Phonon diffraction and dimensionality crossover in phonon-interface scattering

Thermal resistance at interfaces and grain boundaries is important in a range of fields from microelectronics to energy materials. Standard models treat interfaces as structureless even though at the nanoscale they are often better described as arrays of linear defects. Here, we examine several characteristics of heat transport that arise when considering such a structure at the interface. When heat carrying phonons scatter off linear defect arrays, diffraction of phonons occurs. Furthermore, a dimensionality crossover is observed in diffusive transport. Phonons transition from seeing a structureless planar defect when their wavelength is longer than the defect spacing, lambda greater than or similar to D, to seeing the interface as a collection of independently scattering linear defects when lambda less than or similar to D. By applying this theory to grain boundary strain-field scattering, we show that this dimensionality crossover can explain the frequency dependence of grain boundary scattering and transmissivity, which results in the T-2 temperature dependence observed in the low-T thermal conductivity of poly/nanocrystalline materials.