Crystallographic surfaces

Abstract

Nodal surfaces, defined by wave vectors in a reciprocal space, equipotential surfaces, defined by point charges in real space, and periodic minimal surfaces, ‘soap-film’ elements lying smoothly across the asymmetric domains in given crystallographic symmetry groups, are exact mathematical objects which may be of physical significance and which can help with the visualization of significant structure at a level above that of single atoms. They are two-dimensional manifolds, with local metrics different from the euclidean metric of the planar sheets of orthodox crystallography, and are of use in the development of the flexi-crystallography of the ‘soft matter’ proposed by de Gennes.