2D Materials Elastic Properties – AFM-Hertz Methodology

Young's Modulus 2D Materials
Young's Modulus 2D Materials


Young's Modulus 2D Materials

2D materials are single or only few atomic layer thick and posses unique properties with potential in many technological fields. They are highly anisotropic, having significantly different properties in-plane and perpendicular-to-the-plane. For example, graphene, one of the most explored 2D materials, has the in-plane Young’s modulus  E_i=1 TPa , whereas the perpendicular-to-the-plane is only  E_p= 36 GPa . The measurement of Young’s modulus perpendicular-to-the-plane of a few layer thick film of a 2D material is a challenging task. Due to the thickness of just few nanometers, the indentation depth must be less than few Angstroms ( 10^-10 m).

An international team of researchers developed a non-destructive methodology to measure the elastic coupling between the layers of 2D materials.The method is based on the use of Atomic Force Microscope (AFM) to perform extremely high resolution (0.1 Angstrom) indentations. To reach the high resolution, the indentations were performed in modulated nanoindentation mode – the indentation performed in a dynamic AFM mode. The AFM results were analyzed using Semi-Analytical Method (adjusted to anisotropic materials) to obtain the elastic properties of epitaxial graphene and graphene oxide films by fitting experimental force-indentation depth curves.

A perfect agreement was observed between continuum based SAM method and experimentally measured data. The measurement results clearly indicated, that with the sub-nanometer AFM indentations, the the force-indentation curves were very sensitive to the values of  E_p and very slightly depended on  E_i . Along with the large radius of the tip, this allowed to consider the material as isotropic and apply the Hertz analytical model to simplify the fitting procedure.

The results clearly indicate, that the perpendicular-to-the-plane elastic properties can be analyzed using a newly developed methodology. Moreover, the use of Hertz model allows a good approximation to the Young’s modulus of layered 2D materials.

Further details can be found in the original article Elastic coupling between layers in two-dimensional materials, Nature Materials 14,714–720(2015)doi:10.1038/nmat4322.

Credit for image: Elastic coupling between layers in two-dimensional materials, Yang Gao,Suenne Kim,Si Zhou,Hsiang-Chih Chiu, Daniel Nélias,Claire Berger,Walt de Heer,Laura Polloni,Roman Sordan,Angelo Bongiorno& Elisa Riedo.

The comprehensive description of the experimental technique in the supplemental materials makes it useful as a guide for AFM indentation.

Founder of TriboNet, Editor, PhD (Tribology), Tribology Scientist at ASML, The Netherlands. Expertise in lubrication, friction, wear and contact mechanics with emphasis on modeling. Creator of Tribology Simulator.

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