The Burgers Vector and Slip Systems

Characteristics of Dislocations

Dislocations are the carriers of plasticity — when you plastically deform a crystalline material, you are activating the motion of dislocations, which then "slip" through the crystal. While in this introductory class, we want to understand why dislocations are important and how we use them in engineering, actual materials engineers need to be able to describe quantify the stress/strain due to a dislocation and the direction it will move.

1. The Burgers Vector essentially tells you the magnitude and direction of the lattice distortion due to the presence of a dislocation.
2. Slip Systems tell us which directions the dislocations will move. These are the crystallographic directions (Section 5.7) and planes (Section 5.8) we learned about earlier.

The Burgers Vector

Let's first derive the Burgers vector and then consider how we'll use it. Start by looking at a simple 2D array of atoms (Figure 12.5.1) and try to "quantify" the distortion due to the edge dislocation. First, let's think about what the assembly of atoms would look like without the dislocation: the three atoms belonging to the "extra half-plane" would no longer be there, recovering a perfect crystal. So, it is the extra half-plane that is yielding the distortion. Let's measure its influence by constructing the so-called Burgers Circuit:

1. Identify the core of the dislocation (the region where the most distortion occurs, or the area of undercoordinated atoms.
2. Identify an atom (up and to the left is conventional) that does not seem to be influenced by the dislocation. That is, it seems to be in a perfect crystalline coordination.
3. Start drawing a circuit around the dislocation core by jumping from one atomic site to another, making equal numbers of jumps in antiparallel directions.
4. When you've completed the jumps, draw a vector between the starting and ending point of the circuit. This is your Burgers Vector

Lets just show an example, in Figure 12.5.1. 1. The dislocation core is the open space in the middle of the atoms, indicated with a $\bot$. 2. I start at the blue atom up and to the left of the dislocation core and take 3 steps to the right. 3. I take 3 steps down. 4. I take 3 steps to the left (the same number as the steps to the right). 5. I take 3 steps up (the same number as down). 6. I do not return to the origin, so I draw a vector from the end point to the starting point. This is my Burgers Vector, b.

A few observations:

1. If the magnitude of the Burgers vector is 0, then there's no dislocation in the circuit! (Or, you had two dislocations in the circuit... be careful).
2. The Burgers vector points perpendicular to the dislocation core and along the direction the dislocation will slip.
3. The Burgers vector will tell us about the degree of strain that exists in the crystal, which is related to its energy.

Slip Systems

In the simulation of NetLogo model 12.4.1 you saw that the dislocation moved in a particular direction, specifically, a close-packed direction. Slip Systems tell us which directions the dislocations will move. These are the crystallographic directions (Section 5.7) and planes (Section 5.8) we learned about earlier.