The first and easiest material to discuss using band theory is metals. Metals are an aggregate of virtually an infinite number of atoms. Metals are described as having a lustre, good thermal and electrical conductivity and are very malleable. These properties are a direct result of the ability of the atoms to contribute electrons to a common cloud around the atoms. The lustre and conductivity are a result of the mobility of the electrons in this cloud. The malleability is also directly related to the fact that this electron cloud can rearrange itself around any deformations that may result. So let's look at the band structure of a metal.
Now for Band Theory
The figure shown above represents the band structure of metals. It is easily observed that the band contains both full and empty levels. The thermal conductivity arises from the ability of the electron in the full levels near the Fermi Level to jump up into the empty levels, creating a current. Since it is easy for the electrons to jump into the empty levels, it is observed that metals have high conductivity. An example of a metal is copper.
However, one would expect that as metals became warmer, they would conduct even better since the electrons would be excited even more. Quite the opposite happens: as metals are warmed, their conductivity decreases. The reason for this is that even though more electrons are excited into the empty levels, there are more collisions between the moving electrons and the atoms, which scatters the electrons out of their path and results in a lower efficiency in transporting charge. The reason for the increase in collisions is that the temperature increase increases the thermal motion of the atoms making collisions more probable.
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