# Why do most metals have high thermal expansion coefficient although their thermal conductivity are generaly high?

the relationship between thermal conductivity and thermal expansion in metals. Why do most metals have high thermal expansion coefficient although their thermal conductivity are generaly high? Please give detailed explanation.

• Why "although"? Do you have any reason to expect low coefficient of expansion for materials with high thermal conductivity?
– nasu
Commented May 18, 2022 at 17:35

The high thermal conductivity and high thermal expansion of metals have somewhat different origins, although they both can be traced back to the metallic bonding and band formation.

For thermal conductivity, there are roughly two contributions: phonons and quasiparticles (e.g. electrons). Typically in metals, the electronic contribution dominates over the phononic one. Then, metals have high thermal conductivity for roughly the same reason they have high electrical conductivity: there are a lot of free electrons around available to transport energy through the crystal. In fact, in the simplest approximations, the ratio of electrical conductivity to thermal conductivity is a material independent ratio (see Wiedemann-Franz law). This also makes intuitive sense: all of your cookware is made from metal.

Thermal expansion is a bit more subtle and is a result of the anharmonicity of the interaction potential between the atoms making up the lattice. If you had a purely harmonic potential (i.e. Hookes law) between atoms, you actually would not get thermal expansion because the average position of the atoms remains the same regardless of the temperature (you can think of this as you are moving up the parabola that describes the energy, but even if you go to higher energies, because the parabola is symmetric the average position is always the same). But in fact the interaction potential between atoms in a solid is not parabolic, but looks more like the "Lennard-Jones" potential which is increases steeply for low distances but has a long tail for longer distances. This asymmetry means that as you go to higher average energies, the average positions will be further apart, and thus the material expands upon heating. And now you can see why metals have relatively high thermal expansion: the bonds are weak compared to something like a covalently bonded insulator, so it is easier for the atoms to bounce around.

Most metals have high electron shells....this propensity to give off electrons. The reactivity of elements are related to the number of electrons in their outermost shells. Where as the Atoms of metal elements give away electrons often very easily.... in their reactions to form positive ions but also why many light atomic metals below iron are so violent in chemical reactions or ignition (aluminum is used in rocket fuel/explosive, Magnesium, lithium) andnwhy heavy metals are so stable