The relationship between the golden section <z> and the elastic constants of ensembles selected by diffraction methods

Abstract

In polycrystalline materials composed of grains with cubic symmetry, lattice planes whose Miller indices satisfy the condition T(h, k, l) = 1/5 possess average X-ray elastic constants' that depend solely on the crystallographic compliances and not on direction, as shown by Stickforth (1966, Techn. Mitt. Krupp., 24, 89). In analysing particular reflections that satisfy this condition, we discovered that the golden section ф= (1 + √5)/2 ≈ 1-61803, which appears in many branches of the physical and natural sciences, also defines a family of lattice planes (h фh 0) in which isotropic behaviour would be observed through the use of diffraction techniques. This analysis and its extensions are described. © 1996, Taylor & Francis Group, LLC. All rights reserved.