Surface free energy––a possible source of error in nanohardness?

Model calculations for a nanoindentation experiment are presented showing that the surface free energy of the sample contributes to the measured hardness proportional to the inverse of a characteristic length––either the indentation depth or the tip radius––and thus introduces an error which is in principle unlimited. However it is shown that for many cases encountered in practice the error is of the order of a few percent. Large deviations are to be expected if the following conditions are met simultaneously: (a) The dihedral angle of the indenter is small. (b) The sample is metallic with a high surface free energy. (c) And the indentation depth is well below 100 nm. It is shown that tip rounding with radii usual for commercially available indenters does not significantly influence the conclusions. From these considerations it seems that (fused) quartz is a very “safe” reference material with respect to the influence of the surface free energy. Reasons are given why the measurement of the elastic modulus by nanoindentation should not be influenced strongly by the surface free energy.