OK so who wants to look at calcium fluorite?
If you're watching the video, I guess you do.
So let's draw a cube.
It's a cubic unit cell with cubic symmetry.
So we'll start with that.
Give it some perspective, some depth, here.
And there we go, all right.
So I'm trying out some new software here.
So here's calcium fluorite.
This is not calcium fluorite yet.
This is a box.
It's a cube.
So what we're going to do is, we're going
to position some anions here.
As I like to do.
And I usually find that's an easy way
to visualise the structure first.
So I'm putting anions in the corner positions,
OK, in the corner positions.
And then calcium fluorite is-- so this
is CaF2, calcium fluorite.
It's got a simple cubic arrangement of anions.
OK, so we need to draw the anions
in a simple cubic arrangement.
The trouble is, you can see that the ratio between cation
to anion is one to two.
So if we were just to proceed like this,
with a simple cubic lattice with eight corners,
and position a cation in the middle of that,
we'd have a one-to-one ratio.
We'd have one cation in the centre and one anion from
the eight corners, with 1/8 each.
So we can see, hopefully, that we
have to proceed a little bit differently with this.
And so what we do, the customary way
to approach this is to say, all right, well let's
actually consider a slightly larger unit cell.
Now I'm leaving the cube the same size.
But you'll, hopefully, appreciate
that what I'm going to do is, I'm
going to draw more atoms than we would
do for some of the other crystal structures.
So what I've done is I've just broken this down
into eight little subcubes.
OK, eight subcubes, that's not a formal term.
It's just what I like to call it, subcubes, that
make up the entire unit cell.
And then what we're going to do is,
we're going to position an anion at the corner of each
of these subcubes.
OK, so we've still got a simple cubic lattice of anions.
I'm actually not drawing the hidden atoms at this point, OK.
So I'll just write that in over here so
you can appreciate that-- hidden anions not drawn.
Because if you haven't noticed, I'm not a professional artist.
So it would become extremely messy if I tried to do that.
So I've just drawn the ones on the exposed faces.
But you can see that it's a simple cubic lattice.
Or I hope you can.
Now we need to position, then, the cations.
And these are going to go into the simple cubic sites.
But they can only fill half of them
because it has to be twice as many anions.
So, if there's eight little subcubes, that
means we have to have four subcubes
with occupied interstitial sites,
occupied sites, simple cubic sites.
And so we could pick, well we can't just
pick any four of them, actually.
Because the cations must be-- well they're cations.
They've got the same charge, and so they'll
space each other out spatially, as far apart as possible to
reduce the charge repulsion.
So cations must be spaced out as far as possible.
So for example, you wouldn't find
that just the eight subcubes at the top are occupied,
and the eight were empty.
That wouldn't make a lot of sense in 3D space,
in three dimensions.
Because they'd have like charges are
that are quite close together.
So if you occupied, say, this site here,
in the back top left, well maybe you
would occupy the front top right.
And that will be spaced apart as far as possible.
They wouldn't be immediately next to one another.
They'd be in the diagonal subcube.
And if you repeated that diagonal filling
of interstitial sites in three dimensions,
well that's in fact what we find in calcium fluorite,
as far as possible.
Out as far as-- that's what you're
going to write-- as possible.
OK so here we go.
Let's look at one of these subcubes.
And so what I'm going to do here is,
I'm actually going to, for this little subcube here only,
front bottom left, I'm going to actually draw it in.
And the reason that I'm going to do that
is just to make it a little bit more
obvious where these cations exist.
So what I'm going do now is, I am actually
going to draw in the anions.
Because these are the hidden ones now that
I didn't draw earlier there.
They're within this unit cell completely.
This is on that face, that left face, centre position.
This is the left bottom edge position here.
This is the bottom face centred position, OK.
This is the centre of the entire unit cell.
And so then, the interstitial site resides right in the very
centre of that cube, the very centre of that little subcube.
And I like to draw in the direction of contact,
often, with little yellow lines.
And you can see, then, that that cation is touching eight
nearest neighbour anions.
And the final little piece of the puzzle
is, well, if that's where this cation is--
and what I'm going to do here, is
I'm just going to kind of shade in this front face
here of that cube to show you that that has
an occupied interstitial site.
Well then this interstitial site over here in the top front
right would be occupied.
As would this in the back bottom right, and the top back left.
So they're alternating, always across the diagonal
in all three dimensions.
And those are the occupied interstitial sites,
occupied simple cubic sites.
And you can see, it's only four of them.
Only four of them are filled.
And that is, in fact, the calcium fluorite crystal
structure.
So now that you know where they reside,
I could draw these little dots in.
And, hopefully, you realise where that cation exists
in three dimensions, by my shading of the exposed faces
there.
All right well, I hope that helped
you to understand the calcium fluorite crystal structure.