On the Symmetry of Orientation Distribution in Crystal Aggregates

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Abstract
In a number of laboratories data from the X-ray pole-figure goniometer are now processed numerically to obtain a suite of complete and normalized pole- figures. From these pole-figures the preferred orientat ion of the grains in a monomineralic aggregate is determined using spherical harmonic analysis and represented as a frequency distribution of the Euler angles Ψ, θ, ø, termed the “orientation distribution function” (ODF),When the frequency density of grain orientations is plotted in a Cartesian coordinate system with Ψ, θ, ø, as axes,it must have a translation periodicity Of 2π or less along each of the axes, because the Euler Angles are angles of rotation.