Metals
A metal is a material in which the highest occupied electron energy band is only partially filled, or overlaps with the next available band, so that electrons near the Fermi energy can move into neighbouring available states with only an infinitesimally small energy input — allowing metals to conduct electricity and heat far more efficiently than any other class of material.
Curious
The Codex's band theory entry explains that electron energies in a solid form bands separated by gaps. Metals are the specific case where the highest energy band containing electrons is only partially filled (or two bands overlap in energy) — this means there are always plenty of unoccupied electron states immediately adjacent in energy to the occupied ones, so even a vanishingly small applied electric field can shift electrons into these nearby available states, producing an electric current.
This partial band filling is why metals conduct so efficiently compared to insulators and semiconductors, whose electrons must instead overcome a substantial energy gap before becoming mobile — in a metal, essentially no such barrier exists, and conduction electrons behave, to a useful first approximation, almost like a gas of free particles moving through the fixed lattice of positive ions.
Exploring
| Symbol | Name | SI Unit |
|---|---|---|
| κ | Thermal conductivity | W·m⁻¹·K⁻¹ |
| σ | Electrical conductivity | S·m⁻¹ |
| L | Lorenz number (approximately constant across metals) | W·Ω·K⁻² |
Deep Dive
Paul Drude's 1900 classical free-electron model — treating conduction electrons as a classical gas of charged particles scattering off fixed lattice ions — was remarkably successful at explaining basic metallic conductivity and derived an early version of the Wiedemann–Franz law, despite predating quantum mechanics entirely. The model's classical treatment nonetheless produced significant errors (particularly a badly overestimated electronic contribution to specific heat), which Arnold Sommerfeld's 1928 quantum mechanical refinement (incorporating Fermi-Dirac statistics, see the Codex's Fermi energy entry) corrected while preserving Drude's essentially correct qualitative picture of nearly-free conduction electrons.
Electron scattering and resistivity: In a perfectly periodic, defect-free crystal lattice at absolute zero, Bloch's theorem implies electrons would actually travel completely unimpeded, with zero electrical resistance — real metals have finite resistance because of scattering off lattice imperfections (impurities, defects, grain boundaries) and, at any finite temperature, off the lattice's own thermal vibrations (phonons). This is why metal resistance generally increases with temperature (more thermal lattice vibration means more electron scattering) and why extremely pure, carefully prepared metal samples at very low temperatures can achieve remarkably low residual resistance, limited mainly by whatever defects remain.
Not all metallic elements behave identically — transition metals (like iron, with partially filled d-orbital bands) and simple metals (like sodium or aluminium, dominated by simpler s- and p-orbital bands) can show substantially different electronic and magnetic behaviour, reflecting the detailed atomic orbital structure underlying their band formation, a distinction relevant to understanding why some metals (like iron) are also ferromagnetic while most (like copper or aluminium) are not.
Concept Relationship Map
Requires: band theory, Fermi energy
Enables: insulators (by contrast)
Commonly confused with: treating electrical and thermal conductivity as independent properties rather than sharing a common free-electron origin (Wiedemann–Franz law)
Sources
- Drude, P. (1900). Annalen der Physik, 306(3), 566–613.
- Kittel, C. (2004). Introduction to Solid State Physics, 8th ed. Wiley, Ch. 6.