Stress intrepretation of graphene E-2g and A-1g vibrational modes: theoretical analysis (1706.04465v1)

Abstract: We here focus on only one graphene ring and examine to which stress tensor components the E2g and the A1g vibration mode of graphene correspond. These modes are typically related with the G-peak and the D-peak, respectively, and are strongly related to the stress distribution along the specimen. We adopt the theoretical framework of Admal and Tadmor ([1]) for the macroscopic definition of the Cauchy stress tensor and we introduce into this framework the E2g and the A1g as appropriate perturbations. We use these perturbations to the stress tensor expression and evaluate which stress tensor components are related to each vibrational mode. This approach, though qualitative in nature, incorporates all the main physics and reveals that E2g and A1g vibration modes should be related to shear as well as axial stress components when graphene is at rest (i.e. no external applied loading). To bring our framework closer to more concrete results, we evaluate the instantaneous Hardy stress tensor for a pair potential which correspond to the E2g and A1g modes at rest. Our analysis expands to take into account an applied external tensile field. Taking the armchair direction to be along the x-axis, when tension applies along the armchair direction, it is the axial $\sigma$11 stress component which dominates over $\sigma$12, $\sigma$22, which are of smaller order. When tension is along the zig-zag direction, it is the axial $\sigma$22 stress component that dominates over $\sigma$12, $\sigma$11. When tension is at an arbitrary direction between the armchair and the zig-zag direction, all stress components are of the same order and should all be taken into account even at small strains.