Using the quasi-harmonic approximation for atomic vibrations, the macroscopic Grüneisen parameter (γ) can be related to the description of how the vibrational frequencies (phonons) within a crystal are altered with changing volume (i.e. γ i 's). For example, one can show that γ γ = α α K T C V ρ ρ if one defines γ γ as the weighted average γ γ = ∑ ∑ i γ γ i c V , i ∑ ∑ i c V , i , where c V , i 's are the partial vibrational mode contributions to the heat capacity, such that C V = 1 ρ ρ V ∑ ∑ i c V , i .