Entropy Optimization in Texture Goniometry. I. Methodology

Pursuing the approach of finite series expansion to the texture problem of reproducing the orientation distribution function (ODF) from its pole distribution functions (PDF) measured in X‐ray or neutron diffraction experiments, the mathematical model of entropy maximization is introduced and elaborated in a discrete setting. The entropy maximizing solution yields the ODF with the smallest information content consistent with the experimental data, thus avoiding artificial textural components for which there is no evidence in the measured PDF's, especially “ghosts” caused by the specific properties of the diffraction experiment. This solution seems favorable particularly when the data are incomplete or afflicted with experimental errors.