# 11. Dislocation basics

hello this is Jeremy Zimmerman and today I'm going to talk about one dimensional defects and crystals specifically

### dislocation

s so the reason we're talking about these again is crystals are never perfect and there are two types of one dimensional defects there are disinclination x' and these show up in liquid crystal materials and then the topic of today's discussion are### dislocation

s so we have to understand### dislocation

s because they're critical for understanding a lot of mechanical properties and how you get deformation of materials so how you get plastic decra mission of crystalline materials this also allows for relieving strain and it becomes important in things like epitaxial growth and and defects the harm semiconductors so the what a### dislocation

does is it locally breaks kind of the perfection of the translation vector and the### dislocation

is going to distort a large portion of the crystal and it always extends along a line this line typically curves around through the crystal and it either exit the Kirt exits the crystal at two points or it forms a loop there are two major types of### dislocation

s they're edge### dislocation

s and they're screw### dislocation

s and these represent the extremes of the type of### dislocation

s you can have you can also have things that are somewhere in between an edge miss group we call that a mixed### dislocation

so here I'm showing you an edge### dislocation

very far from the center of this you know out towards the edges and...the top and the bottom this crystal looks perfect but what we've done is we have inserted essentially a half layer of atoms into this portion of the crystal you can also see that on this image here where we've added this extra half half plane of atoms into the crystal so there is something called the

### dislocation

core and that is kind of the line that has that sees the maximum strain that's shown here in the blue in order to define the### dislocation

we use something called a burgers circuit so the first thing I'm going to do on this diagram is draw the### dislocation

core here in blue and then we're going to draw a burgers circuit so we're going to kind of circle the core with what we'll call a square loop and so I'm going to pick a starting point and I'm going to move in this case six lattice translation vectors to the left we can move six lattice translation vectors down six lattice translation vectors to the right and six lattice translations vectors back up to towards where we started and what we see is that because we encompassed this### dislocation

core we didn't start and end at the same location so the burgers vector is the vector that goes from the start of the red arrows to the end of the red arrows so we would draw that here as I've done in pink this is the burgers vector for an edge### dislocation

as shown here the burgers vector is perpendicular to the### dislocation

core so### dislocation

s alleviate shear stresses in the material so if...we look at the upper left here this material is strained so we've been applying forces like I'm showing in the red arrows here and this this material is is distorted away from its simple cubic normal self so it takes about an order of magnitude or many orders of magnitude less energy to break a single row of atoms for example along here the bonds on that single row of atoms as opposed to breaking an entire plane of bonds and then letting it reform so this one row of bonds breaks and then you get a little bit of relief of the shear forces here so we've relieved some of the shear forces and we kind of see an offset at the edge of this crystal if this progresses a little bit further what we see is here is if we have bonds have reformed here and we now have this extra plane of atoms inserted into the crystal here so this looks like our

### dislocation

if we continue to apply for shear force to this material this### dislocation

will continue to move so it moves over one more step here another step here and then finally it exits the crystal over here so this motion that I've been showing in this slide is called Glide now I want to talk about screw### dislocation

s so again the lattice is perfect very far from the### dislocation

or the core of this### dislocation

so if you look at the left or the right portions of the crystal or the front or the back it looks pretty much like a perfect crystal but in the middle something messy is going on so I want to you could think of this like a a...parking deck so if we were to be in our car up here at the top of this parking deck and we were to drive down here and we got back to this location we'd end up one unit translation vector deeper into the crystal than we started so if you were to keep driving down this you would eventually go around and around and around and you'd come up the bottom of the parking deck another way of thinking about this is that you have kind of layers of and you show like sheets of paper and you take those sheets of paper and you cut them halfway through and then you tape them back together but each paper is is taped to the one below it so it makes kind of a screw here I have redrawn this screw

### dislocation

and I've kind of flipped it over 90 degrees so we can look down the the### dislocation

core and we can draw the burger circuit for this### dislocation

as well so the first thing we're going to draw on this diagram is the### dislocation

core I'm then going to draw the burger circuit so I'm going to circumnavigate this core in a square loop again so I'm going to pick a starting point in this case I'm going to go pick a starting point and then go up by three left by one two three four five six down by six right by six and up by three and we can see that in this case the arrows again did not meet up and that's because we surrounded a### dislocation

core so the burgers vector is going to be kind of hard to see on this diagram but I'm going to draw it in pink again and...I'm going to drop from this start of the red arrows to the end of the red arrows just right here so this is a screw

### dislocation

and the screwed in a screw### dislocation

the burgers vector is parallel to the### dislocation

core and now I have a few things I'd like you to think about first I'm going to make sure you understand the definitions and symbols for burgers vectors and### dislocation

course and make sure you understand the difference between an edge and a screw### dislocation

I'm going to download the two vesta files of### dislocation

s and I'm going to play with them so I want you to make sure you can see where the### dislocation

is and understand how it distorts the surrounding lattice for an edge### dislocation

I mean I want you to identify the extra half plane of atoms and if you move far to the left or right of the### dislocation

core as I showed on slides three and four of this presentation and you assume that Christel becomes flat how are those two planes oriented relative to each other for the screw### dislocation

if we look at the orientation is drawn in slide 6 how is the section far to the left or far to the right of the screw### dislocation

how are those two parts of the crystal oriented to each other I called this a one dimensional defect but I inserted a half plane of atoms if it's plane of atoms why did we call it one dimension and there are two extremes to### dislocation

types edge and screw can also have mixed### dislocation

s and these have a partial Edge and...partial sphere character so what would the angle between the