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 explore it in VRML. Here we see the two unit cells stacked to form the lattice. Notice that in each case the same overall structure is found.  The VRML below will give you a feel for the overall lattice pattern.
Click on the image to explore it in VRML. 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 to explore it in VRML.

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)=  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 theinterstitial 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 to explore it in VRML.   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
Barbara L. Sauls and Frederick C. Sauls   2000.
Contact the owner for individual permission to use.    blsauls@kings.edu