Diamond Lattice in the Space of Coordination Spheres

An algorithm has been developed for calculating radii, direction vectors, and coordination numbers (c.n.) for an arbitrary number of coordination spheres (CS) of the diamond lattice. It is established that the space of CS of the diamond lattice has imaginary CS in addition to real ones. The imaginary CS are defined by a direction vector, one of the components of which is an imaginary value. The coordination numbers of such CS are zero. For a great number of tabulated CS, we have studied the hierarchies of structural groups (motifs), forming in the space of coordination spheres and determining the X-ray spectra of lattice CS, the crystallomorphological growth forms of diamond crystals, and the forms of diamond fragmentation induced by thermal destruction and melting.