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The physics of heat conduction puts practical limits on many technological fields such as energy production, storage, and conversion. It is now widely appreciated that the phonon-gas model does not describe the full vibrational spectrum in amorphous materials, since this picture likely breaks down at higher frequencies. A two-channel heat conduction model, which uses harmonic vibrational states and lattice dynamics as a basis, has recently been shown to capture both crystal-like (phonon-gas channel) and amorphous-like (diffuson channel) heat conduction. While materials design principles for the phonon-gas channel are well established, similar understanding and control of the diffuson channel is lacking. In this work, in order to uncover design principles for the diffuson channel, we study structurally-complex crystalline Yb₁₄ (Mn,Mg)Sb₁₁, a champion thermoelectric material above 800 K, experimentally using …