Due to technological development, state-of-the-art high-resolution X-ray computed tomography (CT) systems can be developed, enabling the internal visualization of geomaterials in three dimensions. However, in order to obtain structural information one also needs proper three-dimensional (3D) analysis software. In this paper, the potential for petrographic purposes of high-resolution X-ray CT in combination with the 3D analysis software Morpho+ is explored for a Belgian sandstone sample. The advantage of the CT technique is the fact that it is an ideal tool to characterize the internal structure of a rock in three dimensions in a nondestructive way while a limitation of this CT technique is that only small samples can be combined with a high spatial resolution and therefore often many samples will need to be scanned in order to obtain representative volumes. The relationship between sample size and obtained spatial resolution are discussed as well as the influence on the spatial resolution exerted by some important technical aspects like the used X-ray source and detector. This paper focuses in detail on the structures that can be determined by means of micro- and high-resolution X-ray CT in combination with 3D algorithms.
Conventional microstructure analysis of rock samples is usually carried out by studying two-dimensional (2D) polished thin sections with optical microscopy or scanning electron microscopy (SEM). When looking at 2D images, it is necessary to keep in mind that the shape of minerals and their spatial relationships can be much more complex in three dimensions. Although there are powerful quantitative tools to interpret data derived from 2D images for the characterization of three-dimensional (3D) structures, many quantitative and qualitative aspects of structures remain inaccessible from 2D images (Russ, 2002). In order to overcome this problem, several orthogonal sections or serial sectioning coupled with digital image analysis to construct a three-dimensional image of the microstructure can be necessary to reveal 3D mineral structures (Lin and Cohen, 1982; Holt et al., 1996).
Many research topics in geology concern the study of internal structures of geomaterials on a pore-scale level in order to estimate their macroscopic behavior (Bakke and Øren, 1997). In order to compute properties such as permeability and electrical conductivity, there is a need for an adequate description of the complex internal microstructure. Bakke and Øren (1997) developed a process-based reconstruction procedure that incorporates grain-size distribution and other petrographic data obtained from 2D thin sections to reconstruct 3D sandstones. The essence of this approach was to build sandstone models that were analogs of actual sandstones by stochastically modeling the results of the main sandstone forming processes: sedimentation, compaction, and diagenesis. While statistical models based on correlation-function reconstruction retain a similar degree of isotropy and homogeneity as the experimental microstructure, they tend to significantly underestimate the connectivity properties. Although the reconstruction method proposed by Bakke and Øren was promising, it was unclear how accurately it can reproduce more heterogeneous and diagenetically complex sandstones such as those encountered in nature. Øren and Bakke (2002) stated that although X-ray microtomography was extremely useful, it was still not readily available in practice and therefore information about the pore structure of porous materials was often limited to 2D thin-section images. Consequently, the attractive approach was to reconstruct a 3D description of the pore structure from readily available 2D images, by means of statistical models for reconstructing 3D porous media from 2D thin-section images (Joshi, 1974; Adler et al., 1990; Adler et al., 1992; Adler, 1992; Hazlett, 1997; Yeong and Torquato, 1998a, 1998b).
Although statistical and process-based models have their advantages, X-ray microtomography (micro-CT) can also be applied in the study of internal structures of geomaterials. Micro-CT has improved enormously in recent years thanks to rapid technological developments and is more widely available now, with a constantly improving resolution and image quality. This technique enables rapid, nondestructive, 2D and 3D examination and analysis of almost any kind of material, including rock and soil (Carlson, 2006). Tomography-based methods rebuild the internal structural information within an object by mathematically reconstructing it from a series of projections (Russ, 2002). All transmission tomography devices are based on the same principle: the object is positioned between a source and a detector and rotated while transmission images are recorded. Different kinds of probes can be used for the visualization: X-rays, neutrons, gamma rays, etc.
In this paper X-ray computed tomography (CT) is used. A set of 2D radiographs of the sample are collected at a sequence of transmission angles, providing information on X-ray attenuation, which depends on the density and atomic number of the components. By means of reconstruction software the radiographs are converted into a stack of 2D cross sections that allow 3D renderings of the sample. Although in the beginning X-ray computed tomography was mainly used in medicine, it soon became clear that X-ray CT had a large potential for other applications, including palaeontology (Fourie, 1974; Conroy and Vannier, 1984; Haubitz et al., 1988; Chapman et al., 2003; Hlusko et al., 2004), sedimentology (Kenter, 1989; Peyton et al., 1992; Zeng et al., 1996; Boespflug et al., 1995), petrology (Van Geet et al., 2001), soil science (Allan et al., 2002), and fluid-flow research (Wellington and Vinegar, 1987; Géraud et al., 2003; Dunsmuir et al., 1991; Coles et al., 1994; Spanne et al., 1994; Hazlett, 1995; Coles et al., 1996; Coker et al., 1996).
Industrial X-ray CT scanners proved to be successful for research on geomaterials but with a resolution of a few hundreds of μm only. To obtain (sub)micron-scale resolution, currently two options exist: synchrotron sources and laboratory high-resolution X-ray CT (HRXCT) scanners. Synchrotron sources allow submicron resolution with a monochromatic beam of well-defined energy, but prove to be inaccessible for daily use for most research groups. More accessible laboratory equipment includes medical and micro-CT scanners (resolutions varying from roughly 100 to 1 μm, respectively) using X-ray tubes instead of synchrotron sources. HRXCT systems are currently being developed with submicron resolution. The CT scanners with micron or submicron resolution provide an alternative to synchrotron-based research. One of the advantages of CT systems is that they can nondestructively provide stacks of more than 1000 2D cross sections of the sample under investigation much faster than by performing serial sectioning. Since no system is perfect, it is important to understand the advantages and limitations of this technique in order to properly use it to address particular geological questions. An important issue when working with CT is the relationship between sample size and spatial resolution. In HRXCT, the best achievable resolution is related to the spot size of the X-ray source and the magnification of the system. The magnification is limited by the diameter of the sample under investigation. The resolving power of an imaging system is the smallest distance between two features (point, lines) at which these features can be distinguished from one another.
The resolving power that can be achieved within the image is
with R the achievable resolution (Equation 1) in the object, s the spot size of the X-ray source, d the pixel size of the detector, and M the magnification, which is related to the position of the object and the separation between the source and detector:
For low magnifications, the detector pixel size is the limiting factor for the image resolution (Equation 1). For high magnifications, the X-ray source spot size becomes significant, resulting in a fuzzy image. The spot size thus limits the resolution of the whole setup. Furthermore, to achieve high magnification the targeted part of the sample must be positioned very close to the X-ray source, which is impossible for large samples. Moreover, images can contain artifacts if the entire sample width is not imaged. Since X-ray detectors have a limited number of pixels, image resolution is limited to the discretization of the sample width, the latter forming the main practical limit for computed tomography.
As mentioned earlier, a small sample size is crucial for a high spatial resolution. However, working with small rock samples raises the question of the representative volume. In order to obtain an acceptable estimation of the general rock properties, the samples to be analyzed should be representative of the rock body itself, including its normal spatial variations. Theoretically, a sample is only representative when its analysis results are both accurate and reproducible (Gy, 1994). Sampling accuracy is achieved when a few qualitative rules are respected. Correct sampling will provide all constitutive elements to be evaluated with an equal probability of being selected and of belonging to the sample (Gy, 1994). Three major factors influence the accuracy of sampling: the sample grain size, the sample volume, and the amount of samples taken (Smith, 1999). All these factors are in relation with each other. If a rock type has a high internal heterogeneity, a larger amount of samples should be taken. Many studies were performed on sampling by Gy (1967, 1971, 1979), Goodsall and Mathews (1970), and Sedman and Stanley (1990). General rules like the one formulated by Gy (1979) predict that a good estimate of the required sample size is obtained if
where Ms is the sample weight and d is the diameter of the largest particle (Gy, 1979). Depending on the degree of variation in grain size, the parameter K is given a certain value (Gy, 1979). In case of a high degree of variation in grain size, the sample size might have to be doubled compared to samples with a low degree of variation. However, in the case of sampling rocks to be used as building stone, the size of the blocks produced has to be taken into account as well as an estimation of the variation between the blocks themselves. Jefferson (1993) suggests that, as the properties of a block of stone such as its durability are determined by the properties of its constituent parts, the size of these constituent parts can be used as a guide to determining the sample size. Another approach, suggested by Kanit et al. (2003) states that the representative volume element size can be associated with a given precision of the estimation of the wanted overall property and the number of realizations of a given volume of microstructure one is able to consider. For example, Kanit et al. (2003) argue that the overall volume fraction of a phase in a heterogeneous material can be determined either by a few measurements on large volumes, or by measurements of many small volumes of material. They conclude that the representative volume element must be considered as a function of several parameters including the physical property, the contrast of properties, the volume fractions of components, the desired relative precision for the estimation of the effective property, and the number of samples associated with computations that one is ready to carry out. The primary question, however, remains: what characteristic or property does one want to see in 3D by means of X-ray? Is it to determine overall parameters like total porosity to be used as the overall porosity value for the stone in general? Or does one want to look in detail at a certain volume of interest in order to solve some remaining questions? In this paper we will focus on the detail that can be detected with high-resolution X-ray CT rather than on the porosity values or the grain-size distribution results as the overall properties. As an example, we present an analysis conducted on the Bray sandstone. The Bray sandstone has already been characterized in different ways (Cnudde and Jacobs, 2004; Cnudde, 2005; Cnudde et al., 2008), so the results of these experiments can be compared with the results of the high-resolution scan presented here.
Several parameters play a role in the classification of different minerals in 3D derived from X-ray CT scanning: the contrast in X-ray attenuation between those minerals, which is dependent on the density and average atomic number of these minerals, and the size of the minerals in relation to the spatial resolution. Comprehension of the image acquisition technique based on X-ray transmission and of the methods used for extraction of 3D data from a data set is crucial if one is to obtain reliable quantitative measures of features of interest. 3D image analysis starts with high-quality images, since this is essential to retrieve valuable and useful information from the original images. The use of image analysis generally involves the implementation of complex image processing (Starkey and Samantaray, 1994) and of advanced calculation algorithms (Pirard, 1994). Classical image analysis consists of noise reduction, segmentation, and binary image editing. But before performing image analysis, the original images often need to be processed. This image processing is primarily performed to improve the visual appearance of the images and to prepare for measurements of features and structures present. A wide range of different techniques exists for each of these tasks. Several software packages are available for analysis of 2D images. Software for 3D analysis, however, is less frequently available or sometimes not well adapted to specific needs. Therefore the new 3D software Morpho+ (Vlassenbroeck et al., 2007) was developed in order to overcome the existing limitations to analyze (pore) structures inside reconstructed micro-CT images.
In this paper, the potential of high-resolution X-ray CT in combination with the Morpho+ 3D analysis software for petrographic purposes is explored on a Belgian Bray sandstone sample. The advantages and limitations of these techniques are discussed. The data obtained with X-ray CT is compared with results from the more conventional techniques of optical microscopy and scanning electron microscopy.
The Bray Sandstone
The Bray sandstone is a quartz arenite from the Thanetian (Paleocene, Paleogene). This natural building stone has mainly been used for monuments in Binche, Mons, and Bray (Belgium) and in houses (Cnudde, 2005). The Bray sandstone is a heterogeneous accumulation of mostly continental deposits consisting of quartz grains with a siliceous cement. Its color varies from gray to yellowish brown, depending on the amount of iron oxide and/or hydroxides, which occur as a very thin coating around the grains. In addition to monocrystalline quartz grains and sometimes polycrystalline quartz, feldspars, rutile, zircon, some mica, and clays can be identified in thin sections. Some quartz grains show a typical overgrowth; in many cases the shape of the original grain is delineated by a thin iron oxide and/or hydroxides or clay coating between the overgrowth and the grain itself. The presence of the clay minerals in the sandstone can be very significant as it strongly affects rock permeability and porosity. The Bray sandstone is a fine-grained, poorly sorted sandstone (Cnudde et al., 2004). Grains are angular to subrounded, with an average grain size of 0.156 mm and low in sphericity (Cnudde and Jacobs, 2004). According to the formulas of Folk and Ward (1957) (Table 1), the grains could be defined as poorly sorted and positively fine-skewed. To determine the roundness in thin sections, the relation of the various particle diameters (length, width, and thickness) is calculated; specifically the degree to which the shape of a grain approaches that of a sphere (Bates and Jackson, 1980) is of interest. In general, there is no real preferred orientation of the grains; they are also closely packed (Fig. 1). The average open porosity of the Bray sandstone determined with water absorption under vacuum is 14%, with a minimum of 4% and a maximum of 24% (Cnudde, 2005; Cnudde et al., 2008). The average pore diameter determined with mercury intrusion porosimetry (MIP) ranges from 4.7 to 20.1 μm, with an average of 15.7 μm. The average threshold pressure derived from MIP was between 11 μm and 16 μm depending on the degree of cementation. The density of the Bray sandstone is on average 2281 kg/m3 (Cnudde, 2005).
Two different samples of the Bray sandstone were analyzed for this study. A large rectangular sample with a cross section of 6.6 × 7.4 mm2 was scanned. Because of the size of the sample, only part of the sample height could be imaged in order to obtain the desired resolution. The second sample is a drilling core with only 1 mm diameter and a height of ∼500 μm. Its small size allowed scanning at very high resolution.
High-Resolution X-ray CT (HRXCT) Combined with 3D Analysis by Morpho+
A flexible multifunctional high-resolution X-ray CT (HRXCT) scanner allowing 2D radiography and 3D visualization and quantification on a (sub)micron scale was used. The scanner was developed at the “Centre for X-ray Tomography” of the Ghent University, Belgium (Masschaele et al., 2007). The transmission tube head was operated at a high voltage of 100 kV for both samples. The large sample was scanned at a target current of 80 μA, resulting in 8 W target power. In this configuration, the X-ray spot size is ∼5 μm in diameter. A 550-μm-thick aluminum plate was used as a beam-hardening filter. In total 1000 projections were recorded, each projection being an average of three frames at 300 ms exposure time in order to obtain a high signal-to-noise ratio. The total scan time was ∼90 min. A source-to-detector distance of 890 mm and a source-to-object distance of 51.8 mm resulted in a magnification of 17.2, equivalent to a voxel pitch of 7.4 μm (detector pixel pitch of 127 μm). For the small sample, the spot size was set to its minimal size of below 1 μm, limiting the available target current to 9 μA, or ∼1 W target power. A voxel pitch of 700 nm was achieved by a source-to-detector distance of 890 mm and a source-to-object distance of 4.9 mm, equivalent to a magnification of 181.6. Due to the low X-ray flux, no beam-hardening filter was applied. Four frames at an exposure time of 1000 ms were averaged for each of the 1500 projections, extending the total scan time to nearly 3 h. The Varian PaxScan 2520V (a-Si flat panel, CsI screen, 1880 horizontal by 1496 vertical pixels, 127 μm pixel size) recorded images for both samples, although its orientation was changed for the different purposes. This resulted in an image width of 1496 pixels for the low resolution scan, and 1880 pixels to achieve maximum resolution for the small sample. Both samples were reconstructed using the software package Octopus (http://www.inct.be). The software Morpho+ (Vlassenbroeck et al., 2007) was used for the 3D analysis of the pores and the grains of the Bray sandstone. In 3D analysis, a volume composed of voxels is processed to extract quantitative data about the structural composition of the sample. The volume can be represented as a stack of images, although the operations need to be performed in 3D. The objective of the analysis is to obtain parameters such as size, shape, and orientation for each object (for example, a pore or a grain) inside the sample. In Morpho+, the analysis process is composed of several steps, including filtering, phase segmentation or thresholding, labeling, and object separation. By using an algorithm-based dual threshold, the original data was transformed into a binary data set with the aim to extract structural features of the selected pore volume. Dual thresholding uses two intervals; voxels with a gray value in the first interval are classified as foreground voxels, while voxels in the second interval are only defined as foreground voxels if they are connected to voxels from the first interval. This approach reduces the sensitivity to residual image noise. One of the analyzed parameters, which is necessary for our shape analysis, is the maximum opening, which can be extracted from the distance transform. The maximum opening is defined as the diameter of the maximum inscribed sphere which fits inside the object (Fig. 2). For each grain its total volume can be determined as well as its surface. If a sphere with the same total volume of a grain is constructed, its corresponding diameter is defined as the equivalent diameter of the grain. Morpho+ calculates the sphericity S as the ratio of the maximum opening over the equivalent diameter. This parameter gives a rough approximation of the object shape since it expresses how much an object resembles a sphere (S = 1). S ≈ 0 typically corresponds to a large network composed of narrow channels.
Additionally, each object can be modeled as an equivalent ellipsoid which has the same moments of inertia. The three-dimensional moments of the inertia tensor are then calculated and diagonalized. The corresponding rotation of the eigenvectors defines the orientation of the object, while the eigenvalues correspond to the lengths of the principal axes of the equivalent ellipsoid. Since Morpho+ can determine the orientation of the objects of interest such as the grains constituting the sandstone, it is possible to produce a stereoplot derived from the 3D analysis of the grains. The processed volume can be visualized after each step in the analysis process. Since all analysis algorithms operate in three dimensions, cross sections of the volume according to the different principal planes can be visualized.
Micro-CT Scan (Resolution 7.4 μm)
Scanning of the Bray sandstone with a cross section of 6.6 × 7.4 mm2 resulted in a resolution of the micro-CT data of 7.4 μm. Figure 3 represents a reconstructed cross section. Based on the different X-ray attenuation of the composing minerals, different gray values between the different minerals can be detected. Of all minerals present in the Bray sandstone, zircon has the highest attenuation coefficient, while quartz has the lowest (Cnudde, 2005; Gualda and Rivers, 2006). The quartz grains can be clearly detected, as well as some dense inclusions of rutile and zircon, based on a microscopic examination of the samples prior to CT scanning. Besides cross sections, 3D renderings (Fig. 4) can be produced for visual interpretation of the mineral shape and their spatial relationships. However, for quantitative results a 3D analysis is required. Analyzing the pore-volume of the scanned sample with Morpho+ revealed an average porosity of 18 vol% over an analyzed partial volume of 343 mm3. However, all pores smaller than or equal to 7.4 μm are not included in this volume analysis since they are below the resolution.
In addition to determining porosity and overall pore shapes and spatial relationships, each individual grain can be analyzed as well. Therefore grains are first segmented and automatically identified by a watershed separation algorithm based on the Euclidean distance transform (Russ, 2002). Based on analysis of the grain size in the 343 mm3 volume sample, an average equivalent diameter for the Bray sandstone grains of 194 (±53) μm was found together with an average maximum opening of 117 (±34) μm. In this volume, a total of 53,103 grains were analyzed.
Figure 5 shows details of the 3D renderings of the results of Morpho+, where the grains in the selected volume have been relabeled (color coded) based on a selected parameter, such as, e.g., their equivalent diameter. From the grain analysis performed on the micro-CT scan, the largest equivalent diameter found was 375 μm and the largest maximum opening 231 μm. The average sphericity of the analyzed grains based on the micro-CT scan was 0.6. This value indicates that on average the grains are not perfectly spherical. Figure 6 illustrates the frequency distribution of the grain sphericity. The frequency distribution shows a well-sorted curve, which corresponds with the estimation made on the basis of the 2D reconstructed images.
High-Resolution CT Scan (Resolution 0.7 μm)
In order to achieve a resolution on the order of 700 nm, a subsample of the Bray sandstone was selected. This resolution enables one to clearly distinguish the different grains, to assess the intergranular structure, and to identify details inside the grains (Fig. 7). Monocrystalline quartz grains can easily be detected on the reconstructed cross sections as well as mineral inclusions like rutile and zircon, and voids. One has to be very careful when identifying minerals on X-ray CT reconstructed images since X-ray attenuation coefficients are a function of both atomic number and material density. However, based on experience with the material most probably clays and local thin iron oxide coatings can be detected in the reconstructions. Since feldspars and quartz have a more similar attenuation coefficient, they are more difficult to distinguish from one another. A small variation in attenuation coefficient toward the edge of the sample can be seen on Figure 7, caused by phase-contrast. However, this feature is not problematic for the segmentation purpose since by using dual thresholding the correct features can still be segmented.
Based on the reconstructed 2D cross sections, the grains of the Bray sandstone were characterized as subangular over subrounded to rounded. The grain contact varies from point (grains touch each other) to sutured contacts (mutual interpenetration of grains).
Volume rendering of the 2D reconstructions reveals the internal structure of the stone with high 3D detail (Fig. 8). Besides looking at the structures themselves, it is also possible to virtually cut the sample at any desired location and/or angle and to make certain components transparent while rendering other features opaque.
When investigating the images of the high-resolution scan with Morpho+, a total volume of 0.57 mm3 was analyzed, corresponding to a mass of 0.013 g. Although much more detail can be detected in this high-resolution CT scan, many similar samples should be examined in order to obtain a representative element volume. As the subsample volume is so small, only a small amount of grains, a total of 710, could be analyzed on their equivalent diameter, maximum opening, and sphericity. Figure 9 shows a 3D rendering of the results of Morpho+, where each grain has been relabeled (color coded) based on its equivalent diameter. The average grain sphericity calculated based on the high-resolution scan was 0.57. This value indicates that on average the grains are not perfectly spherical, although some grains definitely are (sphericity value = 1).
Comparison of High-Resolution and Micro-CT Scan
The results of the equivalent grain diameter analysis of the high-resolution (0.7 μm) and micro-resolution (7.4 μm) scans are shown in Figure 10, where the ratio of the volume in μm3 of the grains over the total analyzed volume is plotted against their corresponding equivalent diameter results. The 3D analysis demonstrated that in the high-resolution scan on average, more
smaller objects were found, which could not be distinguished in the micro-scan. Also more grains with a lower equivalent diameter were detected than on the micro-CT scan. The average equivalent diameter of the grains scanned at high resolution was 39 (±56) μm and the average maximum opening 24 (±38) μm, which was much lower than the respective values calculated from the micro-CT scan. Based on Equation (3), it is likely that the amount of analyzed volume in the high-resolution scan is too small to correctly characterize the average grain sizes. Additionally, the amount of small grains is much higher than in the micro-scan, where small grains were not detected due to resolution limitations. Based on the frequency distribution curve calculated for the high-resolution scan (Fig. 11), it appears that the amount of examined grains is too low to provide a good estimate of sorting and skewness.
CONCLUSION AND DISCUSSION
In this paper, the potential of high-resolution X-ray CT combined with 3D analysis software for petrographic purposes was explored for a Belgian Bray sandstone sample. The advantages of this technique reside in the fact that X-ray CT is an ideal tool to characterize the internal structure of a rock in three dimensions in a nondestructive way. Besides looking at the structures themselves, CT also allows us to virtually cut through the sample at any given location and to make certain components transparent while rendering other features opaque. Due to rapid technological developments, laboratory equipment at the moment reaches resolutions at submicron scale. The flexible high-resolution X-ray CT scanner at the Centre for X-ray Tomography (Ghent University, Belgium) is capable of imaging at a resolution of 700 nm for rock samples. At this magnification it is possible to clearly distinguish different grains with diameters larger than the resolution, to determine and appreciate their intergranular structure, and to identify details inside the grains. However, the smaller the scanned volume, the higher the detail, but this fact also influences the representative element volume.
The total porosity of the Bray sandstone was determined in two different ways. The average open porosity determined with water absorption under vacuum was 14%, with a minimum of 4% and a maximum of 24%. The average pore diameter determined with MIP ranged from 4.7 to 20.1 μm, with an average of 15.7 μm. When analyzing the pore-volume of the micro-CT scanned sample, its average porosity was 18 vol% over an analyzed volume of 343 mm3. However, all pores smaller than and equal to 7.4 μm are not included in this volume analysis due to the limited resolution. For shape determination a minimum amount of voxels need to be present. In this study objects with a radius equal to or larger than 3 voxels were included in the analysis.
An average grain size between 0.125 and 0.25 mm was determined by means of point counting on thin sections. An average equivalent diameter of 194 (±53) μm and an average maximum opening of 117 (±34) μm were found for the grains scanned with the micro-CT scan while an average equivalent diameter of 39 (±56) μm and an average maximum opening of 24 (±38) μm were detected from the high-resolution scan. Point counting overlooked the smallest grains, which increases the average grain size, bringing it closer to the results of the micro-CT scan. On the other hand, it should be kept in mind that the analyzed volume of the high-resolution scan is too low to provide representative data.
Based on optical microscopy and SEM images, the grains are visually qualified as angular to subrounded, with a low sphericity and poorly sorted. In general, no real preferred orientation of the grains is observed; they are close packed with more concave-convex contacts. The average sphericity of the analyzed grains based on the micro-CT scan was 0.6. The frequency distribution shows a more well-sorted curve, which corresponds with the estimation based on the 2D reconstructed images. On the reconstructed 2D cross sections of the high-resolution scan, the Bray sandstone grains can visually be classified as angular to subrounded. The grain contact varies from point contacts to sutured contacts. The average sphericity of the grains analyzed on the high-resolution scan was 0.57, corresponding to the value determined from the micro-CT scan; on average the grains are not perfectly spherical.
High-resolution CT scans provide more structural detail due to their higher resolution. However, since the volume examined is smaller than for micro-CT scans, the amount of analyzed grains is much smaller, introducing insufficient data to obtain statistically correct grain-size distributions.
A convincing advantage of CT data is formed by the fact that measurement results can be visualized in 3D, where grains in a selected volume can be relabeled (color coded) based on a chosen parameter. Unfortunately CT still has its limitations and should be used for the right purposes in the correct conditions. Problems like a large sample size combined with a high spatial resolution will always be encountered when using X-ray CT and often many samples will need to be scanned in order to obtain representative volumes.
The Fund for Scientific Research—Flanders (FWO) is acknowledged for the post-doctoral grant to V. Cnudde. The Institute for the Promotion of Innovation by Science and Technology in Flanders, Belgium, is acknowledged for the Ph.D. grant to J. Dewanckele.