In a solid, atoms vibrate about their equilibrium position at ordinary temperature and the amplitude of vibration decreases to a minimum at absolute zero of temperature .This vibration of atoms brings elastic distortion in the lattice and, therefore, the waves associated with the vibrations are the elastic waves of varying frequencies.
These waves superimpose to form a wave packet that moves through the solid. The quantum of elastic energy is known as phonon, whose energy is given by E=hυ where υ is frequency of vibration.
The increase in number of vibration of atoms with temperature is represented by increase in number of phonons passing through the crystal. It is the phonons together with valence electrons which are responsible for the transfer of thermal energy from high temperature, region to low temperature region. The property that shows the ability of a material to transfer thermal energy or heat is known as thermal conductivity.
The thermal conductivity of a solid is proportional to its specific heat and to the mean free path of phonons and electrons. The mean free path of electrons is very large in comparison to the mean free path of phonons; as a result, the electrons undergo less number of collisions.
As in metals, the free electrons are sufficiently mobile, metals have shown high thermal conductivity due to the mobility of electrons and phonons as well. On the other hand, in insulators, phonons are the only particles to conduct heat, because the valence electrons are not present.
Conclusions:- It has been concluded that
(a) The thermal conductivity of metals decreases at higher temperatures.
(b) The thermal conductivity of polycrystalline metals is lower than that of a single crystal due to scattering of electrons and phonons along gain boundaries.
(c) The thermal conductivity of metals is lower than their alloys due to scattering of electrons and phonons with the atoms of alloying element.
(d) The thermal conductivity of semi conductors increases with increasing temperature due to flow of excited electrons.
(e) The thermal conductivity of metals, alloys, semiconductors and dielectrics is in the descending order.