Hardness is a measure of a material's resistance to being scratched or dented and is measured using various experimental techniques, including the Vicker's and Knoop tests. However, the values obtained often vary depending on the testing method -- the Knoop diamond, for example, is sharper than the Vicker's and gives a lower hardness. Indeed, experimental values of hardness can vary by more than 10% for the same material. Scientists have therefore been keen to devise a theoretical technique for predicting the hardness of a material with more certainty.

Three years ago, a team led by Faming Gao of Yanshan University in China took an important step towards this goal by developing a semi-empricial formula for the hardness of a material based on the length of the bonds between its components atoms, the number of electrons available for bonding, and the "ionicity", which is the degree to which each pair of atoms shares the electrons between bonds. (In "covalent" materials like silicon the electrons are shared equally, whereas in "ionic" materials one atoms takes over its neighbour's electrons entirely; "polar covalent" materials lie in-between.)

Simunek and Vackar have now taken this work a step further and devised a method for calculating the hardness of single crystals -- both covalent and ionic -- from first principles. Their trick is to introduce a new expression for hardness that describes the strength of a bond based on quantities inherently linked to the atomic structure of the material. Until now, scientists were not able to easily define hardness at the atomic scale.

Their new theory says that the hardness of an ideal single crystal is proportional to the bond strengths and to the number of bonds in a unit cell volume of the crystal. Using simple mathematics, Simunek and Vackar can then calculate the material's hardness. Using their equation, the researchers have also found an unexpected result that contradicts conventional wisdom: atoms surrounded by relatively few other atoms -- that is, those having a lower "co-ordination" number -- are harder than those surrounded by lots of other atoms.

"Our work will lead to a deeper understanding of hardness," Simunek told PhysicsWeb. "The approach will also tell materials scientists how to arrange atoms to make a hard structure for the first time." The team now hopes to develop a complete theory for metallic bonds too.