Nanometer deformation of elastically anisotropic materials studied by nanoindentation

Abstract

The reduced modulus, E_R , of elastically anisotropic materials (Si, CaF₂ and MgF₂) was determined for sub-10 nm, several-10 nm and several-100 nm indentation depths, applying the Hertzian and Oliver–Pharr approaches. The E_R values determined for Si(100), Si(111), CaF₂(100) and MgF₂(100) deforming at sub-10 nm indentations (i.e. 135 GPa, 177 GPa, 142 GPa and 168 GPa) are in good agreement with the theoretical unidirectional E_R values (i.e. 125 GPa, 173 GPa, 135 GPa, 160 GPa). With increasing penetration depth up to several-10 nm, the E_R values gradually deviate from the unidirectional values to the weighted averaged values. E_R remains constant for sub-10 nm and several-10 nm penetration depths, performing the same indentation tests on amorphous organosilicate glass. The results of this study indicate that the modulus determined by nanoindentation depends on the size of indentation (ratio between contact radius and tip radius, a/R), especially in the case of elastically anisotropic materials. It is demonstrated for several-10 nm and several-100 nm penetration depth that the phase transformations in Si during the indentation tests strongly affect the E_R values.

Keywords:

• nanoindentation
• elastic properties
• Hertzian indentation
• phase transformation
• single crystal

Acknowledgements

The authors like to thank Bernd Koehler and Yvonne Ritz, both with the Fraunhofer Institute for Nondestructive Testing, Dresden, Germany, for valuable discussions and for sample preparation. Valuable discussions with William Nix (Stanford University, CA, USA) are acknowledged.