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All sources NASA NTRS DOE OSTI

DOE OSTI2025

Role of pore dilation in molecular transport through the nuclear pore complex: Insights from polymer scaling theory

The nuclear pore complex (NPC), a channel within the nuclear envelope filled with intrinsically disordered proteins, regulates the transport of macromolecules between the nucleus and the cytoplasm. Recent studies have highlighted the NPC’s ability to adjust its diameter in response to the membrane tension, underscoring the importance of exploring how variations in pore size influence molecular transport through the NPC. In this study, we investigated the relationship between pore size and transport rate and proposed a mathematical model describing this connection. We began by theoretically analyzing how the pore size scales with the characteristic dimensions of the mesh-like structure within the pore. By introducing key assumptions about how the meshwork structure influences molecular diffusion, we derived a mathematical expression for the transport rate based on the size of the pore and the transported molecules. To validate our model, we conducted Brownian dynamics simulations using a coarse-grained representation of the NPC. These simulations, performed across a range of pore sizes, demonstrated strong agreement with our model’s predictions, confirming its accuracy and applicability. Our model is specifically tailored for small-to-medium-sized molecules, approximately 5 nanometers in size, making it relevant to a wide range of transcription factors and signaling molecules. It also extends to molecules with weak and transient interactions with FG-Nups, such as importin-β. By presenting this model formula, our study offers a quantitative framework for analyzing the effects of pore dilation on nucleocytoplasmic transport.

Biochemistry & Molecular Biology↗

DOE OSTI2024

Functionalized Graphene via a One-Pot Reaction Enabling Exact Pore Sizes, Modifiable Pore Functionalization, and Precision Doping

Functionalizing graphene with exact pore size, specific functional groups, and precision doping poses many significant challenges. Current methods lack precision and produce random pore sizes, sites of attachment, and amounts of dopant, leading to compromised structural integrity and affecting graphene’s applications. In this work, we report a strategy for the synthesis of functionalized graphitic materials with modifiable nanometer-sized pores via a Pictet–Spengler polymerization reaction. This one-pot, four-step synthesis uses concepts based on covalent organic frameworks (COFs) synthesis to produce crystalline two-dimensional materials that were confirmed by PXRD, TEM measurements, and DFT studies. These new materials are structurally analogous to doped graphene and graphene oxide (GO) but, unlike GO, maintain their semiconductive properties when fully functionalized.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Multi‐Stage Optimization of Pore Size and Shape in Pore‐Space‐Partitioned Metal–Organic Frameworks for Highly Selective and Sensitive Benzene Capture

Abstract Compared to exploratory development of new structure types, pushing the limits of isoreticular synthesis on a high‐performance MOF platform may have higher probability of achieving targeted properties. Multi‐modular MOF platforms could offer even more opportunities by expanding the scope of isoreticular chemistry. However, navigating isoreticular chemistry towards best properties on a multi‐modular platform is challenging due to multiple interconnected pathways. Here on the multi‐modular pacs (partitioned acs) platform, we demonstrate accessibility to a new regime of pore geometry using two independently adjustable modules (framework‐forming module 1 and pore‐partitioning module 2). A series of new pacs materials have been made. Benzene/cyclohexane selectivity is tuned, progressively, from 4.5 to 15.6 to 195.4 and to 482.5 by pushing the boundary of the pacs platform towards the smallest modules known so far. The exceptional stability of these materials in retaining both porosity and single crystallinity enables single‐crystal diffraction studies of different crystal forms (as‐synthesized, activated, guest‐loaded) that help reveal the mechanistic aspects of adsorption in pacs materials.

Chen, Yichong↗

DOE OSTI2026

Pore-Scale Study on the Positive Feedback Between Stress and Porosity Caused by Pressure Solution in Porous Media

Pressure solution is an important process in the evolution of sedimentary rocks, which provide storage space for most of our petroleum resources. It directly influences the generation, migration, and storage of petroleum fluids in subsurface sedimentary rocks. Here, in this paper, we develop a pore-scale, mechanochemical model to demonstrate a possible positive feedback between the local porosity and pore surface stress, in which a higher local porosity causes a higher local pore surface stress, thus enhancing pressure solution and consequently further increasing the local porosity. Pore surface stress represents stress on a solid grain adjacent to a pore. Specifically, the pore-scale, mechanochemical model directly simulates the stress distribution over solid and pore surfaces using a finite element model. The dissolution of solids at the solid-pore interfaces under a far-from-equilibrium condition is simulated using a first-order kinetics model that accounts for the local stress distribution. The updated pore geometry, caused by pore surface dissolution, is then used in the stress simulation in the next numerical iteration. Two types of porous media, the Oriskany sandstone and an artificial porous medium with spherical pores, were tested in the mechanochemical simulation. The positive stress-porosity feedback during pressure solution was observed in both samples. In addition, the model quantitatively illustrated the distribution of local mineral dissolution rates on all pore surfaces, as well as its relation to the effective mineral dissolution rate of the entire sample. Based on the comparison between the two porous media, the local mineral dissolution was regulated by pore space distribution, geometry, and coalescence during pressure solution. This work is the first that uses direct, pore-scale numerical simulation to demonstrate the positive stress-porosity feedback during pressure solution, which has the potential to advance the understanding of the mechanical-chemical (MC) coupling in many geological processes that are relevant to subsurface energy systems, such as the recovery of petroleum hydrocarbons and geothermal energy.

CT scanning↗

DOE OSTI2026

Mechanics of pore array collapse and interaction in shock-compressed polymethyl methacrylate (PMMA)

Recent studies on dynamic pore collapse have revealed significant development of shear localization, which can lead to material failure in porous structures and hot spot generation in energetic materials. These findings have dramatically improved the understanding of failure mechanisms during pore collapse but also prompt further investigation of realistic porous materials. In particular, porous media consist of many pores and porous networks. Even in low-porosity materials, pores can form in close proximity during the manufacturing process, leading to the critical question of pore–pore interaction during collapse under dynamic loading conditions. This study investigates, via plate impact experiments coupled with high-speed internal digital image correlation and shadowgraphy techniques, the collapse of two pores in shock-compressed PMMA at stresses between 0.4 and 1 GPa. The results of these experiments provide new insights into shear localization in pore collapse, in addition to distinct interactions between pores. Shadowgraphy measurements reveal novel, direct visualization of shear band development and crack evolution from pore surfaces. Spacing between adiabatic shear bands is measured over a range of impact stresses and is predicted accurately by the Grady–Kipp model. Pore interactions are found to effect a transition in the impact stress threshold at which different failure mechanisms initiate and are also found to possibly influence preferential sites for shear cracking. Throughout the study, numerical and theoretical models are leveraged to understand shear localization behavior. The role of baroclinicity and wave interactions between the pores is used to elucidate interaction mechanisms between pores.

Lawlor, Barry P. [California Institute of Technolo↗

DOE OSTI2025

A statistical and simulation-informed model for estimating permeability from pore size distribution in saturated geomaterials

Accurate permeability estimation is essential across subsurface engineering applications but remains challenging due to the complex pore structures of natural geomaterials. Traditional empirical methods and simplified theoretical models often inadequately capture the role of pore size distribution and connectivity. Here, this study develops a statistical and simulation-informed permeability model that collapses pore-scale complexity into a compact scaling of the form k = αϕμ d 2 , where ϕ is porosity, μ d is mean pore size, and α is a weakly varying coefficient. By combining pore network simulations with statistical analysis of unimodal and bimodal pore size distributions, we identify three key findings: (i) permeability is much more sensitive to mean pore size than to porosity; (ii) across extensive datasets, the ratio σ d /μ d (standard deviation to mean) clusters around a characteristic value ∼0.4, allowing the effects of the full pore size distribution to be represented by μ d and a narrowly varying α ≈ 0.05; and (iii) for bimodal systems, there exists a critical fraction of small pores ∼0.78 above which flow becomes small-pore dominated, enabling the definition of an effective flow-controlling pore population and facilitating simplified permeability estimation for such systems. The resulting model, which requires only porosity and a representative mean pore size as inputs, is validated against comprehensive experimental datasets (>1700 samples) spanning diverse soils and rocks and achieves good predictive accuracy. Overall, this work provides a physically grounded yet practically simple permeability estimator suitable for subsurface engineering, environmental protection, and resource management applications.

Permeability↗

DOE OSTI2024

Integrated experimental studies of pore structure and fluid uptake in the Bossier Shale in eastern Texas, USA

Within the Haynesville-Bossier Shale complex, the Bossier Shale has not been extensively studied by either industry and academia, despite it being an unconventional gas reservoir and a potential caprock for carbon storage in the underlaying Haynesville Shale. The lack of knowledge of the complex pore structures and fluid-rock interactions hinders the effective extraction of gas and the characterization of fluid reservoirs and sealing capacity. Integrated experimental studies of pore structure and fluid-rock interactions were conducted in seven Bossier Shale core samples collected in eastern Texas. Petrographic, geochemical, and petrophysical properties such as mineral composition, organic richness, thermal maturity, porosity, pore/pore throat diameter distribution, water-accessible pores, liquid water imbibition, and water vapor adsorption were characterized using complementary approaches of thin-section petrography, scanning electron microscopy, X-ray diffraction, total organic matter, pyrolysis, mercury intrusion porosimetry, nuclear magnetic resonance, (Ultra-) small angle X-rays scattering as well as small angle neutron scattering with deuterated liquids and contrast variation. Further, the results show that the thermally mature Bossier Shales are composed of mixed argillaceous mudstone, mixed mudstone, and mixed carbonate mudstone. The shale contains both organic and inorganic pores, with porosities of 3.24-9.37 %, pore-to-throat ratios of 1.65 to 19.4, and water-accessible pores accounting for 28.7-72.6 % of total pores. Approaches of liquid water imbibition and water vapor adsorption, with and without direct contact of water with shale samples, indicate that liquid water first enters the nano-sized pores under high capillary pressures, and water vapor adsorption is mainly controlled by both clay minerals and pores with diameters less than 10 nm. These findings contribute to a better understanding of pore structures and water-shale interactions and their controlling factors in the Bossier Shale.

58 GEOSCIENCES↗

DOE OSTI2025

Solvent Transport in Disordered and Dynamic Membrane Pores: Implications for Reverse Osmosis and Nanofiltration Membranes

Pressure-driven separations with nanoporous membranes, such as reverse osmosis and nanofiltration, play a vital role in addressing water scarcity and enabling resource recovery. Understanding water or solvent transport in membrane pores is essential for advancing membrane separation technologies. A key question in transport modeling is to establish a relationship between solvent permeability and membrane porous structure properties, such as porosity or pore size. The nano- and subnanometer pores in polymeric membranes such as reverse osmosis and nanofiltration membranes are highly tortuous and dynamically connected, which challenges the conventional methods of transport modeling. This study addresses this challenge by developing a theoretical framework to describe solvent transport through membranes with dynamic and disordered porous structure. Specifically, we propose a lattice model to describe the pore network, while preserving the viscous nature of solvent permeation. We further establish a relationship between solvent permeability and membrane porosity or pore size, which is validated by molecular dynamics simulations and experimental data. By integrating this relationship into the solution-friction model, we define pore connectivity and local friction coefficient to quantify the impact of pore structure on solvent permeability. Our analysis highlights the dominant influence of pore connectivity on the permeability of reverse osmosis and nanofiltration membranes, particularly when the pore size approaches the dimensions of solvent molecules. Overall, this study provides critical insights into water and solvent transport mechanisms in nanoporous membranes, opening the door for strategies to substantially enhance membrane performance.

membranes↗

NASA NTRS2020

A 3D Model to Predict Explicit Morphologies and Volume Fraction of Lack-of-Fusion Pores Generated in Selective Laser Melting Processes

The performance of an additively manufactured (AM) component is dependent on the distribution of process-induced defects in addition to the complex microstructure of the material, surface roughness of the component and the process-induced residual stresses. For instance, it has been well demonstrated that lack-of-fusion (LoF) pores produced in the selective laser melting (SLM) AM process can significantly limit the fatigue performance of the material. Although two-dimensional (2D) models exist to predict the 2D profiles of LoF pores, the 2D pore profiles cannot be directly inserted into a three-dimensional (3D) microstructure domain that is output from several prevailing process simulation packages. A few commercial packages that simulate the SLM process can predict LoF pores in a 3D domain, but the morphologies of LoF pores are voxelated and hence do not capture sharp corners of the pores, thereby obviating their use in fatigue crack initiation studies. In order to address the aforementioned gaps, a high-fidelity model that predicts not only the volume fraction, but also the explicit 3D morphologies and spatial distributions of LoF pores has been developed using a computer aided design-based environment. The model has been partially validated for Ti-6Al-4V alloy by comparing the predictions of the volume fraction of LoF pores predicted by the model with experimental data obtained from the literature. Absolute error in predicted volume fraction of LoF pores varied between 5.16% and 1.87% for energy density values between 13 J/mm3 and 45 J/mm3 where a significant amount (over 3% volume fraction) of LoF porosity was measured. The absolute error was within 1.87% for energy density values greater than 45 J/mm3.

Saikumar R. Yeratapally↗

DOE OSTI2026

Pore-Scale Transport Effects in Electrochemical CO 2 Reduction on Gold via Coupled Microkinetic-Transport Modeling

A pore-resolved modeling framework is developed to quantify how pore-scale transport affects the intrinsic microkinetics of CO 2 -to-CO on Au. A DFT-informed microkinetic model is coupled self-consistently to a Generalized-Modified Poisson–Nernst–Planck (GMPNP) transport description in a single, electrolyte-filled cylindrical pore, allowing local concentrations and potential to feed back into site-specific reaction rates. FIB-SEM is used to determine pore sizes within realistic electrode materials. Across pore diameters, d p = 10–6000 nm, the surface-averaged CO 2 reduction rate is systematically reduced relative to the ideal microkinetic baseline where mass transport is not accounted for; the effectiveness factor 𝜂 𝑠,CO 2 , which quantifies this ratio, decreases rapidly at more negative potentials and is about 1% near −1.0 V vs SHE due to reactant depletion. Spatial maps reveal pore-bulk alkalization that emerges at higher cathodic bias, with a small, near-wall pH dip due to electrostatic repulsion of hydroxide at the cathode interface. For a fixed aspect ratio L p /d p , narrower pores exhibit larger 𝜂 𝑠,CO 2 by shortening diffusion paths, whereas variations in the aspect ratio L p /d p play a secondary role. A dimensionless analysis (surface/bulk Damköhler numbers) delineates operating regimes. In conclusion, this work offers a concept for incorporating microkinetic models into homogenized porous-electrode models through effectiveness factors and pore-size distribution.

Au-catalyst↗

DOE OSTI2025

Probing Carbon Mineralization Mechanisms in Pore and Bulk Fluids by Harnessing Architected Calcium Silicates

The ability to synthesize materials with well-controlled pore structures gives us unprecedented control over probing fluid interactions with reactive interfaces and advancing calibrated insights into coupled chemo-morphological interactions. One of the primary challenges in developing crystalline silicate materials lies in achieving ordered pore structures. Existing approaches of producing amorphous mesoporous metal silicates via sol–gel methods and heat-treatment of these materials to produce crystalline phases cause the pore structures in the amorphous phases to collapse. To overcome this challenge, carbon coating of amorphous mesoporous calcium silicate particles is carried out to retain the pore structure, while the material is heated to produce crystalline calcium silicate with calcium sulfate inclusions. The pore diameter in these materials is about 3.9 nm, with a surface area and a pore volume of 28.75 m 2 /g and 0.092 cm 2 /g, respectively. The mechanisms of carbon mineralization are investigated by reacting architected calcium silicate with 1 M Na 2 CO 3 and monitoring the evolution in the structural phases using operando wide-angle X-ray scattering (WAXS) measurements. Formation of stable calcium carbonate polymorph or calcite and metastable calcium carbonate polymorph or vaterite in pore and bulk fluids, respectively, resulting from the reaction between Na 2 CO 3 and CaSiO 3 , are noted. The mechanisms associated with carbon mineralization are delineated using ReaxFF molecular dynamics (MD) simulations. The surface dissolution reaction is initiated by 2H + ions that replace a Ca 2+ ion in the Ca–silicate matrix. Ca 2+ ions in the solution initially react with water to form calcium hydroxide and eventually form calcium (bi)carbonate. A slow and gradual increase in the formation of sodium silicate in the solution resulting from the reactions of silicic acid or the silicon dioxide reaction with sodium hydroxide is noted. When carbon mineralization occurs in environments bearing interfacial fluids, calcite is the dominant calcium carbonate polymorph, as determined using experiments with pore fluids and molecular-scale simulations. In conclusion, these studies provide fundamental insights into the mechanisms underlying the carbon mineralization of calcium silicate informed by experiments and molecular-scale simulations.

Calcium↗

DOE OSTI2026

Effects of confinement and pressure on the structure and dynamics of carbon dioxide in silica slit pores

An understanding of carbon dioxide fluid properties within geological mesopores is important in applications ranging from carbon sequestration to shale oil recovery. Here, a molecular dynamics study is presented that aims to shed light on these systems by simulation of CO 2 fluid confined in β-cristobalite silica slit pores with different pore widths and pressure conditions. The weakly associating nature of carbon dioxide leads to little difference in structural and interfacial dynamical properties for different pore sizes and pressures. Rather, the behavior is found to be dominated by the entropic effects, namely, how the CO 2 organizes next to the silica surface. The CO 2 self-diffusion coefficient shows the strongest pore size dependence. It is strongly diminished in small pores and does not reach the bulk fluid value even in 6 nm pores. It also decreases with pressure, yielding an activation volume that increases with pore size. These results provide new insight into the behavior of a compressible fluid in nanoscale confinement.

Godahewa, Sahan M. [Univ. of Kansas, Lawrence, KS ↗

DOE OSTI2024

Gas pore correlations in laser powder bed fusion of Al6061

Additive manufacturing (AM) of metal materials based on powder bed fusion technology is widely used now in many industries. A known limitation of this type of manufacturing is the formation of gas pores in the bulk material. Here we present a combined X-ray imaging and mid-infrared pyrometry study of pore formation in side-by-side tracks of Al6061 for different processing conditions using both in-situ and post-processing analysis. By carefully quantifying the distributions and correlations of pore positions, we show that an existing pore in one track often catalyzes the formation of another pore in an adjacent track. In a raster scan strategy commonly used to construct bulk material, this phenomenon has the result of forming subsurface perforations, or lines of pores transverse to the scanning direction in a rastered patch. If controlled, this effect can be eliminated to improve the yield strength of the build, or exploited to create programmable failures for specific purposes.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Three-Dimensional Pore Networks in Miocene Stevens Sandstone of California: Implications for CO 2 Geologic Storage

The Miocene Stevens Sandstone in the San Joaquin Basin of California is increasingly recognized as a promising candidate for CO 2 geological storage due to the enormous storage capacity, proven sealing, and existing infrastructure. In this study, computed microtomography imaging and pore network modeling were employed to investigate the influence of pore geometry and wettability on the CO 2 injectivity and residual trapping. Image analysis revealed that a significant fraction of the cement and matrix consists of microporous regions. The microporosity can substantially increase the overall pore space, yet its contribution to permeability remains modest, particularly in samples with low permeability. The intrinsic heterogeneity of turbidite reservoirs further complicates the reservoir properties among different layers. Two-phase flow simulations under varying wettability conditions (water-wet, weak water-wet, and neutral-wet) demonstrated that the CO 2 injection is predominantly controlled by macropores. CO 2 invades microporous regions only after these larger pores are filled. The presence of microporosity leads to a decrease in both initial and residual CO 2 saturations, with the magnitude of the reduction being influenced by wettability. Neutral-wet scenarios exhibit higher CO 2 mobility and thus lower residual trapping than water-wet scenarios. The results imply that heterogeneity in pore geometry and cement distribution across different layers can result in stratified CO 2 flow pathways, complicating efforts to predict injection performance. Overall, the Stevens Sandstone shows considerable promise for CO 2 geologic storage, but effective implementation will require detailed characterization of the pore structure as well as the integration of reactive fluid flow to account for potential mineral dissolution and fines migration.

fluids↗

DOE OSTI2024

The Significant Differences in Solvation Thermodynamics of C1–C3 Oxygenates in Hydrophilic versus Hydrophobic Pores of a Hydrophilic Ti-FAU Zeolite Model

The rates of catalytic reactions have been observed to be dramatically different in zeolites, depending on if they are hydrophobic or hydrophilic. Hypotheses aimed at explaining this behavior have pointed to various solvent molecule and zeolite properties as having influence on entropy. Herein, the influence of various solvent and adsorbate properties on the solvation energies, entropies, and free energies of eleven C1-C3 oxygenates in hydrophobic and hydrophilic pores within a hydrophilic model of Ti-FAU zeolite are tested. The results indicate significant variation in the calculated solvation thermodynamics depending on the adsorbate type, as well as if it is bound within a hydrophobic or hydrophilic pore. Further, while solvation energies are related to solvent-adsorbate interactions, solvation entropies have multiple contributions, and these differ depending on if the adsorbate is in a hydrophobic or hydrophilic pore. Specifically, solvation entropies in hydrophobic pores are related to solvent structural properties, whereas solvation entropies in hydrophilic pores are related to adsorbate polarity. Here, the large range of results obtained from two different pores within one zeolite model with minimal unique adsorption sites suggests that solvation behavior in zeolites is complicated and that the phenomena that control observed performance depend on the zeolite, reaction, and solvent.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Commodity Thermoplastic Elastomer-Enabled Templated Synthesis of Large-Pore Ordered Mesoporous Materials

Fabrication of ordered mesoporous materials (OMMs) has predominantly relied on templating-based methods. However, these methods are constrained by several limitations, especially the limited pore sizes attainable with commercially available surfactants used as structure-directing agents. To unlock the full potential of the OMMs, it is essential to develop synthetic strategies that facilitate the production of large-pore OMMs using scalable processes and cost-effective precursors. This work demonstrates the use of thermoplastic elastomer (TPE)-derived carbon replicas for synthesizing ordered mesoporous silica (OMS) and metal oxides (OMMOs) via precursor infiltration and template removal. The nanostructural evolution of the resulting inorganic materials was systematically investigated. Specifically, using tetraethyl orthosilicate (TEOS) as a silica precursor, this method can produce an OMS with relatively large pores. To establish the generalizability of this process, the fabrication approach was extended to other commercially available TPEs with varied chemical compositions and molecular weights while consistently resulting in ordered structures. Additionally, this synthetic strategy can be successfully applied to the production of OMMOs, including tin and titanium oxide matrix chemistries, yielding pore sizes of 16.0 and 19.2 nm, respectively. By developing a general method and using low-cost precursors, this work presents a scalable approach for fabricating large-pore OMMs with tunable pore textures and matrix chemistries.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Fabrication of model ultrafiltration membranes with uniform, high aspect ratio pores

Here, in this manuscript, we report the facile fabrication of large-area model membranes with highly uniform and high aspect ratio pores with diameters <20 nm. These membranes are useful for fundamental investigations of separation by size exclusion in the ultrafiltration regime, where species to be separated from solution have dimensions of 1–100 nm. Such investigations require membranes with narrow pores and high aspect ratios such that the Hagen–Poiseuille equation is followed, enabling well-known models such as the hindered transport model to be evaluated and other affecting factors to be ignored. We demonstrate that the sub-20 nm pores in the membrane are of sufficiently high aspect ratio such that water flux through the membrane is consistent with the Hagen–Poiseuille equation. The fabrication relies on self-assembling block copolymers to form uniform, densely packed patterns with sub-20 nm resolution, sequential infiltration synthesis to convert the block copolymer in situ into a mask with adequate contrast to etch pores with an aspect ratio >5, and low-resolution photolithography to transfer the pattern over a large area into a silicon nitride membrane. Model membranes with narrow pore-size distribution fabricated in this way provide the means to investigate parameters that impact size-selective ultrafiltration separations such as the relationships between solute or particle size and pore size, their distributions, and rejection profiles, and, therefore, test the validity or limits of separation models.

Chen, Wen↗

NASA NTRS1992

Extreme value statistics analysis of fracture strengths of a sintered silicon nitride failing from pores

Statistical analysis and correlation between pore-size distribution and fracture strength distribution using the theory of extreme-value statistics is presented for a sintered silicon nitride. The pore-size distribution on a polished surface of this material was characterized, using an automatic optical image analyzer. The distribution measured on the two-dimensional plane surface was transformed to a population (volume) distribution, using the Schwartz-Saltykov diameter method. The population pore-size distribution and the distribution of the pore size at the fracture origin were correllated by extreme-value statistics. Fracture strength distribution was then predicted from the extreme-value pore-size distribution, usin a linear elastic fracture mechanics model of annular crack around pore and the fracture toughness of the ceramic. The predicted strength distribution was in good agreement with strength measurements in bending. In particular, the extreme-value statistics analysis explained the nonlinear trend in the linearized Weibull plot of measured strengths without postulating a lower-bound strength.

Chao, Luen-Yuan↗