Minkowski Tensor Shape Analysis of Cellular, Granular and Porous Structures

Peukert W, Schröder-Turk G, Mickel W, Kapfer S, Klatt M, Schaller F, Hoffmann M, Kleppmann N, Inayat A, Armstrong P, Hug D, Reichelsdorfer M, Schwieger W, Mecke K (2011)

Publication Language: English

Publication Type: Journal article

Publication year: 2011

Journal

Advanced Materials Wiley-VCH Verlag

Book Volume: 23

Pages Range: 2535--2553

Volume: 23

Issue: 22-23

Journal Issue: 22-23

DOI: 10.1002/adma.201100562

Abstract

Predicting physical properties of materials with spatially complex structures is one of the most challenging problems in material science. One key to a better understanding of such materials is the geometric characterization of their spatial structure. Minkowski tensors are tensorial shape indices that allow quantitative characterization of the anisotropy of complex materials and are particularly well suited for developing structure-property relationships for tensor-valued or orientation-dependent physical properties. They are fundamental shape indices, in some sense being the simplest generalization of the concepts of volume, surface and integral curvatures to tensor-valued quantities. Minkowski tensors are based on a solid mathematical foundation provided by integral and stochastic geometry, and are endowed with strong robustness and completeness theorems. The versatile definition of Minkowski tensors applies widely to different types of morphologies, including ordered and disordered structures. Fast linear-time algorithms are available for their computation. This article provides a practical overview of the different uses of Minkowski tensors to extract quantitative physically-relevant spatial structure information from experimental and simulated data, both in 2D and 3D. Applications are presented that quantify (a) alignment of co-polymer films by an electric field imaged by surface force microscopy; (b) local cell anisotropy of spherical bead pack models for granular matter and of closed-cell liquid foam models; (c) surface orientation in open-cell solid foams studied by X-ray tomography; and (d) defect densities and locations in molecular dynamics simulations of crystalline copper.

Authors with CRIS profile

Wolfgang Peukert Lehrstuhl für Feststoff- und Grenzflächenverfahrenstechnik Gerd Schröder-Turk Professur für Theoretische Physik Sebastian Kapfer Lehrstuhl für Theoretische Physik Michael Klatt Lehrstuhl für Theoretische Physik Fabian Schaller Lehrstuhl für Theoretische Physik Matthias Hoffmann Lehrstuhl für Theoretische Physik Amer Inayat Professur für Technische Chemie (Reaktionstechnik) Patrick Armstrong Lehrstuhl für Feststoff- und Grenzflächenverfahrenstechnik Martin Reichelsdorfer Lehrstuhl für Theoretische Physik Wilhelm Schwieger Professur für Technische Chemie (Reaktionstechnik) Klaus Mecke Lehrstuhl für Theoretische Physik

Additional Organisation(s)

Exzellenz-Cluster Engineering of Advanced Materials

Involved external institutions

Technische Universität Berlin DE Germany (DE) Karlsruhe Institute of Technology (KIT) DE Germany (DE)

How to cite

APA:

Peukert, W., Schröder-Turk, G., Mickel, W., Kapfer, S., Klatt, M., Schaller, F.,... Mecke, K. (2011). Minkowski Tensor Shape Analysis of Cellular, Granular and Porous Structures. Advanced Materials, 23(22-23), 2535--2553. https://dx.doi.org/10.1002/adma.201100562

MLA:

Peukert, Wolfgang, et al. "Minkowski Tensor Shape Analysis of Cellular, Granular and Porous Structures." Advanced Materials 23.22-23 (2011): 2535--2553.

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