In this lesson we're going to continue talking about these two types of structures, the FCC and HCP, but we're going to visualize them slightly differently. We'll start out with our A row, and the spheres are all touching one another. And then what we do is we add the B row. And those are going to touch, and will develop a complete row of B that sits in the interstitial positions of the A. And now, on top of that, we're going to include the row that we're referring to as C. So now we have our ABC stacking. And what I'd like to do then, is to indicate the directions that tell us where the spheres are touching. So, I have those two sets of arrows. And now what I'm going to do, is to go back to the unit cube that we've been using in the past, and I'm indicating on the cube where those two arrows that are in the lower visual appear inside of the unit cell. And now, what I'll do is to place on top of that triangle, in the FCC structure, I'll place the positions of the spheres as indicated below. And so, now what we have is the ABCABC stacking. And it leads to the FCC structure. And you can see the alternative description that we have of stacking with the unit cell that ultimately develops. Now when we look at the HCP structure, we get again, our A row. And now we're going to put a B row. And now instead of putting a C row, this time we're putting another row, which is just above the A. And we're going to refer to this as the A row. So now we have ABA, and our structure then becomes the ABA hexagonal close-packed structure. When we consider the two sets of arrangements, that is the FCC, what we see first is, there is a direction that's indicated on this visual and that direction is telling us the direction of stacking. And what we have is a vector that we can refer to as a unit. So this is the unit that tells us the repeat distance in the FCC structure. Now when we look at the HCP structure, that vector that takes us from the first A to the second A is two-thirds of that which is in the first visual. So that distance between the repeat layers for the ABC are 1, and the AB sequence for HCP are two-thirds of that. So now what we can do is we can relate the HCP directly to the FCC. And by doing that, what we can do is, we can describe the c-axis of the hexagonal closed pack in terms of the magnitude of the direction with respect to the FCC. Remember that the FCC is along a direction of the body diagonal and so, therefore, it's going to be a0 onto the square root 3, but now it's two-thirds of that, since we're in the HCP structure. Now when we look at the a, the A is the in-plane distances between the spheres. And now when we go back on the right-hand side, this relates directly to the distances that we see in the FCC, which is one-half of Aa0 onto the square root of 2. And if we make that ratio, what we get is the C over A ratio of the square root of 8 over the square root of 3. What that means is, it tells us that for ideal spheres packed in the sequence ABAB, what we're getting is, a C over A ratio that represents the square root of 8 over the square root of 3. We refer to this, then, as ideal HCP packing. Now when we look at traditional metals what we see is, in this table, we see the ideal packing, which is the 1.633. And now what we can do, is we can make some comparisons of the ideal to actual metals that we see in practice. Cadmium and zinc, for example. If you look at the C over A ratio, that value is larger. Which means that there is a change in the spherical symmetry and it would suggest perhaps that the spheres are elongated in the C. As opposed to being in the A direction. On the other hand, when we look at the elements magnesium through barillium what we see is a reduction. And as a consequence of that, when we deviate from this ideal positioning, we're going to see that the structure is changing. And that's going to have an affect on ultimately the mechanical behavior of these materials. Thank you.