metals crystal lattice structure

SIMPLE CUBIC METAL

In a metal the atoms are all identical, and most are spherical (the bonding does not depend on direction). Metals thus tend to adopt relatively simple structures. The simplest is:

Simple Cubic (sc)

Here are two ways to draw a unit cell for the simple cubic structure. In the unit cell on the left, the atoms at the corners are cut because only a portion (in this case 1/8) belongs to that cell. The rest of the atom belongs to neighboring cells, as shown in the stacking below.
Click on the left unit cell above to view a movie of it rotating. Here we see the two unit cells stacked to form the lattice.

Notice that in each case the same overall structure is found.

The movie below will give you a feel for the overall lattice pattern. Click on the image to view it.

We can think of this lattice as layers of square packed spheres. The layers are stacked so that each sphere is directly above the one in the layer beneath.

Although we have shown space between the spheres, this is only to "open up" the structure to view. In the real crystal, the spheres touch as shown in the unit cell and lattice below.

Thus, the edge length of the cell is 2x the sphere radius.

Click on the unit cell and lattice above to view them rotating.

In 3-D the packing efficiency is given by:

P.E. = (volume of spheres) / (volume of cell)

For a simple cubic lattice, this is: P.E. = (1/8x8)(4/3 pi r³) / (2r)³= pi/6 = 52.35%.

This low value is not suprising. Remember that a 2-D square lattice uses space inefficiently. A simple cubic lattice is its 3-D analog, and also contains much empty space.

Let us shift our attention to the empty spaces in the lattice. Each unit cell contains one large interstitial site in its center (47.65% of the volume). There are 8 atoms touching this space, so the interstitial coordination number is 8, and its geometry is cubic (a cube has 8 corners).

Since each unit cell contains (8 x 1/8 =) 1 atom and 1 interstitial site, the number of atoms and interstitial sites is the same.

Examine the structure below which shows the arrangement about any single atom in the simple cubic lattice; note that each atom has 6 neighbors, so the atomic coordination number is 6. The coordination geometry is octahedral (an octahedron has 6 corners).

Octahedral coordination of an atom. An octahedron.

Since both the coordination number and packing efficiency are low, a simple cubic lattice uses space inefficiently. Very few examples of simple cubic lattices are known (alpha - polonium is one of the few known simple cubic lattices).

Below we again see a section of the simple cubic lattice as it "really" is - with the atoms touching one another. Note the channels formed by the alignment of the interstitials. These empty spaces can allow other small atoms to enter the crystal.

Click on the image below to view the lattice.

Click here to go to the next page.

Structure of Crystals Crystal Lattices Unit Cells From Unit Cell to Lattice From Lattice to Unit Cell Stoichiometry Packing & Geometry

Simple Cubic Metals

Close Packed Structures Body Centered Cubic Cesium Chloride Sodium Chloride Rhenium Oxide Niobium Oxide

Except as otherwise noted, all images, movies and VRMLs are owned and copyright by Dr. Barbara L. Sauls and Dr. Frederick C. Sauls 1998. Contact the owners for individual permission to use. barbarasauls@kings.edu