The number of space lattices possible for the crystalographic dimensions `alpha ne beta ne gamma`

Options

A. 1
B. 2
C. 3
D. 4

Answer

To solve the question regarding the number of space lattices possible for the crystallographic dimensions where α ≠ β ≠ γ, we can follow these steps:

### Step 1: Understand the Definitions
- **Crystallographic Dimensions**: These refer to the lengths of the edges of the unit cell (a, b, c) and the angles between them (α, β, γ).
- **Space Lattice**: A three-dimensional arrangement of points that represents the positions of the atoms in a crystal.

### Step 2: Identify the Crystal System
- When α ≠ β ≠ γ, the crystal system in question is the **triclinic system**. This is characterized by having no symmetry and all sides and angles being different.

### Step 3: Determine the Type of Unit Cell
- In the triclinic system, there is only one type of unit cell, which is the **primitive unit cell**. This means that the lattice points are located only at the corners of the unit cell.

### Step 4: Conclude the Number of Space Lattices
- Since the triclinic system has only one type of unit cell (primitive), the number of space lattices possible for the given conditions (α ≠ β ≠ γ) is **1**.

### Final Answer
The number of space lattices possible for the crystallographic dimensions α ≠ β ≠ γ is **1**.

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