Some statistical investigations of feldspar structures

Abstract

The usual statistical tests for detecting a centre of symmetry cannot be directly applied to certain feldspar structures because of the occurrence of "translational pseudosymmetry" in them. An examination of the problem of intensity distribution in pseudosymmetric structures shows that a certain class of reflections (the "a" type in feldspars) exhibits, as a first approximation, the nature of the distribution corresponding to the "average structure". This is illustrated with six of the plagioclases, all of which are found to have centrosymmetric distributions. A simple method is suggested for estimating the extent of pseudosymmetry in such structures, and this is illustrated with an example. The recently proposed statistical tests for relatedness or isomorphism have also been applied to the plagioclase feldspars. These tests confirm the general earlier ideas concerning the structural relatedness of the different members of the series. They show good agreement with other approximate measures of structural relatedness available for these structures. The advantage of these methods is that they are based only on the observed intensities, and one is therefore able to obtain quantitative statistical measures of the relatedness amongst structures without having to wait for the ultimate structure analysis.