Kapitza thermal resistance across individual grain boundaries in graphene
Graphical abstract
Introduction
Graphene [1], the famous two-dimensional allotrope of carbon, has been demonstrated to have extraordinary electronic [2], mechanical [3], and thermal [4] properties in its pristine form. However, large-scale graphene films, which are needed for industrial applications are typically grown by chemical vapor deposition [5] and are polycrystalline in nature [6], consisting of domains of pristine graphene with varying orientations separated by grain boundaries (GB) [7], [8], [9]. They play a significant or even dominant role in influencing many properties of graphene [10], [11].
One of the most striking properties of pristine graphene is its extremely high heat conductivity, which has been shown to be in excess of 5000 W/mK [4], [12]. Grain boundaries in graphene act as line defects or one-dimensional interfaces which leads to a strong reduction of the heat conductivity in multigrain samples [13], [14]. The influence of GBs can be quantified by the Kapitza or thermal boundary resistance R. The Kapitza resistance of graphene grain boundaries has been previously computed using molecular dynamics (MD) [15], [16] and Landauer-Bütticker [17], [18] methods, and has also been measured experimentally [19]. However, these works have only considered a few separate tilt angles, and a systematic investigation on the dependence of the Kapitza resistance on the tilt angle between any two pristine grains is still lacking. The relevant questions here concern both the magnitude R for different tilt angles and possible correlations between the structure or line tension of the GBs and the corresponding value of R.
Modelling realistic graphene GBs has remained a challenge due to the multiple length and time scales involved. Recently, an efficient multiscale approach [20] for modelling polycrystalline graphene samples was developed based on phase field crystal (PFC) models [21], [22]. The PFC models are a family of continuum methods for modelling the atomic level structure and energetics of crystals, and their evolution at diffusive time scales (as compared to vibrational time scales in MD). The PFC models retain full information about the atomic structure and elasticity of the solid [22]. It has been shown [20] that using the PFC approach in two-dimensional space one can obtain large, realistic and locally relaxed microstructures that can be mapped to atomic coordinates for further relaxation in three-dimensional space with the usual atomistic simulation methods.
In this work, we employ the multiscale PFC strategy of Ref. [20] to generate large samples of tilted, bicrystalline graphene with a well-defined GB between the two grains. These samples are then further relaxed with MD at T = 300 K. A heat current is generated across the bicrystals using nonequilibrium MD (NEMD) simulations, and the Kapitza resistance is computed from the temperature drop across the GB. We map the values of R(θ) for a range of different tilt angles θ and demonstrate how R correlates with the structure of the GBs. Finally, we demonstrate that quantum corrections need to be included in R to obtain quantitative agreement with experiments and lattice dynamical calculations.
Section snippets
PFC models
PFC approaches typically employ a classical density field to describe the systems. The ground state of ψ is governed by a free energy functional that is minimized either by a periodic or a constant ψ, corresponding to crystalline and liquid states, respectively. We use the standard PFC modelwhere the model parameters ε and τ are phenomenological parameters related to temperature and average density, respectively. The component penalizes for
Results and discussion
It is well known [15], [16], [33] that the calculated Kapitza resistance depends on the sample length in NEMD simulations. Fig. 4 shows the calculated Kapitza resistance R in the case as a function of the sample length Lx. Using fixed boundary conditions as described above, R saturates at around Lx = 400 nm. On the other hand, using periodic boundaries as described in Ref. [15], R converges more slowly. To this end, we have here used fixed boundary conditions and a sample length of
Summary and conclusions
In summary, we have employed an efficient multiscale modelling strategy based on the PFC approach and atomistic MD simulations to systematically evaluate the Kapitza resistances in graphene grain boundaries for a wide range of tilt angles between adjacent grains. Strong correlations between the Kapitza resistance and the tilt angle, the grain boundary line tension, and the defect density are identified. Quantum effects, which have been ignored in previous studies, are found to be significant.
Acknowledgements
This research has been supported by the Academy of Finland through its Centres of Excellence Program (Project No. 251748). We acknowledge the computational resources provided by Aalto Science-IT project and Finland's IT Center for Science (CSC). K. A. acknowledges the financial support from Iran Ministry of Science and Technology. P.H. acknowledges financial support from the Foundation for Aalto University Science and Technology, and from the Vilho, Yrjö and Kalle Väisälä Foundation of the
References (48)
- et al.
Structure, energy, and structural transformations of graphene grain boundaries from atomistic simulations
Carbon
(2011) - et al.
Thermal transport in nanocrystalline graphene investigated by approach-to-equilibrium molecular dynamics simulations
Carbon
(2016) - et al.
Accelerated molecular dynamics force evaluation on graphics processing units for thermal conductivity calculations
Comput. Phys. Commun.
(2013) - et al.
Efficient molecular dynamics simulations with many-body potentials on graphics processing units
Comput. Phys. Commun.
(2017) - et al.
Anomalous thermal transport along the grain boundaries of bicrystalline graphene nanoribbons from atomistic simulations
Carbon
(2014) - et al.
Electric field effect in atomically thin carbon films
Science
(2004) - et al.
The electronic properties of graphene
Rev. Mod. Phys.
(2009) - et al.
Measurement of the elastic properties and intrinsic strength of monolayer graphene
Science
(2008) - et al.
Superior thermal conductivity of single-layer graphene
Nano Lett.
(2008) - et al.
Large-area synthesis of high-quality and uniform graphene films on copper foils
Science
(2009)
Grains and grain boundaries in single-layer graphene atomic patchwork quilts
Nature
Topological defects in graphene: dislocations and grain boundaries
Phys. Rev. B
Cones, pringles, and grain boundary landscapes in graphene topology
Nano Lett.
Polycrystalline graphene and other two-dimensional materials
Nat. Nanotech.
Charge transport in polycrystalline graphene: challenges and opportunities
Adv. Mater.
Tailoring the thermal and electrical transport properties of graphene films by grain size engineering, Nature Communications
8
Thermal transport across twin grain boundaries in polycrystalline graphene from nonequilibrium molecular dynamics simulations
Nano Lett.
Kapitza conductance of symmetric tilt grain boundaries in graphene
J. Appl. Phys.
Thermal transport in grain boundary of graphene by non-equilibrium green's function approach
Appl. Phys. Lett.
Effect of grain boundaries on thermal transport in graphene
Appl. Phys. Lett.
Bimodal phonon scattering in graphene grain boundaries
Nano Lett.
Multiscale modeling of polycrystalline graphene: a comparison of structure and defect energies of realistic samples from phase field crystal models
Phys. Rev. B
Modeling elasticity in crystal growth
Phys. Rev. Lett.
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