Which of the following sets of axial angles and axial lengths represent maximum number in Bravais lattices?

Options

A. `alpha = beta = gamma = 90° and a = b ne c`
B. `alpha = beta = gamma = 90° and a ne b ne c`
C. `alpha = beta = gamma ne 90° and a = b = c`
D. `alpha = beta = gamma = 90° and a = b = c`

Answer

To solve the question regarding which set of axial angles and axial lengths represents the maximum number in Bravais lattices, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Bravais Lattices**:
Bravais lattices are the distinct lattice structures that can be formed in three-dimensional space. There are 14 types of Bravais lattices categorized into seven crystal systems.

2. **Identify Axial Lengths and Angles**:
The axial lengths refer to the lengths of the unit cell edges (a, b, c), and the axial angles refer to the angles between these edges (α, β, γ).

3. **Orthorhombic Crystal System**:
In the orthorhombic crystal system:
- The lengths of the axes are not equal: \( a \neq b \neq c \).
- The angles between the axes are all 90 degrees: \( \alpha = \beta = \gamma = 90^\circ \).

4. **Determine the Maximum Number of Lattices**:
The orthorhombic system has four types of Bravais lattices:
- Primitive (P)
- Body-centered (I)
- Face-centered (F)
- Base-centered (C)

5. **Conclusion**:
Since the question asks for the set of axial angles and lengths that represent the maximum number in Bravais lattices, the answer is the orthorhombic system, which has the properties of \( a \neq b \neq c \) and \( \alpha = \beta = \gamma = 90^\circ \).

### Final Answer:
The set of axial angles and axial lengths that represent the maximum number in Bravais lattices is the orthorhombic system.

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