodium Chloride (NaCl)**:
- In NaCl, sodium ions (Na⁺) occupy octahedral voids, and chloride ions (Cl⁻) are at the corners. The coordination number here is 6 for both Na⁺ and Cl⁻.
- **Zinc Sulfide (ZnS)**:
- In ZnS, the zinc ions (Zn²⁺) and sulfide ions (S²⁻) have a coordination number of 4 for both ions in the sphalerite structure.
- **Aluminium Trioxide (Al2O3)**:
- In Al2O3, the aluminum ions (Al³⁺) and oxide ions (O²⁻) also do not have a coordination number of 8.

4. **Conclusion**:
- Based on the analysis, the only structure that has both A and B atoms with a coordination number of 8 is Cesium Chloride (CsCl). Therefore, the unit cell of the compound AB belongs to the **Cesium Chloride structure**.

### Final Answer:
The crystal class to which the unit cell of compound AB belongs is **Cesium Chloride structure**.

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