Geometric modeling of force equilibria in crystals: the “equal distance – equal force” formalism (EDEF)

Abstract

Abstract For a broad class of symmetric compounds a formalism is presented which allows detection and proof of physical force equilibria on the basis of purely geomet ric considerations. To represent the atomic interactions be tween structural fragments, the traditional concept of coor dination is generalized by means of the Cartesian product of the sets of atomic coordinates of the fragments. If the physical forces between the atom pairs in the generalized coordination shells are of the same kind, translational and rotational equilibrium between fragments can be read from the geometric directions of the interactions rather than from quantitative physical laws. Partial force equilibrium, as a weaker notion of total force equilibrium, opens up a way to qualitative considerations of dynamic phenomena. Here the basic concepts of this “EDEF model” are defined and il lustrated. We also study the relationship between the EDEF formalism and the underlying symmetry and prove condi tions which are sufficient to conclude EDEF equilibria from the common symmetry elements of the fragments involved. The geometric model enables us to consider the structure of crystals from the point of view of their inner forces.