Anisotropy of spatial phase distributions

The spatial distribution of mineral phases or pores in magmatic, metamorphic and deformed rocks bear genetic information on crystallization, reaction or transport processes amongst others. In general, the spatial distribution of phases can be categorized into random, clustered or anti-clustered types. For example anti-clustered distributions in a deformed, metamorphic rock can be related to heterogeneous nucleation, while clustered distributions can originate from transport limited mineral reactions. Similarly, crystallization processes have the potential to produce either random or clustered phase distributions hinting on crystallization sequence or reaction history. The deviation from randomness towards (anti-)clustering in bi- or multiphase system can be measured in a quantitative way giving the opportunity to address involved processes not only limited to a descriptive way.

Many metamorphic rocks exhibit an either deformation- and/or reaction-induced foliation and also primary foliations may be present in magmatic rocks. Addressing the phase distribution in an isotropic way may degrade the result of a microstructure quantification by camouflaging the spatial ordering of a phase with respect to one specific sample direction in an otherwise isotropic distribution. For example, K-feldspar may appear regularly spaced within quartz-rich layers, while in any other sample direction, this periodicity of K-feldspar is not present. In order to tackle anisotropy of spatial phase distributions, extensions of isotropic methods are presented. Newly derived descriptions of anisotropic phase distributions based on contact normals, a modified center-to-center method and a Fourier transform-based approach will be compared and based on natural examples, their advantages and shortcomings will be discussed.