Coincidence Coefficients of Two Space Lattices and Their Lattice Planes

Abstract

Universal and straight-forward formulae to find the coincidence coefficients of two space lattices and their lattice planes are given by means of elementary theory of numbers. The coincidence coefficient of two space lattices is α2 = kk/d3, and that of their lattice planes is α = α2(CH(2)). Eine universelle und direkte Formel zur Auffindung der Koinzidenzkoeffizienten zweier Gitter und ihrer Gitterebenen wird mittels elementarer Zahlentheorie angegeben. Der Koinzidenzkoeffizient zweier Raumgitter betragt α2 = kk/d3 und der ihrer Gitterebenen α = α2(CH(2)).