The 𝐶 𝜆 and 𝒗 𝜆 = 𝜕𝜔 𝜆 𝜕𝐪 λ ⁄ (𝜔 𝜆 = 2𝜋𝑓 𝜆 ) are calculated within the harmonic approximation, while the 𝜏 𝜆 are calculated based on a perturbative model for the phonon-phonon interactions. A detailed overview of this method is given in Ref. and in the following section.