Pore REconstruction and Segmentation (PORES) method for improved porosity quantification of nanoporous materials
Introduction
Although electron tomography provides valuable three-dimensional visualizations of the sample under interest, accurate quantification of pore sizes in nanoporous materials remains a difficult problem, especially if the pores are irregularly shaped.
Quantification of nanoporous materials is important in many applications in the field of sorption/separation or catalysis, in which size selectivity often plays an important role [1], [2]. This makes a reliable and accurate knowledge of the pore size distribution indispensable.
Microporous () and mesoporous () materials are usually characterized by N2-sorption experiments at a temperature of 77 K [3]. However, the quantification of the pore size distribution based on these measurements is carried out using models that assume a regular pore size, i.e., cylindrical or slit-shaped pores. Unfortunately, no model is available for materials with irregular pores. In this publication, an alternative and reliable approach to determine the pore size in nanoporous materials is proposed.
Transmission electron microscopy (TEM) is an ideal technique to investigate nanoporous materials at a local scale, but conventional TEM is limited to providing two-dimensional (2D) projections of a three-dimensional (3D) microscopy sample [4]. To measure the pore size distribution, a 3D representation of the sample is required, which can be obtained using electron tomography. This technique combines the information of a tilt series of 2D TEM images in a 3D voxel-based reconstruction [5]. The quality of the 3D reconstruction is of critical importance, since it influences further quantification. Computing accurate reconstructions from TEM projection images with classical analytical algorithms such as weighted back-projection (WBP) [6] or algebraic algorithms like the simultaneous iterative reconstruction technique (SIRT) [7] is a difficult task, mainly because of two issues. First, the limited tilt range of the sample (usually about ±75°) causes elongation of the 3D reconstruction and smearing of the voxel values, often referred to as the “missing wedge” artifact. Secondly, the reconstruction quality also depends on the number of TEM projection images, which is often relatively small to avoid beam damage, especially for sensitive materials.
It has been shown recently that the quality of a 3D reconstruction can be improved by incorporating prior knowledge in the reconstruction process. Assuming that the sample contains just a few a priori known compositions, each occurring in homogeneous regions, the discrete algebraic reconstruction technique (DART) has been able to strongly reduce missing wedge artifacts [8], [9]. The partially discrete algebraic reconstruction technique (PDART) exploits the existence of dense homogeneous particles of which the grey value is known by incorporating this knowledge in the reconstruction algorithm, resulting in more accurate reconstruction quality [10]. Other methods minimize the total variation of the reconstruction, where the sample is assumed to have a sparse gradient, i.e., the number of boundary pixels in the sample is relatively small compared to the total number of pixels [11], [12]. However, the prior knowledge assumptions incorporated in the reconstruction algorithms of the previous examples are not always applicable to nanoporous materials, since the reconstruction may consist of a continuous range of grey values with non-sparsity of the gradient image. In this paper, we propose an approach that exploits a different kind of prior knowledge, which is related uniquely to porous materials: the existence of many local regions of void space.
After the reconstruction step, individual pores can be extracted. To that end, a segmentation step should be applied to separate the pores from the material matrix. Manually or automatically selecting global thresholds can produce satisfactory results if there is a clear separation between the background and the material matrix [13]. However, due to reconstruction artifacts, this separation is not straightforward in practice. In particular for the segmentation of pores that are small compared to the voxel size, this approach is error prone. It can therefore be expected that further analysis of the pores with individual pore statistics such as size, orientation, and eccentricity will be strongly influenced by the results of the two previous steps, i.e., reconstruction and segmentation.
To overcome the limitations discussed above, we present a tailor-made, integral approach, for the reconstruction, segmentation, and quantification of porous nanomaterials: the PORES “POre REconstruction and Segmentation” algorithm. The PORES data processing chain outperforms conventional approaches, since it is optimized for nanoporous structures. The PORES processing chain starts by calculating a porous sample specific reconstruction with the new SUPPRESS “Simultaneous Update of Pore Pixels by iterative REconstruction and Simple Segmentation” algorithm. SUPPRESS reduces artifacts by exploiting prior knowledge about the porous structure of the material, while automatically classifying the interior of the pores. The PORES method continues by applying a watershed algorithm directly to the reconstruction, resulting in accurate segmentation of the pores. This segmentation permits accurate quantification of individual pores, which is employed to generate full sample pore statistics.
The PORES method is described in Section 2. In Section 3, the method is validated with both simulation and real experiments. The paper is concluded in Section 4.
Section snippets
Method
This section describes the entire PORES algorithm, which is displayed in the flowchart in Fig. 1. It consists of two parts: the reconstruction algorithm (described in Section 2.1 and displayed in the uppermost part of the flowchart in Fig. 1) and the segmentation and quantification (described in Section 2.2 and displayed in the bottommost part of the flowchart in Fig. 1).
Experiments and results
In this section, a range of experiments to evaluate our approach and their corresponding results are discussed. First, in Section 3.1, the TEM acquisition set-up for an aluminosilicate sample is described. Next, various simulation experiments are reported in Section 3.2. In Section 3.3, different figures of merit for the validation of our approach are introduced. In Section 3.4, the results of all experiments are reported. Finally, the PORES algorithm is applied to the real data in Section 3.5.
Conclusions
In conclusion, the PORES algorithm was proposed; it is an integral approach for the reconstruction, segmentation and quantification of nanoporous materials. As the proposed processing chain is tailored specifically for nanoporous materials, accurate quantification becomes possible. The first step, i.e., the SUPPRESS reconstruction, significantly reduced missing wedge artifacts in the reconstruction by the incorporation of prior knowledge in the reconstruction algorithm. Individual pores were
Acknowledgments
The authors acknowledge the Concerted Research Project (CRP) sponsored by the Special Fund for Research at the University of Antwerpen on ‘Optimization of the structure-activity relation in nanoporous materials’. J. Sijbers acknowledges the IWT SBO TOMFOOD project (120033). K.J. Batenburg was supported by the Netherlands Organisation for Scientific Research (NWO), programme 639.072.005. S. Bals acknowledges financial support from the European Research Council (ERC Starting Grant
References (27)
- et al.
Electron tomography
Mater. Today
(2004) - et al.
3D imaging of nanomaterials by discrete tomography
Ultramicroscopy
(2009) - et al.
Accurate segmentation of dense nanoparticles by partially discrete electron tomography
Ultramicroscopy
(2012) - et al.
Electron tomography based on a total variation minimization reconstruction technique
Ultramicroscopy
(2012) - et al.
Compressed sensing electron tomography
Ultramicroscopy
(2013) Topographic distance and watershed lines
Signal Process.
(1994)- et al.
Zeolite β nanoparticles based bimodal structuresmechanism and tuning of the porosity and zeolitic properties
Microporous Mesoporous Mater.
(2014) - et al.
3D electron microscopy in the physical sciencesthe development of z-contrast and EFTEM tomography
Ultramicroscopy
(2003) - et al.(2002)
- et al.(2008)
Practical cone-beam algorithm
J. Opt. Soc. Am. A
Cited by (7)
Quantitative analysis of mesoporous structures by electron tomography: A phantom study
2023, UltramicroscopyCitation Excerpt :The segmentation can also be integrated into iterative reconstruction procedures. For example, watershed segmentation has been combined with SIRT reconstruction with the prior knowledge that there exist many local regions of void space [22]. For a sample consisting of just a few priori known components, each with homogeneous known density, it is well known that DART can directly result in a segmented 3D structure [18].
Sphericity and roundness computation for particles using the extreme vertices model
2019, Journal of Computational ScienceCitation Excerpt :Sphericity related indices have also been computed at nanoscopic scale. An equivalent spherical diameter is used to obtain a pore size distribution in nanoporous materials [18]. Si NCs are analyzed with 2D software, ImageJ, to obtain the equivalent diameter [19] and circularity index [28], and a 3D software, Amira, is used to compute size and Lent measurements [25] of quantum dot particles.
Pore size effects on convective flow and diffusion through nanoporous silica gels
2015, Colloids and Surfaces A: Physicochemical and Engineering AspectsCitation Excerpt :On the nanoscale, however, the gel liquid is firmly kept within the gel by capillary forces, and any attempts to extract a liquid by force would result in gel breakage [16], making said liquid porosimetry techniques inapplicable. Gas adsorption methods are also not applicable here, since the necessary drying of the samples would affect the material structure severely [27]. Studies have shown that the abovementioned methods differ both in the position of the PSD peak, and with respect to which size category of pores that is numerically over- or underestimated [20,24].
Three-Dimensional Reconstruction of Interface Roughness and Alloy Disorder in Ge/GeSi Asymmetric Coupled Quantum Wells Using Electron Tomography
2024, ACS Applied Materials and InterfacesSegmentation criteria in the problem of porosity determination based on CT scans
2020, Proceedings of SPIE - The International Society for Optical Engineering