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Flake thickness is one of the defining properties of graphene-related 2D materials (GR2Ms), and therefore requires reliable, accurate, and reproducible measurements with well-understood uncertainties. This is needed regardless of the production method or manufacturer because it is important for all GR2M products to be globally comparable. An international interlaboratory comparison on thickness measurements of graphene oxide flakes using atomic force microscopy has been completed in technical working area 41 of versailles project on advanced materials and standards. Twelve laboratories participated in the comparison project, led by NIM, China, to improve the equivalence of thickness measurement for two-dimensional flakes. The measurement methods, uncertainty evaluation and a comparison of the results and analysis are reported in this manuscript. The data and results of this project will be directly used to support the development of an ISO standard., (Creative Commons Attribution license.)

Finite element analysis (FEA) is used to model nanoindentation by a rigid, spherically shaped indenter, axially indenting an elastic two phase polymer system comprised of a cylindrical nanoparticle of compliant polymer set in a semi-infinite matrix of stiffer polymer. The cylindrical nanoparticle is normal to the sample surface. An axisymmetric finite element model is used to determine the reduced modulus measured as a function of the indentation depth for various nanoparticle radii and extensions below the surface. We show how the previous simple analytical equations may be extended to describe these situations with accuracy. This gives excellent agreement with the FEA and provides a clear guide to the maximum indentation depth as a function of both the nanoparticle radius and its thickness consistent with a choice of either computation from the analytical equations or direct measurement with a maximum of 10% error in the measured reduced modulus.

Finite element analysis (FEA) is used to investigate the effect of the Poisson's ratios of both the overlayer and the substrate on the nanoindentation of an elastic two-phase system where the elastic overlayer is more compliant than the underlying elastic substrate. A rigid spherical indenter is used as a probe. It is found that nanoindentation results may be expressed analytically using a simple extension of the previously described equation (Clifford and Seah 2006 Nanotechnology 17 5283). This simple function describes the reduced modulus value measured using Oliver and Pharr's method (1992 J. Mater. Res. 7 1564) for any modulus values or Poisson's ratio values of the overlayer and substrate, overlayer thickness or indenter tip radius. This equation and the FEA behind it are tested using experimental published data for the nanoindentation of a silicon dioxide layer on silicon.