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Scattering of flexural acoustic phonons at grain boundaries in graphene

Edit E. Helgee, Andreas Isacsson

Abstract

We investigate the scattering of long-wavelength flexural phonons against grain boundaries in graphene using molecular dynamics simulations. Three symmetric tilt grain boundaires are considered: one with a misorientation angle of $17.9^\circ$ displaying an out-of-plane buckling 1.5 nm high and 5 nm wide, one with a misorientation angle of $9.4^\circ$ and an out-of-plane buckling 0.6 nm high and 1.7 nm wide, and one with a misorientation angle of $32.2^\circ$ and no out-of-plane buckling. At the flat grain boundary, the phonon transmission exceeds 95 % for wavelengths above 1 nm. The buckled boundaries have a substantially lower transmission in this wavelength range, with a minimum transmission of 20 % for the $17.9^\circ$ boundary and 40 % for the $9.4^\circ$ boundary. At the buckled boundaries, coupling between flexural and longitudinal phonon modes is also observed. The results indicate that scattering of long-wavelength flexural phonons at grain boundaries in graphene is mainly due to out-of-plane buckling. A continuum mechanical model of the scattering process has been developed, providing a deeper understanding of the scattering process as well as a way to calculate the effect of a grain boundary on long-wavelength flexural phonons based on the buckling size.

Scattering of flexural acoustic phonons at grain boundaries in graphene

Abstract

We investigate the scattering of long-wavelength flexural phonons against grain boundaries in graphene using molecular dynamics simulations. Three symmetric tilt grain boundaires are considered: one with a misorientation angle of displaying an out-of-plane buckling 1.5 nm high and 5 nm wide, one with a misorientation angle of and an out-of-plane buckling 0.6 nm high and 1.7 nm wide, and one with a misorientation angle of and no out-of-plane buckling. At the flat grain boundary, the phonon transmission exceeds 95 % for wavelengths above 1 nm. The buckled boundaries have a substantially lower transmission in this wavelength range, with a minimum transmission of 20 % for the boundary and 40 % for the boundary. At the buckled boundaries, coupling between flexural and longitudinal phonon modes is also observed. The results indicate that scattering of long-wavelength flexural phonons at grain boundaries in graphene is mainly due to out-of-plane buckling. A continuum mechanical model of the scattering process has been developed, providing a deeper understanding of the scattering process as well as a way to calculate the effect of a grain boundary on long-wavelength flexural phonons based on the buckling size.

Paper Structure

This paper contains 12 sections, 17 equations, 14 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Method
  3. Grain boundaries
  4. Wave packet method
  5. Results
  6. Grain boundaries
  7. Phonon scattering
  8. Continuum mechanical model
  9. Theory
  10. Method of solution
  11. Results
  12. Conclusion

Figures (14)

  • Figure 1: (Color online) Grain boundary with misorientation angle $32.2^\circ$, seen from the $y$ direction (top) and from the $z$ direction (bottom). Figure created using VMDHUMP96.
  • Figure 2: (Color online) Grain boundary with misorientation angle $17.9^\circ$, seen from the $y$ direction (top) and from the $z$ direction (bottom). Figure created using VMDHUMP96.
  • Figure 3: (Color online) Grain boundary with misorientation angle $9.4^\circ$, seen from the $y$ direction (top) and from the $z$ direction (bottom). Figure created using VMDHUMP96.
  • Figure 4: Buckling height (top) and width (bottom) for the $9.4^\circ$ boundary plotted against the length of the simulated system in the $x$ direction.
  • Figure 5: Buckling height (top) and width (bottom) for the $17.9^\circ$ boundary plotted against the length of the simulated system in the $x$ direction.
  • ...and 9 more figures