Abstract

The inter-atomic bonds in metals are (I) strong covalent bonds, but (II) metals are malleable and ductile, with the bonding structure re-arranging rather easily. (III) Metals usually have one of the closely packed crystal structure, and (IV) often have phase transitions between them at rather modest temperatures or pressures. (V) The formation energy of an atomic vacancy is only about half of what one might expect from counting the net number of broken bonds. (VI) Metals tend to speed up and change chemical reactions (catalysis) at their surfaces.

All the above can be found and explained in a simple model, but treated rigorously quantum mechanically, for a metal of one type of electron (e.g. atomic s-electrons or d-electrons) only, the latter being quite a good approximation for the transition metals. A short quantum mechanical calculation shows the energy to be proportional to the square root of the coordination number C of near neighbours, which accounts for the properties II to VI. Total energy calculations for aluminium with its mixture of atomic 3s and 3p electrons are found to give similar results.

The analysis shows that a metal atom is bonded to its surrounding cluster of close neighbours as a whole in a ‘cluster bond’. When the metal is deformed, the cluster of close neighbours just shuffles around the central atom without breaking the cluster bond.