Continuous Pore Size Distribution Research Articles

Pore structure evolution due to loess collapse: A comparative study using MIP and X-ray micro-CT

Loess is a structured soil that tends to undergo collapse when loaded and wetted. X-ray micro-computed tomography (μ-XCT) is increasingly employed to study loess collapse, but some questions still need to be addressed including the method’s capabilities to effectively characterize loess micro-fabrics and how this can be best achieved. This study addresses these questions by investigating the evolution of pore structure during loess collapse through a combined approach involving the oedometer test, mercury intrusion porosimetry (MIP) and X-ray micro-computed tomography (μ-XCT). The pore size distribution (PSD) in terms of entrance diameter was obtained from μ-XCT images. This PSD corresponds well with that obtained from MIP. For the characterisation of pore evolution during loess collapse, a voxel size of 1 μm is shown to provide good results relevant to the evolution of PSD as a result of loess collapse. The effectiveness of PSD characterization for loess materials progressively deteriorates and rapidly loses significant value when the voxel size is increased. Different geometry concepts and pore size descriptors were evaluated and the discrete PSD approach was found to result in larger pore sizes compared to the continuous PSD method. A so-called ‘ink-bottle’ effect (where the volume of large pores that are only accessible through smaller pore entrances is incorrectly associated with the smaller pore fraction) was observed in both intact and collapsed samples. This highlights that the hierarchal morphology of loess pore structure is preserved during collapse. The PSD evolution due to loess collapse can be captured by either continuous or discrete descriptor demonstrating that μ-XCT forms a powerful complementary tool in characterizing loess pore structure and its evolution caused by mechanical loading or wetting.

Multiscale Research on Pore Structure Characteristics and Permeability Prediction of Sandstone

The random existence of many irregular pore structures in geotechnical materials has a decisive influence on its permeability and other macroscopic properties. The analysis and characterization of the micropore structure of the material and its permeability are of great significance for geotechnical engineering. In this study, digital images with different magnifications were used to examine the pore structure and permeability of sandstone samples. The image processing method is used to obtain binary images, and then, the pore size distribution method is used to calculate the pore size distribution. Therefore, based on the Hagen-Poiseuille formula, we get the prediction value of material’s permeability and compare it with the value obtained from mercury intrusion porosimetry (MIP). It is found that different microscopic images with different magnification and various statistical methods of pore size have a specific influence on the characterization of pore structure and permeability prediction. The porosity of different magnifications is not the same, and the results obtained at higher magnifications are more consistent with the results obtained with MIP. With the increase of magnification, we can observe more pores in large sizes. The effect of CPSD (continuous pore size distribution) in pore size statistics is better than that of DPSD (discrete pore size distribution). In permeability prediction, the prediction result of higher magnification images are closer to the instrument test value, and the value of DPSD is more significant than that of CPSD. In future research, an appropriate method should be selected to obtain a reasonable prediction of the permeability of the target material.

Particle classification and intra-particle pore structure of carbonate sands

Carbonate soils, known as bioclastic deposits, have been classified as ‘problematic soils’ in many offshore and ocean engineering applications. Carbonate soils have many complicated mechanical properties, e.g., low shear strength and high compressibility, mainly determined by their unique microstructures that include weak carbonate minerals, complex particle morphology, and abundant intra-particle pores. However, current knowledge of these microstructures, especially regarding intra-particle pore structure, does not yet match our understanding of the complicated behaviors of the soils. In this context, this paper presents a detailed quantitative study of the particle morphology and intra-particle pore structure of carbonate sand particles based on the results of X-ray micro-computed tomography (μCT) scanning and image processing techniques. By investigating particle shape, this paper first introduces a triangular classification method for carbonate particles in terms of their aspect ratios. The continuous pore size distribution, fractal dimension, and Euler characteristic are then defined to characterize the cumulative volume fraction, complexity, and connectivity of the precisely reconstructed intra-particle pore structure, respectively. The classification results indicate that the proposed classification method is a significant step toward the establishment of a novel classification framework for carbonate soils in engineering applications. The quantitative results characterizing the topological properties of the intra-particle pore structure and their statistical analysis provide deep insight into the hydro-physical permeability and biogeologic origins of carbonate soils.

Methane Absolute Adsorption in Kerogen Nanoporous Media with Realistic Continuous Pore Size Distributions

Accurate estimation of CH4 absolute adsorption amount is essential for shale gas-in-place (GIP) evaluation as well as well productivity. Recent studies have shown that pore size distribution (PSD) ...

Nitrogen-doped porous carbon via ammonothermal carbonization for supercapacitors

In this study we demonstrate a cheap and sustainable ammonothermal approach towards nitrogen-doped porous carbons. Sodium borate (borax) is employed as a catalyst during the synthesis resulting in the formation of small interconnected primary particles of 99%. Comparison of different pore systems indicates that a continuous pore size distribution may explain improved rate performances.

Visualizing the Carbon Binder Phase of Battery Electrodes in Three Dimensions

This study presents a technique to directly characterize the carbon and binder domain (CBD) in lithium-ion (Li-ion) battery electrodes in three dimensions and use it to determine the effective transport properties of a LiNi0.33Mn0.33Co0.33O2 (NMC) electrode. X-ray nanocomputed tomography (nano-CT) is used to image an electrode composed solely of carbon and binder, whereas focused ion beam–scanning electron microscopy is used to analyze cross-sections of a NMC electrode to gain morphological information regarding the electrode and CBD porosity. Combining the information gathered from these techniques reduces the uncertainty inherent in segmenting the nano-CT CBD data set and enables effective diffusivity of its porous network to be determined. X-ray microcomputed tomography (micro-CT) is then used to collect a NMC data set that is subsequently segmented into three phases, comprised of active material, pore, and CBD. The effective diffusivity calculated for the nano-CT data set is incorporated for the CBD present in the micro-CT data set to estimate the ensemble tortuosity factor for the NMC electrode. The tortuosity factor greatly increases when compared to the same data set segmented without considering the CBD. The porous network of the NMC electrode is studied with a continuous pore size distribution approach that highlights median radii of 180 nm and 1 μm for the CBD and NMC pores, respectively, and with a pore throat size distribution calculation that highlights median equivalent radii of 350 and 700 nm.

A new method to establish NMR T2 spectrum based on bimodal Gaussian density function: A case study of tight sandstone in East China Sea Basin

The identification and evaluation of tight sandstone reservoirs has been very difficult due to their low porosity, low permeability, complex pore structure and strong heterogeneity. In order to evaluate the quality of tight sandstone reservoir, priority should be given to the quantitative evaluation of pore size. Nuclear magnetic resonance (NMR) log is frequently employed in pore size evaluation; however, due to its high technical costs and other limitations, it can only be conducted in very few wells and the wide application can never be found. In this study, 12 core samples from the tight sandstone in East China Sea Basin have been collected to conduct centrifugal NMR experiments. Based on the analysis of data obtained from experiments, it is discovered that the bimodal Gaussian density function is well fitted to the NMR T2 spectrum and can be applied to the fitting of NMR T2 spectrum. Furthermore, in the analysis of physical property parameters of reservoir and each individual parameter of bimodal Gaussian density function, it is indicated that the porosity and permeability are best correlated with them. Therefore, the empirical formula between porosity, permeability and the parameters of bimodal Gaussian density function were established to construct pseudo NMR T2 spectrum by using bimodal Gaussian density function and it has been verified by the comparison between the result and experimental data. In order to achieve the more accurate and wide application of this method, the NMR T2 spectrum versus proportion frequency curve was transformed into the pore radius R versus porosity component Pφ curve before the fitting. When used in exploration field, the method can construct continuous pore size distribution curve which can be used for the quantitative evaluation of tight sandstone reservoir's quality. Compared with the method of NMR logging, this technique can be applied to the evaluation of pore structure of tight sandstone reservoirs more widely.

Characterization and comparison of capillary pore structures of digital cement pastes

More and more studies are based on digital microstructures of cement pastes obtained either by numerical modelling or by experiments. A comprehensive understanding of the their pore structures, therefore, becomes significant. In this study, the pore structure of a virtual cement paste (HYMO-1d) generated by cement hydration model HYMOSTRUC 3D is characterized. The pore structure of HYMO-1d is compared to the one of CT-1d that is reconstructed by using X-ray computed tomography technique (CT scan). Both HYMO-1d and CT-1d have the same porosity. Various parameters are taken into account, viz., the specific surface area, the pore size distribution (PSD), the connectivity and the tortuosity of water-filled pores. Regarding the PSD, two concepts (i.e., the “continuous PSD” and the “PSD by MIP simulation”) are adopted. The “continuous PSD” is believed to be a “realistic” PSD; while the “PSD by MIP simulation” is affected by the “throat” and “ink bottle” pores. The results show that HYMO-1d and CT-1d exhibit a similar curve of “continuous PSD”, but distinct curves of “PSD by MIP simulation” and different specific surface areas. A lower complexity of the pore structure of HYMO-1d is indicated by a higher tortuosity of water-filled pores with reference to CT-1d. This study indicates that the comparison of pore structures between the digital microstructures should be based on multiple parameters. It also gives an insight into further studies on digital microstructures, i.e. transport properties of unsaturated materials.

Porosity and permeability determination of organic-rich Posidonia shales based on 3-D analyses by FIB-SEM microscopy

Abstract. The goal of this study is to better understand the porosity and permeability in shales to improve modelling fluid and gas flow related to shale diagenesis. Two samples (WIC and HAD) were investigated, both mid-Jurassic organic-rich Posidonia shales from Hils area, central Germany of different maturity (WIC R0 0.53 % and HAD R0 1.45 %). The method for image collection was focused ion beam (FIB) microscopy coupled with scanning electron microscopy (SEM). For image and data analysis Avizo and GeoDict was used. Porosity was calculated from segmented 3-D FIB based images and permeability was simulated by a Navier Stokes–Brinkman solver in the segmented images. Results show that the quantity and distribution of pore clusters and pores (≥ 40 nm) are similar. The largest pores are located within carbonates and clay minerals, whereas the smallest pores are within the matured organic matter. Orientation of the pores calculated as pore paths showed minor directional differences between the samples. Both samples have no continuous connectivity of pore clusters along the axes in the x, y, and z direction on the scale of 10 to 20 of micrometer, but do show connectivity on the micrometer scale. The volume of organic matter in the studied volume is representative of the total organic carbon (TOC) in the samples. Organic matter does show axis connectivity in the x, y, and z directions. With increasing maturity the porosity in organic matter increases from close to 0 to more than 5 %. These pores are small and in the large organic particles have little connection to the mineral matrix. Continuous pore size distributions are compared with mercury intrusion porosimetry (MIP) data. Differences between both methods are caused by resolution limits of the FIB-SEM and by the development of small pores during the maturation of the organic matter. Calculations show no permeability when only considering visible pores due to the lack of axis connectivity. Adding the organic matter with a background permeability of 1 × 10−21 m2 to the calculations, the total permeability increased by up to 1 order of magnitude for the low mature and decreases slightly for the overmature sample from the gas window. Anisotropy of permeability was observed. Permeability coefficients increase by 1 order of magnitude if simulations are performed parallel to the bedding. Our results compare well with experimental data from the literature suggesting that upscaling may be possible in the future as soon as maturity dependent organic matter permeability coefficients can be determined.

Fabrication of conductive carbonaceous spherical architecture from pitch by spray drying

Continuous spray drying used to synthesize amphiphilic sulfonated pitch-based spherical nanoparticles was reported in this study. The spherical particles were further carbonized and activated by KOH to obtain porous spheres. N2 adsorption–desorption, mercury porosimetry and Raman spectroscopy were used to investigate the pore structure and electron conductivity of the resulting spherical activated carbon particles. The results show that the porous spheres had a high specific surface area (e.g., up to 2550m2g−1) and a continuous pore size distribution that varied from micropores to macropores. This interconnected 3-D carbonaceous architecture efficiently improved the electrical conductivity and facilitated a better utilization of the inner-pores for energy storage. These two aspects combine together to guarantee a low internal resistance and a good rate performance to an EDLC using these spherical nanoporous carbons as the electrodes. In 1M TEA-BF4/PC solution, such EDLC showed a specific capacitance of 173Fg−1 at 0.05Ag−1 and 115Fg−1 at 10Ag−1. Its energy density gets to 43.8Whkg−1 and maintains at 24.16Whkg−1 even the power density rises up to 25kWkg−1.

Nonparametric pore size distribution using d-PFG: Comparison to s-PFG and migration to MRI

Here we present the successful translation of a pore size distribution (PSD) estimation method from NMR to MRI. This approach is validated using a well-characterized MRI phantom consisting of stacked glass capillary arrays (GCA) having different diameters. By employing a double pulsed-field gradient (d-PFG) MRI sequence, this method overcomes several important theoretical and experimental limitations of previous single-PFG (s-PFG) based MRI methods by allowing the relative diffusion gradients’ direction to vary. This feature adds an essential second dimension in the parameters space, which can potentially improve the reliability and stability of the PSD estimation. To infer PSDs from the MRI data in each voxel an inverse linear problem is solved in conjunction with the multiple correlation function (MCF) framework, which can account for arbitrary experimental parameters (e.g., long diffusion pulses). This scheme makes no a priori assumptions about the functional form of the underlying PSD. Creative use of region of interest (ROI) analysis allows us to create different underlying PSDs using the same GCA MRI phantom. We show that an s-PFG experiment on the GCA phantom fails to accurately reconstruct the size distribution, thus demonstrating the superiority of the d-PFG experiment. In addition, signal simulations corrupted by different noise levels were used to generate continuous and complex PSDs, which were then successfully reconstructed. Finally, owing to the reduced q- or b- values required to measure microscopic PSDs via d-PFG MRI, this method will be better suited to biomedical and clinical applications, in which gradient strength of scanners is limited.

Revisiting poromechanics in the context of microporous materials

Poromechanics offers a consistent theoretical framework for describing the mechanical response of porous solids, fully or partially saturated with a fluid phase. When dealing with fully saturated microporous materials, which exhibit pores of the nanometre size, aside from the fluid pressure acting on the pore walls additional effects due to adsorption and confinement of the fluid molecules in the smallest pores must be accounted for. From the mechanical point of view, these phenomena result into volumetric deformations of the porous solid: the so-called “swelling” phenomenon. The present work investigates how the poromechanical theory should be refined in order to describe adsorption and confinement induced swelling in microporous solids. Firstly, we report molecular simulation results that show that the pressure and density of the fluid in the smallest pores are responsible for the volumetric deformation of the material. Secondly, poromechanics is revisited in the context of a microporous material with a continuous pore size distribution. Accounting for the thermodynamic equilibrium of the fluid phase in the overall pore space, the new formulation introduces an apparent porosity and an interaction free energy. We use a prototype constitutive relation relating these two quantities to the Gibbs adsorption isotherm, and then calculate the induced deformation of the solid matrix. Agreement with experimental data found in the literature is observed. As an illustrating example, we show the predicted strains in the case of adsorption of methane on activated carbon.

Physicochemical properties and structural evolutions of gas-phase carbonization chars at high temperatures

The gas-phase carbonization chars from hydrocarbons with low molecular weight (anthracene oil and petroleum ether) were prepared using a drop tube reactor at 1000–1200 °C, and their physicochemical properties and structural evolutions (elemental composition, carbon crystallite structure, surface morphology, pore structure and chemical composition of volatile matters) were mainly investigated. The chars obtained in the high temperature region, which appeared with high C/H atomic ratio and poor carbon crystallite structure far from natural graphite, could be used as high carbonaceous materials. The chars were composed of uniform spherical particles with a continuous pore size distribution. The average pore diameters of the chars were much smaller and in the rage of 5.0–8.7 nm. The increasing carbonization temperature led to an initial increasing and a sequent decreasing of specific surface areas from mico–meso-pores and an increasing of those from meso–macro-pores in the chars. The volatile matters in the chars were composed of an easily-extracted fraction (CS 2-soluble compounds with three to six aromatic rings) and a hard-extracted fraction (CS 2-insoluble compounds with higher aromaticity). The elevated carbonization temperature led to diminish the two volatile fractions. A liquid core formation mechanism was proposed to explain the gas-phase carbonization process of hydrocarbons.

3D-microstructure analysis of hydrated bentonite with cryo-stabilized pore water

In saturated bentonite, free water is hosted in the meso- and macropores. Microscopic characterization of free water and the associated pore structure is very difficult because of the swelling- and shrinking-behaviour of montmorillonite. In this article, we present state of the art cryo-preparation techniques including high pressure freezing and low temperature freeze substitution, which enable the stabilization of bentonite microstructures. Microscopic analyses of cryo-stabilized bentonite samples are then performed with conventional SEM, with cryo-SEM and with FIB-nanotomography. From the resulting 2D- and 3D-images, so-called “continuous pore size distributions” are calculated and the 3D-connectivities of the mesopores are documented. Furthermore, from the comparison with pore size analyses that are based on conventional preparation techniques (oven drying and freeze drying), it is shown that high pressure freezing leads to more reliable results. Overall, it is demonstrated that reliable quantitative 3D-characterization can be achieved from the bentonite pore structure when high resolution 3D-imaging by FIB-nanotomography is combined with modern cryo-preparation techniques (i.e. high pressure freezing).

Preparation and magnetic properties of spindle porous iron nanoparticles

Spindle porous iron nanoparticles were firstly synthesized by reducing the pre-synthesized hematite (α-Fe 2O 3) spindle particles with hydrogen gas. The products were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), X-ray photoelectron spectroscopy (XPS), nitrogen adsorption/desorption isotherms and vibrating sample magnetometry (VSM). A lattice shrinkage mechanism was employed to explain the formation process of the porous structure, and the adsorbed phosphate was proposed as a protective shell in the reduction process. N 2 adsorption/desorption result showed a Brunauer–Emmett–Teller (BET) surface area of 29.7 m 2/g and a continuous pore size distribution from 2 nm to 100 nm. The magnetic hysteresis loop of the synthesized iron particles showed a saturation magnetization of 84.65 emu/g and a coercivity of 442.36 Oe at room temperature.

Stochastic theory of size exclusion chromatography by the characteristic function approach

A general stochastic theory of size exclusion chromatography (SEC) able to account for size dependence on both pore ingress and egress processes, moving zone dispersion and pore size distribution, was developed. The relationship between stochastic-chromatographic and batch equilibrium conditions are discussed and the fundamental role of the ‘ergodic’ hypothesis in establishing a link between them is emphasized. SEC models are solved by means of the characteristic function method and chromatographic parameters like plate height, peak skewness and excess are derived. The peak shapes are obtained by numerical inversion of the characteristic function under the most general conditions of the exploited models. Separate size effects on pore ingress and pore egress processes are investigated and their effects on both retention selectivity and efficiency are clearly shown. The peak splitting phenomenon and peak tailing due to incomplete sample sorption near to the exclusion limit is discussed. An SEC model for columns with two types of pores is discussed and several effects on retention selectivity and efficiency coming from pore size differences and their relative abundance are singled out. The relevance of moving zone dispersion on separation is investigated. The present approach proves to be general and able to account for more complex SEC conditions such as continuous pore size distributions and mixed retention mechanism.

Prediction of Permeability-Surface Area Product Data by Continuous-Distribution Pore Models

Objective: To investigate the ability of continuous-distribution pore models to accurately predict permeability-surface area product (PS) experimental data in skeletal muscle. Methods: Models having a water-only (WO) pathway and continuous distributions of microvascular transport-pathway sizes were fit to solute reflection-coefficient (σ) experimental data (∼0.5–16 nm Stokes radii) obtained from skeletal muscle to determine optimal parameter values. Without further modification, these models were used to predict experimental PS values obtained from the literature for small solutes ranging in size from NaCl to inulin and for three proteins, α-lactalbumin, ovalbumin, and albumin (∼ 0.23–3.7 nm radii). The protein PSs were determined from fluorescent tracer-diffusion curves and a nonlinear model of tracer diffusion in the cat hindlimb preparation. The model's PS predictions were compared to those of a discrete-pore model previously developed and a fiber-matrix (FM) model. Results: A log-normal (LN) continuous pore-size distribution plus WO-pathway model (three free parameters) fit the σ data to within the 95% confidence intervals of each of eight solutes spanning a 32-fold size range and was nearly as close to the data as was the two discrete-pore plus WO-pathway model (four free parameters). Both models closely described the PS data for nine solutes spanning a 14-fold size range. The fit of a fiber-matrix plus WO-pathway model (three free parameters) to the σ data was much poorer than for the other models. Conclusions: The LN and two-discrete-pore models accurately describe σ and PS experimental data in cat and human skeletal muscle. Therefore, experimental data resulting from complex microvascular transport processes are well characterized by simple pore models.

Prediction of Permeability‐Surface Area Product Data by Continuous‐Distribution Pore Models

To investigate the ability of continuous-distribution pore models to accurately predict permeability-surface area product (PS) experimental data in skeletal muscle. Models having a water-only (WO) pathway and continuous distributions of microvascular transport-pathway sizes were fit to solute reflection-coefficient (sigma) experimental data (approximately 0.5-16 nm Stokes radii) obtained from skeletal muscle to determine optimal parameter values. Without further modification, these models were used to predict experimental PS values obtained from the literature for small solutes ranging in size from NaCl to inulin and for three proteins, alpha-lactalbumin, ovalbumin, and albumin (approximately 0.23-3.7 nm radii). The protein PSs were determined from fluorescent tracer-diffusion curves and a nonlinear model of tracer diffusion in the cat hindlimb preparation. The model's PS predictions were compared to those of a discrete-pore model previously developed and a fiber-matrix (FM) model. A log-normal (LN) continuous pore-size distribution plus WO-pathway model (three free parameters) fit the sigma data to within the 95% confidence intervals of each of eight solutes spanning a 32-fold size range and was nearly as close to the data as was the two discrete-pore plus WO-pathway model (four free parameters). Both models closely described the PS data for nine solutes spanning a 14-fold size range. The fit of a fiber-matrix plus WO-pathway model (three free parameters) to the sigma data was much poorer than for the other models. The LN and two-discrete-pore models accurately describe sigma and PS experimental data in cat and human skeletal muscle. Therefore, experimental data resulting from complex microvascular transport processes are well characterized by simple pore models.

Pore size distribution determination from liquid permeation through microporous membranes

Knowledge of the pore size distribution of a microfiltration or ultrafiltration membrane is necessary in order to accurately predict membrane performance in any given application. The liquid permeation technique presented in this paper has been used to obtain data for determining pore size distribution for nearly sixty years. However, the mathematical technique presented in this paper to interpret the experimental data has not been used since its conception in the early nineteen-thirties. This paper examines the merits of this mathematical technique which, when coupled with modern computing capabilities and precise data acquisition, can be used to effectively determine accurate, continuous pore size distributions of hydrophobic membranes.

Effects of Addition of Polyacrylic Ammonium on Colloidal Processing of α-Alumina

Effects of addition of polyacrylic ammonium (shorten as PAN) on colloidal processing of ceramics were investigated with aqueous suspensions of α-alumina powder with an equivalent spherical diameter of 0.35μm. The added PAN was completely adsorbed onto the alumina surface below a critical amount of -3.5×10-6mol carboxyl group per m2 of alumina surface at pH9.0. The zeta potential of alumina powder (-24mV at pH9.0) reached -40mV with addition of the critical amount of negatively charged polymer, and free polymer above the critical amount didn't affect the zeta potential.The viscosities of PAN-added alumina suspensions showed a first minimum at the critical amount of PAN, and increased with increasing free polymer content. Further addition of PAN caused the secondary minimum of viscosity as a function of PAN content. It was possible to prepare a highly concentrated fluid alumina suspension of ≈63vol% solids by addition of the critical amount of PAN. However, it was difficult to increase the solids content above 53vol% at pH2.5 in electrostatic stabilization with HCl solution.The green densities of alumina compacts consolidated by filtration of electrostatically stabilized suspensions were independent of solids content in suspension stage, while the green densities for electrosteric stabilization with PAN showed a minimum at around solids content of 40vol%. The pore size distributions depended on both green densities and consolidation processes of powder (filtration or doctor blade method). A narrow pore size distribution was measured in a high-density green compact consolidated by filtration. The median size of pore in a green compact was small for electrostatic stabilization than electrosteric stabilization at a similar density, but PAN-addition was effective to produce a more continuous pore size distribution and a more uniform green structure.Although the densification behavior was mainly dominated by green density, PAN-addition in suspension stage was effective in achieving a higher density and a more fine texture than electrostatic stabilization at the final stage of sintering. The densification of a high-density green compact proceeded with disappearance of closed pores which were formed at around 92-95% T. D. The low-density green compacts were densified without the significant formation of closed pores. The texture of sintered alumina was greatly affected by the pore size distribution of a green compact. A wide pore size distribution formed a small number of large pores at the grain boundaries of large grains, while a narrow pore size distribution gave a microstructure with many small closed pores located at the grain boundaries of small grains.