Coordination Number, Packing Factor And Slip Systems In Bcc, Fcc And Hcp Structures
Hello, this is Andy from the engineers Academy and today, we're going to revisit the crystalline structures of body center cubic and face Center cubic we're also going to introduce a third crystalline structure called hexagonal close-packed. So what we have on the screen here is the information sheet for this learning outcome. And pictured we see our body center or BCC, our face center FCC and our hexagonal close-packed, HCP structures, directly underneath each of those diagrams. We've got some. Additional information about each of those repeating elements. So let's begin on the left-hand side with our body centered, cubic structure. And the first things that we're going to discuss are coordination number and packing factor.
So we see from the information that BCC has a coordination number of 8. And what that literally means is if we were to take our central atom here, and we were to work out how many other atoms are in direct contact with that atom. Then that number would be 8 I want you to. Imagine that each of the atoms on the corner move towards the central atom. And what you would notice is that all of those 8 atoms on the corner would be in contact with the central atom. Hence, a coordination number of 8 now, packing factor refers to how much atom versus how much free space is within that unit cell.
So imagine once again, that all of those atoms on the corners, move towards the central atom. And what we're left with is a unit cube within that unit cube naught point, six eight or sixty. Eight percent will be atom. And the remaining thirty-two percent will be free space. So the packing factor is a ratio of atom to free space, let's move on and repeat that for the face centered cubic structure and the atom that we're going to refer to when looking at coordination number is the atom on the top surface now, you're going to need to use a little of visualization here.
Because once again, we need to imagine all the atoms moving towards that central atom. And in doing so they're going. To come into contact with the atom. Now we can immediately see that there's going to be four atoms in contact without central atom. One, two, three, four.
But if we also refer to the layer below, we can see that there's going to be another one. Two three on this central face is not pictured to simplify the diagram and fall on the back face. So that's, an additional four atoms in contact with that central atom.
But what we also need to consider is the subsequent layer or the layer that would be above this. Unit cell, and what we would have is another one, two, three, four atoms in contact with that central atom, because the next layer will be a repeat of that central layer. Therefore, we have four plus four, plus four atoms in contact given us a coordination number of twelve. Now once again, for packing factor, we need to imagine all of those atoms in that unit cube being drawn in together.
And when they're all drawn in together to form that unit what we would have in this case is 74% atom and only 26% free. Space so the face centered cubic is more densely packed or more closely packed than the body center cubic structure. And in fact, a body centered cubic structure, isn't, truly closely packed as we'll see in a moment, but a face centered cubic structure is closely packed or close packed so let's move on to our hexagonal close-packed structure. And what we immediately notice is that we have the same coordination number as we had with face centered, cubic coordination numbers, 12, but let's just check that. By taking the central atom on the top face. Now what we can immediately see is that if all of those atoms were drawn together that atom on the top face would be in contact with one two, three, four, five, six atoms.
But what we would also notice is that it would be in contact with a further one, two, three on the layer below now. Once again, we need to visualize these three repeating as part of the next cell. So our central atom would be in contact with another one. Two three as a result, three plus six, plus. Three gives us our coordination number of 12 for the hexagonal close-packed structure.
Now, although we don't have a unit cube here, we have a hexagonal structure. The packing factor is determined in exactly the same one. So imagine all of those atoms being drawn closely together within that unit.
And what we would be left with is 26% free space and 74% atom. So it's packed in exactly the same way as our face Center cubic structure, I'll just clear some space on each of these diagrams to explain this. Point so if we inspect our HCP structure a little more closely on the top surface, we see one atom, surrounded by four at the corners in the same plane.
And if we compare that to our FCC structure, we see exactly the same. We see a central atom, surrounded by four at the corners. And in actual fact, FCC and HCP are almost identical, except for something called the stacking sequence. So the difference here lies in what happens on that second layer, we know in face Center cubic this atom.
Here is going to. Sit on the same face as these two atoms here, this atom here is going to sit on the same face as this atom and this atom. But when we close up our hexagonal close-packed structure, we don't see the same happening in our second layer. So in actual fact, the repeating unit in a hexagonal close-packed structure is a hexagon, whereas in face and body center cubic is a cubic structure. So let's move on now and look at slip systems, which are made up of slip planes and slip directions.
So in an earlier, Tutorial we talked about how the things that make a material soft malleable and ductile is how easily the layers slide over each other. And although that was a simplistic view, the principle is the same when we look at slip planes and slip directions as a starting point let's, look at our face, Center cubic material and face Center cubic materials have four slip lines, and I'm going to draw the first of these on for you, and then we'll discuss it. So the first slip line runs from corner to corner and.
Then in to the back corner of the cube. So in effect, the slip plane is at a diagonal to the cube itself. Now the easiest way to think about slip planes is it's where the atoms are most closely packed, or it's, where the atoms are going to have the least resistance to motion. If you like all the atoms on that surface are sitting in exactly the same plane. So it's easy for them to slide across the next layer, I'm going to throw a second slip plane on this cube.
But please note there are an additional. Two which I won't draw wrong because I don't want the diagram to become too crowded. So we have a second slip line, which runs from corner to corner and then into the far back corner here, again, producing a diagonal plane. So face Center cubic has four slip planes, let's just go back to our first slip plane, and now we're going to discuss slip directions. So we've already established that face Center cubic has four slip planes.
And each of those four slip planes can move in three directions, because we. Have three slip directions. Now, the directions that this can move in is it can move in this direction here it can move in this direction here, or it can move in this direction here.
So if each of our four planes can move in three directions that gives us a total of twelve separate slip systems. All we need to do is multiply the number of planes by the number of directions, each of those planes can move in. And that gives us the number of slip systems. It is worth mentioning that in order to be soft.
Malleable and ductile by definition, a material requires five slip planes or more. So we can see that face Center cubic is a soft malleable and ductile material. So let's move on to body center cubic. So the first thing to point out about body center cubic is that it's, not too closely packed, not the same senses, face Center cubic and HCP structures. And the reason being is if we were to draw each of these atoms to the center once again, then all of those atoms would touch the central atom.
But none of.Then would touch each other. So what we don't have is any planes where these atoms are very tightly packed. Whereas we do see that in the face Center cubic material that said, body center, cubic materials actually have a total of 18 slip planes. So there are twelve slip planes, which can move in two directions. 12 times 2 is 24 and there's additional six slip planes, which can move in four directions.
Six times four is also 24. Adding those together gives us 48 slip systems. So you would on first.
Inspection expect BCC to be soft malleable and ductile, but because it isn't closely packed, those slip planes actually have a tendency to interfere with each other. They prevent each other from slipping. Now, when we looked at a more simplified model, we talked about interlocking of the layers, and it's, a very similar principle here, the layers interlock, and they prevent each other from moving, even though we have the 48 slip planes.
The key thing to remember is that this is because BCC is not a closely. Packed structure, okay. So let's move on. And look at our final example, which is hexagonal close-packed.
And we notice there that HCP structures only have one slip plane, which is capable of moving in three directions, giving it three slip systems. So the slip plane in hexagonal close-packed is this plane here we know that if we draw all of those atoms into the center we're going to have a very densely packed layer, and the directions that this can move in is this direction, this direction or this. Direction here now you may be wondering why this bottom surface here, isn't also a slip plane. And the reason is because it's in the same plane as out surface. So we only have one slip plane because the two planes are reminded you may also be wondering why this isn't a slip direction and this isn't the slip direction and this isn't a slip direction. And again, the reasoning is very similar.
If we call this direction, one, then this direction here is also direction. Once they're in the same direction as. Each other and by the same reasoning, if we call this direction, turn then this here is also direction too. So we only have one slip plane, and we only have three slip directions in HCP structures, because we don't have the required five slip systems in HCP structures. They tend to be very hard non-malleable and non-ductile. So just a quick summary, then we have faced Center cubic materials with twelve slip systems because that's closely packed.
We end up with a very soft malleable and ductile material. Next we have body center cubic it isn't closely packed. So what we end up with is a relatively hard non-malleable, non-ductile material, but the hardest most non-malleable and non-ductile material or structure is the hexagonal close-packed, because we only have three slip systems. The likelihood of layers slipping past each other in the HCP structure is greatly reduced.