| |||
| The face centered cubic (FCC) unit cell begins with a totally different layer, one that is
packed much more efficiently. This figure shows the basic layer that will be repeated throughout
the entire lattice. Let's think about what we are about to do. We want to place the second
layer in the indentations of the first layer. Notice that the indentations are too close to
one another for us to fill them all. In other words, if we were to place an atom in each
indentation, they would not all fit. Because of this, the second layer will only cover half of
the holes in the first layer. Reset Lattice |
| Notice that having placed the second layer on top of the first still leaves a lot of holes. You
can see all the way through them in this figure. There is no way that you could have
placed another atom (in this same layer) to cover even one of these holes because it simply does
not fit. The question then becomes, where do we place the third layer? There are two options,
both of which are equally efficient. We will show both of them, but will concentrate on only one. Reset Lattice |
| The first option places the third layer such that it eclipses the first one, that is, the ABA
pattern. This leads to a different unit cell: the Hexagonal Unit Cell, and this type of packing
is referred to as hexagonal closest packing (hcp). Although it may be difficult to see, demonstrate
to yourself that it has a coordination number of 12 by picking one atom in the center of a hexagon
and seeing that it touches 12 other atoms. Reset Lattice |
| The other option places the third layer in the indentations of the second layer (the holes that
were still clearly visible in the two-layer (AB) figure). This generates an ABC pattern. Reset Lattice |
| The fourth layer, eclipsing the first, creates the ABCA
pattern shown here. Since I realize that it is difficult to pin point the actual unit cell from
the lattice, let's cut
some of the atoms from the end of the lattice in order to facilitate this. This figure will allow
you to see the FCC unit cell. First, rotate the lattice straight up until you align the blue, green,
and pink atoms at the far left. One of the faces of the unit cell should be clearly visible. Now
slowly rotate the lattice diagonally to the right (NE) until you see another face. This face is part
of the same unit cell . Reset Lattice |
| To make it even easier, let's cut most of the atoms out of the lattice and just leave enough to
see the FCC unit cell. Rotate straight up until the two blue atoms are aligned north and south.
These are the only two atoms remaining from the original layer (A). Continue rotating and you
will see that you have only the 14 lattice points that form the unit cell. This figure clearly
shows the atoms from each layer that make up the FCC unit cell. Reset Lattice |
Return to Cubic Unit Cells