Dr. Michael Katz - Porous Materials

Close Packed Structures

Let's take a step back from bonding. Think about an atom as just a sphere. Don't worry about how a sphere would interact with another sphere.

If it helps, imagine that you work in the packing plant of a baseball manufacturing store. The more baseballs you can pack in a box, the cheaper it is to ship the box. In this analogy, the baseball is an atom, the box is a crystal, and the shipping cost is the energy of the system.

Let's start by trying to pack one layer of atoms (baseballs) in a crystal (a box). What is the most efficient (lowest energy) way of packing the atoms in one layer? Before you move on, stop and think about this question. Let's call this layer, Layer A.

Layer A is a close packed array of atoms. It should look like a hexagon array of atoms.

With your first layer complete, we want to start adding a second layer (Layer B). Layer B will have the same atom arrangement as Layer A. However, what is the best way of aligning Layer B on top of Layer A? The goal is to minimize the energy by maximizing the packing (density) of the layers? Stop and think about this before you go on.

To maximize the packing of the atoms (density), Layer B should sit in the divots created in Layer A. You will notice that there is still unoccupied space between Layer A and Layer B, but this is the best way to have the closest packing (close packed layers) and thus maximize density and minimize energy. What if you had to add a third layer? How would you organize it? Take a minute to think about it.

There are two answers to the last question. You can pack the third layer such that it looks just like Layer A, or you can pack the third layer such that it looks like a new layer (Layer C). In the former, we create an ABABAB set of layers that form a Hexagonal Close Packed structure (HCP). In the latter, we create an ABCABC set of layers that form a Cubic Close Packed structure (CCP). The term Hexagonal and Cubic come from the type of unit cell that is formed from this packing.

Let's imagine that the atoms that we packed in either an HCP or CCP array are anions. This means that we must pack some cations into the unit cell. Cations are often smaller than anions. Where would the cations go? What coordination geometry would the cations be in? Take some time to think about this.

Returning to our analogy, your boss comes down and wants to add golf balls to the box because there should be space to send golf balls and baseballs without having to use a larger box. Where do you put the golf balls?

If you recall, there is some space between neighbouring layers that is unoccupied. These interstitial positions are ideal for cations. There are tetrahedral sites and octahedral sites. Some of the tetrahedral sites point up. Some of the tetrahedral sites point down. Not all the sites have to be filled. Depending on the charges of the anions and cations, the size of the cations, and the coordination chemistry of the cations, the structure may prefer to utilize some of the interstitial sites and not the others. It is worth noting that sometimes we get reverse structures where the cation is bigger and forms the close packed array and the anions are smaller and sit in the interstitial positions; this is less common.

Below is a 3D close packed structure that you can rotate, zoom in on, and toggle on and off various layers/features. Play around with it. Learn from it. Can you recognize the difference between the two types of tetrahedral geometries (+ vs -)? can you recognize the octahedral interstitial sites? What are the fractional coordinates of all the atoms? what Miller planes are the layers on? What questions do you have when you play with this?