On configurational weak phase transitions in graphene

Abstract

We report a study on configurational weak phase transitions for a freestanding monolayer graphene. Firstly, we characterize weak transformation neighborhoods by suitably bounding the metric components. Then, we distinguish between structural and configurational phase changes and elaborate on the second class of them. We evaluate the irreducible invariant subspaces corresponding to these phase changes and lay down symmetry-breaking as well as symmetry-preserving stretches. In the reduced bifurcation diagram, symmetrypreserving stretches are related to a turning point with a change of stability but not of symmetry. Symmetrybreaking stretches are related to a first-order weak phase transition. We evaluate symmetry-breaking stretches as well as their generating cosets. The reduced bifurcation diagram consists of three transcritical bifurcating curves which are all unstable but can be stabilized producing a subcritical bifurcation. We, also, shortly comment on the hysteretical behavior that might appear in this case.

Influence of partial blistering on the global and the local stress and couple stress field for a monolayer graphene resting on substrate

“…The mathematical framework for describing the graphene-substrate system is presented in the work by Sfyris et al [4]. There, we consider simple loading/deformation histories for three classes of problems within the linear framework [5,6] of modeling graphene as a hexagonal 2-lattice [7][8][9][10][11]. The first class of problems pertains to in-surface motions only, while the second class are where we also have out-of-surface motions.…”

Nonlinear electro-magneto-mechanical constitutive modelling of monolayer graphene

“…From the theoretical point of view, the electronic properties of graphene are due ultimately to its crystal structure, which is a honeycomb lattice of carbon atoms that can be regarded as a hexagonal 2-net [1][2][3][4][5][6][7][8]. The s 2 p 2 configuration of the atomic carbon hybridizes in graphene into a configuration in which the 2s, 2p x and 2p y orbital of each carbon are sp 2 -hybridized to form in-plane σ bonds with its three nearest neighbours.…”

“…The above models of electro-magneto-elasticity are at the continuum level. At the discrete level, graphene is a multilattice [1][2][3][4][5][6][7][8]39], i.e. it is a hexagonal 2-lattice and there is a standard procedure for obtaining a continuum model starting from lattice considerations.…”

“…Also since graphene is a real 2-d material the curvature tensor should be included in the list of independent arguments of the energy to take into account out-of-surface motions. This framework tackles solely the mechanical effects [1][2][3][4][5][6][7][8]. To include the electric effects, we first need an expression of the Cauchy-Born rule for the electronic structure of the crystal.…”

“…Secondly, we note that graphene's change from a conductor to insulator is an interesting case of a phase transition that may be described by the loss of positive-definiteness of some of the elasticities deriving from our energy. At the purely mechanical level, criteria for the initiation of configurational weak phase transitions [8] are given in [7].…”