0:04

We're going to describe in more detail what we mean by the Burgers vector,

Â and also what we mean by the concept of a slip plane.

Â First, let's go back and consider a perfect crystal.

Â When we have a perfect crystal, and we look at and go around the circuit that

Â we're referring to as a Burgers circuit, what we're doing here is to make a circuit

Â around beginning at a particular point, counting over a certain number,

Â coming down, going back to the left, and then going back up again.

Â When the crystal is perfect what happens is we start and

Â we end at exactly the same position.

Â Now when we add a extra half-plane of atoms from the top of our Structure.

Â Now what we have is when we begin at the start,

Â we move around in a clockwise fashion.

Â We count over a certain number of atom positions.

Â Down a certain number, back over to the left and then back up to the right again.

Â When we do that, we find that we have

Â the end position is not at the same part as the starting position.

Â So what we do then is we define this as our Burgers Vector.

Â The Burgers Vector connects the failure of the start and

Â end points as a result of the introduction of the half-plane of atoms.

Â These atoms are the adjacent atoms.

Â So this distance then represents the shortest distance

Â associated with that closure failure.

Â Again we take a look at our picture that we just went through,

Â where we have the Burgers Vector as a result of going around that circuit.

Â Now, what we can do is turn the picture a bit too, so

Â we can the three dimensional nature of the image that's up on the screen right now.

Â 1:59

And so here we are.

Â We've created a projection.

Â And now what we'll do is we can see the dislocation line.

Â That dislocation line winds up going into the depth of the crystal.

Â But another thing that becomes important is that line lies on a plane,

Â which is made up of the atoms that are moving as a consequence

Â of the sheer of the upper part of the crystal, with respect to the bottom part.

Â So, that line on the diagram, then, represents the trace of the plane.

Â And we're going to refer to that plane as the slip plane.

Â So we have our dislocation line, we have our slip plane and what we also see is

Â that the Burgers Vector is perpendicular to the line of the dislocation.

Â 3:00

Again here is our image of our crystal with an extra half plane of atoms.

Â So all along that dislocation line we are missing bonds

Â associated with the bottom portion of that added extra half plane.

Â What we can do is we can create an analogue between

Â the picture that we have up here on the screen,

Â along with the problem of the ripple of the rug on the floor.

Â 3:29

Let's say you've just moved in to a new apartment and

Â you put your rug down on a floor before you put all your furniture in.

Â What you find is that the rug is not exactly square with respect

Â with the corner.

Â Now what you could do is to try to slide the whole rug across the floor.

Â Now there's a bit of a problem, especially if you're by yourself.

Â What you have to do is to overcome the force associated

Â with the weight of the rug on to the floor and the friction that has to

Â be overcome as a result of pushing the rug around on the floor.

Â However, if you introduce a ripple in the rug which is indicated in the rug that

Â I've illustrated here.

Â What you can easily do is kick that ripple around so

Â what you can in fact do is to move the lower portion of the rug so

Â it becomes parallel with one of the walls that are forming your corner.

Â So this is very much similar to what happens with respect to the dislocations.

Â The dislocations then allow for easy motion

Â of the slip that occurs when we shear the top and

Â the bottom of the crystal with respect to one another.

Â We have another way that we can describe a dislocation.

Â We can do this by use of a flexible tube.

Â What we do is we take a tube that's hollow and what we can do is slice it and

Â we're slicing it with respect to A, E, F, and B.

Â And then if we take one side of the tube with respect to the other and push it so

Â we're pushing it normal to the z axis, parallel to the x axis.

Â What we will do is to create a displacement and

Â that displacement then is represented by the plane EDCF.

Â 5:25

So, that is our plane where we have our displacement.

Â In this particular model, that plane then represents the shear that has

Â occurred as a result of that force that I've applied and

Â the direction in which that body has moved with respect to

Â the applied shear then gives us the slip direction.

Â And we see that the slip direction is perpendicular and

Â we refer to this as the edge dislocation.

Â 6:01

Now when we take that same material and this way what we do is to again cut it so

Â we go from A to B to C to D and then what we do is to create a displacement and

Â this time the displacement is parallel to Z and what we then

Â are doing is describing something we refer to as a screw dislocation.

Â A screw dislocation Is where the displacement and

Â the direction of slip are parallel to one another,

Â unlike what we have on the left, where the edge dislocation and

Â the slip direction are perpendicular to one another.

Â So we've now been able to describe another type of dislocation.

Â This type of dislocation we refer to as a screw dislocation.

Â It gets its name by recognizing that if we start at position D and

Â we go all the way around that outer surface at the top of the figure,

Â we wind up at position E.

Â And position E is at a different level than is position D.

Â So consequently, we've had a displacement in the direction of the axis Z.

Â 7:23

Now what I'd like to do is to talk about the presence of

Â a dislocation line that lies inside of a crystal.

Â So I have a line here and the line is very specific.

Â I've drawn it so that at position A on one side of the crystal,

Â you see that the line is the result of adding an extra half plane of atoms.

Â Now when you look to the left side, what you see is,

Â when that line terminates at the surface, what I now see with respect to that

Â perpendicular surface is I've created a screw dislocation at that surface.

Â And the line that connects them is referred to as a mixed dislocation.

Â So, inside of a crystal, terminating at two surfaces,

Â what I have is a dislocation line which has a variety of characters to it.

Â First of all, on the A side the character of the dislocation is an edge.

Â We look at the B side where it terminates.

Â We find that the dislocation now is acting as a screw.

Â When we connect those with a line between A and

Â B that forms a dislocation line, which is actually a mixed dislocation.

Â We can describe this behavior as we go around the circuit,

Â starting at the edge, where we see the tangent vector.

Â And the tangent vector that we have with respect to the position a,

Â is perpendicular to the dislocation B.

Â 9:09

As we look along the line at the position where we have a mixed dislocation,

Â the Burgers vector and the tangent vector are at an angle,

Â which is not either 90 degrees or parallel.

Â So what we've then been able to do is to describe the behavior of the line,

Â and how a particular line in a dislocation can have different characters,

Â and can be screw, edge, or mixed.

Â It's also possible to have a dislocation that lies wholly inside of the crystal and

Â closes on itself and in that particular case, it's referred to as

Â a dislocation loop, and the character changes as you go around the loop.

Â Thank you.

Â