A Review of Particle Size Analysis with X-ray CT
Abstract
:1. Introduction
- What materials and particle sizes have been analysed with this method?
- What are the options for sample preparation, and are they influenced by the particles to be measured?
- What influence does the image processing methodology have on the results?
- Where are the limits of the method in terms of material suitability and particle size range?
1.1. History of Particle Analysis with X-ray CT
1.2. Summary of Materials Examined
1.3. Particle Size Ranges
2. Scanning Protocol for Particle Size Analysis
2.1. Step 1: Sample Preparation
2.2. Step 2: Data Acquisition and Reconstruction
2.3. Step 3: Image Pre-Processing
2.4. Step 4: Image Binarisation and Segmentation
2.5. Step 5: Measurements and Quantification
Sketch | Measure | Methods of Calculation |
---|---|---|
Volume | Counting of all voxels belonging to a particle [89], integral over SH functions [87], integral over the surface covered by a mesh [90]. | |
Surface Area | Counting all faces of surface voxels, estimation of the surface area [84,85], measuring a surface mesh (marching cubes [90]), or calculated from the SH functions [87]. | |
Three dimensions of the particle—length (L), width (W), and breadth (B) (also called depth or thickness). These are mutually orthogonal and L ≥ W ≥ B | Derived from the moments of inertia (with mass represented by voxel intensity) [52,87], edge length of the smallest box that contains the particle [91,92], searching the SH parameters [52], or by calculating length as the maximum Feret [93] or caliper diameter, the maximum distance between two tangential planes of the particle surface and finding W and B orthogonally [94]. | |
Position of the particle within the dataset | Centroid (centre of mass) position [89], as the origin of a square box containing the particle, or as the first point of the particle encountered in the searching direction. | |
Orientation of principal axes, , | Principal axis orientation derived from moments of inertia (or volume) tensor [87]. | |
Local Thickness | The diameter of the largest sphere that fits inside the particle at a local point. [95]. The local thickness differs from the total thickness especially in cases of porous or cup-shaped particles. | |
Equivalent Diameter of a sphere of the same volume as the particle | Derived measure from volume (V): Equivalent diameter | |
Sphericity measures between 0 and 1, and shows how closely the shape matches a perfect sphere | Derived measure from volume (V) and surface area (A): Sphericity |
3. Outlook and Limits of the Method
3.1. Limits of Particle Size and Resolution
3.2. Limits of Material Suitability
3.3. Outlook and Future Developments
4. Conclusions
- 1
- Particle characterisation with X-ray CT has become a widely used method over the last 20 years.
- 2
- The advantages of X-ray CT are the ease of sample preparation, and the available measures of the 3D size and morphology of the particles, as well as internal features such as intra-particle porosity and sample heterogeneity.
- 3
- Since each X-ray CT scan typically encompasses tens of thousands of particles, it is easy to achieve statistically significant results.
- 4
- Modern sub-micrometre X-ray CT systems are able to scan particles as small as 5 µm, or potentially as small as 2 to 3 µm, if the particles are spaced apart.
- 5
- Using theoretical approximations, we have shown that X-ray CT is suitable for characterising materials with atomic numbers up to Z = 40 when the sample is prepared in form of loose particles in a capillary.
- 6
- Materials with an atomic number greater than 40 need special sample preparation methods such as diluting in epoxy in order to achieve enough X-ray transmission from a typical laboratory source.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Behnsen, J.G.; Black, K.; Houghton, J.E.; Worden, R.H. A Review of Particle Size Analysis with X-ray CT. Materials 2023, 16, 1259. https://doi.org/10.3390/ma16031259
Behnsen JG, Black K, Houghton JE, Worden RH. A Review of Particle Size Analysis with X-ray CT. Materials. 2023; 16(3):1259. https://doi.org/10.3390/ma16031259
Chicago/Turabian StyleBehnsen, Julia G., Kate Black, James E. Houghton, and Richard H. Worden. 2023. "A Review of Particle Size Analysis with X-ray CT" Materials 16, no. 3: 1259. https://doi.org/10.3390/ma16031259
APA StyleBehnsen, J. G., Black, K., Houghton, J. E., & Worden, R. H. (2023). A Review of Particle Size Analysis with X-ray CT. Materials, 16(3), 1259. https://doi.org/10.3390/ma16031259