Here Φ λ ,λ ′ ,λ ′′ are the temperature-independent three-phonon interaction strengths determined perturbatively from the harmonic frequencies and displacement vectors (eigenvectors) and the third-order force constants Φ Φ Φ . These are how phonon anharmonicity is formally introduced in this model. The functions δ (x) = 1 if x = 0 and zero otherwise enforce the conservation of energy, while the Φ λ ,λ ′ ,λ ′′ contain an analogous function ∆(x) which enforces conservation of (crystal) momentum. These "selection rules" for the conservation of energy (and also momentum) are a product of the harmonic phonon frequency spectrum, as are the occupation numbers n λ which also contribute to the scattering probabilities (c.f. Eq. 4). A complete description of the method used to calculate the linewidths can be found in Ref. . Following Ref. , we define an approximate linewidth Γλ as: