Parameters in trigonal structure are

Options

A. `alpha=beta=gamma ne90^(@)`
B. `alpha=beta=gamma=90^(@)`
C. `alphane beta ne gammane90^(@)`
D. `alpha=gamma=90^(@) beta gt 90^(@)`

Answer

To determine the parameters in a trigonal (or rhombohedral) structure, we can break down the information step by step.

### Step-by-Step Solution:

1. **Understanding the Trigonal Structure**:
- The trigonal structure is also referred to as a rhombohedral lattice. This means that it has specific geometric properties that distinguish it from other crystal systems.

**Hint**: Remember that the trigonal structure is one of the seven crystal systems and has unique characteristics.

2. **Lattice Parameters**:
- In a trigonal structure, there are three lattice parameters, which are the lengths of the sides of the unit cell. These sides are denoted as 'a', 'b', and 'c'.

**Hint**: Lattice parameters are essential for defining the dimensions of the unit cell in a crystal structure.

3. **Equality of Sides**:
- In the trigonal structure, all three sides (a, b, and c) are of equal length. Therefore, we can write:
\[ a = b = c \]

**Hint**: This equality of sides is a key feature of the trigonal structure.

4. **Angles Between the Sides**:
- The angles between the sides are denoted as alpha (α), beta (β), and gamma (γ). In the trigonal structure, these angles are also equal, but they are not equal to 90 degrees:
\[ \alpha = \beta = \gamma \neq 90^\circ \]

**Hint**: The angles being equal but not equal to 90 degrees is crucial in identifying the trigonal structure.

5. **Final Parameters Summary**:
- To summarize, the parameters in a trigonal structure can be defined as:
- Lattice parameters: \( a = b = c \)
- Angles: \( \alpha = \beta = \gamma \neq 90^\circ \)

**Hint**: Make sure to remember that all sides are equal and that the angles are equal but not right angles.

### Conclusion:
The parameters of a trigonal structure (or rhombohedral lattice) are characterized by equal side lengths and equal angles that are not 90 degrees. This unique arrangement defines the trigonal crystal system.