Question

The Burgers vector in a perfect dislocation represents

• A. Grain boundary direction
• B. Magnitude and direction of lattice distortion
• C. Crystal orientation
• D. Slip plane normal

Hint:

The elastic strain energy per unit length of a dislocation is proportional to the square of its Burgers vector (\( E \propto G b^2 \)). This explains why dislocations split into partial dislocations to minimize their energy.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks for the physical definition and significance of the Burgers vector (\( \vec{b} \)) associated with a perfect dislocation in a crystal lattice.

Step 2: Detailed Explanation:

• Definition of Burgers Vector: The Burgers vector (\( \vec{b} \)) is a fundamental vector that characterizes a dislocation.
It represents the magnitude and direction of the lattice distortion (or slip distance) associated with the dislocation line.

• Burgers Circuit Method: The Burgers vector is determined by constructing a closed loop (Burgers circuit) around the dislocation line in a real, distorted crystal, and comparing it to an identical loop made in a perfect, defect-free crystal.
The vector required to close the loop in the perfect crystal is the Burgers vector.

• Dislocation Types:
- In an

edge dislocation, the Burgers vector is perpendicular to the dislocation line (\( \vec{b} \perp \vec{t} \)).
- In a

screw dislocation, the Burgers vector is parallel to the dislocation line (\( \vec{b} \parallel \vec{t} \)).
- In a perfect (or unit) dislocation, the magnitude of the Burgers vector is equal to one repeat distance of the crystal lattice in that crystallographic direction.

• Analysis of Incorrect Options:
- It does not represent grain boundary direction (Option A), crystal orientation (Option C), or the normal to the slip plane (Option D, which is defined by the cross product of the dislocation line vector and the Burgers vector).


Step 3: Final Answer:
Therefore, the Burgers vector represents the magnitude and direction of lattice distortion, matching Option (B).