We're going to describe in more detail what we mean by the Burgers vector, and also what we mean by the concept of a slip plane. First, let's go back and consider a perfect crystal. When we have a perfect crystal, and we look at and go around the circuit that we're referring to as a Burgers circuit, what we're doing here is to make a circuit around beginning at a particular point, counting over a certain number, coming down, going back to the left, and then going back up again. When the crystal is perfect what happens is we start and we end at exactly the same position. Now when we add a extra half-plane of atoms from the top of our Structure. Now what we have is when we begin at the start, we move around in a clockwise fashion. We count over a certain number of atom positions. Down a certain number, back over to the left and then back up to the right again. When we do that, we find that we have the end position is not at the same part as the starting position. So what we do then is we define this as our Burgers Vector. The Burgers Vector connects the failure of the start and end points as a result of the introduction of the half-plane of atoms. These atoms are the adjacent atoms. So this distance then represents the shortest distance associated with that closure failure. Again we take a look at our picture that we just went through, where we have the Burgers Vector as a result of going around that circuit. Now, what we can do is turn the picture a bit too, so we can the three dimensional nature of the image that's up on the screen right now. And so here we are. We've created a projection. And now what we'll do is we can see the dislocation line. That dislocation line winds up going into the depth of the crystal. But another thing that becomes important is that line lies on a plane, which is made up of the atoms that are moving as a consequence of the sheer of the upper part of the crystal, with respect to the bottom part. So, that line on the diagram, then, represents the trace of the plane. And we're going to refer to that plane as the slip plane. So we have our dislocation line, we have our slip plane and what we also see is that the Burgers Vector is perpendicular to the line of the dislocation. Again here is our image of our crystal with an extra half plane of atoms. So all along that dislocation line we are missing bonds associated with the bottom portion of that added extra half plane. What we can do is we can create an analogue between the picture that we have up here on the screen, along with the problem of the ripple of the rug on the floor. Let's say you've just moved in to a new apartment and you put your rug down on a floor before you put all your furniture in. What you find is that the rug is not exactly square with respect with the corner. Now what you could do is to try to slide the whole rug across the floor. Now there's a bit of a problem, especially if you're by yourself. What you have to do is to overcome the force associated with the weight of the rug on to the floor and the friction that has to be overcome as a result of pushing the rug around on the floor. However, if you introduce a ripple in the rug which is indicated in the rug that I've illustrated here. What you can easily do is kick that ripple around so what you can in fact do is to move the lower portion of the rug so it becomes parallel with one of the walls that are forming your corner. So this is very much similar to what happens with respect to the dislocations. The dislocations then allow for easy motion of the slip that occurs when we shear the top and the bottom of the crystal with respect to one another. We have another way that we can describe a dislocation. We can do this by use of a flexible tube. What we do is we take a tube that's hollow and what we can do is slice it and we're slicing it with respect to A, E, F, and B. And then if we take one side of the tube with respect to the other and push it so we're pushing it normal to the z axis, parallel to the x axis. What we will do is to create a displacement and that displacement then is represented by the plane EDCF. So, that is our plane where we have our displacement. In this particular model, that plane then represents the shear that has occurred as a result of that force that I've applied and the direction in which that body has moved with respect to the applied shear then gives us the slip direction. And we see that the slip direction is perpendicular and we refer to this as the edge dislocation. Now when we take that same material and this way what we do is to again cut it so we go from A to B to C to D and then what we do is to create a displacement and this time the displacement is parallel to Z and what we then are doing is describing something we refer to as a screw dislocation. A screw dislocation Is where the displacement and the direction of slip are parallel to one another, unlike what we have on the left, where the edge dislocation and the slip direction are perpendicular to one another. So we've now been able to describe another type of dislocation. This type of dislocation we refer to as a screw dislocation. It gets its name by recognizing that if we start at position D and we go all the way around that outer surface at the top of the figure, we wind up at position E. And position E is at a different level than is position D. So consequently, we've had a displacement in the direction of the axis Z. Now what I'd like to do is to talk about the presence of a dislocation line that lies inside of a crystal. So I have a line here and the line is very specific. I've drawn it so that at position A on one side of the crystal, you see that the line is the result of adding an extra half plane of atoms. Now when you look to the left side, what you see is, when that line terminates at the surface, what I now see with respect to that perpendicular surface is I've created a screw dislocation at that surface. And the line that connects them is referred to as a mixed dislocation. So, inside of a crystal, terminating at two surfaces, what I have is a dislocation line which has a variety of characters to it. First of all, on the A side the character of the dislocation is an edge. We look at the B side where it terminates. We find that the dislocation now is acting as a screw. When we connect those with a line between A and B that forms a dislocation line, which is actually a mixed dislocation. We can describe this behavior as we go around the circuit, starting at the edge, where we see the tangent vector. And the tangent vector that we have with respect to the position a, is perpendicular to the dislocation B. As we look at the screw side of the face, what we find is that the tangent factor to the line is parallel to the burgers vector B. As we look along the line at the position where we have a mixed dislocation, the Burgers vector and the tangent vector are at an angle, which is not either 90 degrees or parallel. So what we've then been able to do is to describe the behavior of the line, and how a particular line in a dislocation can have different characters, and can be screw, edge, or mixed. It's also possible to have a dislocation that lies wholly inside of the crystal and closes on itself and in that particular case, it's referred to as a dislocation loop, and the character changes as you go around the loop. Thank you.