Impact of grain boundary characteristics on thermal transport in polycrystalline graphene: Analytical results

Abstract

The effect of grain boundary (GB) structure, size and shape on thermal conductivity of polycrystalline graphene is studied in the framework of the deformation potential approach. Precise analytical expressions for the phonon mean free path (MFP) are obtained within the Born approximation. We found exactly two types of behavior in the long-wavelength limit: MFP varies as ω −1 for open GBs of any shape while it behaves as ω −3 for closed configurations (loops). In the short-wavelength limit MFP tends to a constant value for any configuration. Oscillatory behavior is observed for all GBs which indicates that they serve as diffraction grating for phonons. This property is also inherent in GBs with irregularities caused by partial disclination dipoles. The thermal conductivity is calculated in the framework of Callaway's approach with all main sources of phonon scattering taken into account. Reduction of the heat conductivity with decreasing grain size is obtained in a wide temperature range. Most interesting is that we found a marked decrease in the thermal conductivity of polycrystalline graphene containing GBs with changes in their misorientation angles.

Efficient modulation of thermal transport in two-dimensional materials for thermal management in device applications

“…In fact, the GBs in the actual structure are often complex and irregular, which violates the ideal constancy of misorientation and leads to a significant decrease in κ. 100 Considering BC-G, the effect of the misorientation angle to κ is more obvious, as shown in Fig. 3(c).…”

Electrical resistivity of polycrystalline graphene: effect of grain-boundary-induced strain fields

“…Earlier, in the study of heat transport in graphene (see Ref. 23 ), we have shown the possibility, within the framework of our approach, of taking into account any number of PDDs (including those with different ω ) inside the GB wall. Which is important in calculations, one can consider many built-in PDDs as one with a total arm length.…”

“…It is well known that the effect of strain field can be described within the deformation potential theory 26 . In our approach, the total strain field caused by the GB at any point of graphene sheet is determined through a sum of strain fields from all 5-7 pairs 23 . In this way, for a GB oriented in the x-direction, the deformation potential V ǫ (r) takes the form where TrE ij (r) is the trace of the strain tensor, G is the deformation potential constant, is the modulus of the Frank vector which, for the chosen geometry, is directed along the z axis, p is the number of 5-7 pairs in the GB, ζ is the is Poisson's ratio, ( x ni , y ni ) are coordinates of i-th disclination in n-th dipole.…”

“…This allowed us to describe the features of electron and phonon scattering in polycrystalline materials due to long-range strain fields 22 . Recently, we presented a general scheme that allows us to calculate strain fields in graphene caused by GB of any size and shape as a sum of strains of 5-7 disclination dipoles 23 . This approach has been applied to the analysis of heat transport in polycrystalline graphene 23 and allows us to consider any possible configurations of GBs including closed defects like the Stone-Walles 24 .…”

Electrical Resistivity of Polycrystalline Graphene: Effect of Grain-Boundary-Induced Strain Fields

“…It is well known that the effect of strain field can be described within the deformation potential theory [26]. In our approach, the total strain field caused by the GB at any point of graphene sheet is determined through a sum of strain fields from all 5-7 pairs [23]. In this way, for a GB oriented in the x-direction, the deformation potential V (r) takes the form…”