where 𝐶 𝜆 are the modal heat capacities, 𝒗 𝜆 are the model group velocities, 𝜏 𝜆 are the phonon lifetimes, 𝑁 is the number of wavevectors included in the summation, and 𝑉 0 is the unit cell volume. 𝐶 𝜆 and 𝒗 𝜆 are calculated within the harmonic approximation as: