Which of the following statement/statements is/re correct?

Options

A. in the `NaCl` structures, each `Na^(+)` ion is surrounded by `6Cl^(-)` ions as nearest neighbours and twelve `Na^(+)` ions as next nearest neighbours.
B. the co-ordination number of cation generally increases as the radius ratio increases
C. packing efficiencies higher than `0.74` are possible only with cation and anion of different sizes
D. during a crystal defect electrical neutrality should be maintained.

Explanation

To determine which statements are correct regarding the properties of ionic compounds and their structures, we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Statement 1: NaCl Structure**
- In the NaCl structure, each Na⁺ ion is surrounded by 6 Cl⁻ ions as nearest neighbors and 12 Na⁺ ions as next nearest neighbors.
- **Analysis**: In the face-centered cubic (FCC) lattice of NaCl, each Na⁺ ion indeed has 6 Cl⁻ ions as nearest neighbors. The next nearest neighbors are the Na⁺ ions located at the corners of the cube, which totals to 12.
- **Conclusion**: This statement is **correct**.

2. **Statement 2: Coordination Number and Radius Ratio**
- The coordination number of cations generally increases with the radius ratio.
- **Analysis**: According to the radius ratio rule, as the radius ratio of cation to anion increases, the coordination number also increases. For example, a radius ratio of 0.225 to 0.414 corresponds to a coordination number of 4 (tetrahedral), and a ratio of 0.732 to 1 corresponds to a coordination number of 6 (octahedral).
- **Conclusion**: This statement is **correct**.

3. **Statement 3: Packing Efficiency**
- Packing efficiency higher than 0.74 is possible only when there is a significant difference between cation and anion sizes.
- **Analysis**: In ionic crystals, a higher packing efficiency can be achieved when there is a significant size difference between cations and anions. This allows for more efficient packing of ions in the crystal lattice.
- **Conclusion**: This statement is **correct**.

4. **Statement 4: Crystal Defects and Electrical Neutrality**
- During crystal defects, electrical neutrality is maintained.
- **Analysis**: In Frenkel defects, a cation is displaced but the overall charge remains balanced. In Schottky defects, equal numbers of cations and anions are removed from the lattice, maintaining electrical neutrality.
- **Conclusion**: This statement is **correct**.

### Final Conclusion:
All statements (A, B, C, and D) are correct.