Metallic Bonding

Every other bonding model you meet has bonds in it — a pair of electrons, two named atoms, a direction. Metallic bonding has none of these. It proposes a lattice of positive ions sitting in a pool of electrons that belong to no atom in particular and move freely through the whole structure.

That is an unusual kind of explanation, and it deserves suspicion. This page sets out what the model gets right, which is a great deal, and then what it gets wrong, which courses rarely mention and which is where the interesting chemistry is.

Where the electrons go

A metal atom holds its outer electrons loosely — that is essentially the definition of a metal. Pack a great many such atoms together and the outer electrons are no longer bound to any individual nucleus. They occupy states spread across the entire crystal.

What remains behind is a regular array of cations, and what holds it together is the attraction between those cations and the negative charge distributed among them. The bonding is non-directional: no ion has a partner, and no direction through the crystal is privileged. Everything characteristic about metals follows from that one structural fact.

One pool of electrons, four properties

Electrical conductivity. Apply a voltage and the delocalised electrons drift. Nothing has to break, no ions move, and the metal is unchanged by the current passing through it — unlike a molten salt, where conduction moves matter as well as charge.

Thermal conductivity. The same electrons carry kinetic energy from hot regions to cold ones, which is why metals feel cold to the touch: they are removing heat from your hand efficiently. The link between the two conductivities is quantitative and quite tight, and it has a name — the Wiedemann–Franz law, which says their ratio is nearly the same constant for all metals at a given temperature. Silver is the best electrical conductor of the elements and also the best thermal one, which is exactly what a shared mechanism predicts.

Malleability and ductility. Push one plane of ions past another and every ion arrives in a position identical to the one it left, still surrounded by the same electron pool. The bonding survives the deformation completely intact. This is why a metal can be beaten into foil or drawn into wire, and it is the sharpest possible contrast with the cleavage behaviour of ionic crystals, where the same displacement is catastrophic.

Lustre. Delocalised electrons can absorb photons across a continuous range of energies and immediately re-emit them, so a clean metal surface reflects almost all visible light. The absence of a fixed energy gap is why metals are reflective at every wavelength rather than coloured.

Why gold is gold-coloured

Which raises the obvious question: if metals reflect everything, why are gold and copper not silver-white like the rest?

Because in those two, one specific electronic transition happens to fall inside the visible range. In copper it is a jump from the filled 3d levels up to the partly filled 4s band; in gold it is 5d to 6s. Both absorb the blue and violet end of the spectrum, so what reflects back is weighted toward yellow and red.

Gold's case has an extra layer. Its 6s orbital is drawn in and lowered in energy by relativistic effects — the innermost electrons of a nucleus with 79 protons move fast enough for relativistic corrections to matter — which shrinks the 5d-to-6s gap until it lands in the visible. Without relativity, gold would look like silver. Cesium is faintly golden for a related reason, and with gold and copper it completes a list of exactly three warm-tinted elements.

Charge density sets the melting point

The strength of metallic bonding scales with how much positive charge each ion contributes and how tightly the resulting structure packs — essentially, charge divided by size.

Sodium contributes one electron per atom from a large ion, and it melts at 98 °C. Cesium, larger still, melts at 28.5 °C, which is below body temperature. Magnesium contributes two electrons from a smaller ion and needs 650 °C; calcium, 842 °C.

Transition metals sit far above both, because their d electrons participate in the bonding as well, giving several electrons per atom from compact ions. Tungsten melts at 3,422 °C, higher than any other metal.

The trend runs the other way for the softest metals: alkali metals can be cut and are among the least dense solids known, and it is the same low charge density that makes them so reactive.

Alloys work by making the layers awkward

Pure metals are usually too soft to be useful, and the fix is to spoil the regularity that makes their planes slide so easily.

Substitutional alloys replace some atoms with atoms of a similar size. Brass is copper with zinc; bronze is copper with tin. Sterling silver is 92.5% silver with 7.5% copper, added purely because pure silver deforms too readily to hold a shape.

Interstitial alloys wedge much smaller atoms into the gaps. Steel is iron with a small proportion of carbon — often well under 1% — occupying spaces between iron atoms.

Both work the same way. A plane of atoms slides easily when everything in it is identical and evenly spaced. Introduce atoms of a different size and the plane snags, so far more force is needed to deform the metal. The alloy is harder and stronger, and correspondingly less malleable: you cannot have both, and every alloy is a chosen point on that trade-off.

Bands, and what the sea cannot see

The electron sea is a picture. The theory underneath it is band theory, and it explains things the picture cannot.

When N atoms combine, their N atomic orbitals become N molecular orbitals spread over the whole crystal. For any real crystal N is astronomical, so the levels are packed so closely that they form a continuous band. Whether the material conducts depends on how that band is filled:

• A metal has a partly filled band, or two bands that overlap. An electron can move into a higher state using an arbitrarily small amount of energy, so a tiny voltage produces a current.
• An insulator has a completely filled band and a large empty one above it, separated by a gap. Diamond's gap is about 5.5 eV — far more than thermal energy can supply.
• A semiconductor has the same arrangement with a small gap. Silicon's is 1.12 eV and germanium's 0.67 eV, small enough that heat alone promotes some electrons across, which is why semiconductor conductivity rises with temperature.

That last contrast is the one to hold on to, because it exposes the sea model's biggest failure. Metals conduct worse as they get hotter. The sea picture, with its freely moving electrons, predicts the opposite. The real reason is that heat makes the lattice vibrate and vibrating ions scatter the electrons out of their drift — a mechanism that requires the wave description and is invisible in the picture of a fluid.

Six things this model gets wrong

Stating the limits is not a criticism of the model; it is what tells you when to stop trusting it.

• It cannot explain why conductivities differ so much between metals — a factor of sixty between silver and manganese.
• It gets the temperature dependence backwards, as above.
• It says nothing about magnetism. Iron, cobalt and nickel are ferromagnetic and their immediate neighbours are not; nothing in a uniform electron pool distinguishes them.
• It cannot explain why mercury is a liquid while its neighbours are solid. That answer also lies in relativistic effects, and is the subject of a separate article.
• It offers no account of superconductivity, where resistance vanishes entirely below a critical temperature.
• It treats metallic bonding as a sharply distinct category when it is really the end of a continuum. Tin makes the point better than any argument: below 13.2 °C its stable form is grey tin, a brittle semiconductor with the diamond structure, while above that temperature it is ordinary white tin, a malleable metal. Same element, same pressure, and bonding that changes character with temperature alone.