E106 Lecture Problem 174

1
E106 Lecture Problem - 174

• Nikhil Sonde
• 2/6/07

2
The Problem

• The energy necessary to generate a dislocation
  is proportional to the square of
• the length of the Burgers vector, b2. This
  means that the most stable (lowest
• energy) dislocations have the minimum length,
  b. For the bcc metal structure,
• calculate (relative to Eb111) the dislocation
  energies for Eb110 and Eb100.

3
What is important?

• The length of the Burgers vector is the distance
  between two lattice points in a given direction.

b1002 a2 b1102 2a2 b1112 0.75a2
111
Eb100 1.33Eb111 Eb110 2.66Eb111

100
110
4
Physical interpretation

• It takes less energy to form a dislocation in the
  111 direction
• Chapter 8.5 Slip systems
• Slip plane Plane with the highest packing
  density
• Slip direction Plane with the highest linear
  density
• For a BCC structure, there are many slip planes
  (110,211,321) but only one slip direction
  lt111gt