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DOE OSTI2025

Porosity in nuclear graphite and its impact on nuclear reactor science and criticality safety applications

Porosity in nuclear-grade graphite significantly influences its low-energy neutron scattering, yet its effect on underlying phonon properties remains debated. Here, this work integrates inelastic and small-angle neutron scattering (INS/SANS) experiments, advanced atomistic simulations with a novel machine-learned potential (DeepMD), total cross-section measurements, and neutronics calculations (SCALE, MCNP, OpenMC) to investigate porosity’s impact on neutron thermalization. INS measurements on diverse graphite grades reveal no discernible porosity effect on phonon spectra, which align with crystalline graphite. Conversely, total cross-section data below ≈10 meV show increased scattering attributable to SANS. Our DeepMD simulations demonstrate that realistic micropores do not distort phonon spectra, challenging the assumptions in current ENDF/B-VIII.1 porosity thermal scattering laws (TSLs). These TSLs, based on random atom removal, produce unphysical phonon spectra and inflate inelastic cross-sections. Augmenting a crystalline TSL with an SANS component accurately captures experimental total cross-sections. Neutronics benchmarks (ICSBEP/IRPhE) show ENDF porosity TSLs unphysically increase neutron multiplication factor, keff. Crucially, incorporating SANS physics (NCrystal/OpenMC) indicates accurately modeled porosity negligibly affects keff, reactor physics, or criticality safety.

Critical benchmarks↗

DOE OSTI2016

Urban flood modeling using shallow water equations with depth-dependent anisotropic porosity

The shallow water model with anisotropic porosity conceptually takes into account the unresolved subgrid-scale features, e.g. microtopography or buildings. This enables computationally efficient simulations that can be run on coarser grids, whereas reasonable accuracy is maintained via the introduction of porosity. This article presents a novel numerical model for the depth-averaged equations with anisotropic porosity. The porosity is calculated using the probability mass function of the subgrid-scale features in each cell and updated in each time step. The model is tested in a one-dimensional theoretical benchmark before being evaluated against measurements and high-resolution predictions in three case studies: a dam-break over a triangular bottom sill, a dam-break through an idealized city and a rainfall-runoff event in an idealized urban catchment. The physical processes could be approximated relatively well with the anisotropic porosity shallow water model. The computational resolution influences the porosities calculated at the cell edges and therefore has a large influence on the quality of the solution. The computational time decreased significantly, on average three orders of magnitude, in comparison to the classical high-resolution shallow water model simulation.

finite volume method↗

DOE OSTI2016

A method to improve the sensitivity of neutron porosity measurement based on D-T source

Compensated porosity logging tool utilizing deuterium-tritium (D-T) source shows a lower sensitivity to the variation of formation porosity compared with that adopting Am-Be source. In order to improve the sensitivity, the factors of an infinite homogeneous formation influencing slowing-down length and the near to far counts ratio are analyzed in this paper. Then Monte Carlo simulation method is used to build well logging models to study the responses of a neutron porosity logging tool to hydrogen index and formation density. It shows that in addition to hydrogen index, the variation of the density also has a great impact on slowing-down length and the ratio which reduces the response sensitivity to porosity. A new model depicts the relationship between the count ratio and porosity is proposed. Finally, when the model is used to process the measured ratio, the ratio shows improved dynamic range and sensitivity to porosity compared with the values without processing.

47 OTHER INSTRUMENTATION↗

DOE OSTI2023

Porosity evolution in proton irradiated microfine-grained POCO graphite

This work investigated the porosity evolution of POCO ZXF-5Q graphite that has been irradiated by 340 kW, 120 GeV protons inside NT02 target system in Fermilab's NuMI beamline. This POCO graphite has undergone direct bulk dimensional swelling at low dose irradiation and its local microstructural change is still not well-understood during this process. In this work, the (sub-) micrometre scale porosity from six locations across proton beam fluence and temperature gradients have been studied using focused ion beam-scanning electron microscopy (FIB-SEM) tomography. Here, a deep learning-based tomographic image segmentation technique has been established and implemented for porosity segmentation and quantification. It has been found that there is a decrease in the total volumetric percentage of the porosity at proton beam centre (~ 8 – 8.4 vol.%), by comparing to un-irradiated POCO (~ 12 – 13vol.%) and to beam 2σ and 5σ radii (~ 12vol.%). This decrease in porosity volume percentage was found to be caused by the reduction in pores with volumes > 0.1 μm 3 induced by material bulk dimensional swelling at proton beam centre area. The porosity reduction in relation to dimensional change and irradiation creep was discussed among with other contributing factors, and further investigations through well-controlled irradiation experiment are still needed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Porosity, swelling, and composition evolution in high-burnup monolithic U-Mo fuel

The microstructural progression of very high-burnup (>8 × 10 21 fissions/cm 3 ) monolithic uranium-molybdenum (U-10wt.%Mo) was analyzed, providing crucial insights into the behavior of post-recrystallized nuclear fuel, where scant data exists. Three focused ion beam cuboids sourced from a fuel plate with varying local burnups of 8.86 × 10 21 , 9.05 × 10 21 , and 9.36 × 10 21 fissions/cm 3 were characterized. The porosity and composition of the samples were evaluated to characterize the evolution of the microstructure as a function of fission density and different locations on the fuel plate, while simultaneously isolating plate-specific parameters such as Zr diffusion barrier thickness, hot-isostatic-pressing conditions, enrichment, and reactor conditions. The porosity was segmented, and the three-dimensional distribution of the porosity was extrapolated from the two-dimensional segmentation. The composition was assessed and quantified using energy-dispersive X-ray spectroscopy areal mapping. The porosity fraction increased as a function of the burnup from 27.77±0.51, 35.12±1.54, and 37.71±0.44 % for 8.86 × 10 21 , 9.05 × 10 21 , and 9.36 × 10 21 fissions/cm 3 , respectively. When compared to literature, the porosity volume fraction plateaus at burnups greater than 6 × 10 21 fissions/cm 3 , while the pore size grows linearly as a function of fission density. The number of large pores increased in number density as a function of burnup, while the smallest pores (<0.3 µm) increased up to 9.05 × 10 21 fissions/cm 3 , followed by a decrease at 9.36 × 10 21 fissions/cm 3 . The delamination and cracking in the fuel plate propagated through an interconnected porosity sublayer identified ∼5 µm from the diffusion barrier. The local swelling of the specimens was within or near the prediction bounds of the Robinson-Williams model for local swelling. The fission products, strontium, barium, cerium, and cesium, precipitated into the pores, while neodymium accumulated adjacent to the pores. Furthermore, these findings have direct implications for the development of fuel performance codes and the accurate documentation of the microstructure evolution in high burnup U-Mo, thus enhancing the safety and efficiency of nuclear fuel usage.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2014

Effects of porosity on corrosion resistance of Mg alloy foam produced by powder metallurgy technology

Magnesium alloy foams have the potential to serve as structural material for regular light-weight applications as well as for biodegradable scaffold implants. However, their main disadvantage relates to the high reactivity of magnesium and consequently their natural tendency to corrode in regular service conditions and in physiological environments. The present study aims at evaluating the effect of porosity on the corrosion resistance of MRI 201S magnesium alloy foams in 0.9% NaCl solution and in phosphate buffer saline solution as a simulated physiological electrolyte. The magnesium foams were produced by powder metallurgy technology using space-holding particles to control the porosity content. Machined chips were used as raw material for the production of Mg alloy powder by milling process. The microstructure of the foams was examined using optical and scanning electron microscopy, X-ray diffraction, and X-ray photoelectron spectroscopy analysis. The corrosion behavior was evaluated by immersion test and potentiodynamic polarization analysis. The results obtained clearly demonstrate that the porosity has a significant effect on the corrosion resistance of the tested foams. Foams with 14–19% porosity have a corrosion rate of 4–10 mcd and 7–15 mcd in NaCl and phosphate buffer saline solution, respectively, compared to only 0.10 mcd for the same alloy in as cast conditions. This increased corrosion degradation of the Mg foams by more than one order of magnitude compared to the cast alloy may limit their potential application in regular and physiological environments. - Highlights: • Porosity has a detrimental effect on corrosion resistance of MRI 201S Mg foams. • 14–19% porosity increases the corrosion rate by more than one order of magnitude. • Accelerated corrosion limits the use of foams in regular/physiological environments.

36 MATERIALS SCIENCE↗

DOE OSTI2016

X-ray tomography studies on porosity and particle size distribution in cast in-situ Al-Cu-TiB{sub 2} semi-solid forged composites

X-ray computed tomography (XCT) was used to characterise the internal microstructure and clustering behaviour of TiB{sub 2} particles in in-situ processed Al-Cu metal matrix composites prepared by casting method. Forging was used in semi-solid state to reduce the porosity and to uniformly disperse TiB{sub 2} particles in the composite. Quantification of porosity and clustering of TiB{sub 2} particles was evaluated for different forging reductions (30% and 50% reductions) and compared with an as-cast sample using XCT. Results show that the porosity content was decreased by about 40% due to semi-solid forging as compared to the as-cast condition. Further, XCT results show that the 30% forging reduction resulted in greater uniformity in distribution of TiB{sub 2} particles within the composite compared to as-cast and the 50% forge reduction in semi-solid state. These results show that the application of forging in semi-solid state enhances particle distribution and reduces porosity formation in cast in-situ Al-Cu-TiB{sub 2} metal matrix composites. - Highlights: •XCT was used to visualise 3D internal structure of Al-Cu-TiB{sub 2} MMCs. •Al-Cu-TiB{sub 2} MMC was prepared by casting using flux assisted synthesis method. •TiB{sub 2} particles and porosity size distribution were evaluated. •Results show that forging in semi-solid condition decreases the porosity content and improve the particle dispersion in MMCs.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Gradient porosity electrodes for fast charging lithium-ion batteries

The tendency of Li plating at the surface of thick graphite electrodes greatly limits their application in electrical vehicle (EV) batteries for fast charging applications. To address this concern, we proposed an innovative gradient porosity architecture to facilitate mass transport and suppress Li plating in the thick anodes for fast charging applications. This concept was approved through a thick 3-layered graphite electrode with the highest porosity in the top layer and the lowest porosity in the bottom layer, in contact with the current collector. Here, the gradient porosity structure in the 3-layered graphite electrodes was confirmed by electron microscopy and mercury porosimetry measurements. Used as the anodes of lithium-ion batteries, 3-layered graphite electrodes demonstrated unprecedentedly rate capability and durability superior to 1-layered electrodes. The post-mortem analysis on the cycled cells shows that 3-layered electrodes can significantly suppress Li plating at a high rate up to 4C, which might be responsible for the improved performance of the derived cells. The excellent electrochemical behaviors of 3-layered graphite electrodes are associated with the favored mass transport originating from the unique gradient porosity structure. This is consistent with theoretical studies showing that gradient porosity lowers the Li-ion concentration gradient in the electrolyte in the region close to the separator and slows down the process of reaching the Li plating threshold.

25 ENERGY STORAGE↗

DOE OSTI2016

Experimental Study of Porosity Changes in Shale Caprocks Exposed to CO 2 -Saturated Brines I: Evolution of Mineralogy, Pore Connectivity, Pore Size Distribution, and Surface Area

Carbon capture, utilization, and storage, one proposed method of reducing anthropogenic emissions of CO 2 , relies on low permeability formations, such as shales, above injection formations to prevent upward migration of the injected CO 2 . Porosity in caprocks evaluated for sealing capacity before injection can be altered by geochemical reactions induced by dissolution of injected CO 2 into pore fluids, impacting long-term sealing capacity. Therefore, long-term performance of CO 2 sequestration sites may be dependent on both initial distribution and connectivity of pores in caprocks, and on changes induced by geochemical reaction after injection of CO 2 , which are currently poorly understood. This paper presents results from an experimental study of changes to caprock porosity and pore network geometry in two caprock formations under conditions relevant to CO 2 sequestration. Pore connectivity and total porosity increased in the Gothic Shale; while total porosity increased but pore connectivity decreased in the Marine Tuscaloosa. Gothic Shale is a carbonate mudstone that contains volumetrically more carbonate minerals than Marine Tuscaloosa. Carbonate minerals dissolved to a greater extent than silicate minerals in Gothic Shale under high CO 2 conditions, leading to increased porosity at length scales <~200 nm that contributed to increased pore connectivity. In contrast, silicate minerals dissolved to a greater extent than carbonate minerals in Marine Tuscaloosa leading to increased porosity at all length scales, and specifically an increase in the number of pores >~1 μm. Mineral reactions also contributed to a decrease in pore connectivity, possibly as a result of precipitation in pore throats or hydration of the high percentage of clays. Finally, this study highlights the role that mineralogy of the caprock can play in geochemical response to CO 2 injection and resulting changes in sealing capacity in long-term CO 2 storage projects.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRSDate not supplied

Porosity Prediction and Detection During Composite Cure Using Simulation and Ultrasonic In-Situ Inspection Inside and Autoclave

Composite materials offer unique benefits in aerospace applications such as increased strength-to-weight ratio and improved fatigue properties. They are increasingly being used in major commercial aircraft programs. However, current processing methods can lead to defects in composite parts, which are currently identified using post-manufacturing inspection methods. A cure defects process model has been developed to predict the formation of manufacturing defects (e.g., porosity and fiber waviness) in composites based on the cure parameters and part geometry. However, a capability to directly validate porosity during cure did not exist. Validation methods included comparing resin pressure measured during cure with predictions by the process model and inspection/microscopy after cure. This study developed a high-temperature ultrasonic inspection system to detect porosity defects in composites during autoclave cure and experimentally verify the predictions of the model. The system operated inside an autoclave within an enclosure cooled by intermittent liquid nitrogen(LN2) injections. A high-temperature 2.25 MHz ultrasonic transducer was utilized to transmit ultrasonic waves through the tool plate and into the composite material and to measure the amplitude and time of flight of the reflected waves with a 1 mm × 1 mm resolution. Porosity was observed via the ultrasonic reflections, which experienced increased attenuation in regions of high porosity. Distinct regions of increased porosity were present due to uneven pressure across the panel, which was driven by an intentional misfit between the flat caul plate and the tapered composite panel with ply drops. These observations matched the predictions of the model using the inputs from the experiment (e.g., part material and geometry, cure cycle) and were validated by post-cure ultrasonic inspection and micrographs. The in-situ inspection system was able to successfully provide defect detection and localization and can be applied to future manufacturing of composite structure for aerospace applications.

Porosity↗

NASA NTRS2024

Correlations of Additive Manufacturing Model-Based Process Metrics With Spatter-Induced Porosity in the Powder Bed Fusion-Laser Beam/Metallic Process

Components fabricated using the powder bed fusion laser beam metallic (PBF-LB/M) additive manufacturing (AM) process comprise a multitude of sequential weld passes. Qualifying materials for components in critical applications requires a thorough understanding of pertinent processing-microstructure-property relationships. Porosity defects have a strong adverse effect on the mechanical properties of a material. The morphology of porosity defects created by lack of fusion in PBF-LB/M often exhibit high aspect ratios that can act as stress concentrators and become crack initiation sites. The occurrence of spatter induced porosity is studied using synchronized AM model-based process metrics and porosity measured by high-resolution X-ray computed tomography. A novel AM process metric is introduced to quantify the relative exposure to spatter ejecta impacts and incorporation throughout the sequence of the PBF-LB/M process. Further characterization using optical metallography and scanning electron microscopy indicated that both keyhole and lack of fusion porosity correlated statistically with the spatter ejecta impact field of the PBF-LB/M process. Both keyhole and lack of fusion porosity can be predicted by the spatter exposure process metric, which can be exploited to control the fusion sequence.

Additive Manufacturing↗

DOE OSTI2017

Push-pull tests for estimating effective porosity: expanded analytical solution and in situ application

The analytical solution describing the one-dimensional displacement of the center of mass of a tracer during an injection, drift, and extraction test (push-pull test) was expanded to account for displacement during the injection phase. The solution was expanded to improve the in situ estimation of effective porosity. The truncated equation assumed displacement during the injection phase was negligible, which may theoretically lead to an underestimation of the true value of effective porosity. To experimentally compare the expanded and truncated equations, single-well push-pull tests were conducted across six test wells located in a shallow, unconfined aquifer comprised of unconsolidated and heterogeneous silty and clayey fill materials. The push-pull tests were conducted by injection of bromide tracer, followed by a non-pumping period, and subsequent extraction of groundwater. The values of effective porosity from the expanded equation (0.6–5.0%) were substantially greater than from the truncated equation (0.1–1.3%). The expanded and truncated equations were compared to data from previous push-pull studies in the literature and demonstrated that displacement during the injection phase may or may not be negligible, depending on the aquifer properties and the push-pull test parameters. The results presented here also demonstrated the spatial variability of effective porosity within a relatively small study site can be substantial, and the error-propagated uncertainty of effective porosity can be mitigated to a reasonable level (< ± 0.5%). The tests presented here are also the first that the authors are aware of that estimate, in situ, the effective porosity of fine-grained fill material.

58 GEOSCIENCES↗

DOE OSTI2018

Quantification of Porosity in Ceramic Matrix Composites Using Thermography

Thermography is one of the Non-Destructive Evaluation methods used to qualitatively estimate the amount of porosity in as-manufactured ceramic matrix composite (CMC) parts. Through-transmission (TT) thermography allows for comparison of thermal diffusivity caused by differences in material density and porosity at different locations in the part. In this study, volume fraction of pores and its distribution in CMC samples containing different amounts of porosity was quantified using optical microscopy and X-ray computed tomography scans. TT thermography was done on the same specimens and images were analyzed to determine the distribution of thermal diffusivity. Comparison of porosity measurements and thermal diffusivity images shows an inverse correlation. A simple two-phase analytical model describing this relationship is derived for composites and its solution is shown to compare favorably with experimental data. In the absence of porosity data, the model can be used to estimate porosity directly from thermal diffusivity data.

36 MATERIALS SCIENCE↗

DOE OSTI2019

The Effects of Shear Strain, Fabric, and Porosity Evolution on Elastic and Mechanical Properties of Clay-Rich Fault Gouge

The elastic and mechanical properties of fault gouge are key controls on fault zone stiffness, strength, damage, healing, and sliding stability. Clay minerals are prevalent in fault zones and have significant effects on friction, porosity, elastic properties, and shear fabric development. Although clay-rich gouges are well studied, the roles of porosity evolution and fabric formation in modulating elastic and mechanical properties are unclear. We have found that with progressive shear, the role of strain localization and fabric development may compete with densification to control the evolution of friction and elastic moduli. We report on a suite of double-direct shear experiments on synthetic gouge composed of 50% Ca-montmorillonite and 50% granular quartz at a normal stress of 25 MPa. We measure the coefficient of friction, porosity, P and S wave speeds, and bulk and shear moduli, and their evolution with shearing, to shear strains up to ~25. We find that the evolution of Vp, Vs, and elastic moduli are controlled by the interplay of porosity loss, shear fabric development, and particle contact stiffness. In general, V p , V s , and elastic moduli increase with shear strain and are accompanied by gradual densification and porosity loss. However, at intermediate shear strains (~2–8) a decrease in V p , V s , and elastic moduli is superimposed on this overall trend. Based on previous microstructural studies, we hypothesize that fabrics develop parallel to shear direction (perpendicular to wave propagation) over this range of strains, leading to reduced fault stiffness and competing with porosity loss as the dominant control on elastic properties.

58 GEOSCIENCES↗

DOE OSTI2021

Porosity-Permeability Evolution During Simultaneous Mineral Dissolution and Precipitation

Permeability in reactive porous media evolves in complex ways that are hard to predict. Macroscopic empirical equations are often used to estimate permeability evolution but fail to reflect the impact of pore scale reactions on permeability. This work aims to understand the evolution of permeability in systems where mineral dissolution and precipitation occur simultaneously. Pore network models are used for permeability simulation of a Paluxy sandstone using pore and pore-throat size distributions from the analysis of X-ray CT images. Pore and pore-throat radii are increased and decreased to reflect the effects of dissolution and precipitation reactions. Varying spatial distributions of reactions are simulated and the resulting porosity and permeability values compared with commonly used macroscopic equations. It is observed that when dissolution occurs at the inlet and precipitation at the outlet, porosity increases while permeability decreases. Similar results are also observed in the respective opposite scenario where precipitation occurs at the inlet and dissolution at the outlet. When dissolution and precipitation reactions are randomly distributed throughout the network, porosity increases with little change in permeability that is not captured by the empirical equations. When reactions are controlled by pore and pore-throat sizes, such as dissolution occurring in pores and pore-throats of small size and precipitation in pores and pore-throats of larger size, porosity and permeability decrease. When precipitation occurs in pores and pore-throats of smaller size and dissolution in pores and pore-throats of larger size, porosity and permeability increase and is described relatively well by the Verma-Pruess porosity-permeability equation.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

A historical overview of the activation and porosity of metal–organic frameworks

Since the first reports of metal–organic frameworks (MOFs), this unique class of crystalline, porous materials has garnered increasing attention in a wide variety of applications such as gas storage and separation, catalysis, enzyme immobilization, drug delivery, water capture, and sensing. A fundamental feature of MOFs is their porosity which provides space on the micro- and meso-scale for confining and exposing their functionalities. Therefore, designing MOFs with high porosity and developing suitable activation methods for preserving and accessing their pore space have been a common theme in MOF research. Reticular chemistry allows for the facile design of MOFs from highly tunable metal nodes and organic linkers in order to realize different pore structures, topologies, and functionalities. With the hope of shedding light on future research endeavors in MOF porosity, it is worthwhile to examine the development of MOFs, with an emphasis on their porosity and how to properly access their pore space. In this review, we will provide an overview of the historic evolution of porosity and activation of MOFs, followed by a synopsis of the strategies to design and preserve permanent porosity in MOFs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Porosity Determination and Classification of Laser Powder Bed Fusion AlSi10Mg Dogbones Using Machine Learning [Slides]

Angular pores (lack of fusion) pores are more detrimental to the health of the part due to induced stress concentrations. Three types of porosity found in AM parts: keyhole porosity, gas porosity, and lack of fusion porosity. In this research, we address the question, "Which machine learning and/or machine vision techniques work best to segment porosity and determine the type of porosity observed in the sample?"

42 ENGINEERING↗

NASA NTRS1974

Effects of porosity on weld-joint tensile strength of aluminum alloys

Tensile properties in defect-free weldments of aluminum alloys 2014-T6 and 2219-T87 (sheet and plate) are shown to be related to the level or concentration of induced simulated porosity. The scatter diagram shows that the ultimate tensile strength of the weldments displays the most pronounced linear relationship with the level of porosity. The relationships between yield strength or elongation and porosity are either trivial or inconsequential in the lower and intermediate levels of porosity content. In highly concentrated levels of porosity, both yield strength and elongation values decrease markedly. Correlation coefficients were obtained by simple straight line regression analysis between the variables of ultimate tensile strength and pore level. The coefficients were greater, indicating a better correlation, using a pore area accumulation concept or pore volume accumulation than the accumulation of the pore diameters. These relationships provide a useful tool for assessing the existing aerospace radiographic acceptance standards with respect to permissible porosity. In addition, these relationships, in combination with known design load requirements, will serve as an engineering guideline in determining when a weld repair is necessary based on accumulative pore level as detected by radiographic techniques.

Lovoy, C. V.↗