Equi-biaxial compressive strain in graphene: Grüneisen parameter and buckling ridges

Abstract

Strain and defects in graphene have critical impact on morphology and properties of graphene. Here we report equi-biaxial compressive strain in monolayer graphene on SiO2 and Si3N4 substrates induced by thermal cycling in vacuum. The equi-biaxial strain is attributed to the mismatch in coefficient of thermal expansion between graphene and the substrate and sliding of graphene on the substrate. The sliding occurs during heating at the temperatures of 390 and 360 K for graphene on SiO2 and Si3N4 substrates, respectively. The biaxial Grüneisen parameter is determined to be 1.95 and 3.15 for G and 2D Raman bands of graphene, respectively. As the heating temperature exceeds a threshold temperature (1040 K for graphene/SiO2 and 640 K for graphene/Si3N4), buckling ridges are observed in graphene after the thermal cycle, from which the biaxial buckling strain of graphene on SiO2 and Si3N4 substrates are obtained as 0.21% and 0.22%, respectively. Importantly, the induced buckling ridges in graphene exhibit a pattern representing the symmetry of graphene crystal structure, which indicates that graphene relieves the compressive stress mainly along its lattice symmetry directions. These thermally induced graphene ridges are also found reminiscent of those in the synthesized graphene, suggesting the same origin of formation of the buckling ridges under biaxial compression.

Delamination of multilayer graphene stacks from its substrate through wrinkle formation under high pressures

“…These displacements are likely to be dissipated through out-ofplane displacements of the membrane, leading to the observed wrinkling. Similar wrinkling effects were observed in several previous works in which graphene was strained through thermal expansion mismatch with the substrate [24,25], or through the use of a flexible polymer substrate or matrix [23,26]. This first mechanical consideration can explain the formation of wrinkles, but does not explain why these are observed with pure methanol PTM (as well as with pure ethanol in the low pressure regime) but not with other PTMs, such as water, nitrogen or paraffin oil.…”

“…In ref. 25, the buckling threshold identified corresponds to a compressive strain of 0.21% in the graphene sheet when graphene is on a SiO 2 /Si substrate. In the case of high pressure experiments, a value of ε S (P ) = 0.21% at the SiO 2 /Si substrate surface is achieved at pressure as low as ∼ 0.7 GPa.…”

“…The development of an elaborated, inhomogeneous strain field at the nanoscale due to rippling and/or sliding of graphene over the substrate has been proposed, providing in-plane strain dissipation during the compression mechanism [13]. Graphene buckling and crumpling under compression have indeed been reported in various experimental works on graphene mechanics [22][23][24][25][26]. In ref.…”

Configurational Effects on Strain and Doping at Graphene-Silver Nanowire Interfaces

“…−2 is the Grüneisen parameter, is the doping shift constant, and is the no-strain no-doping peak position. Literature reveals = 1.95, = 3.15, = −1.407 10 , and = −0.285 10 [15,24]. This linear transformation of -space to the space of G and 2D realises a correlation plot of 2D against G , with inclined isolines (grey dashed lines) representing equal strain and doping.…”

Dynamic Local Strain in Graphene Generated by Surface Acoustic Waves

“…However, in the case of graphene, there is still a large dispersion of values reported in the literature, with γ G and γ 2D in the ranges of 0.69 − 2.4 and 2.98 − 3.8, respectively [5,14,[53][54][55]. This variation can be attributed to the different type of strain applied, as well as to the quality of the graphene, the substrate used [56], and the effective adhesion of the graphene to the substrate [57]. The smaller value of γ 2D than of γ G obtained in this study seems to be an artifact related to the less efficient SAW-induced modulation of the 2D band due to its broader nature, as it has been discussed in figure 4.…”