Practical Assessment of Quartz Crystallographic Preferred Orientation Strength

Abstract

The ordering strength of crystallographic preferred orientation data can be assessed in different ways, however, the appropriateness of the methodology used to do so can depend on the geometry of the distributions. Eigenvector-based ordering evaluation methods, for example, may not be appropriate for data that comprise multiple, variably oriented distributions such as those commonly found in quartz c-axis crystallographic preferred orientations. Examination of artificial data that represent a variety of different potential c-axis distributions shows a significant correlation between the relative orientations of those distributions (i.e., the opening angle in a cross-girdled quartz c-axis pole figure) and the strengths calculated using eigen-vector based evaluation methods; larger pole figure opening angles correlate with decreasing distribution ordering strength. The same correlation does not exist when strength is evaluated using the l² - norm of the estimated probability density function (J_PF) of the same data. The direct correlations between pole figure c-axis opening angles and ordering strength noted in the artificial distributions are also demonstrated in the evaluation of real-world data, though significant complications related to heterogeneous nature, and/or deformation, of the natural specimens can partially obfuscate the relationship. Regardless, given the potential effect of geometry on eigenvector-based evaluation methods we recommend that the ordering strength of pole figure data be evaluated using J_PF.