The Foundations of Chemistry

Plan

We visualize the simple cubic cell.

13-16 Bonding in Solids 521

Solution

(a) One face of the cubic unit cell is shown in the left-hand drawing, with the atoms touching.
The centers of the nearest neighbor atoms are separated by one unit cell edge, at the distance
6.30 Å. (b) A three-dimensional representation of eight unit cells is also shown. In that drawing
the atoms are shown smaller for clarity. Some atoms are represented with different colors to
aid in visualizing the arrangement, but all atoms are identical.Consider the atom shown in red
at the center (at the intersection of the eight unit cells). Its nearest neighbors in all of the unit
cell directions are shown as light red atoms. As we can see, there are six nearest neighbors.
The same would be true of any atom in the structure.

EXAMPLE 13-8 Nearest Neighbors

Silver crystals are face-centered cubic, with a cell edge of 4.086 Å. (a) What is the distance
between centers of the two closest Ag atoms? (b) What is the atomic radius of silver in this
crystal? (c) How many nearest neighbors does each atom have?

Plan

We reason as in Example 13-7, except that now the two atoms closest to each other are those
along the face diagonal.

One face of the simple

cubic unit cell

Several unit cells

(atoms shown smaller for clarity)

6.30 Å

6.30 Å

6.30 Å

One face of four adjacent unit cells

(x-y plane)

One face of the face-centered

cubic unit cell

4.086 Å

4.086 Å h