Theoretically, the heat capacity, which is a measure of how much energy it takes to raise the temperature of a solid, is related to the lattice vibrations or phonons. Lattice vibrations are the collective motions of atoms of a crystal, and the heat capacity is proportional to the change of the average energy of these collective vibrational modes. Within a harmonic approximation of lattice vibrations, the heat capacity is formulated as a summation over the contribution of these lattice vibrations via: