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Engineering

Three-Dimensional Particle Shape Analysis Using X-ray Computed Tomography: Experimental Procedure and Analysis Algorithms for Metal Powders

Published: December 04, 2020
doi:
10.3791/61636
,
1Applied Chemicals and Materials Division, MS647,National Institute of Standards and Technology

Summary

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.

Abstract

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.

Introduction

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.

Protocol

NOTE: The following protocol is written for metal powder particles with size, according to a volume-equivalent spherical diameter (VESD, diameter of sphere with same volume as particle) approximation, between 10 µm and 100 µm. Assume that the metal has a density in units of g/cm3. Gloves should be worn during the sample preparation steps, along with eye protection. It is important to read over all the steps in Protocol 1, as some equipment needs to be ready before starting the Protocol. <p class=…

Representative Results

ASTM has initiated a proficiency testing program (AMPM, Additive Manufacturing Powder Metallurgy) for metal powder used for laser powder bed fusion, where participants carry out a battery of standard metal powder tests and ASTM compiles the statistical distribution of these results in a report to the participants61. Samples of metal powder are distributed twice per year to all participants. NIST personnel serve as some of the technical advisors to this program, and so have received similar metal p…

Discussion

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…

Disclosures

The authors have nothing to disclose.

Acknowledgements

The authors would like to acknowledge the long-term support of NIST for 3D powder analysis.

Materials

Epoxy Ellsworth Adhesives https://www.ellsworth.com/products/adhesives/epoxy/hardman-doublebubble-extra-fast-set-epoxy-red-package-3.5-g-packet/ Hardman Part # 4001 case of 100
DOWNLOAD MATERIALS LIST

References

  1. Allen, T. . Powder Sampling and Particle Size Determination, 1st edition. , (2003).
  2. Rodriguez, J., Edeskär, T., Knutsson, S. Particle shape quantities and measurement techniques: a review. Electron Journal of Geotechnical Engineering. , 18 (2013).
  3. Garboczi, E. J., Douglas, J. F. Intrinsic conductivity of objects having arbitrary shape and conductivity. Physical Review E. 53, 6169-6180 (1996).
  4. Mansfield, M. L., Douglas, J. F., Garboczi, E. J. Intrinsic viscosity and the electrical polarizability of arbitrarily shaped objects. Physical Review E. 64, 61401-61416 (2001).
  5. Garboczi, E. J., Douglas, J. F., Bohn, R. B. A hybrid finite element-analytical method for determining the intrinsic elastic moduli of particles having moderately extended shapes and a wide range of elastic properties. Mechanics of Materials. 38, 786-800 (2006).
  6. Garboczi, E. J., Douglas, J. F. Elastic Moduli of Composites Containing a Low Concentration of Complex-Shaped Particles Having a General Property Contrast with the Matrix. Mechanics of Materials. 5, 53-65 (2012).
  7. Audus, D. J., Hassan, A. M., Garboczi, E. J., Hudson, S. D., Douglas, J. F. Interplay of particle shape and suspension properties: A study of cube-like particles. Soft Matter. 11, 3360-3366 (2015).
  8. Garboczi, E. J., Bullard, J. W. Shape analysis of a reference cement. Cement and Concrete Research. 34, 1933-1937 (2004).
  9. Masad, E., Saadeh, S., Al-Rousan, T., Garboczi, E. J., Little, D. Computations of particle surface characteristics using optical and x-ray CT images. Computational Materials Science. 34, 406-424 (2005).
  10. Cheok, G. S., Stone, W. C., Garboczi, E. J. Using LADAR to characterize the 3-D shape of aggregates: Preliminary results. Cement and Concrete Research. 36, 1072-1075 (2006).
  11. Mahmoud, E., Gates, L., Masad, E., Garboczi, E. J. Comprehensive Evaluation of AIMS Texture, Angularity, and Dimensions Measurements. Journal of Materials in Civil Engineering. 22, 369-379 (2010).
  12. Erdoğan, S. T., Nie, X., Stutzman, P. E., Garboczi, E. J. Micrometer-scale 3-D imaging of eight cements: Particle shape, cement chemistry, and the effect of particle shape on laser diffraction size analysis. Cement and Concrete Research. 40, 731-739 (2010).
  13. Holzer, L., Flatt, R., Erdoğan, S. T., Nie, X., Garboczi, E. J. Shape comparison between 0.4 µm to 2.0 µm and 20 µm to 60 µm cement particles. Journal of the American Ceramic Society. 93, 1626-1633 (2010).
  14. Erdoğan, S. T., Fowler, D. W., Garboczi, E. J. Shape and size of microfine aggregates: X-ray microcomputed tomography vs. laser diffraction. Powder Technology. 177, 53-63 (2007).
  15. Garboczi, E. J., Liu, X., Taylor, M. A. The Shape of a Blasted and Crushed Rock Material over More than Three Orders of Magnitude: 20 µm to 60 mm. Powder Technology. 229, 84-89 (2012).
  16. Cepuritis, R., Wigum, B. J., Garboczi, E. J., Mørtsell, E., Jacobsen, S. Filler from crushed aggregate for concrete: Pore structure, specific surface, particle shape and size distribution. Cement and Concrete Composites. 54, 2-16 (2014).
  17. Cepuritis, R., Garboczi, E. J., Jacobsen, S., Snyder, K. A. Comparison of 2-D and 3-D shape analysis of concrete aggregate fines from VSI crushing. Powder Technology. 309, 110-125 (2017).
  18. Cepuritis, R., Garboczi, E. J., Jacobsen, S. Three-dimensional shape analysis of concrete aggregate fines produced by VSI crushing. Powder Technology. 308, 410-421 (2017).
  19. Cepuritis, R., Garboczi, E. J., Ferraris, C. F., Jacobsen, S., Sørensen, B. E. Measurement of particle size distribution and specific surface area for crushed concrete aggregate fines. Advanced Powder Technology. 28, 7065 (2017).
  20. Erdogan, S. T., Forster, A. M., Stutzman, P. E., Garboczi, E. J. Particle-based characterization of Ottawa sand: Shape, size, mineralogy, and elastic moduli. Cement and Concrete Composites. 83, 36-44 (2017).
  21. Olivas, A., et al. Certification of SRM 2493: Standard Reference Mortar for Rheological Measurements. NIST Special Publication. , 260 (2017).
  22. Martys, N., Peltz, W., George, W., Toman, B., Garboczi, E. J. . Certification of SRM 2497: Standard Reference Concrete for Rheological Measurement, NIST SP1237. , (2019).
  23. Estephane, P., Garboczi, E. J., Bullard, J. W., Wallevik, O. H. Three-dimensional shape characterization of fine sands and the influence of particle shape on the packing and workability of mortars. Cement and Concrete Composites. 97, 125-142 (2019).
  24. Slotwinski, J. A., et al. Characterization of Metal Powders Used for Additive Manufacturing. Journal of Research of the National Institute of Standards and Technology. 119, (2014).
  25. Grell, W. A., et al. Effect of powder oxidation on the impact toughness of electron beam melting Ti-6Al-4V. Additive Manufacturing. 17, 123-134 (2017).
  26. Garboczi, E. J., Hrabe, N. Particle shape and size analysis for metal powders used for additive manufacturing: Technique description and application to a gas-atomized Ti64 powder and a plasma-atomized Ti64 powder. Additive Manufacturing. 31, 100965 (2020).
  27. Garboczi, E. J. Three-Dimensional Shape Analysis of JSC-1A Simulated Lunar Regolith Particles. Powder Technology. 207, 96-103 (2011).
  28. Chiaramonti, A. N., Goguen, J. D., Garboczi, E. J. Quantifying the 3-Dimensional Shape of Lunar Regolith Particles Using X-Ray Computed Tomography and Scanning Electron Microscopy at Sub-λ Resolution. Microscopy and Microanalysis. 23, (2017).
  29. Escobar-Cerezo, J., et al. An Experimental Scattering Matrix for Lunar Regolith Simulant JSC-1A at Visible Wavelengths. The Astrophysical Journal Supplement Series. 235, 19 (2018).
  30. Hu, M., Zhang, T., Stansbury, J., Neal, J., Garboczi, E. J. Determination of Porosity and Thickness of Biofilm Attached on Irregular-Shaped Media. Journal of Environmental Engineering. 139 (7), 923-931 (2013).
  31. Garboczi, E. J., Riding, K. A., Mirzahosseini, M. Particle shape effects on particle size measurement for crushed waste glass. Advanced Powder Technology. 28, 648-657 (2017).
  32. Baidya, S., et al. Analysis of Different Computational Techniques for Calculating the Polarizability Tensors of Stem Cells with Realistic Three-Dimensional Morphologies. IEEE Transactions on Biomedical Engineering. , (2018).
  33. Vargas-Lara, F., Hassan, A. M., Garboczi, E. J., Douglas, J. F. Intrinsic Conductivity of Carbon Nanotubes and Graphene Sheets Having a Realistic Geometry. Journal of Chemical Physics. 143, 204902 (2015).
  34. Hassan, A. M., Vargas-Lara, F., Douglas, J. F., Garboczi, E. J. Electromagnetic Resonances of Individual Single-Walled Carbon Nanotubes with Realistic Shapes: A Characteristic Modes Approach. IEEE Transactions on Antennas and Propagation. 64, 2743 (2016).
  35. Durbhakula, K. C., et al. Electromagnetic Scattering From Individual Crumpled Graphene Flakes: A Characteristic Modes Approach. IEEE Transactions on Antennas and Propagation. 65, 6035 (2017).
  36. Hassan, A. M., et al. Electromagnetic Scattering from Multiple Single-Walled Carbon Nanotubes Having Tumbleweed Configurations. IEEE Transactions on Antennas and Propagation. 65, (2017).
  37. Malavé, V., Killgore, J. P., Garboczi, E. J., Berger, J. R. Decoupling the effects of surface topography and material heterogeneity on indentation modulus: A simple numerical linear-elastic model. International Journal of Solids and Structures. 124, 235-243 (2017).
  38. Garboczi, E. J. The influence of particle shape on the results of the electrical sensing zone method as explained by the particle intrinsic conductivity. Powder Technology. 322, 32-40 (2017).
  39. Garboczi, E. J. Three-dimensional mathematical analysis of particle shape using x-ray tomography and spherical harmonics: Application to aggregates used in concrete. Cement and Concrete Research. 32, 1621-1638 (2002).
  40. Erdoğan, S. T., et al. Three-dimensional shape analysis of coarse aggregates: New techniques for and preliminary results on several different coarse aggregates and reference rocks. Cement and Concrete Research. 36, 1619-1627 (2006).
  41. Taylor, M. A., Garboczi, E. J., Erdoğan, S. T., Fowler, D. W. Some properties of irregular particles in 3-D. Powder Technology. 162, 1-15 (2006).
  42. Garboczi, E. J., Bullard, J. W. Contact function, uniform-thickness shell volume, and convexity measure for 3D star-shaped random particles. Powder Technology. 237, 191-201 (2013).
  43. Bullard, J. W., Garboczi, E. J. Defining shape measures for 3D star-shaped particles: Sphericity, roundness, and dimensions. Powder Technology. 249, 241-252 (2013).
  44. Jia, X., Garboczi, E. J. Advances in shape measurement in the digital world. Particuology. 26, 19-31 (2016).
  45. Garboczi, E. J., Bullard, J. W. 3D analytical mathematical models of random star-shape particles via a combination of X-ray computed microtomography and spherical harmonic analysis. Advanced Powder Technology. 28, 325-339 (2017).
  46. Qian, Z., Garboczi, E. J., Ye, G., Schlangen, E. Anm: A geometrical model for the composite structure of mortar and concrete using real-shape particles. Materials and Structures. 49 (1), 149-158 (2015).
  47. Thomas, S., Lu, Y., Garboczi, E. J. Improved model for 3-D virtual concrete: Anm model. Journal of Computing in Civil Engineering. , (2015).
  48. Zuo, Y., Qian, Z., Garboczi, E. J., Ye, G. Numerical simulation of the initial particle parking structure of cement/geopolymer paste and the dissolution of amorphous silica using real-shape particles. Construction and Building Materials. 185, 206-219 (2018).
  49. Lu, Y., Islam, A., Thomas, S., Garboczi, E. J. Three-dimensional mortar models using real-shaped sand particles and uniform thickness interfacial transition zones: Artifacts seen in 2D slices. Construction and Building Materials. 236, 117590 (2020).
  50. Grigoriu, M., Garboczi, E. J., Kafali, C. Spherical harmonic-based random fields for aggregates used in concrete. Powder Technology. 166, 123-138 (2006).
  51. Liu, X., Garboczi, E. J., Grigoriu, M., Lu, Y., Erdoğan, S. T. Spherical harmonic-based random fields based on real particle 3D data: Improved numerical algorithm and quantitative comparison to real particles. Powder Technology. 207, 78-86 (2011).
  52. Stauffer, D., Aharony, A. . Introduction To Percolation Theory: Revised, second edition. , (1994).
  53. Bentz, D. P., Garboczi, E. J. Percolation of phases in a three-dimensional cement paste microstructural model. Cement and Concrete Research. 21, 325-344 (1991).
  54. Garboczi, E. J., Snyder, K. A., Douglas, J. F., Thorpe, M. F. Geometrical percolation threshold of overlapping ellipsoids. Physical Review E. 52, 819-828 (1995).
  55. Garboczi, E. J., Bentz, D. P., Stauffer, D. Computer simulation and percolation theory applied to concrete, in. Annual Reviews of Computational Physics VII. , 85-123 (2000).
  56. Garboczi, E. J. Percolation phase diagrams for multi-phase models built on the overlapping sphere model. Physica A: Statistical Mechanics and its Applications. 442, 156-168 (2016).
  57. Fernlund, J. M. R. The effect of particle form on sieve analysis: a test by image analysis. Engineering Geology. 50 (1), 111-124 (1998).
  58. Otsu, N. A Threshold Selection Method from Gray-Level Histograms. IEEE Transactions on Systems, Man, and Cybernetics. 9, 62-66 (1979).
  59. . Horiba Available from: https://www.horiba.com/fileadmin/uploads/Scientific/Documents/PSA/Manuals/CAMSIZER_Characteristics_Nov2009.pdf (2020)
  60. . Malvern MORPHOLOGI G3 Available from: https://www.malvernpanalytical.com/en/support/product-support/morphologi-range/morphologi-g3 (2020)
  61. . ASTM Available from: https://www.astm.org/STATQA/Additive_Manufacturinng_Powder_Metallurgy.htm (2020)
  62. Bain, E., Garboczi, E. J., Seppala, J., Parker, T., Migler, K. AMB2018-04: Benchmark Physical Property Measurements for Powder Bed Fusion Additive Manufacturing of Polyamide 12. Integrating Materials and Manufacturing Innovation. , (2019).
  63. du Plessis, A., Sperling, P., Beerlink, A., du Preez, W., le Roux, S. G. Standard method for microCT-based additive manufacturing quality control 4: Metal powder analysis. MethodsX. 5, 1336-1345 (2018).
  64. DeCost, B. L., Jain, J., Rollett, A. D., Holm, E. A. Computer vision and machine learning for autonomous characterization for AM powder feedstocks. JOM. 69, 456-465 (2017).
  65. DeCost, B. L., Holm, E. A. Characterizing powder materials using keypoint-based computer vision methods. Computational Materials Science. 126, 438-445 (2017).

Tags

3D Particle AnalysisX-ray Computed Tomography (XCT)Particle ShapeParticle SizePowder CharacterizationMetal Powders3D ImagingMathematical ClassificationParticle Shape ParametersParticle Size Parameters
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Garboczi, E. J., Hrabe, N. Three-Dimensional Particle Shape Analysis Using X-ray Computed Tomography: Experimental Procedure and Analysis Algorithms for Metal Powders. J. Vis. Exp. (166), e61636, doi:10.3791/61636 (2020).
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