In a trigonal crystal

Options

A. `a = b = c, alpha = beta = gamma != 90^@`
B. `a = b != c, alpha = beta = gamma = 90^@`
C. `a != b != c, alpha = beta = gamma = 90^@`
D. `a = b != c, alpha = beta = 90^@, gamma = 120^@`

Answer

To solve the problem regarding the trigonal crystal system, we need to understand the parameters that define its structure. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Parameters of a Trigonal Crystal System
In crystallography, a trigonal crystal system is defined by three edge lengths (a, b, c) and three angles (α, β, γ).

### Step 2: Identify Edge Lengths
For a trigonal crystal system:
- The edge lengths are defined as follows:
- \( a = b \) (the lengths of two edges are equal)
- \( c \) is different from \( a \) and \( b \) (the third edge length is different)

### Step 3: Identify Angles
The angles between the edges in a trigonal system are defined as:
- \( \alpha \) (angle between b and c)
- \( \beta \) (angle between c and a)
- \( \gamma \) (angle between a and b)

For the trigonal system:
- \( \alpha = \beta \) (the angles between the edges are equal)
- \( \gamma = 90^\circ \) (the angle between the other two edges is 90 degrees)

### Step 4: Summarize the Characteristics
From the above points, we can summarize the characteristics of a trigonal crystal system:
- Edge lengths: \( a = b \neq c \)
- Angles: \( \alpha = \beta \) and \( \gamma = 90^\circ \)

### Step 5: Conclusion
Based on the definitions and characteristics of a trigonal crystal system, we can conclude that the correct option matches the conditions of edge lengths and angles as described.