In this screencast we're going to define
some crystal systems and then give an example of a
ceramic crystal structure. So there are
7 basic crystal systems
What these depend on
are what are known
as lattice constants and the lattice constants
are "a", "b", "c"
and in this case this is
"a", this is "b"
and this is "c". So they're these
lengths. In addition we
look at the inter axial
angles and we define these
as
alpha beta and gamma
and these are these angles
right here. Changing our lattice constants
and our inter axial
angles will change the
type of system. So here
we have what's known as a
tetragonal or tetragonal or however you want to pronounce it
and in here "a" equals
"b" but does not equal
"c". So this is an elongated
type of structure. However all the angles
are the same and equal 90 degrees
We compare that with our
cubic structure up here where
"a" equals "b" equals "c"
and alpha equals beta equals gamma
equals ninety degrees, and this should be
a gamma. So each system
can have more than one unit cell.
So for example a cubic system
can have three types of unit cells
simple, face centered cubic,
and body centered cubic. The
tetragonal system has two unit cells
If you look at all 7
basic crystal systems and add up
the number of unit cells within each one
what you find is you end up with
14 Bravais Standard
unit cells. And these can describe
all possible lattice networks
So we're going to look at a more complicated
structure and those are known
as ceramic. So these ceramic
crystal structures are identified
by the following constraints. First of all
they have to have out least two elements.
Second, if they are ionic
they consist of cations and anions.
The Crystal has to be
neutral and as we know
cations because they lose
an electron, or more than one, are less
than the anions and therefore the ratio of the radius
of the radius of the cation to that of the anion
has to be less than 1. And what this
ratio does is it describes the coordination number
which are the number of atoms
that one atom can touch. And they want to touch as many of
each other as they can. So we have
different types of ceramic
structures and the most basic one
is what's known as
the A-X structure.
So an example of that is
sodium chloride. There's one anion
for each cation
In addition we can have a system
such as Am
Xp such
that "M" and/or "P"
do not equal one. Thus an example of this would be something like
calcium fluoride. We also have
a system that is a little bit more complex
"Am" "Bn" "Xp".
And let's show an example of that
right here. This is what's known
as
the perovskite crystal structure
an example here has a barium
titanium O3. So first let's check
that it is neutral. So barium has a plus two,
titanium is plus four
and oxygen is minus 2
So that's 2 plus
4 plus 3 times negative
2 for the oxygen which equals 0.
So it is neutral. So
the structure for this is that
we have one oxygen here
on each face. We have a barium
on each corner and finally
we have one titanium in the middle
Let's make sure that this adds up
to the relationship of barium to titanium
to oxygen. If we look at one
oxygen on each face, each face has 1/2
an atom. There are 6 faces
so there are in our unit cell
3 atoms of oxygen.
Now we look at the barium. Each corner is 1/8
of an atom. There are eight corners
so there is one atom of
barium. And finally we have titanium
which is just one atom in the center
therefore we have barium, titanium
and thee atoms of
oxygen. So there are a number of different
ceramic crystal geometries. What determines
the type of geometry is first of all this ratio
of the cation to the anion, and that leads to
our coordination number which then
leads to the geometry. So for example
if you have a coordination number
of 4 then you have
one cation, for example,
in the middle and it's surrounded by
4 anions in a tetrahedral
type of geometry