Characterising the Morphology of Disordered Materials

Abstract

We introduce Minkowski functionals to characterise, reconstruct and discriminate different complex material microstructures, for instance, experimental data sets generated from X-ray computer tomography imaging; samples include a suite of Fontainebleau sandstone, and a heterogeneous cross-bedded sandstone. Three distinct classes of digitised complex microstructure are considered: particle based Boolean models, structures generated by level-cuts through Gaussian fields, and models based on a Voronoi tesselation of space. One can define a set of measures for random composite media from a single image at any phase fraction ø which allows one to accurately reconstruct the medium for all other phase fractions and to predict, for instance, the percolation threshold p c . The evolution of the Minkowski functions during erosion and dilation operations on non-convex morphologies leads to a very accurate discrimination of morphology — better than commonly used techniques such as structure functions or chord length distributions.