Heterogeneity, and the secret of the sea

TL;DR

This paper introduces tools for analyzing the heterogeneity of solid specimens, with applications in microscopy and material characterization, providing new methods for measuring compositional variability.

Contribution

It presents novel analytical tools and expressions for modeling and measuring heterogeneity, inspiring further research in microscopy and material analysis.

Findings

Development of intuitive heterogeneity plots

Formulas for containment probability and sample bias

Applications to microscopy data analysis

Abstract

This paper explores tools for modeling and measuring the compositional heterogeneity of a rock, or other solid specimen. Intuitive ``variation per decade'' plots, simple expressions for containment probability, generalization for familiar error-in-the-mean expressions, and a useful dimensionless sample bias coefficient all emerge from the analysis. These calculations have also inspired subsequent work on log-log roughness spectroscopy (with applications to scanning probe microscope data), and on angular correlation mapping of lattice fringe images (with applications in high resolution transmission electron microscopy). It was originally published as Appendix E of a dissertation on ``Microcharacterization of interplanetary dust collected in the earth's stratosphere''.