For a cubic crystal structure which one of the following relations indicating the cell characterstic is correct?

Options

A. `a != b != c` and `alpha != beta` and `gamma != 90^(@)`
B. `a != b != c` and `alpha != beta = gamma = 90^(@)`
C. `a = b =c` and `alpha != beta != gamma = 90^(@)`
D. `a = b=c` and `alpha = beta = gamma = 90^(@)`

Answer

To solve the question regarding the correct relation indicating the cell characteristics of a cubic crystal structure, we will follow these steps:

### Step 1: Understand the cubic crystal structure
A cubic crystal structure is defined by its unit cell, which is a cube. In a cubic structure, the lengths of the edges of the cube are equal.

### Step 2: Identify the parameters of the cubic cell
For a cubic crystal structure, the following characteristics hold true:
- The lengths of the edges are equal: \( A = B = C \)
- The angles between the edges are all equal to 90 degrees: \( \alpha = \beta = \gamma = 90^\circ \)

### Step 3: Analyze the options provided
Given the characteristics of the cubic structure, we need to check which of the options provided reflects these properties correctly.

### Step 4: Determine the correct relation
Since we established that for a cubic crystal structure:
- \( A = B = C \)
- \( \alpha = \beta = \gamma = 90^\circ \)

The correct relation indicating the cell characteristics will be the one that states these equalities.

### Conclusion
Based on the analysis, the correct option indicating the cell characteristics for a cubic crystal structure is the one that states \( A = B = C \) and \( \alpha = \beta = \gamma = 90^\circ \).

---