CLOSE PACKED STRUCTURES
Face Centered Cubic (fcc)
Cubic Close Packed (ccp)
These are two different names for the same lattice.
We can think of this cell as being made by inserting another atom into each face of the simple cubic lattice - hence the "face centered cubic" name.
The reason for the various colors is to help point out how the cells stack in the solid. Remember that the atoms are all the same.
The unit cell is again shown expanded for visibility. Actually, the corner atoms touch the one in the center of the face. The name "close packed" refers to the packing efficiency of 74.05%. No other packing can exceed this efficiency (although there are others with the same packing efficiency).
If we stack the cells into a lattice we notice that the atoms form
diagonal layers - the reason for the colors is to make these stand out.
Note that diagonal layers also form along our line of sight. Since these
cut across the other layers, each layer will contain all three colors.
A different and better way of looking at this structure focuses on those layers.
We start with a hexagonal array of spheres (the blue "A" layer).
Notice that this is a close-packed arrangement - there is no way to pack
more spheres into a given area.
We then place a second close-packed layer (the gold "B" layer) atop the the first, so they nestle into the left-pointing holes in the first.
All spheres are actually the same atom, the colors are to help
you keep track of the layers.
Notice that there are 2 separate choices for the second layer; in the animation below, we have arbitrarily chosen to cover the left-pointing holes. We can put them over either all the "left-pointing" interstices or all the "right-pointing" interstices.
If we put them over the right-pointing interstices we generate a different layer, labeled the green or "C" layer.
Remember there are twice as many interstitial sites as spheres. (One left-pointing and one right-pointing).
We can continue to stack these layers in any order, providing that
no 2 identical layers are adjacent.
The cubic close packed structure can be constructed from the
A - B - C - A - B - C . . . . . sequence.
An alternate sequence might be B - A - C - B - A - C ...
The resulting structure is a 3-D analog of the hexagonal packing in a plane - it is the most efficient way to pack spheres.
Click on the images below to view the structure in horizontal and vertical rotation.
However, the internal structures and relationships can be examined by moving the spheres apart slightly.
Click on the image below to explore the lattice in VRML.
There are two types of interstitial sites in an fcc lattice. Let us consider a pair of layers - blue and gold.
Remember, the gold atoms cover all the left-pointing interstices
in the blue layer, and none of the right-pointing ones.
Under each gold atom is a small space surrounded by 4 atoms in a tetrahedral arrangement. This is a 4 - coordinate tetrahedral interstitial site.
If we look at the right-pointing holes in the blue layer, we see that the gold layer does not nestle into them as it does the left-pointing ones. These cavities are surrounded by 6 atoms in octahedral geometry. This is a 6 - coordinate octahedral interstitial site.
Go back and look at the lattice again and locate the tetrahedral
and octahedral interstitial sites.
Are there any cubic sites?
Examples of fcc / ccp metals include nickel, silver, gold, copper,
Another way of stacking these layers is to omit the "C" layers altogether - simply alternate "A" and "B". This is also a close-packed array, but the symmetry is different. It is called:
Hexagonal Close Packed (hcp)
The hexagonal close packed structure can be made by piling layers
A - B - A - B - A - B . . . . . sequence.
An alternative sequence would be A - C - A - C - A ...
The resulting HCP structure is shown below.
Click on the images below to view the lattice structure in horizontal and vertical rotation.
The VRML below is the same structure slightly
expanded to improve visibility.
The unit cell for hcp is shown below. Remember that the different colors are used only to make the spatial relationships clearer. In the solid, the atoms are all identical.
These unit cells stack together like this:
Examples of hcp metals include zinc, titanium, and cobalt.
The coordination geometry about each atom is shown below. Note that while both structures have CN = 12 the arrangements are slightly different. In hcp, the top and bottom three are directly above one another. In ccp, they are staggered.
Another difference arises from the packing order. In the hcp, there
are never any atoms over the "left-pointing" holes. Thus, if we look directly
down on the animated structures above we can see tiny channels through
the hcp lattice. These are absent in ccp. In some materials, channels
provide a pathway for other substances to enter the lattice and react.
In the hcp lattice the channels are too small to have much practical importance.
Below you see an actual STM image of a Ni surface. This is NOT a simulation, but a genuine picture. Note the hexagonal arrangement of atoms.
This image is the property of IBM Research
Almaden Research Center
Click here to go to the next page.
Structure of Crystals
From Unit Cell to Lattice
From Lattice to Unit Cell
Packing & Geometry
Simple Cubic Metals
Close Packed Structures
Body Centered Cubic
Except as otherwise noted, all images, movies and
VRMLs are owned and copyright
Barbara L. Sauls and Frederick C. Sauls 2000.
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