Representation quadrics for crystal structures. I. Metallic elements with no variable coordinates

Summation of the components of interactomic vectors, r_n, normal to a crystallographic plane, (hkl), divided by the area of the periodic repeat unit over which the vectors operate, provides a quantity, σ_n, (hkl), defined as an interaction factor. If all values of σ_n for a given interatomic vector are plotted in the directions normal to all planes in the structure, the result is a structural quadric, with geometric properties analogous to representation quadrics for single-crystal properties. All the atomic interactions in a crystal can thus be represented by a group of quadrics having common semiaxes. It is proposed that crystal properties are a function or functions of the structural quadrics and calculations incorporating some simplifying assumptions are presented to indicate possible applications of the concept.