On the new characteristics of Miller indices for centered lattices

摘要

This work proposes and justifies a clarification of the description of the crystal structure with the use of centered lattices,and concerns also the following:(1)the graphical and analytical criterion for the existence of lattice planes,described by selected Miller indices,(2)the correct way to use the parametric equation of families of planes,(3)"geometric derivation of the integral reflection conditions"and"Laue indices of Bragg peaks versus Miller indices of families of lattice planes",(4)the characteristics of Miller indices describing nodes of reciprocal lattices for centered direct lattices,(5)the characteristics of Miller indices describing the faces of single crystals and also(6)the characteristics of the information included in Miller indices.Reciprocal lattice nodes associated with families of lattice planes in direct lattices do not form the centered lattices in the reciprocal space themselves.The centered lattices in reciprocal space are created by points with coordinates equal to the Laue indices of Bragg reflections,which are allowed by the integral systematic absences.Parts of them are not associated with any of the direct lattice planes.