Which of the following characteristic features match(es) with the crystal systems: simple cubic and face centred cubic?

Options

A. Both have the cell parameters a = b = c and `alpha=beta=gamma`
B. Both belong to different crystal systems
C. Both have only two crystallographic angles of `90^(@)`
D. Both belong to same crystal system

Answer

To determine which characteristic features match with the crystal systems of simple cubic and face-centered cubic, we need to analyze the properties of both structures.

### Step-by-Step Solution:

1. **Identify the Crystal Systems**:
- The simple cubic (SC) and face-centered cubic (FCC) structures are both types of cubic crystal systems.

2. **Analyze the Lattice Parameters**:
- In both simple cubic and face-centered cubic structures, the edge lengths (a) are equal. Therefore, the lattice parameters are the same.
- Both structures have three equal edge lengths (a = b = c) and all angles (α, β, γ) are equal to 90 degrees.

3. **Determine the Crystallographic Angles**:
- For both simple cubic and face-centered cubic systems, the crystallographic angles are 90 degrees. This means they have the same angular relationships.

4. **Identify the Crystal System**:
- Both simple cubic and face-centered cubic belong to the cubic crystal system. However, they are different types of cubic lattices.

5. **Conclusion**:
- The characteristic features that match for both simple cubic and face-centered cubic are:
- They both have equal edge lengths.
- They both have angles of 90 degrees.
- They both belong to the cubic crystal system.

### Final Answer:
The correct characteristics that match with both simple cubic and face-centered cubic are:
- Both have equal edge lengths (a = b = c).
- Both have angles of 90 degrees (α = β = γ).
- Both belong to the cubic crystal system.