Particle Shape Analysis Research Articles

Particle shape analysis of calcareous sand based on digital images

Particle geometric is a key parameter that defines the eometric attributes of calcareous sand particles and is intricately related to their mechanical traits, such as compression and shear. The scanning electron microscopy and digital imaging were applied to capture the microscopic properties and geometric projections of calcareous sand. The qualitative analysis, conventional statistical methods and fractal theory were employed to describe the geometric morphology of sand particles. Additionally, we analyzed the structural and physical traits of calcareous sand based on its unique biological genesis. We developed a hypothetical structural-physical model for calcareous sand. Our findings revealed the interwoven reticulation on the surface of calcareous gravel particles, along with an uneven distribution of pores on the external surface. As the particle size increased, the global profile factor decreased and the angularity increased. The critical threshold for the variations in flatness, surface roughness, and circularity was observed at a particle size of 5 mm, with the particle size having a relatively minor effect on these characteristics for particles smaller than 5 mm. The shape of the calcareous sand particles exhibited fractal characteristics, with fractal dimension serving as a measure of surface smoothness, particle breakage, and strength. These experimental results could significantly enhance our understanding of the mechanical behavior of calcareous sand.

The Diatomite Grinding Technology Concept for the Protection of Diatomite Shells and the Control of Product Grading.

Diatomite deposits in Poland are located in the Podkarpackie Voivodeship, and the only active deposit is in Jawornik Ruski. Therefore, it is a unique material. Improved rock processing methods are constantly in demand. In the research presented here, we have used research methods such as X-ray diffraction (XRD), scanning electron microscope (SEM), particle shape analysis, and appropriate sets of crushing machines. Diatomite comminution tests were carried out on test stands in different crushers (jaw crusher, hammer crusher, high-pressure roller press, ball mill) using different elementary crushing force actions: crushing, abrasion, and impact, occurring separately or in combination. The machines were tested with selected variable parameters to obtain products with a wide range of grain sizes ranging from 0 to 10 mm. The ball mill (yield 87%, system C3) and the hammer crusher with HPGR (high-pressure grinding roller) (yield 79%, system D2 + D3) have the greatest impact on diatom shell release and accumulation in the finest 0-5 μm and 5-10 μm fractions. For commercial purposes, it is important to obtain very fine fractions while keeping the shells undisturbed.

Magnetic polyamide 11 powder for the powder bed fusion process by liquid-liquid phase separation and crystallization

Herein, we demonstrate the preparation of magnetic polyamide 11 feedstock powders for powder bed fusion (PBF) using liquid-liquid phase separation and crystallization. By adding magnetic nanomaterials during the precipitation process, the particulate additive is incorporated into the polymer matrix. This enables the production of filled systems at single particle level, which is advantageous in terms of the adjustable magnetic strength and homogeneity of the powder. Thermogravimetric analysis is used to determine the additive content and onset temperature of decomposition of composite powders, where additive-enhancement of PA11 powders with magnetic iron oxide nanoparticles showed a positive influence on the thermal stability of the feedstock. Successive analysis of particle size distribution, shape, colour, crystal structure, magnetic properties and thermal properties of the composite powders are carried out and their properties are discussed with respect to the PBF process. A decrease in particle size, width of the thermal process window and isothermal crystallization time can be attributed to the nucleating effect of the magnetic additive. The PBF processability of the composite feedstock is demonstrated by the production of magnetic tensile bar specimens from additive-enhanced PA11 powders with 1 wt.-% magnetic iron oxide.

X-ray tomography applied to tsunami deposits: Optimized image processing and quantitative analysis of particle size, particle shape, and sedimentary fabric in 3D

The analysis of particle size, shape, size, and their spatial arrangement (i.e. fabric) in a sedimentary deposit plays a significant role in their interpretation in terms of transport mechanism, flow conditions, and sediment source. The present work focuses on the use of X-ray computed tomography (X-CT) to analyze tsunami deposits (core samples), as examples of complex sedimentary assemblages. A workflow of image processing is proposed to measure 3D parameters of particle size, shape, and orientation using two different software packages (Fiji-ImageJ, and IPSDK) and two different methods of image segmentation. The semi-automated method provides better segmentation quality of the tsunami deposit, as compared with the poor performance of fully-automated image segmentation. We also provide some clues to reduce the computational time. This workflow is applied to two examples of tsunami deposits on the coasts of the Algarve (1755 Lisbon tsunami, southern Portugal). Optimized processing of X-CT images gives access to detailed vertical variations of grain size, grain shape, and componentry (clayey matrix, silicates, and carbonates, including marine bioclasts), as well as information on flow directions inferred from the sedimentary fabric in 3D. High-resolution analysis of the bedforms and vertical grain size grading allows determining the flow conditions during the inundation phase of the tsunami.

Characterization of Particle Shape with an Improved 3D Light Scattering Sensor (3D-LSS) for Aerosols

To characterize fine particulate products in industrial gas–solid processes, insights into the particle properties are accessible via various measurement techniques. For micron particles, online imaging techniques offer a fast and reliable assessment of their size and shape. However, for the shape analysis of submicron particles, only offline techniques, such as SEM and TEM imaging, are available. In this work, an online sensor system based on the principle of elastic light scattering of particles in the gas phase is developed to measure the shape factor of non-spherical particles in the size range of 500 nm to 5 µm. Single aerosol particles are guided through a monochromatic circularly polarized laser light beam by an aerodynamic focusing nozzle, which was developed based on the CFD simulation of the flow and particle movement. The intensity of the scattered light is measured at several discrete positions in the azimuthal direction around the particles. An algorithm computes the sphericity of the particles based on the distribution of the intensity signals. The sensor construction, data processing and analysis are described. Model aerosols with particles of different shapes are investigated to test the developed sensor and show its performance in the determination of the sphericity distribution of particles.

New approach for particle size and shape analysis of iron-based oxygen carriers at multiple oxidation states

One of the crucial issues in the chemical looping technology lies in its bed material: the oxygen carrier. Particle size analysis of an oxygen carrier is important since in a fluidized bed the material can only work well within a specific size range. While the favorable size ranges for oxygen carrier materials have already been reported, none of the published studies has analyzed the particle size and shape of oxygen carriers in detail. Furthermore, the effect of oxygen carriers' oxidation degree on such properties has not been considered either. This study aimed to report the particle size and shape analysis of five iron-based oxygen carriers, one natural ore, one synthetic material, and three residue products, at different oxidation degrees using dynamic image analysis (DIA). The oxygen carriers were prepared at different mass conversion degrees in a fluidized bed batch reactor. The size distribution, sphericity, and aspect ratio of the oxygen carrier particles were examined experimentally using a Camsizer instrument. Our results show that the DIA method was successfully able to analyze the particle size and shape of our oxygen carriers with satisfying accuracy for comparison. The oxidation state of the investigated materials seems to only affect the particle size and shape of oxygen carriers to a minor extent. However, exposures to redox cycles in a fluidized bed reactor may alter the particle size and shape of most oxygen carriers.

Particle size and shape analyses for powder bed additive manufacturing

Technical advances in dynamic imaging have enabled routine sampling and analysis of particle shape and shape distributions. Size and shape distributions are relevant to many particulate processes involving flow, spreading, packing and densification. Powder bed additive manufacturing is a prime example requiring uniform spreading, packing and sintering of fine metal powders. This study focuses on quantitative representations of shape described in the International Standards Organization specifications and considers three aspects for improvement thereof: (1) reduced-order mapping of shape distributions using principal component analysis of shape descriptors; (2) uncertainty of shape distribution statistics based on pixel resolution; and (3) opportunities for analysis using machine learning for enhanced image resolution.

Exploring particle breakage in sand under triaxial shearing using combined X-ray tomography and particle tracking method

In this paper, a novel investigation of the particle breakage behaviour of sands is made using combined techniques of X-ray micro-computed tomography (μCT) and sand particle tracking. First, an in situ μCT triaxial test on a miniature sand specimen is conducted to allow the visualisation of particle-scale morphology and movement. Then a two-step particle tracking method is developed and applied to track the sand particles that experience a zero or slight degree of particle breakage. Making use of the power of the particle tracking method, the individual intact particles within a sheared sand specimen containing a mixture of crushed and uncrushed particles were tracked for the first time. The results show that the degree of particle breakage in the consolidation stage is very low, and before the peak stress is reached, more than half of the particles were crushed for the first time; also significant particle breakage occurred at the centre of the specimen during the post-peak stage. The particle shape and gradation analyses reveal that larger grains with lower values of sphericity and convexity are prone to breakage, with the angularities of the crushed particles being closely related to their mother particles.

Shape analysis of sand particles based on Fourier descriptors

Particle shape greatly influences the mechanical behavior of geotechnical materials. For a specific material, for example, a sand particle, it remains an open question how to provide a comprehensive quantitative information about the particle shape. While Fourier descriptors, as a sequence of good shape descriptors, are well addressed in the literature, approaches mainly aim at pattern recognition in the field of computer vision. In this paper, Fourier descriptors are used to analyze the particle shape of geotechnical material. A total of 600 sand particles were collected from the Hutuo River, the main water resource of Shijiazhuang County, Hebei Province. Several shape descriptors, elongation, circularity, convexity, and roughness, are identified and further analyzed statistically. The Andrews plot of Fourier descriptors can be used to discriminate the sand samples. And it is convenient to use Fourier descriptors to reconstruct sand particles. A functional relationship between Fourier descriptors Dk and k, the frequency of the kth components is proved to exist. Moreover, the relationship between shape descriptors and Fourier descriptors is investigated in a correlation analysis. The elongation has a moderate correlation with Fourier descriptors of D1.

A Hydrothermal Phase Diagram for the Low-Temperature Synthesis of Nonstoichiometric Nickel Ferrite Nanoparticles

Corrosion products in pressurized water reactors are challenging to study in situ, yet understanding their properties is key to improving reactor performance and radiation reduction. In this study, a hydrothermal synthesis technique was used to produce nickel ferrite (NiFe2O4) particles from goethite (α-FeOOH) and nickel nitrate hexahydrate [Ni(NO3)2 6H2O] in the presence of sodium hydroxide (NaOH). X-ray diffraction was used for phase identification, with scanning electron microscopy used for particle shape and size analysis. By varying the [Ni]:[Fe] ratio of the precursors and synthesis temperature between 100°C to 250°C, a phase diagram was developed to determine the stability field in both composition and temperature for obtaining a single-phase, nonstoichiometric nickel ferrite product. The compositional boundaries of the single-phase region of the diagram are a function of temperature, consistent with the increased solubility and reaction rates at temperatures above 125°C. The single-phase nickel ferrite encompasses [Ni]:[Fe] ratios in a very narrow range at 150°C, only 0.35 to 0.375, but widens as a function of temperature and reaches its greatest breadth at 250°C. At this temperature, a single-phase product is obtained for a range of starting compositions from 0.30 to 0.425. Outside of this window, additional nanoparticles are obtained whose identity and composition vary with both temperature and starting mixture. On the lower nickel content side of the single-phase region, the mixture contains either unreacted goethite (for temperatures below 200°C) or hematite (α-Fe2O3) at 200°C or higher. On the Ni-rich side of the single-phase region, theophrastite [β-Ni (OH)2] was obtained along with the nickel ferrite, at all temperatures studied. The single-phase window was widest at 250°C, resulting in nickel ferrites with a Ni mole fraction between 0.23 and 0.31.

Influences of Ferric Ions and Fe as a Minor Element in the Lattice on the Floatability of Cassiterite.

In this study, synthetic pure cassiterite and cassiterite doped with two different Fe contents were successfully recrystallized by means of sintering. Their crystal structure and chemical compositions were characterized by X-ray powder diffraction (XRD) as well as scanning electron microscopy (SEM) combined with energy-dispersive X-ray (EDX) analysis. Their floatability was studied by microflotation with a diphosphonic acid surfactant named Lauraphos301 as a collector. Unlike the addition of ferric ions in solution, which strongly depressed the floatability of all of the cassiterite samples, a much higher flotation efficiency of the Fe-doped cassiterite samples was found especially at lower collector concentrations. The cassiterite floatability is proportional to the Fe content in cassiterite at a broad range of pH, and the recovery has the following order: cassiterite with 1417 ppm Fe > cassiterite with 1165 ppm Fe > pure cassiterite. The electrokinetic behavior of the cassiterite samples with and without the collector was studied by electrophoretic measurements and revealed that the chemical interaction dominated the adsorption. With the help of the particle shape analysis, a more angular shape was found for the Fe-doped cassiterite samples. Moreover, without the influence of particle shape, much abundant adsorption of Lauraphos301 was found on the Fe-doped cassiterite samples by AFM topography imaging. The minor amount of Fe in the cassiterite lattice and a more angular shape of the Fe-doped cassiterite samples were believed to enhance floatability collectively. The study reveals that the influence of the chemical composition of the minerals on flotation was almost inextricably bound up with particle morphology and emphasizes the importance of considering both factors and investigating them individually for the flotation study.

Development of Mid‐Way Testing Contingencies for Solid Rocket Motor Processing

AbstractPolyurethane based composite solid propellant (CSP) having aluminium as fuel and ammonium perchlorate (AP) as oxidizer is used in present day solid rocket motors (SRMs). Mechanical and burn rate properties of CSP are wholly dependent on the composition and packing fraction of bimodal AP. Any process deviation or anomalous behavior of propellant slurry at the end of pre/final mixing will result in unacceptable mechanical and ballistic properties leading to rejection of these mixes. Hence, it becomes essential to investigate for possible causes of anomalous behavior such as incorrect content and Coarse/Fine AP ratio (CAP/FAP), contamination with foreign materials, etc. Though suitable test procedures are already available for homogeneity/composition analysis and in vogue, there is no regular test procedures in case of interchange of raw materials of different formulations, to check for contamination of pre‐mixes and to verify AP content in the mixes after mixing the curing agent. Herein, simple contingency procedures have been developed to estimate CAP/FAP in the pre‐mix and AP content in pre/finalmix slurries. The CAP (before its use in premix and after CAP/FAP estimation) was examined using a particle size and shape analyzer and an optical microscope. Contamination checks were also carried out on the samples of premixes usingFT‐IR and DSC. In addition, propellant samples cured under standard conditions were checked for possible deviations with respect to expected mechanical, interfacial, physical and ballistic properties. Conclusions drawn from the investigation can be used to clear the pre/final mix batches for further processing.It is to be noted that these cost‐saving contingency procedures will hereafter form part of analytical testing routines during the processing of solid propellant segments.

Simulating Grain Shape Effects and Damage in Granular Media Using PeriDEM

We provide a numerical platform for the analysis of particle shape and topology on the bulk behavior of granular media using a peridynamic based discrete element method, where the deformation and damage of individual particles are taken into account. To accommodate arbitrary particle shapes including nonconvex ones as well as particle topology, a method is developed to detect peridynamic bonds that extend outside the domain boundary. To avoid numerical oscillation on contact, Coulomb's law is modified for small velocity and a node-level damping is introduced. Particle contact with the rigid boundary wall is computed analytically to avoid treating the wall a peridynamic domain to improve simulation. Moreover, to generate an initial jammed particle distribution, a optimization-based method is used.

Time-Dependent Size and Shape Evolution of Gold and Europium Nanoparticles from a Bioproducing Microorganism, a Cyanobacterium: A Digitally Supported High-Resolution Image Analysis

Herein, the particle size distributions (PSDs) and shape analysis of in vivo bioproduced particles from aqueous Au3+ and Eu3+ solutions by the cyanobacterium Anabaena sp. are examined in detail at the nanoscale. Generally, biosynthesis is affected by numerous parameters. Therefore, it is challenging to find the key set points for generating tailored nanoparticles (NPs). PSDs and shape analysis of the Au and Eu-NPs were performed with ImageJ using high-resolution transmission electron microscopy (HR-TEM) images. As the HR-TEM image analysis reflects only a fraction of the detected NPs within the cells, additional PSDs of the complete cell were performed to determine the NP count and to evaluate the different accuracies. Furthermore, local PSDs were carried out at five randomly selected locations within a single cell to identify local hotspots or agglomerations. The PSDs show that particle size depends mainly on contact time, while the particle shape is hardly affected. The particles formed are distributed quite evenly within the cells. HR-PSDs for Au-NPs show an average equivalent circular diameter (ECD) of 8.4 nm (24 h) and 7.2 nm (51 h). In contrast, Eu-NPs preferably exhibit an average ECD of 10.6 nm (10 h) and 12.3 nm (244 h). Au-NPs are classified predominantly as "very round" with an average reciprocal aspect ratio (RAR) of ~0.9 and a Feret major axis ratio (FMR) of ~1.17. Eu-NPs mainly belong to the "rounded" class with a smaller RAR of ~0.6 and a FMR of ~1.3. These results show that an increase in contact time is not accompanied by an average particle growth for Au-NPs, but by a doubling of the particle number. Anabaena sp. is capable of biosorbing and bioreducing dissolved Au3+ and Eu3+ ions from aqueous solutions, generating nano-sized Au and Eu particles, respectively. Therefore, it is a low-cost, non-toxic and effective candidate for a rapid recovery of these sought-after metals via the bioproduction of NPs with defined sizes and shapes, providing a high potential for scale-up.

Characterization of a Vision-Based Tool for the Investigation of Geometric Characteristics of Ground-Deposited Volcanic Ash

With the support of public authorities and research institutions, volcanic ash fallout and its impact on the safety of people, infrastructure and services are addressed with the aim of defining protocols and instruments for the reliable and effective handling of related emergencies. Most of the solutions proposed in the literature on ash fallout monitoring suffer from high cost and are demanding in terms of installation and maintenance. The approach suggested in this work is based on the use of a low-cost vision embedded system and a dedicated algorithm which automatically processes acquired frames of ground-deposited volcanic ash in order to estimate the main geometric properties of each particle identified in the work area. A complete characterization of the system is presented, along with a robustness analysis of particle shapes, their orientation and their position in the inspected frame. An accuracy of ±40.2 µm (with a 3σ limit) and a resolution of 32.9 µm (in the worst case), over a framed area of 130 mm by 100 mm, were estimated; these values would fulfill the objectives of the application.

Microscopic Insights into the Inhomogeneous Degradation of Pt Alloy Catalysts in PEM Fuel Cells

Fuel cell electric vehicles (FCEVs) powered by proton exchange membrane fuel cells (PEMFCs) offer a sustainable, low-carbon alternative to the world’s current energy structure based on fossil fuels. Recently, application of PEMFC to heavy-duty vehicles (HDVs) has attracted significant interest for reducing greenhouse gas emissions in this market. Relative to passenger vehicles, HDVs require extended lifetimes and high operating costs, leading to an increased emphasis on the durability and efficiency of membrane electrode assembly components [1].Degradation of the oxygen reduction reaction (ORR) cathode catalyst is one of the main challenges for heavy duty applications. Several degradation mechanisms have been identified, such as Ostwald ripening, particle coalescence/migration, and particle detachment, the observation of which relies on transmission electron microscopy (TEM) [2,3]. Through TEM, inhomogeneous degradation at the micro- and nanoscale during operation have been observed: (1) the Pt loading decreases toward the cathode/membrane interface and creates a depletion zone adjacent to the interface [2,4] and (2) different rates of electrochemical surface area loss of PtCo supported on various porous carbons,[5] leading to the speculation of different degradation rates for particles at the exterior vs. interior carbon surfaces.To elucidate these inhomogeneous degradation mechanisms, we employ high-throughput image analysis and electron tomography methods to analyze fuel cell cathodes before and after accelerated stress tests (ASTs) performed in both nitrogen and air environments. An automated, high-throughput method was developed that provides statistically relevant analysis of PtCo particle size, shape, and loading distribution. This method combines automated image or energy-dispersive spectroscopy (EDS) map acquisition using a commercial software (MAPS, Thermo Fisher Scientific) and custom Python codes to analyze high-angle annular dark field (HAADF) and EDS spectrum images. With the high-throughput method, we reveal the inhomogeneous distribution of PtCo particle size, Pt loading, and Co content across the entire electrode. In addition, an electron tomography workflow is under development to measure PtCo particle size and composition on the exterior and interior of the porous carbon support. The effect of cathode gaseous environment on the distribution of particle size, loading, and composition is discussed at the microscale across the electrode and at the nanoscale for exterior and interior surfaces of primary carbon particles. Findings from this study will provide new mitigation strategies and design principles to enable durable fuel cell catalysts.[6]References[1] DA Cullen et al., Nat. Energy. 6 (2021), p. 462.[2] PJ Ferreira et al., J. Electrochem. Soc. 152 (2005), p. A2256.[3] R Borup et al., Chem. Rev. 107 (2007), p. 3904.[4] H Yu et al., Electrochim. Acta 247 (2017), p. 1169.[5] M Ko et al., J. Electrochem. Soc. 168 (2021), p. 24512.[6] This material is based on work performed by the Million Mile Fuel Cell Truck (M2FCT) Consortium, technology managers Greg Kleen and Dimitrios Papageorgopoulus, which is supported by the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, Hydrogen and Fuel Cell Technologies Office, and by U.S. Department of Energy, Office of Nuclear Energy, Fuel Cycle R&D Program, and the Nuclear Science User Facilities. Electron microscopy research was supported by the Center for Nanophase Materials Sciences (CNMS), which is a US Department of Energy, Office of Science User Facility at Oak Ridge National Laboratory.This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).

Novel Dynamic Technique, Nano-DIHM, for Rapid Detection of Oil, Heavy Metals, and Biological Spills in Aquatic Systems.

Numerous anthropogenic and natural particle contaminants exist in diverse aquatic systems, with widely unknown environmental fates. We coupled a flow tube with a digital in-line holographic microscopy (nano-DIHM) technique for aquatic matrices, for in situ real-time analysis of particle size, shape, and phase. Nano-DIHM enables 4D tracking of particles in water and their transformations in three-dimensional space. We demonstrate that nano-DIHM can be automated to detect and track oil spills/oil droplets in dynamic systems. We provide evidence that nano-DIHM can detect the MS2 bacteriophage as a representative biological-viral material and mercury-containing particles alongside other heavy metals as common toxic contaminants. Nano-DIHM shows the capability of observation of combined materials in water, characterizing the interactions of various particles in mixtures, and particles with different coatings in a suspension. The observed sizes of the particles and droplets ranged from ∼1 to 200 μm. We herein demonstrate the ability of nano-DIHM to characterize and distinguish particle-based contaminants in water and their interactions in both stationary and dynamic modes with a 62.5 millisecond time resolution. The fully automated software for dynamic and real-time detection of contaminants will be of global significance. A comparison is also made between nano-DIHM and established techniques such as S/TEM for their different capabilities. Nano-DIHM can provide a range of physicochemical information in stationary and dynamic modes, allowing life cycle analysis of diverse particle contaminants in different aquatic systems, and serve as an effective tool for rapid response for spills and remediation of natural waters.

Particle breakage and shape analysis of calcareous sand under consolidated-undrained triaxial shear

Particle breakage and shape analysis of calcareous sand under consolidated-undrained triaxial shear

Correction to: Fractal dimension, particle shape, and particle breakage analysis for calcareous sand

Correction to: Fractal dimension, particle shape, and particle breakage analysis for calcareous sand

Particle shape characterizations for energetic materials by computational geometry and stereology method

Particle shapes significantly affect viscosity and flow behavior of energetic materials, and therefore affect their packability and processability. This study presents a computational geometry framework for automatically quantifying two-dimensional (2D) and three-dimensional (3D) particle shapes of energetic materials. A specimen by mixing three typical energetic materials including HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine), RDX (1,3,5-Trinitroperhydro-1,3,5-triazine) and AP (Ammonium Perchlorate) particles is used in this study. This specimen is scanned by high-resolution X-ray computed tomography (X-ray CT), yielding a volumetric image. An improved watershed analysis algorithm is used to process the volumetric image to identify individual 3D particles. The stereology sampling method is used to obtain 2D projections of 3D particles. Computational geometry techniques are developed by this study to analyze 2D particle projections and 3D particle geometries to compute seven commonly used shape descriptors, including convexity, circularity, intercept sphericity, area sphericity, diameter sphericity, circle ratio sphericity, and surface area sphericity. Results show that those different shape descriptors of energetic materials can be divided into three groups based on their numerical ranges. This study also evaluates the effectiveness and accuracy of 2D shape descriptors for quantifying the true 3D shapes. The inconsistent characterization results between 2D and 3D shape descriptors suggest that researchers should be cautious when using 2D images to characterize 3D particle shapes of energetic materials. The computational geometry framework and particle shape analysis results presented in this study can be potentially useful in numerical modeling, experimental analysis, and theoretical investigation for energetic materials.