Design of hard crystals

Hardness is measured by indenting, or by scratching, a solid. In general, it is a measure of structural stability which, in turn, is determined by elastic stiffness, plastic resistance, resistance to structure change; all of which vary with chemical bonding type (electronic structure). For maximum hardness, the key properties must be simultaneously maximized. Furthermore, hardness is a three-dimensional property, so the properties must be maximized in three-dimensions. Resistance to elastic strain depends primarily on valence-electron volumetric density, VED (electrons/unit volume). For sp bonding, the number of valence electrons simply equals the column number (I, II, III, or IV) of the Periodic Table. For the transition elements, there is no reliable rule. The bulk modulus increases with the VED, while the shear moduli are more complex. Resistance to plastic deformation depends primarily on dislocation mobility. This is determined by intrinsic factors in covalently bonded solids (semiconductors) and by extrinsic factors in metals. When a dislocation moves, the atomic symmetry at its core changes. This has a little effect in sp-bonded metals, but it profoundly affects the chemical bonding in covalent crystals. For maximum hardness, dislocation mobility must be minimized. The above principles have been applied to create a new material that easily scratches sapphire; namely, OsB 2. It is believed that they can be used to create even harder materials.