THE RELATIONSHIP BETWEEN THE GOLDEN SECTION-PHI AND THE ELASTIC-CONSTANTS OF ENSEMBLES SELECTED BY DIFFRACTION METHODS

In polycrystalline materials composed of grains with cubic symmetry, l attice planes whose Miller indices satisfy the condition Gamma(h,k,l) = 1/5 possess average X-ray elastic constants that depend solely on th e crystallographic compliances and not on direction, as shown by Stick forth (1966, Techn. Mitt. Krupp., 24, 89). In analysing particular ref lections that satisfy this condition, we discovered that the golden se ction Phi = (1 + root 5)/2 approximate to 1.61803, which appears in ma ny branches of the physical and natural sciences, also defines a famil y of lattice planes (h Phi h 0) in which isotropic behaviour would be observed through the use of diffraction techniques. This analysis and its extensions are described.