Linus Pauling: There is another aspect of the theory of valence that I should mention now, and this is one that has been understood, at
any rate understood to the extent that we shall discuss now, only during the last few years. This is the matter of metallic
What is it? What is the nature of the forces that hold the copper atoms together in the metal copper, in the crystal of copper?
Well, let us consider copper. I think that I would prefer to consider aluminum. Let us consider the metal aluminum. It
has the same structure as copper – cubic closest packing as shown here. Each atom of aluminum has, each atom of aluminum
here is surrounded by twelve neighbors that are equally distant from it; six in this layer, three in the layer behind, three
in the layer in front.
Now, aluminum has atomic number thirteen. It has three electrons outside of the neon shell, plenty of orbitals, four orbitals
in the argon shell, so that we would expect it to form three covalent bonds using its three electrons. In order that it be
bonded equally to twelve neighbors, we may describe the three bonds as resonating among the twelve structures and holding
the aluminum atoms together.
The same sort of resonance of covalent bonds among a large number of alternative positions occurs in other elements. For
example, in the metals potassium, calcium, scandium, titanium, vanadium, chromium, the properties of these metals correspond
nicely to the idea that we have one, two, three, four, five, six electrons, six bonds formed by each atom and resonating around
the positions connecting the atom with the neighboring atoms. The malleability and ductility can be understood in terms of
this resonance, also the property of electric conduction, the ability of the metal to conduct the electric current. I may
mention that there are two kinds, or two common kinds, of closest packing of spheres that are represented by the metals.
In, this is cubic closest packing, analogous to this structure, along a three-fold axis of the structure, there is repetition
after three layers. There are two alternative ways of placing any layer above the layer beneath it: this way, or this way.
In cubic closest packing, these layers, these ways, repeat so as to give repetition after three layers, in hexagonal closest
packing, there is repetition after two layers. This gives a hexagonal crystal. Magnesium and many other metals have this
structure. Aluminum, copper, silver, gold, many other metals have this structure, cubic closest packing.
I think that it is interesting that in 1890, many years before x-ray diffraction was discovered, the English amateur scientist,
William Barlow, had assigned this hexagonal, closest packed structure to magnesium on the basis of the knowledge that magnesium
crystallizes at hexagonal crystals, with the right, with a certain dis-, ratio, this distance to this in the crystal, and
had assigned cubic closest packing to aluminum, copper, silver, gold, and other metals. In fact, he had assigned the sodium
chloride structure to sodium chloride and other alkali halogenides, the cesium chloride structure to cesium chloride, the
sphalerite structure to the cubic form of zinc sulfide, the wortzite structure to the hexagonal form of zinc sulfide, the
fluorite structure to fluorite, CaF2, and he was right on all of these assignments. He wasn’t, wasn’t sure, of course, that he was right, but it has turned out
that his ideas about closest packing of spheres and so on were right and permitted him to find the correct structures.