- What metals have the closest packing structures?
- What metals have the body centered cubic structure?
- Is there any metal adopting the simple cubic structure?
- What are the features of rareearth metals?

On this page, we give a brief discussion on metal structures. Namely, metals have closest packing (fcc and hcp) structures, the body centered cubic (bcc), simple cubic (sc) and complicated closest packing structures.

We will only scratch the surface on the subject on metal structures, but the basic concepts presented here let you understand why metals behave they way they do (properties).

Since the periodic table is a useful tool for representing information, the structure types of metals can be displayed using a period table.

*Solution*

Assume the radius of gold *spheres* to be *r*, and the edge
of the face centered unit cell to be *a*. There are four gold
(atomic mass 197.0, Avogadro's number = 6.023x10^{23}) atoms
per unit cell, thus

= 19.3 g / cm

a = 4.0774*10

= 2 * 2

r = 1.442 *10

*Discussion*

A handbook did give the radius of gold as 144 pm (1 pm = 10^{12}).

Copper has a sepcific gravity of 8.92, evaluate its atomic radius.

The atomic radius of silver Ag is listed as 145 pm. Evaluate its density.

This type of structure has two atoms per unit cell, and it is slightly less densely packed as the fcc or hcp types as shown by Example 1.

**
Example 2
**

*Solution*

Assume the radius of *spheres* be *r*, and the edge
of the body centered unit cell to be *a*. There are two
spheres per unit cell, thus

= 3

V

V

Fraction of volume occupied by spheres = 2*V

= 3

= 0.68 or 68%.

*Discussion*

The fraction of 0.68 is slightly less than those (0.74) of closest packed
structures. Thus, the bcc structures are less densely packed according to the
hardsphere model.

The cubic unit cell contains only one sphere, and the edge length is exactly equal to the diameter of the sphere. In the diagram, we choose the origin to be the center of an atom, but if you choose the origin to be the center among 8 spheres, your cube enclose a whole atom.

You can work out the fraction of space occupied by spheres in such an arrangement to be p/6 (0.52), much less than the bcc structure type.

Actually, the hc (4 H) type has a complicated packing sequence such as ABAC, ABCB, etc. That is why they are designated as (4 H). Actually, the structure of Sm (samarium) has a very complicated sequence of ACACBCBAB ACACBCBAB .... (see page 309 of The Crystal Chemistry and Physics of Metals and Alloys by W.B. Pearson, Wiley Interscience, 1972)

© cchieh@uwaterloo.ca