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.