Indentation Depth-Dependent Hardness of Metal-Organic Framework Crystals: The Effect of Local Amorphization Induced by Indentation

The hardness of metal-organic frameworks (MOFs) is an important mechanical property metric measuring their resistance to the permanent plastic deformation. The hardness of most MOFs measured from nanoindentation experiments usually exhibits the similar unique indentation depth dependence feature, the mechanism of which still remains unclear. In order to explain the effect of the indentation depth on the hardness of MOFs, we conducted nanoindentation simulations on HKUST-1 by using reactive molecular dynamics simulations. Our simulations reveal that the HKUST-1 material near the indenter can transform from the parent crystalline phase to a new amorphous phase due to the high pressure generated, while its counterpart far from the indenter remains in the crystalline phase. By considering the crystalline-amorphous interface in the energy analysis of MOFs, we derived an analytical expression of the hardness at different indentation depths. It is found that the interface effect can greatly increase the hardness of MOFs, as observed in nanoindentation simulations. Moreover, the proposed analytical expression can well explain the indentation depth-dependent hardness of many MOF crystals measured in nanoindentation experiments. Overall, this work can provide a better understanding of the indentation depth dependence of the hardness of MOFs.