A superlattice — alternating layers of two materials — filters phonons by Bragg reflection. Coherent phonons with wavelengths matching the period are reflected; others transmit. A gradient superlattice varies the layer period across the structure. The question: does the gradient scatter phonons like disorder, or does the gradual variation preserve coherence?
Atomistic wave-packet simulations reveal the answer: long-range disorder dominates. The number of distinct period sizes, the number of repetitions of each size, and whether periods increase or decrease all affect phonon transmission — but the primary determinant is how disordered the sequence of interfaces appears at long range. Short-range order (how many identical periods repeat before the next size) matters much less than the global arrangement.
Coherent phonon mode-conversion — where a phonon enters the superlattice at one frequency and exits at another through nonlinear interaction with the varying periodicity — depends on the same long-range structure. The conversion efficiency peaks when the gradient introduces enough long-range disorder to break the translational symmetry that would otherwise forbid mode mixing, but not so much disorder that the phonon loses coherence entirely.
Phonon transmission in gradient superlattices falls between the fully ordered limit (strong Bragg reflection, sharp transmission bands) and the fully disordered limit (diffuse scattering, no coherence). The gradient is neither order nor disorder — it's structured variation, and the thermal transport responds to the structure at the longest scales. Engineering the long-range interface pattern, not the local layer thickness, is the effective control parameter for thermal conductivity.