Analytical methods for representing complex textures by biaxial pole figures

Abstract

Three angular variables which give the relative orientation between two sets of axes have been defined and their angular range specified for important classes of symmetry. All possible orientations are contained within this angular volume. Continuous ranges of orientations require a continuous density function defined over this volume; this representation is termed a biaxial pole figure. Such figures are a complete representation of the texture since the population of all possible orientations are given. The intensity of diffraction of x rays from any plane is equal to the average density over a defined path through the volume. The problem is one of transforming the x-ray data into the biaxial pole figure. Those methods which have been used for the fiber case are directly extendable to the biaxial case but the increased complexity restricts their usefulness. An iterative method which directly relates the density at any point to only those values of intensity to which it can contribute has been defined and implemented. The method converges to a minimum variance solution for positive values of density. Otherwise the density is zero since negative values are physically inadmissible. A comparison shows this method to give superior results. © 1968 The American Institute of Physics.