For some ceramic materials, why does the thermal conductivity first decrease and then increase with rising temperature?

Thermal conductivity is a material property that represents the ability to conduct heat. In ceramics, heat conduction mainly happens through two processes: lattice vibrations (phonons) and electronic conduction. Phonons in the lattice transmit vibrational energy, while a small amount of heat is conducted via free electrons.

In the initial phase, as the temperature increases, lattice vibrations or phonons become more energetic and frequent. However, at the same time, these more energetic phonons are more likely to scatter off each other and other lattice defects, such as grain boundaries, dislocations, and impurities. This scattering causes the phonons to lose their coherence and disrupts the efficient transmission of heat, which leads to a decrease in the overall thermal conductivity.

After reaching a certain temperature, the increasing thermal energy in the ceramic material starts to reduce the effects of scattering and enables more efficient heat conduction. This is due to a redistribution of energy between different phonon modes and a reduction in the influence of lattice defects and grain boundaries on the phonon scattering. As a result, the thermal conductivity of the ceramic material starts to increase with further rise in temperature. In conclusion, the variation in thermal conductivity of some ceramic materials with temperature can be attributed to the balance between phonon scattering and the redistribution of energy among phonon modes. Initially, as the temperature increases, the increased scattering leads to a decrease in thermal conductivity. After a certain temperature threshold is reached, the reduced scattering effect and the redistribution of energy among phonon modes allow for more efficient heat conduction, leading to an increase in thermal conductivity.