# Ballistic-diffusive Phonon Heat Transport across Grain Boundaries

## TL;DR

This study uses atomistic-continuum simulations to explore how phonons propagate across grain boundaries, revealing a coexistence of ballistic and diffusive heat transport and the dominant role of long-wavelength phonons in thermal conduction.

## Contribution

It introduces a combined atomistic-continuum method with a coherent phonon pulse model to quantitatively analyze phonon transport across grain boundaries, including the effects on thermal resistance and GB reconstruction.

## Key findings

- Long-wavelength phonons travel ballistically across GBs.
- Grain boundaries modify thermal transport, favoring coherent phonons.
- GB interactions can lead to GB reconstruction.

## Abstract

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.

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Source: https://tomesphere.com/paper/1704.08415