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Characterising the Morphology of Disordered Materials

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Morphology of Condensed Matter

Part of the book series: Lecture Notes in Physics ((LNP,volume 600))

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.

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Author information

Authors and Affiliations

  1. School of Petroleum Engineering, University of New South Wales, Sydney, NSW, 2052, Australia

    Christoph H. Arns & Mark A. Knackstedt

  2. Department of Applied Mathematics, Research School of Physical Sciences and Engineering, Australian National University, Canberra, ACT, 0200

    Mark A. Knackstedt

  3. MPI für Metallforschung, Heisenbergstr. 3, 70569, Stuttgart, Germany

    Klaus R. Mecke

  4. ITAP, Fakultät für Physik, Universität Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany

    Klaus R. Mecke

Authors
  1. Christoph H. Arns
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  2. Mark A. Knackstedt
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  3. Klaus R. Mecke
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Editor information

Editors and Affiliations

  1. Max-Planck-Institut für Metallforschung, Heisenbergstrasse 1, 70569, Stuttgart, Germany

    Klaus Mecke

  2. Fakultät für Mathematik und Informatik Institut für Stochastik, TU Bergakademie Freiberg, 09596, Freiberg, Germany

    Dietrich Stoyan

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Arns, C.H., Knackstedt, M.A., Mecke, K.R. (2002). Characterising the Morphology of Disordered Materials. In: Mecke, K., Stoyan, D. (eds) Morphology of Condensed Matter. Lecture Notes in Physics, vol 600. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45782-8_2

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  • DOI: https://doi.org/10.1007/3-540-45782-8_2

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  • Print ISBN: 978-3-540-44203-5

  • Online ISBN: 978-3-540-45782-4

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