So this crystal structure we can see at first glance,
it looks like it's based on some kind of hexagonal symmetry.
Let's take a closer look and make sure
that we understand it.
So the first thing you should recognise about this is that
this arrangement of atoms is a close-packed arrangement in one
plane, or in two dimensions.
So this area, if these were just circles,
these would be packed as closely as they possibly can.
So this is a close-packed plane that I'm
running my hand over right now.
That's a close-packed plane.
Now if I turn it 90 degrees, we can see along this way
is a close-packed plane.
There's another close-packed plane in a different position.
And here's another close-packed plane on the bottom,
in another position.
So we can see, in fact, that if we look at these planes at 90
degrees to the planes, we can see the close-packed planes are
stacked in an ABA arrangement, or the positions of atoms
in this top plane are actually in the same position
as the ones in the bottom if you look straight down.
And that's in this direction right here.
So if we see close-packed planes stacked up
in an ABA arrangement, we know right off the bat it's HCP.
Now, if we just look at a close-packed plane
like this one right here-- these are close-packed atoms
in two dimensions.
And then we see another close-packed plane.
Again, this is a close-packed arrangement--
these atoms are close-packed-- and we position them
on top of each other, any time we
do that, we actually create interstitial sites between them
and we create two different types.
We create octahedral, where the interstitial site is actually
touching one, two, three, four, five, six atoms.
And we also create tetrahedral, where the interstitial site
is touching one, two, three, and in the back there, four.
So this interstitial site right here is tetrahedral.
And that octahedral.
And in fact, if you look normal to the surface
of a close-packed plane, that is,
we look this way, if you can see right through-- so
this interstitial site right here
and this one and this one-- that's
an octahedral interstitial site.
And if you can see the plane immediately below or see
the atom immediately below, that's
a tetrahedral interstitial site.
And those alternate-- octahedral, tetrahedral,
octahedral.
This crystal structure here, at first glance,
take a look at it.
Can see a cubic arrangement-- atoms at the corners.
And if you look straight on to any one of the faces,
you'll see that there's an atom right
in the middle of the face.
So this is in fact FCC, or face-centered cubic.
And you can see as well, cut away,
if there was another atom here and here,
this little spot right here, in fact, the place where
this flag is indicated, is an octahedral interstitial site--
one, two, three, four, plus one, two more--
six atoms touching that.
Course, there's also an octahedral interstitial site
in the very centre of this structure-- one, two, three,
four atoms, five, six.
So in the very centre there is an octahedral interstitial
site.
And there are also tetrahedrals.
If you look at one, two, three, four, between those atoms
right there is a tetrahedral interstitial site.
With this model, we can see again,
the stacking of close-packed planes.
These six atoms belong to a close-packed plane.
They're arranged in a close-packed arrangement
in two dimensions, as are the plane of atoms
on this surface of the table and the one
just above it, these eight atoms right there.
Now, if we stack up the third layer of atoms,
you'll see we actually have two different positions that we
could put the atoms into, either these spots right here
or we could put them into these spots right here.
You can't occupy them both at the same time.
The atoms don't fit into those two spots at the same time.
But you can fit them in either of these.
So we can form this structure here or this structure here.
Again, that's this one or this one.
And with our knowledge of the stacking
of close-packed planes, we can actually
determine which structure is which.
Again, if we look perpendicular to these close-packed planes
and you see that this plane here on the top and the plane
on the bottom are directly over each other,
that's an ABA rearrangement of close-packed planes.
And this is HCP.
Now if we move to this interstitial site right here,
you can see these atoms are no longer directly
over the top of the bottom ones.
And this is a FCC arrangement, A, B, C positions.
There's three different positions
normal to the close-packed plane.
Another interesting thing you can see about FCC--
this is again made FCC again-- if we
look normal to this, this top plane
is not in the same position as the bottom.
We can also see we've made a close-packed plane that we
can face, see, this way which is not parallel
to this close-packed plane.
We've stacked up close-packed planes in this direction.
But we've also created a non-parallel close-packed
plane.
Anytime you see non-parallel close-packed planes,
you know it cannot be HCP.
In HCP, the only close-packed planes
are the basal planes stacked up one on top of each other.
So this is FCC.
So what's this funny looking structure here?
To what crystal structure to these atoms belong?
Well, you may be tempted at first to say, well, look,
there's a plane.
There's another one.
And this atom belongs to another plane up at the top.
And it looks like it should be A, B, A, because this atom here
resides directly over the top of this atom right here.
So you may be inclined at first glance to think this is HCP.
But remember, these planes are not close-packed.
That arrangement right there, this square arrangement,
is not close-packed.
In fact, this is the face, the conventional face,
of an FCC unit cell, or one 1, 0, 0 planes.
These are close-packed directions,
but this is not a close-packed plane.
So the trick to this structure is identifying the close-packed
plane which is here and here and here and here,
realising that you have now close-packed planes that are
not parallel to each other.
This is FCC.
It cannot be HCP.
It's FCC.
And in fact, these four non-parallel planes all
belong to the 1, 1, 1 family of planes
and they're in fact unique 1, 1, 1 planes.
Here's another funny little structure.
We've got some planes, appear to be
stacked on top of each other.
And at first glance, as before you may think,
this is an arrangement of A, B, A.
But we can only use that approach
of stacking sequence when we're referring
to close-packed planes.
These atoms are not part of a close-packed plane.
Again, they're part of the faces of the FCC unit cell,
or the 1, 0, 0 family of planes, which is not close-packed.
So we can't look at the stacking of these planes
to determine if it is FCC or HCP.
But once we've identified that this is actually
one of the 1, 0, 0 or faces of the unit cell,
it becomes a little bit more clear that this is in fact FCC.
This is one face.
If we turn it this way, we're looking at a portion
of the structure here.
The other face, if you imagine you remove these two atoms,
you would have another FCC face.
At 90 degrees to that, along the back,
we've got another traditional FCC face.
And here, if we remove these two atoms,
you'd see the conventional 1, 0, 0 type face of this unit cell.
So this structure is FCC.
Another way to look at this is to realise that you've got
close-packed directions that are crossing each other at 90
degrees.
And if you think through the structures that we've covered,
FCC and HCP and BCC, in BCC, the close-packed directions
cross across the cube diagonals, or the 1, 1, 1 directions.
And those are not crossing at 90 degrees.
In HCP, the close-packed directions cross at 60 degrees.
But along the face diagonals of FCC,
the close-packed directions do in fact cross at 90 degrees.
So once you see the close-packed directions
crossing at 90 degrees, you're fairly certain that it's FCC.
The only exception, of course, I suppose could be simple cubic.
Simple cubic would have close-packed directions
at 90 degrees.
But it will be fairly easy to identify
that if you saw the planes stacked one
on top of each other.
It would be almost as if you took this midpoint out
and squished these two down.
That would be simple cubic.
If we look at this arrangement here,
again, the directions are crossing
at 90 degree-- the close-packed directions are
crossing at 90 degrees.
This is one of the 1, 0, 0 faces of FCC or it could be.
And in fact if we stack the atoms out this way,
it's the exact same structure as we saw with this little model
in one of the other clips.
So by stacking these up, we formed an FCC structure.
And I just wanted to show you what the simple cubic structure
would look like.
If you stacked these directly on top of each other,
you'd see a simple cubic arrangement.
Again, the close-packed directions
are still at 90 degrees.
But it's fairly easy to identify that the structure is
simple cubic.
This is a tetrahedral interstitial site, so named
because it forms a four-sided solid.
So the solid that it actually forms
looks like this little solid that I have here
that's stuck to the table.
But this is a four-sided solid.
And then right in the very centre of that is
the tetrahedral interstitial site.
And this is a tetrahedral solid.
So here we have six atoms forming an octahedral site
at their centre.
So the octahedral site has a coordination number of six.
At the centre of these six atoms is a little space that you
could fit another atom.
And this is the octahedral interstitial site.
It's named octahedral not because it
has eight atoms touching it, but because it
forms an eight-sided solid.
So I've just made that little solid right here.
If you imagine a face across each of these triangles,
you'd have an eight-sided solid-- one, two, three, four.
So four on this side and then four--
I just broke it-- four on this side.
So this is an octahedral interstitial site,
right in the centre, right there where the tip of my finger is.
And that's the same space that is in the centre of this
interstitial site.