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When interatomic interactions are purely harmonic, normal modes cannot interact, and therefore no phonon scattering occurs, thus resulting in infinite thermal conductivity.

But why is anharmonicity required for phonons to interact/scatter?

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Coupled harmonic oscillators result in a linear equation for waves on beaded strings etc. Also in three dimensions. This means that when $\Psi(\vec{r}, t)$ and $\Phi(\vec{r}, t)$ are solutions, then also any linear combination (for example their sum) is a solution.

With coupled anharmonic oscillators, the wave equation is not linear anymore, and superposition cannot be exact. The waves interact, difference and sum frequencies are generated, which is inelastic scattering.

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  • $\begingroup$ To apply your answer to my question, is it safe to say that purely harmonic modes, arising from a purely harmonic potential, do not interact at all and therefore result in perfectly elastic scattering? $\endgroup$ Commented Apr 18, 2019 at 14:18
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    $\begingroup$ @Drew They do not even scatter. In such systems one can observe ballistic phonon transport. $\endgroup$
    – user137289
    Commented Apr 18, 2019 at 18:11

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