Hardness of materials: studies at levels from atoms to crystals

Based on the electron-holding energy per unit volume, we extend the concept of hardness to atomic stiffness, ionic stiffness and bond hardness, investigating the nature of material hardness at these three levels. We find that the stiffness of isolated atoms or ions has no direct connection with the hardness of materials, whereas material hardness is directly related to bond hardness, which is essentially determined by the electron-holding energy of its constituent chemical bonds per unit volume. We establish a model for identifying the hardness of materials on the basis of bond hardness. This work offers a deeper understanding of the nature of material hardness at the atomic level, and provides a practical guide in the search for new superhard materials.