Effective phonon mean free path in polycrystalline nanostructures

Abstract

We have calculated the mean free path (MFP) of phonons associated with grain boundary scattering in polycrystalline nanostructures, by developing a Monte Carlo ray tracing transmission model that can be applied to arbitrary geometries. The calculations for various log-normal grain-size distributions realized by Voronoi diagrams and genetic algorithms show that the boundary-scattering MFP in a polycrystalline nanostructure is 20%–30% longer than that in a simple cubic structure with the same average grain size (defined by matching grain volumes). The impact on thermal conductivity is quantified for nanocrystalline silicon by using Matthiessen's rule to combine boundary scattering with intrinsic phonon-phonon scattering. The result reveals that the thermal conductivity depends strongly on the average grain size but only weakly on the breadth of the grain-size distribution, and thus, the simple cubic structure is a reasonable approximation for the polydisperse grain structure of actual materials.

Investigation of phonon coherence and backscattering using silicon nanomeshes

“…We obtain the long length limit Λ B from the slope of L / Λ against L , which isolates the intrinsic diffusive boundary scattering from the ballistic end effects4748. We have validated the ray tracing code against analytical solutions for Λ B , including nanowires44 and cross-plane transport in diffuse superlattices49, as well as previously published BTE simulation results for two nanomeshes21 (see Supplementary Note 4 and Supplementary Fig. 4).…”

“…Analytical results for are known for simple geometries such as nanowires4243, but Λ B is generally unknown for complicated structures such as the nanomesh1520. To rigorously determine Λ B we use a ray tracing technique44. From the Landauer-Büttiker formalism4546, the thermal conductance G is…”

Probing length-scale separation of thermal and spin currents by nanostructuring YIG

“…However, the maximum thermal conductivity in the sample with average grain size of 0.55 μm, 5.2 Wm -1 K -1 , is much lower than that in 190 nm-thick film, 23 Wm -1 K -1 [23], which indicates suitability of nanostructuring for reducing thermal conductivity. Note that the previous phonon transport calculations of silicon nanocrystalline structures have shown that the grain-size dependence of thermal conductivity is insensitive to the width of size distribution and determined by the average size [24].…”

The use of strain and grain boundaries to tailor phonon transport properties: A first-principles study of 2H-phase CuAlO2. II

“…At grain/phase boundaries that are comparable to grain size, a significant amount of heat is transported through the interface by phonons [56], therefore studying the high pressure 2H phase of CuAlO2 can help elucidate phonon transport in nano--grained structures of the 3R phase as well. The grain boundary scattering term is the only term that depends on the direction of the phonon group velocity explicitly, which can generally be expressed as the frequency independent equation [57],…”