  The propagation of a heat pulse in a single crystal and across grain
boundaries (GBs) is simulated using a concurrent atomistic-continuum method
furnished with a coherent phonon pulse model. With a heat pulse constructed
based on a Bose-Einstein distribution of phonons, this work has reproduced the
phenomenon of phonon focusing in single and polycrystalline materials.
Simulation results provide visual evidence that the propagation of a heat pulse
in crystalline solids with or without GBs is partially ballistic and partially
diffusive, i.e., there is a co-existence of ballistic and diffusive thermal
transport, with the long-wavelength phonons traveling ballistically while the
short-wavelength phonons scatter with each other and travel diffusively. To
gain a quantitative understanding of GB thermal resistance, the kinetic energy
transmitted across GBs is monitored on the fly and the time-dependent energy
transmission for each specimen is measured; the contributions of coherent and
incoherent phonon transport to the energy transmission are estimated.
Simulation results reveal that the presence of GBs modifies the nature of
thermal transport, with the coherent long-wavelength phonons dominating the
heat conduction in materials with GBs. In addition, it is found the phonon-GB
interaction can result in the reconstruction of the GBs.
