section_path: Properties/Electrical and thermal
section_name: Electrical and thermal
paragraph_text: Electrical and thermal
  
  The electronic structure of metals means they are relatively good conductors of electricity. The electrons all have different momenta, which average to zero when there is no external voltage. When a voltage is applied some move a little faster in a given direction, some a little slower so there is a net drift velocity which leads to an electric current. This involves small changes in which wavefunctions the electrons are in, changing to those with the higher momenta. Quantum mechanics dictates that one can only have one electron in a given state, the Pauli exclusion principle. Therefore there have to be empty delocalized electron states (with the higher momenta) available at the highest occupied energies as sketched in the Figure. In a semiconductor like silicon or a nonmetal like strontium titanate there is an energy gap between the highest filled states of the electrons and the lowest unfilled, so no accessible states with slightly higher momenta. Consequently, semiconductors and nonmetals are poor conductors, although they can carry some current when doped with elements that introduce additional partially occupied energy states at higher temperatures.
  
  The elemental metals have electrical conductivity values of from 6.9 × 10 S /cm for manganese to 6.3 × 10 S/cm for silver. In contrast, a semiconducting metalloid such as boron has an electrical conductivity 1.5 × 10 S/cm. With one exception, metallic elements reduce their electrical conductivity when heated. Plutonium increases its electrical conductivity when heated in the temperature range of around −175 to +125 °C, with anomalously large thermal expansion coefficient and a phase change from monoclinic to face-centered cubic near 100 °C.
  
  All of the metallic alloys as well as conducting ceramics and polymers are metals by the same definition; for instance titanium nitride has delocalized states at the Fermi level. They have electrical conductivities similar to those of elemental metals. Liquid forms are also metallic conductors or electricity, for instance mercury. In normal conditions no gases are metallic conductors. However, a plasma (physics) is a metallic conductor and the charged particles in a plasma have many properties in common with those of electrons in elemental metals, particularly for white dwarf stars.
  
  Metals are relatively good conductors of heat, which in metals is transported mainly by the conduction electrons. At higher temperatures the electrons can occupy slightly higher energy levels given by Fermi–Dirac statistics. These have slightly higher momenta (kinetic energy) and can pass on thermal energy. The empirical Wiedemann–Franz law states that in many metals the ratio between thermal and electrical conductivities is proportional to temperature, with a proportionality constant that is roughly the same for all metals.
  
  The contribution of a metal's electrons to its heat capacity and thermal conductivity, and the electrical conductivity of the metal itself can be approximately calculated from the free electron model. However, this does not take into account the detailed structure of the metal's ion lattice. Taking into account the positive potential caused by the arrangement of the ion cores enables consideration of the electronic band structure and binding energy of a metal. Various models are applicable, the simplest being the nearly free electron model. Modern methods such as density functional theory are typically used.