The size and shape of powder particles are not independent quantities. Usual measurement techniques do not measure these intertwined parameters in three dimensions (3D). A 3D measurement/analysis technique is described, based on X-ray computed tomography, which can measure size and shape and classify powder particles according to both parameters.
Measuring the size distribution of the particles in a powder is a common activity in science and industry. Measuring the shape distribution of the particles is much less common. However, the shape and size of powder particles are not independent quantities. All known size/shape measurement techniques either assume a spherical shape or measure the shape in two dimensions only. The X-ray computed tomography (XCT) based method presented here measures both size and shape in 3D without making any assumptions. Starting from a 3D image of particles, the method can mathematically classify particles according to shape, for example particles composed of several smaller particles welded together as opposed to single particles that are not necessarily spherical. Of course, defining a single number as the "size" or "shape" of a random non-spherical particle is not possible in principle, leading to many ways to estimate particle size and shape via various interlinked parameters, which can all be generated from this complete 3D characterization in the form of averages and distributions. The necessary experimental procedures, mathematical analysis, and computer analysis are described and an example is given for a metal powder. The technique is limited to particles that can be imaged by XCT with a minimum of about 1000 voxels per particle volume.
Measuring the size distribution of the particles in a powder is a common activity in science and industry1,2. Measuring the shape distribution of the particles is less common, but both size and shape, along with the material the particles are made from, determine their properties, either alone or in some kind of matrix material3,4,5,6,7. Materials whose particle size and shape are of interest include portland cement, sand, and gravel8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23, metal powders for powder metallurgy and additive manufacturing24,25,26, lunar soil27,28,29, shredded automotive tires30, crushed waste glass31, stem cells32, and carbon nanotubes and graphene33,34,35,36,37. However, the shape and size of powder particles are not independent quantities26. For example, suppose one has a geometrically regular particle whose "size" is said to be d. Without saying whether this particle is a sphere, a cube, or a thin rod of length d, one does not really know how the size applies to this particle. By saying that the particle is a sphere, cube, or rod, one is really specifying the particle's shape, and without this extra information, the size information is meaningless.
For these three examples, a sphere, cube, or thin rod, particle size can be specified by a single number. But even if the rod had a circular cross-section, one would need to also measure the diameter of this cross-section, so two size parameters would really be needed for the thin rod particle. What about particles shaped like ellipsoids, or rectangular boxes? For each of these, three numbers are needed to specify the size, and still the shape must be given as either an ellipsoid or a rectangular box in order for the three size parameters to have meaning. For a randomly-shaped particle, an infinite number of size parameters (e.g., the length of chords across the particle) would be needed to completely characterize the "size" of the particle, and yet these would be meaningless without a "shape characterization," knowing at what angles relative to the center of mass of the particle these chords were drawn.
There are many techniques used for measuring the size distribution of the particles in a powder, employing different physical principles1,2. What is not usually recognized, however, is that in order to extract particle size, information about particle shape, whether assumed or measured, must be used. Current techniques can be classified as: (I) measurements of three-dimensional (3D) particle size while assuming 3D shape, and (II) measurements of both size and shape but only of two dimensional (2D) projections, using 2D image analysis techniques. For spherical particles, all 2D projections are circles, with the same diameter as the original particles, and all these measurement techniques, both Class I and Class II, within measurement uncertainty, give the same results for perfect spheres. For non-spherical particles, the 2D projections are much less closely related to the original particles. If a particle has internal porosity that does not break the particle surface, these pores will not be measured at all by any of these 3D or 2D measurement techniques. Class I includes laser diffraction, electrical sensing volume (ESV)38, sieve analysis, and sedimentation; and Class II covers transmission and scanning electron microscopy, atomic force microscopy, and dynamic and static image analysis with optical techniques. Neither class accurately measures the size and shape of non-spherical particles in 3D.
Since around 200239, a new method of particle analysis has been developed40,41,42,43,44,45 that images a 3D particle in 3D, and then uses several forms of mathematical analysis to represent and classify each particle. A 3D image is saved for each individual particle, which can be compared to the geometrical and mathematical information that is also saved for each particle. This mathematical information can be used to re-generate the particle as desired in any kind of 3D model46,47,48,49, at any location and orientation, or to generate virtual particles that are forced to have the same statistics50,51. This particle analysis method is based on XCT scans of particles dispersed in epoxy or some other such medium. The XCT scans are operated on by specialized software that employ the burning algorithm52,53,54,55,56 to identify particles, and then either spherical harmonic series fitting or voxel counting to generate and store particle shape and size, 3D images of the particles, and, in a second step, geometrical information for each particle. Each particle analyzed has a unique alphanumeric label, which is used to track each particle, the information about each particle, and link each particle to its 3D image. During this analysis process, pores that are inside a particle are analyzed and the total porosity in that particular particle is stored, since XCT reconstruction gives a complete 3D view of a sample.
Three (out of many) geometrical size/shape parameters have been found to be particularly useful in analyzing and classifying particles in 3D: the length, L, the width, W, and the thickness, T. L is defined as the longest surface point to surface point distance across a particle, W is defined similarly as L with the additional constraint the unit vector along W must be perpendicular to the unit vector along L, and T is also defined similarly as L with the additional constraint that the unit vector along T must be perpendicular to both the unit vector along L and the unit vector along W12. These three parameters define the minimum rectangular or bounding box that just contains the particle, and the ratios of these three parameters give valuable but approximate shape information about each particle. Distributions can be made of any of these. It is possible that W correlates well with the "sizes" measured with sieve analysis57, while the "sizes" measured with laser diffraction correlate to a mixture of L, W, and T31.
Finally, the 3D images of a test sample of 100-200 of the particles are visually checked to determine where the cutoffs in L/T are that enable the method to distinguish between single, near-spherical (SnS) particles, and non-spherical (NS) particles, which could be multiple particles welded together, or what are clearly single particles but with an odd shape.
The XCT-based method for characterizing the 3D size and shape of metal particles has more possible applications but also some limitations. The limitations will be addressed first.
A fast-curing epoxy is used so that the viscosity of the epoxy is high enough to prevent the powder from settling under gravity while the epoxy is curing, or at least reducing the time during which settling could happen and the initial well-spaced dispersion degraded. Some settling can still take place, especially fo…
The authors have nothing to disclose.
The authors would like to acknowledge the long-term support of NIST for 3D powder analysis.
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