Indentation size effect in barium titanate with spherical tipped nanoindenters

Nanoindentation tests in an 90°-ac-domain area of an ${001}$ orientated barium titanate single crystal were performed using four different indenters (two with cube corner and two with spherical shape) with tip radii from $61nm$ to $1.9μm$⁠. Extensive calibrations of the tips on fused quartz and sapphire defined the penetration depth range for approximately spherical contact prior to indentation of barium titanate $(BaTiO3)$⁠. The measured elastic modulus is independent of the different indenters. The measurements showed plastic deformation after “pop-in”. The calculated mean pressure remained constant for each indenter, but clearly depends upon the indenter radius. The indenter radius dependence of the hardness support the concept of “geometrically necessary dislocations”, proposed by W. D. Nix and H. Gao [J. Mech. Phys. Sol., 46, 411 (1998)] and its extension to spherical tipped indenters [J. G. Swadener, E. P. George, G. M. Pharr, J. Mech. Phys. Solids, 50, 681 (2002)]. The results show this concept fits the data generated with indenter radii which are at least an order of magnitude lower than investigated by Swadener. Furthermore, the results agree with estimates of the statistically stored dislocation density determined for $BaTiO3$⁠.