Quantifying Particle Shape in 3D

Experimental and Mathematical Considerations

E. J. Garboczi

100 Bureau Drive Stop 8615National Institute of Standards and TechnologyGaithersburg, Maryland 20899-8615 USAedward.garboczi@nist.gov

ABSTRACT. Quantifying the shape of particles in three dimensions (3D) is important in particle technology. In concrete, the 3D shape of particles like sand, gravel and cement is of great interest for applications including suspension rheology, mechanical properties and realistic microstructure models. When particles are classified as star-shaped, a weaker condition than convexity, a combination of x-ray computed tomography (CT) and spherical harmonic series analysis can quantitatively describe their 3D shape. Since this analysis results in an analytic function for the particle’s surface, one can perform almost any kind of volume or surface integral and so compute many geometrical properties. This paper reviews how 3D particle shape can be measured and analyzed and gives examples for the classes of particles found in construction. Some data will also be given on how particle shape can influence particle size measurement.


KEYWORDS: particle, shape, 3D, spherical harmonics, x-ray tomography, concrete

1. Introduction to particle shape in 3D

The geometry of particles is of interest to researchers in many fields. For regular objects like spheres, cubes, ellipsoids and rectangular boxes, relationships between their dimensions and their shape parameters (e.g. ...

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