A method for predicting the structural deformations of 2D materials under strain

In a recent Journal of Physics: Condensed Matter paper, Zacharias Fthenakis and Nektarios Lathiotakis propose a fast and accurate description of the mechanical response of any 2D structure under any strain conditions. Here we find out more from the authors in their own words:

The isolation of graphene by Geim and Novoselov in 2004 gave rise to the field of 2D materials, and the possibility that their properties are relevant for future nanotechnology applications. Many such novel structures (e.g. h-BN, MoS2, WS2, CdS, AlN, C2BN, Si2BN, h-SiC, silicene, germanene, phosphorene etc.) have been theoretically predicted and/or experimentally derived and their properties studied. They continue to fuel significant research interest.

It is therefore important to develop theories and models to describe certain properties of these materials, especially using analytical mathematical expressions. This, however, is not always achievable, due to the complexity of the underlying physics. In our recent paper, we propose a theoretical method which provides such analytic expressions for the structural deformation (i.e. bond length and bond angle deformation) of any 2D planar structure under uniaxial strain along any strain direction.  The required input is the deformation for uniaxial strain along specific strain directions. The method can be easily generalized to analytically describe the mechanical response of any 2D planar structure under any kind of strain conditions, including out of plane deformations, as well as the mechanical response of 2D structures under strain which are not entirely planar.

Figure caption: (a) Graphene stretched uniaxially under strain ε along a strain direction which forms angle θ0 with x-axis. Bond lengths r01, r02, r03 are deformed by δl1, δl2 and δl3, respectively. Bond angles θ01, θ02 and θ03 with respect to the strain direction, are deformed by δθ1, δθ2 and δθ3, respectively. According to the method proposed by Fthenakis and Lathiotakis, δli = 3α0λiε, where λi = ξ1cos2θ0i + ξ2 and δθj – δθi=μijε, where and (i,j,k)=(1,2,3) or (2,3,1) or (3,1,2). (b) λi and μjk as a function of cos2θ0i and cos2θ0ι respectively and the fitting lines according to the above equations, for several strain directions. Image taken from J. Phys. Cond. Mat. 175401 © IOP Publishing 2017.

We applied our method to graphene, deriving general analytic expressions for bond angle and bond length deformations under uniaxial strain in any strain direction. We showed that these analytical expressions fit extremely well with results obtained from ab-initio density functional theory calculations.

The method is very useful for researchers who need a fast and accurate description of the mechanical response of a 2D structure under specific strain conditions, avoiding extensive ab-initio calculations, which are expensive and time consuming.

About the Authors
Zacharias Fthenakis received his PhD in Physics from the University of Crete, Greece. He has been postdoctoral researcher at the Michigan State Univerity, USA and the Institute of Electronic Structure and Laser of the Foundation for Research and Technology, Greece and now he is postdoctoral researcher at the Physics Department of the University of South Florida, USA. His main scientific interests include mechanical, electronic, magnetic and transport properties of materials, with emphasis in two dimensional materials and novel carbon allotropes, as well as  the properties of ferroelectric materials.

Nektarios Lathiotakis received his PhD in Physics from the University of Crete, Greece. He has been a postdoctoral researcher at the University of Bristol, Universität Würzburg and Freie Universität Berlin. He is a Senior Researcher at the Theoretical and Physical Chemistry Institute of the National Hellenic Research Foundation, Greece. He is interested in the development of theoretical electronic structure methods like the reduced density matrix functional theory and the structural, mechanical, optical, magnetic properties of molecular and periodic systems.

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Categories: Journal of Physics: Condensed Matter, JPhys+

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