Characterising the Morphology of Disordered Materials

  • Christoph H. Arns
  • Mark A. Knackstedt
  • Klaus R. Mecke
Part of the Lecture Notes in Physics book series (LNP, volume 600)


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.


Porous Medium Percolation Threshold Phase Fraction Voronoi Tesselation Sandstone Sample 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Christoph H. Arns
    • 1
  • Mark A. Knackstedt
    • 1
    • 2
  • Klaus R. Mecke
    • 3
    • 4
  1. 1.School of Petroleum EngineeringUniversity of New South WalesSydneyAustralia
  2. 2.Department of Applied Mathematics, Research School of Physical Sciences and EngineeringAustralian National UniversityCanberra
  3. 3.MPI für MetallforschungStuttgartGermany
  4. 4.ITAP, Fakultät für PhysikUniversität StuttgartStuttgartGermany

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