Thermal Properties of Crystals
In Chapter 5, we built simple mathematical models to describe the vibrations of atoms, first in a one-dimensional system and then extended to a three-dimensional harmonic crystal. These models, in the quantum description, led us to introduce a quasi-particle called the phonon, with an associated momentum and energy spectrum. Many of the phenomena measured in crystals can be traced back to phonons. In this Chapter, we will employ the results of the phonon formalism used in Chapter 5 to interpret the thermal properties of crystals, in particular their heat capacity, thermal expansion and thermal conductivity.