First-principles local stress in crystalline and amorphous metals

Atomic size is perhaps the most commonly used concept to describe material properties. Advances in the understanding of materials are hindered by the available choices of simplifying concepts that can be used. However, the precise definition of atomic size is not easy, and often controversial. Atomic level stress provides a new interpretive tool that draws on the rich formalism of solid mechanics for use with density functional calculations to advance a deeper understanding of the properties of materials. We discuss atomic level stresses in liquids and glasses and make comparisons with ordered and disordered crystals. Somewhat surprisingly, even ordered compounds that are under no macroscopic stress and whose individual atoms are completely relaxed, i.e., no force acting on them, can have substantial atomic level stresses. On top of concepts such as the ionicity or covalency, the atomic level stresses add to the arsenal of analysis tools that are available to interpret the results of density functional calculations.