Structure-specific mode-resolved phonon coherence and specularity at graphene grain boundaries

Zhun-Yong Ong, Georg Schusteritsch, and Chris J. Pickard

Phys. Rev. B 101, 195410 – Published 5 May 2020

Abstract

In spite of their importance for understanding phonon transport phenomena in thin films and polycrystalline solids, the effects of boundary roughness scattering on phonon specularity and coherence are poorly understood because there is no general method for predicting their dependence on phonon momentum, frequency, branch, and boundary morphology. Using the recently formulated atomistic $S$ -matrix method, we develop a theory of boundary roughness scattering to determine the mode-resolved phonon coherence and specularity parameters from the scattering amplitudes. To illustrate the theory, we apply it to phonon scattering in realistic nonsymmetric graphene grain boundary (GB) models derived from atomic structure predictions. The method is validated by comparing its predictions with frequency-resolved results from lattice dynamics-based calculations. We prove that incoherent scattering is almost perfectly diffusive. We show that phonon scattering at the graphene GB is not diffuse, although coherence and specularity are significantly reduced for long-wavelength flexural acoustic phonons. Our approach can be generalized to other atomistic boundary models.

Received 15 March 2019
Accepted 14 April 2020

DOI:https://doi.org/10.1103/PhysRevB.101.195410

Physics Subject Headings (PhySH)

Grain boundaries Lattice dynamics Phonons

Graphene Polycrystalline materials Solid-solid interfaces

Nonequilibrium Green's function

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Zhun-Yong Ong ^*

Institute of High Performance Computing, A*STAR, Singapore 138632, Singapore

Georg Schusteritsch and Chris J. Pickard

Department of Materials Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom and Advanced Institute for Materials Research, Tohoku University 2-1-1 Katahira, Aoba, Sendai 980-8577, Japan

^*ongzy@ihpc.a-star.edu.sg

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Issue

Vol. 101, Iss. 19 — 15 May 2020

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Images

Figure 1
Depiction of (a) perfectly specular versus (b) perfectly diffuse scattering at a boundary, and (c) the graphene GB between armchair- and zigzag-edge graphene. The shape and orientation of their respective Brillouin zones are also shown.
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Figure 2
(a) Atomistic structure of the (4,4)|(7,0) GB-II and GB-III interfaces. (b) Schematic of atomistic $S$ -matrix calculation with the scattering region comprising the (32,32)|(56,0) grain boundary (GB). We generate an ensemble of 256 GB configurations derived from structure predictions. Each GB configuration is inserted into the scattering region between the left and right leads and its corresponding $S$ matrix is computed using Ref. [22].
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Figure 3
Comparison of the Zhao-Freund specularity parameters $p_{α, L}$ (dashed lines) from Eq. (7) with the branch-averaged specularity parameters ${\bar{P}}_{α, L}$ (solid lines) from Eq. (8) for $α =$ LA (green symbols), TA (red symbols), and ZA (blue symbols) phonons in armchair-edge graphene.
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Figure 4
(a)–(c) Phonon dispersion, (d)–(f) coherence $(C_{n})$ and the estimated (g)–(i) total, and (j)–(l) coherent and (m)–(o) incoherent mode-resolved specularity parameters $(P_{n}^{total}, P_{n}^{coh}$ , and $P_{n}^{incoh})$ for the ZA, TA, and LA phonons in armchair-edge graphene impinging on the grain boundary. The modes in the incoming phonon flux are filled circles colored according to their numerical value, while the modes in the outgoing flux are hollow squares. The frequency range is $ω = ω_{0}$ to $25 ω_{0}$ where $ω_{0} = 10^{13}$ rad/s, with the maximum frequency $(ω_{max})$ for the ZA, TA, and LA phonons equal to $12 ω_{0}, 21 ω_{0}$ , and $25 ω_{0}$ , respectively. The isofrequency contours are indicated in intervals of $Δ ω = ω_{0}$ in (d)–(o) using solid gray lines. The phonon dispersions in (a)–(c) are indicated with color contours in intervals of $Δ ω = ω_{0} / 2$ .
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Figure 5
Main scattering transitions for an incoming (a) ZA and (b) TA phonon, labeled $Ψ_{in}$ , at normal incidence to the grain boundary from the armchair-edge graphene on the left at $ω = 5 \times 10^{13}$ rad/s. The bulk LA, TA, and ZA phonon channels on the armchair-edge (left subpanel) and zigzag-edge (right subpanel) graphene side are displayed within their respective first Brillouin zones. The color scales indicate the transition probability from $W_{total} (ω)$ for the dominant outgoing channels, with the transitions indicated by dotted lines and transition probabilities written in italic font.
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