three-dimensional-particle-shape-analysis-using-x-ray-computed

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

Measuring the size distribution of the particles in a powder is a common activity in science and industry. Measuring the shape distribution of the ...

National Institute of Standards and Technology

Differential effective medium theory (D-EMT) has been used by a number of investigators to derive expressions for the shear viscosity of a colloidal suspension or an emulsion as a function of the volume fraction of the dispersed phase. Pal and Rhodes [R. Pal, E. Rhodes, J. Rheol. 33 (7) (1989) 1021-1045] used D-EMT to derive a viscosity-concentration expression for non-Newtonian emulsions, in which variations among different oil-water emulsions were accommodated by fitting the value of an empirical solvation factor by matching the volume fraction at which the ratio of each emulsion was experimentally observed to have a viscosity 100 times greater than that of the pure solvent. When the particles in suspension have occluded volume due to solvation or flocculation, we show that the application of D-EMT to the problem becomes more ambiguous than these investigators have indicated. In addition, the resulting equations either do not account for the limiting behavior near the critical concentration, that is, the concentration at which the viscosity diverges, or they incorporate this critical behavior in an ad hoc way. We suggest an alternative viscosity-concentration equation for emulsions, based on work by Bicerano and coworkers [J. Bicerano, J.F. Douglas, D.A. Brune, J. Macromol. Sci., Rev. Macromol. Chem. Phys. C 39 (4) (1999) 561-642]. This alternative equation has the advantages that (1) its parameters are more closely related to physical properties of the suspension and (2) it recovers the correct limiting behavior both in the dilute limit and near the critical concentration for rigid particles. In addition, the equation can account for the deformability of flexible particles in the semidilute regime. The proposed equation is compared to the equation proposed by Pal and Rhodes.

A comparison of viscosity-concentration relationships for emulsions.

Minimization of free energy is used to calculate the equilibrium vertical rise and meniscus shape of a liquid column between two closely spaced, parallel planar surfaces that are inert and immobile. States of minimum free energy are found using standard variational principles, which lead not only to an Euler-Lagrange differential equation for the meniscus shape and elevation, but also to the boundary conditions at the three-phase junction where the liquid meniscus intersects the solid walls. The analysis shows that the classical Young-Dupré equation for the thermodynamic contact angle is valid at the three-phase junction, as already shown for sessile drops with or without the influence of a gravitational field. Integration of the Euler-Lagrange equation shows that a generalized Laplace-Young (LY) equation first proposed by O'Brien, Craig, and Peyton [J. Colloid Interface Sci. 26, 500 (1968)] gives an exact prediction of the mean elevation of the meniscus at any wall separation, whereas the classical LY equation for the elevation of the midpoint of the meniscus is accurate only when the separation approaches zero or infinity. When both walls are identical, the meniscus is symmetric about the midpoint, and the midpoint elevation is a more traditional and convenient measure of capillary rise than the mean elevation. Therefore, for this symmetric system a different equation is fitted to numerical predictions of the midpoint elevation and is shown to give excellent agreement for contact angles between 15 degrees and 160 degrees and wall separations up to 30mm . When the walls have dissimilar surface properties, the meniscus generally assumes an asymmetric shape, and significant elevation of the liquid column can occur even when one of the walls has a contact angle significantly greater than 90 degrees . The height of the capillary rise depends on the spacing between the walls and also on the difference in contact angles at the two surfaces. When the contact angle at one wall is greater than 90 degrees but the contact angle at the other wall is less than 90 degrees , the meniscus can have an inflection point separating a region of positive curvature from a region of negative curvature, the inflection point being pinned at zero height. However, this condition arises only when the spacing between the walls exceeds a threshold value that depends on the difference in contact angles.

Capillary rise between planar surfaces.

With advances in anisotropic particle synthesis, particle shape is now a feasible parameter for tuning suspension properties. However, there is a need to determine how these newly synthesized particles affect suspension properties and a need to solve the inverse problem of inferring the particle shape from property measurements. Either way, accurate suspension property predictions are required. Towards this end, we calculated a set of dilute suspension properties for a family of cube-like particles that smoothly interpolate between spheres and cubes. Using three conceptually different methods, we numerically computed the electrical properties of particle suspensions, including the intrinsic conductivity of perfect conductors and insulators. We also considered hydrodynamic properties relevant to particle solutions including the hydrodynamic radius, the intrinsic viscosity and the intrinsic solvent diffusivity. Additionally, we determined the second osmotic virial coefficient using analytic expressions along with numerical integration. As the particles became more cube-like, we found that all of the properties investigated become more sensitive to particle shape. 

Interplay of particle shape and suspension properties: a study of cube-like particles.

Additive manufacturing techniques can produce complex, high-value metal parts, with potential applications as critical metal components such as those found in aerospace engines and as customized biomedical implants. Material porosity in these parts is undesirable for aerospace parts - since porosity could lead to premature failure - and desirable for some biomedical implants - since surface-breaking pores allows for better integration with biological tissue. Changes in a part's porosity during an additive manufacturing build may also be an indication of an undesired change in the build process. Here, we present efforts to develop an ultrasonic sensor for monitoring changes in the porosity in metal parts during fabrication on a metal powder bed fusion system. The development of well-characterized reference samples, measurements of the porosity of these samples with multiple techniques, and correlation of ultrasonic measurements with the degree of porosity are presented. A proposed sensor design, measurement strategy, and future experimental plans on a metal powder bed fusion system are also presented. 

Porosity Measurements and Analysis for Metal Additive Manufacturing Process Control.

The addition of carbon nanotubes (CNTs) and graphene sheets (GSs) into polymeric materials can greatly enhance the conductivity and alter the electromagnetic response of the resulting nanocomposite material. The extent of these property modifications strongly depends on the structural parameters describing the CNTs and GSs, such as their shape and size, as well as their degree of particle dispersion within the polymeric matrix. To model these property modifications in the dilute particle regime, we determine the leading transport virial coefficients describing the conductivity of CNT and GS composites using a combination of molecular dynamics, path-integral, and finite-element calculations. This approach allows for the treatment of the general situation in which the ratio between the conductivity of the nanoparticles and the polymer matrix is arbitrary so that insulating, semi-conductive, and conductive particles can be treated within a unified framework. We first generate ensembles of CNTs and GSs in the form of self-avoiding worm-like cylinders and perfectly flat and random sheet polymeric structures by using molecular dynamics simulation to model the geometrical shapes of these complex-shaped carbonaceous nanoparticles. We then use path-integral and finite element methods to calculate the electric and magnetic polarizability tensors (αE, αM) of the CNT and GS nanoparticles. These properties determine the conductivity virial coefficient σ in the conductive and insulating particle limits, which are required to estimate σ in the general case in which the conductivity contrast Δ between the nanoparticle and the polymer matrix is arbitrary. Finally, we propose approximate relationships for αE and αM that should be useful in materials design and characterization applications. 

Intrinsic conductivity of carbon nanotubes and graphene sheets having a realistic geometry.

A microstructure model has been applied to simulate near-surface degradation of portland cement paste in contact with a sodium sulfate solution. This new model uses thermodynamic equilibrium calculations to guide both compositional and microstructure changes. It predicts localized deformation and the onset of damage by coupling the confined growth of new solids with linear thermoelastic finite element calculations of stress and strain fields. Constrained ettringite growth happens primarily at the expense of calcium monosulfoaluminate, carboaluminate and aluminum-rich hydrotalcite, if any, respectively. Expansion and damage can be mitigated chemically by increasing carbonate and magnesium concentrations or microstructurally by inducing a finer dispersion of monosulfate.

Microstructural Origins of Cement Paste Degradation by External Sulfate Attack.

This paper lays the groundwork for linking Hounsfield unit measurements to the International System of Units (SI), ultimately enabling traceable measurements across X-ray CT (XCT) machines. We do this by characterizing a material basis that may be used in XCT reconstruction giving linear combinations of concentrations of chemical elements (in the SI units of mol/m3) which may be observed at each voxel. By implication, linear combinations not in the set are not observable.

Preliminary X-ray CT investigation to link Hounsfield unit measurements with the International System of Units (SI).

Using a commercial X-ray tomography instrument, we have obtained reconstructions of a graded-index optical fiber with voxels of edge length 1.05 µm at 12 tube voltages. The fiber manufacturer created a graded index in the central region by varying the germanium concentration from a peak value in the center of the core to a very small value at the core-cladding boundary. Operating on 12 tube voltages, we show by a singular value decomposition that there are only two singular vectors with significant weight. Physically, this means scans beyond two tube voltages contain largely redundant information. We concentrate on an analysis of the images associated with these two singular vectors. The first singular vector is dominant and images of the coefficients of the first singular vector at each voxel look are similar to any of the single-energy reconstructions. Images of the coefficients of the second singular vector by itself appear to be noise. However, by averaging the reconstructed voxels in each of several narrow bands of radii, we can obtain values of the second singular vector at each radius. In the core region, where we expect the germanium doping to go from a peak value at the fiber center to zero at the core-cladding boundary, we find that a plot of the two coefficients of the singular vectors forms a line in the two-dimensional space consistent with the dopant decreasing linearly with radial distance from the core center. The coating, made of a polymer rather than silica, is not on this line indicating that the two-dimensional results are sensitive not only to the density but also to the elemental composition.

Edward J. Garboczi

Applied Chemicals and Materials Division,
MS647,
Applied Chemicals and Materials Division, MS647

National Institute of Standards and Technology

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

Edward J. Garboczi

.css-o250i3{font-size:18px;font-family:Open Sans,sans-serif;line-height:21.6px;}Applied Chemicals and Materials Division,MS647,Applied Chemicals and Materials Division, MS647

National Institute of Standards and Technology

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

Applied Chemicals and Materials Division,
MS647,
Applied Chemicals and Materials Division, MS647