## Structure of Materials

### Close Packed Layer

Materials are different from simple molecules because bonding extends over a longer range and, because of this, we must consider the placement of atoms relative to many others.

Imagine that the atoms in some material can be represented by hard spheres like marbles. If you add as many marbles as you can to a container so that they form one layer, you'll have a packing scheme as shown at right. This is a close-packed layer.

In any close-packed layer, every atom is surrounded by six other atoms.

A material is 3-dimensional so we have to consider the layers above and below as well. The second layer of marbles would fit into the depressions of the first layer. They cover 1/2 of the holes in the first layer. Some of the atoms (or marbles) in the second layer are shown in blue.

### Hexagonal Close Packed

There are a couple of possibilities for the third layer.

You could put the third row of atoms in depressions of the second row so that they are directly over the first row.

Third row atoms are shown in red in the figure at right. Note that there are holes that go through all three layers.

Now extend this in 3-dimensions so that you have infinite layers stacked so that alternate layers have the same position:

...A-B-A-B-A-B-A-B...

### Cubic Close Packed

Another possibility is that the atoms in the third can sit so that they cover the other 1/2 of holes in the first layer.

The third layer is again shown in red at right. Note that all the holes between atoms in the third layer are over atoms in either the second or first layers. There are no holes that extend over all three layers.

The third layer is in a different position as the first. Extending this over 3-dimensions we have:

...A-B-C-A-B-C-A-B-C...

### Unit Cells

The close packed layers in any material extend for millions of atoms. It is frequently useful though to think about the smallest repeat unit. We call this the unit cell of the material.

To find the smallest repeat unit for the hexagonal close packing, we need to look at part of 3 layers. Take a diamond-shaped unit of 4 atoms in layer one. Add one atom in layer 2 that is sitting over a depression formed by 3 of the layer 1 atoms. Then add 4 atoms from layer 3 that have identical positions as layer one. This is the unit cell. Note that it isn't a cube. The angles in the diamond-shaped layers are 60 degrees and 120 degrees.

For the smallest repeat unit in cubic close packing, we need parts of 4 layers. One atom from the first layer sits below a triangle of 6 atoms in the second row. There is an inverted triangle of 6 atoms in the third row. The fourth row includes atoms in the same position as the first layer.

### Diamond Structure

The diamond structure is a very common form. This structure is based on the cubic close packed structure with 4 additional atoms (pictured as green balls) in holes within the structure.

The form of carbon in diamonds has this structure. It is also the structure of crystalline silicon. Note that each atom in the diamond material has 4 bonds to other atoms and these 4 bonds form a tetrahedral array.

### Other Packing Forms

Not all materials are close packed. A non-close packed array of atoms is pictured below. There is a greater amount of empty space within these layers than in the close packed arrays.

The second layer can either go directly above the first layer (cubic) or it can go into the holes of the first layer (body-centered cubic). The third layer goes directly above the first in either case.

The unit cell, that is the smallest repeat unit for each type is below. The cubic unit cell atoms from 2 layers and the body-centered cubic unit cell has atoms from 3 layers.

Professor Patricia Shapley, University of Illinois, 2012