Reversible Loss of Bernal Stacking during the Deformation of Few-Layer Graphene in Nanocomposites

The deformation of nanocomposites containing graphene flakes with different numbers of layers has been investigated with the use of Raman spectroscopy. It has been found that there is a shift of the 2D band to lower wavenumber and that the rate of band shift per unit strain tends to decrease as the number of graphene layers increases. It has been demonstrated that band broadening takes place during tensile deformation for mono- and bilayer graphene but that band narrowing occurs when the number of graphene layers is more than two. It is also found that the characteristic asymmetric shape of the 2D Raman band for the graphene with three or more layers changes to a symmetrical shape above about 0.4% strain and that it reverts to an asymmetric shape on unloading. This change in Raman band shape and width has been interpreted as being due to a reversible loss of Bernal stacking in the few-layer graphene during deformation. It has been shown that the elastic strain energy released from the unloading of the inner graphene layers in the few-layer material (∼0.2 meV/atom) is similar to the accepted value of the stacking fault energies of graphite and few layer graphene. It is further shown that this loss of Bernal stacking can be accommodated by the formation of arrays of partial dislocations and stacking faults on the basal plane. The effect of the reversible loss of Bernal stacking upon the electronic structure of few-layer graphene and the possibility of using it to modify the electronic structure of few-layer graphene are discussed.


S1. Deformation of Graphene Nanocomposites
In this present study we followed the effect of deformation upon the 2D band in the Raman spectra of a number of model nanocomposites consisting of exfoliated monolayer, bilayer, trilayer and few-layer graphene flakes embedded in a polymer matrix on a poly(methyl methacrylate) (PMMA) beam. The flakes were sandwiched between thin layers of cured SU-8 (spin-coated to ∼300 nm thick) as shown schematically in the diagram below (not to scale).
Full details of the specimen preparation and test procedures are given elsewhere. [1][2][3] The Raman spectra were excited using a 785 nm (1.59 eV) laser with a Renishaw 2000 Raman spectrometer and obtained from the middle of a number of different flakes on the PMMA beam, with a laser power at the sample of < 1 mW. The beam was deformed in steps of ∼0.05% strain to 0.4% strain (monitored using a resistance stain gauge fixed to the beam) using a four-point bending rig and then unloaded.
Two types of deformation experiments were undertaken: • Spectra were obtained at each strain level from points on the central regions of each the flakes being monitored. • A series of spectra were obtained at different positions along a flake of trilayer graphene to map the behaviour at different positions on the flake at different strain levels. Figure S1. Shift of the 2D Raman band with strain for a graphene monolayer flake in a model nanocomposite. (a) Overall band shift for the monolayer, (b) Details of the band for the monolayer, (c) Shift with strain of the bands fitted to a single peak, (d) The variation with strain of the FWHM (full width at half maximum height) of the bands fitted to a single peak.    Figure S6. Variation of position and FWHM of the 2D band for the middle of the flake (green spot) shown in Figure S5. The shift of the 2D band to lower wavenumber accompanied by band narrowing can be clearly seen.  Figure S5 at different levels of applied strain, 0%, 0.3% and relaxed. Figure S7 shows the variation of FWHM along the trilayer flake at different levels of applied strain. In the undeformed state (0%) the average FWHM across the flake is 77.8 cm -1 with a standard deviation of 1.2 cm -1 . At 0.3% strain the FWHM narrows to 76.3 ± 0.9 cm -1 over the central region of the flake. The values of FWHM are higher at the ends of the flake as a result of the lower strain at the free edges, as has been found before 1 . When the strain on the flake is relaxed after being loaded up to 0.4% strain ( Figure S6) the average FWHM increases to 79.3 ± 2.1 cm -1 . The larger standard deviation in the relaxed state could be due to local fluctuations in strain due to the presence of defects in the flake that have not disappeared completely upon unloading.

S3.1 Loss of Bernal Stacking for Few-layer Graphene
For N layers of graphene under deformation, the elastic stored energy U s of the middle layers is given by where E g is the Young's modulus of the graphene (∼ 1 TPa), e g is the elastic strain in the graphene and V is the volume of a single graphene layer.
The volume of the graphene layer is given by where l 0 , w 0 and d are the length, width and thickness of the graphene layer (d = 0.34 nm).
Upon the loss of Bernal stacking, the increase in van der Waals energy U SF by forming N non-AB Bernal-stacked layers is where ∆u is the stacking fault energy per atom of the non-Bernal stacked graphene, A = When the stored elastic energy U s exceeds the stacking fault energy U SF , the loss of Bernal stacking will become energetically favorable. Thus the critical situation is when U s = U SF which leads to As discussed in the text, the loss of Bernal stacking normally occurs at around 0.4% strain. In the simplest case of trilayer graphene (N = 3) it is possible use this equation to estimate the stacking fault energy of graphene as This value is in agreement with that obtained by Shibuta and Elliott 4 who showed that for the interaction between two graphene sheets with a turbostratic orientational relationship, the loss of AB stacking through either rotation or displacement of the two sheets relative to each other, the energy gap between AB and AA stacking is the order of 0.36 meV/atom.

S3.2 Dislocation Energetics
There is accumulated evidence from studies upon graphite 5,6 that such deformation will lead to arrays of basal plane stacking faults and partial dislocations.
The Burgers vector of the partial dislocation is where c is the Burgers vector of the complete dislocation and x is the fraction of c. Along the armchair direction of graphene |c| = 3a, where a = 0.142 nm is the bond length.
In the vicinity of a dislocation, the loss of perfect AB stacking leads to an increase of the van der Waals energy by 2∆uwl/A where ∆u is the stacking fault energy difference per atom, and w and l are the width and length of the partial dislocation and A is the area per atom in the graphene lattice.
The elastic energy due to the deformation around a partial dislocation can be written approximately as which leads to the optimum width of the partial dislocation as nm 40 For an elongation of 0.4%, the distance between to neighbouring partial dislocations is given by (0.142/0.004) nm ∼ 35 nm. This means that the separation of the partial dislocations will be of the order of their width and that regular stacking will be effectively lost in the whole area.