Phonon mean free path and thermal conductivity in grain size- and shape-controlled polycrystalline nanostructures via Laguerre tessellation

We systematically investigate the effects of grain size and sphericity distributions on phonon mean free path and thermal conductivity using phonon transport simulations. Polycrystalline nanostructures are generated via Laguerre tessellation, enabling independent control of grain size and shape through seed-point coordinates and weights. The boundary-limited phonon mean free path is evaluated as a function of grain size and sphericity distributions. The results show that broader grain size distributions increase the phonon mean free path and consequently enhance thermal conductivity due to increased variability in phonon transport paths. In contrast, grain shape affects thermal transport primarily through the mean sphericity, while the width of the sphericity distribution has a negligible impact. In particular, structures with higher sphericity exhibit reduced phonon–boundary scattering and higher thermal conductivity. Furthermore, differences between coordinate-based and weight-based control approaches are identified, arising from their distinct grain shape characteristics. These findings demonstrate that while grain size distribution governs thermal transport, grain shape provides an additional degree of control. The present study offers practical guidelines for the design of polycrystalline materials with tailored thermal properties.