X-ray computed tomography using partially coherent Fresnel diffraction with application to an optical fiber.

A reconstruction algorithm for partially coherent x-ray computed tomography (XCT) including Fresnel diffraction is developed and applied to an optical fiber. The algorithm is applicable to a high-resolution tube-based laboratory-scale x-ray tomography instrument. The computing time is only a few times longer than the projective counterpart. The algorithm is used to reconstruct, with projections and diffraction, a tilt series acquired at the micrometer scale of a graded-index optical fiber using maximum likelihood and a Bayesian method based on the work of Bouman and Sauer. The inclusion of Fresnel diffraction removes some reconstruction artifacts and use of a Bayesian prior probability distribution removes others, resulting in a substantially more accurate reconstruction.

Design of a 3000-Pixel Transition-Edge Sensor X-Ray Spectrometer for Microcircuit Tomography.

Feature sizes in integrated circuits have decreased substantially over time, and it has become increasingly difficult to three-dimensionally image these complex circuits after fabrication. This can be important for process development, defect analysis, and detection of unexpected structures in externally sourced chips, among other applications. Here, we report on a non-destructive, tabletop approach that addresses this imaging problem through x-ray tomography, which we uniquely realize with an instrument that combines a scanning electron microscope (SEM) with a transition-edge sensor (TES) x-ray spectrometer. Our approach uses the highly focused SEM electron beam to generate a small x-ray generation region in a carefully designed target layer that is placed over the sample being tested. With the high collection efficiency and resolving power of a TES spectrometer, we can isolate x-rays generated in the target from background and trace their paths through regions of interest in the sample layers, providing information about the various materials along the x-ray paths through their attenuation functions. We have recently demonstrated our approach using a 240 Mo/Cu bilayer TES prototype instrument on a simplified test sample containing features with sizes of ∼ 1 µm. Currently, we are designing and building a 3000 Mo/Au bilayer TES spectrometer upgrade, which is expected to improve the imaging speed by factor of up to 60 through a combination of increased detector number and detector speed.

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 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.

Electromagnetic resonance analysis of asymmetric carbon nanotube dimers for sensing applications.

In this work, we study the electromagnetic scattering characteristics of asymmetric carbon nanotube (CNT) dimers with rigorous computational experiments. We show that the configurational asymmetry in the CNT dimer assembly creates a unique field distribution in the vicinity of the dimer, which in turn generates two distinct resonances representing the bonding and anti-bonding modes. The sensitivity of these two modes towards CNT lengths, orientations, and shapes, is studied. We also show the ability of asymmetric CNT dimer for the contactless detection of nanoparticles (NP). The presence of a NP in the vicinity of the CNT dimer perturbs the dimer's field distribution and causes unequal shifts in the bonding and anti-bonding resonances depending on the NP location, material, size and shape. By studying the differences in these resonance shifts, we show that the relative location and orientation of the NP can be reconstructed. The computational experiments performed in this work have the potential to guide the use of asymmetric CNT dimers for novel sensing applications.

Dynamic Laser Absorptance Measured in a Geometrically Characterized Stainless-Steel Powder Layer.

The relationship between real powder distributions and optical coupling is a critical building block for developing a deeper physical understanding of laser-additive manufacturing and for creating more reliable and accurate models for predictable manufacturing. Laser-light absorption by a metal powder is distinctly different from that of a solid material, as it is impacted by additional parameters, such as particle size, shape distribution, and packing. Here, we use x-ray computed tomography to experimentally determine these parameters in a thinly spread austenitic stainless-steel powder on a metal substrate, and we combine these results with optical absorptance measurements during a 1 ms stationary laser-light exposure to simulate the additive-manufacturing process. Within the thinly spread powder layer, the particle volume fraction changes continuously from near zero at the powder surface to a peak value of 0.72 at a depth of 235 µm, with the most rapid increase taking place in the first 100 µm. The relationship between this particle volume fraction gradient and optical absorptance is investigated using an analytical model, which shows that depth-averaged absorptance measurements can measure the predicted average value, but will fail to capture local effects that result from a changing powder density. The time-averaged absorptance remains at levels between 0.67 and 0.80 across a two orders of magnitude range in laser power, which is significantly higher than that observed in solid stainless-steel experiments. The dynamic behavior of the absorptance, however, reveals physical phenomena, including oxidation, melting, and vapor cavity (keyhole) formation, as well as quantifying the effect of these on the absorbed energy.

AMB2018-03: Benchmark Physical Property Measurements for Material Extrusion Additive Manufacturing of Polycarbonate.

Material extrusion (MatEx) is finding increasing applications in additive manufacturing of thermoplastics due to the ease of use and the ability to process disparate polymers. Since part strength is anisotropic and frequently deviates negatively with respect to parts produced by injection molding, an urgent challenge is to predict final properties of parts made through this method. A nascent effort is underway to develop theoretical and computational models of MatEx part properties, but these efforts require comprehensive experimental data for guidance and validation. As part of the AM-Bench framework, we provide here a thorough set of measurements on a model system: polycarbonate printed in a simple rectangular shape. For the precursor material (as-received filament), we perform rheology, gel permeation chromatography, and dynamical mechanical analysis, to ascertain critical material parameters such as molar mass distribution, glass transition, and shear thinning. Following processing, we conduct X-ray computed tomography, scanning electron microscopy, depth sensing indentation, and atomic force microscopy modulus mapping. These measurements provide information related to pores, method of failure, and local modulus variations. Finally, we conduct tensile testing to assess strength and degree of anisotropy of mechanical properties. We find several effects that lead to degradation of tensile properties including the presence of pore networks, poor interfacial bonding, variations in interfacial mechanical behavior between rasters, and variable interaction of the neighboring builds within the melt state. The results provide insight into the processing-structure-property relationships and should serve as benchmarks for the development of mechanical models.

Multi-Energy X-Ray Tomography of an Optical Fiber: The Role of Spatial Averaging.

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.

The Influence of X-Ray Computed Tomography Acquisition Parameters on Image Quality and Probability of Detection of Additive Manufacturing Defects.

X-ray computed tomography (XCT) is a promising nondestructive evaluation technique for additive manufacturing (AM) parts with complex shapes. Industrial XCT scanning is a relatively new development, and XCT has several acquisition parameters that a user can change for a scan whose effects are not fully understood. An artifact incorporating simulated defects of different sizes was produced using laser powder bed fusion (LPBF) AM. The influence of six XCT acquisition parameters was investigated experimentally based on a fractional factorial designed experiment. Twenty experimental runs were performed. The noise level of the XCT images was affected by the acquisition parameters, and the importance of the acquisition parameters was ranked. The measurement results were further analyzed to understand the probability of detection (POD) of the simulated defects. The POD determination process is detailed, including estimation of the POD confidence limit curve using a bootstrap method. The results are interpreted in the context of the AM process and XCT acquisition parameters.

Comparison of Models for Heat Transfer in High-Density Fibrous Insulation.

This study evaluated different models for calculating the effective thermal conductivity of fibrous insulation by comparing predicted values with certified values of Standard Reference Material 1450c, Fibrous Glass Board. This comparison involved the coupled effects of radiation and conduction heat transfer. To support these comparisons, the fiber diameter distribution was measured using X-ray computed tomography, and this distribution was used in several heat transfer models considered in this paper. For the evaluation of the radiative heat transfer, the diffusion approximation, the Schuster-Schwarzschild approximation, and the Milne-Eddington approximation were considered. The conduction of the gas and the fibers was treated by the kinetic theory and a semi-empirical model, respectively. Two models were considered for the evaluation of the radiative properties: the large specular reflecting approach and the application of Mie theory for media composed of infinite cylinders.

AMB2018-04: Benchmark Physical Property Measurements for Powder Bed Fusion Additive Manufacturing of Polyamide 12.

Laser sintering (LS) of polyamide 12 (PA12) is increasingly being adopted for industrial production of end-use parts, yet the complexity of this process coupled with the lack of organized, rigorous, publicly available process-structure-physical property datasets exposes manufacturers and customers to risks of unacceptably poor part quality and high costs. Although an extensive scientific literature has been developed to address some of these concerns, results are distributed among numerous reports based on different machines, materials, process parameters, and users. In this study, a single commercially important LS PA12 feedstock has been processed along four build dimensions of a modern production LS machine, characterized by a wide range of physical techniques, and compared to the same material formed by conventional melt processing. Results are discussed in the context of the literature, offering novel insights including distributions of particle size and shape, localization of semicrystalline phase changes due to LS processing, effect of chemical aging on melt viscosity, porosity orientation relative to LS build axes, and microstructural effects on tensile properties and failure mechanisms. The resulting datasets will be made publicly available to modelers and practitioners for the purpose of improving certifiability and repeatability of end-use parts manufactured by LS.

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

PURPOSE: 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. METHODS AND MATERIALS: We formulated a model for our material basis with a set of measurements of elemental powders at four tube voltages, 80 kV, 100 kV, 120 kV, and 140 kV, on a medical XCT. The samples included 30 small plastic bottles of powders containing various compounds spanning the atomic numbers up to 20, and a bottle of water and one of air. Using the chemical formulas and measured masses, we formed a matrix giving the number of Hounsfield units per (mole per cubic meter) at each tube voltage for each of 13 chemical elements. We defined a corresponding matrix in units we call molar Hounsfield unit (HU) potency, the difference in HU values that an added mole per cubic meter in a given voxel would add to the measured HU value. We built a matrix of molar potencies for each chemical element and tube voltage and performed a singular value decomposition (SVD) on these to formulate our material basis. We determined that the dimension of this basis is two. We then compared measurements in this material space with theoretical measurements, combining XCOM cross section data with the tungsten anode spectral model using interpolating cubic splines (TASMICS), a one-parameter filter, and a simple detector model, creating a matrix similar to our experimental matrix for the first 20 chemical elements. Finally, we compared the model predictions to Hounsfield unit measurements on three XCT calibration phantoms taken from the literature. RESULTS: We predict the experimental HU potency values derived from our scans of chemical elements with our theoretical model built from XCOM data. The singular values and singular vectors of the model and powder measurements are in substantial agreement. Application of the Bayesian Information Criterion (BIC) shows that exactly two singular values and singular vectors describe the results over four tube voltages. We give a good account of the HU values from the literature, measured for the calibration phantoms at several tube voltages for several commercial instruments, compared with our theoretical model without introducing additional parameters. CONCLUSIONS: We have developed a two-dimensional material basis that specifies the degree to which individual elements in compounds effect the HU values in XCT images of samples with elements up to atomic number Z = 20. We show that two dimensions is sufficient given the contrast and noise in our experiment. The linear combination of concentrations of elements that can be observed using a medical XCT have been characterized, providing a material basis for use in dual-energy reconstruction. This approach provides groundwork for improved reconstruction and for the link of Hounsfield units to the SI.

Analysis of Different Computational Techniques for Calculating the Polarizability Tensors of Stem Cells with Realistic Three-Dimensional Morphologies.

Recently, the National Institute of Standards and Technology has developed a database of three-dimensional (3D) stem cell morphologies grown in ten different scaffolds to study the effect of the cells' environments on their morphologies. The goal of this work is to study the polarizability tensors of these stem cell morphologies, using three independent computational techniques, to quantify the effect of the environment on the electric properties of these cells. We show excellent agreement between the three techniques, validating the accuracy of our calculations. These computational methods allowed us to investigate different meshing resolutions for each stem cell morphology. After validating our results, we use a fast and accurate Pad' approximation formulation to calculate the polarizability tensors of stem cells for any contrast value between their dielectric permittivity and the dielectric permittivity of their environment. We also performed statistical analysis of our computational results to identify which environment generates cells with similar electric properties. The computational analysis and the results reported herein can be used for shedding light on the response of stem cells to electric fields in applications such as dielectrophoresis and electroporation and for calculating the electric properties of similar biological structures with complex 3D shapes.

A Q-Band Free-Space Characterization of Carbon Nanotube Composites.

We present a free-space measurement technique for non-destructive non-contact electrical and dielectric characterization of nano-carbon composites in the Q-band frequency range of 30 GHz to 50 GHz. The experimental system and error correction model accurately reconstruct the conductivity of composite materials that are either thicker than the wave penetration depth, and therefore exhibit negligible microwave transmission (less than -40 dB), or thinner than the wave penetration depth and, therefore, exhibit significant microwave transmission. This error correction model implements a fixed wave propagation distance between antennas and corrects the complex scattering parameters of the specimen from two references, an air slab having geometrical propagation length equal to that of the specimen under test, and a metallic conductor, such as an aluminum plate. Experimental results were validated by reconstructing the relative dielectric permittivity of known dielectric materials and then used to determine the conductivity of nano-carbon composite laminates. This error correction model can simplify routine characterization of thin conducting laminates to just one measurement of scattering parameters, making the method attractive for research, development, and for quality control in the manufacturing environment.

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

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.

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

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.

Microstructural Origins of Cement Paste Degradation by External Sulfate Attack.

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.

Porosity Measurements and Analysis for Metal Additive Manufacturing Process Control.

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.

Capillary rise between planar surfaces.

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.

A comparison of viscosity-concentration relationships for emulsions.

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.