Evaluation of tomographic methods for limestone characterization: Using synchrotron-based X-ray tomography todetermine porosity, internal structure andinternal distributions in limestone

Evaluation of tomographic methods for limestone

characterization

Using synchrotron-based X-ray tomography to determine porosity, internal structure and

internal distributions in limestone

Albert Askengren

Department of Physics Linnaeus väg 20

901 87 Umeå Sweden

www.physics.umu.se

Abstract

Limestone is a raw material in the cement and quicklime industry and knowledge about limestone characteristics can help improve and optimize production processes.

In the end this can lead to a reduction in CO 2 emissions from the industry.

In this project X-ray tomography (XRT) was used to examine limestone samples.

The aim was to determine if XRT, including synchrotron-based XRT, is a reliable method to determine porosity, pore structure and internal distributions of pores and pyrite (FeS 2 ) grains in limestone. The aim also included to determine if XRT could be used to resolve material variations, fine-grained and larger crystals in limestone.

In total, there were ten limestone samples and the performed XRT was done by Advanced Light Source (ALS) in Berkeley, California and by Luleå University of Technology. A brief comparison between ALS and Luleå was also done by inspecting samples that have been through XRT at both facilities. The main software used for analysis was Avizo v.9.2.0.

The results showed that XRT is a suitable method for determining porosity and pore distribution. Interactive thresholding was used in Avizo for measuring porosity.

The porosity was determined as a single value and as a narrow range, where a narrow range was more reliable. XRT was also found to be a suitable method for visually determining a variety of textures within the samples. Areas with different materi- als (such as dolomite) and/or newly-formed crystals were visually distinguishable but individual newly-formed crystals were not as clear when compared to scanning electron microscopy. Individual older fine-grained and larger crystals were hard to resolve.

Internal distributions in 3D of both pores and pyrite grains were possible to

obtain with XRT. The analysis of internal distributions was found to be a clear

advantage with the method of XRT. The equivalent diameter of pores and pyrite

grains was also measured and plotted in histograms. The XRT performed at ALS

had higher resolution than the XRT performed in Luleå (0.65 vs 2 µm). Lower

resolution over-estimated the average equivalent diameter of pores, and boundaries

of pores and cavities were harder to see. Therefore, the higher resolution from ALS

was preferable. These results contribute to understanding limestone characteristics.

Sammanfattning

Kalksten är ett råmaterial i bränd kalk och cementindustrin och kunskap om kalk- stenens egenskaper kan bidra till att förbättra och optimera produktionsprocessen.

I slutändan kan detta leda till en minskning av koldioxidutsläppen från industrin.

I detta projekt användes röntgentomografi för att studera kalkstensprover. Syftet var att bestämma ifall röntgentomografi, inklusive synkrotronbaserad röntgento- mografi, är en pålitlig metod för att bestämma porositet, porstruktur och intern fördelning av porer och pyritkorn (FeS 2 ) i kalksten. Syftet inkluderade också att undersöka ifall röntgentomografi kunde urskilja materialvariationer, finkorniga och större kristaller i kalksten. Totalt fanns det tio kalkstensprover och röntgentomo- grafin utfördes hos Advanced Light Source (ALS) i Berkeley, California och hos Luleå Tekniska Universitet. En kort jämförelse mellan ALS och Luleå gjordes också genom att inspektera prover som hade genomgått röntgentomografi vid båda anläg- gningarna. Den huvudsakliga programvaran som användes vid analysen var Avizo v.9.2.0.

Resultatet visade att röntgentomografi är en lämplig metod för att bestämma porositet och distribution av porer. Binär segmentering användes i Avizo för att mäta porositeten. Porositeten bestämdes som ett specifikt värde och som ett smalt intervall, där ett smalt intervall var mer pålitligt. Röntgentomografi var också en pålitlig metod för att visuellt granska en mängd olika strukturer inuti proverna.

Områden med andra material (t.ex. dolomit) och/eller nybildade kristaller var urskiljbara men enskilda nybildade kristaller syntes inte lika tydligt i jämförelse med svepelektronmikroskop. Enskilda äldre finkorniga och större kristaller var svåra att urskilja.

Det var möjligt att ta fram interna distributioner i 3D av både porer och pyritkorn

med röntgentomografi. Analysen av interna distributioner visade sig vara en klar

fördel med metoden röntgentomografi. Den ekvivalenta diametern av porer och

pyritkorn uppmättes också och plottades i histogram. Röntgentomografin som ut-

fördes vid ALS hade högre upplösning än röntgentomografin utförd i Luleå (0.65 vs

2 µm). Lägre upplösning överskattade den genomsnittliga ekvivalenta diametern av

porer och gränserna till porer och hålrum var svårare att se. Därför var den högre

upplösningen från ALS att föredra. Dessa resultat bidrar till att förstå kalkstenens

egenskaper.

Acknowledgements

I would like to thank the Thermochemical Energy Conversion Laboratory (TEC- Lab) and the Centre for Sustainable Cement and Quicklime Production at Umeå University for creating the opportunity to perform an interesting project as my Master’s Thesis. I’ve had a competent reference group to support me in my work and they have been helpful regarding any questions that I’ve had.

I would also like to thank Markus Carlborg at Umeå University and Anna Strand- berg at Swedish University of Agricultural Sciences for letting me take part of scan- ning electron microscopy images taken at the Umeå Centre for Electron Microscopy (UCEM).

This research used resources of the Advanced Light Source, a U.S. DOE Office of

Science User Facility under contract no. DE-AC02-05CH11231. Research scientist

Dr Dula Parkinson at Beamline 8.3.2 is gratefully acknowledged for performing the

analyses at ALS.

CONTENTS CONTENTS

Contents

Abbreviations vi

1 Introduction 1

2 Method 4

2.1 X-ray tomography . . . . 4

2.1.1 Synchrotron X-ray microtomography . . . . 6

2.2 Material . . . . 6

2.3 Experimental setup . . . . 7

2.3.1 Setup at ALS . . . . 8

2.3.2 Setup at LTU . . . . 8

2.4 Analysis of X-ray tomography data . . . . 8

2.4.1 Image and analysis difficulties . . . . 8

2.4.2 Specific software used . . . . 9

2.4.3 Imaging operations in this study . . . . 9

3 Results & Discussion 11 3.1 Porosity . . . 11

3.2 Texture and structure . . . 13

3.2.1 Texture variations . . . 13

3.2.2 Grains and crystals . . . 14

3.2.3 Comparison with SEM imaging . . . 16

3.3 Comparison between ALS and LTU . . . 17

3.4 Internal distributions . . . 19

3.4.1 Pyrite distribution . . . 20

3.4.2 Variations in distributions . . . 22

4 Conclusion 24 4.1 Porosity . . . 24

4.2 Texture interpretation . . . 24

4.3 Resolution dependence . . . 24

4.4 When X-ray tomography shines . . . 24

5 Future work 25

6 References 26

A XRD data of limestone samples 29

Abbreviations

ALS - Advanced Light Source

EDS - Energy-dispersive X-ray spectrometer FOV - Field of view

ICP - Inductively Coupled Plasma Mass Spectrometry LTU - Luleå University of Technology

NK - Nordkalk AB

SEM - Scanning electron microscope SMA - SMA Mineral AB

VP-SEM - Variable-pressure scanning electron microscopy XRD - X-ray diffraction

XRF - X-ray fluorescence

XRT - X-ray tomography/X-ray microtomography

1 INTRODUCTION

1 Introduction

In 2019, just over 7.7 billions of people were estimated to live on planet earth [1]. The world population grows and requires more resources and materials in order to build and expand cities in terms of buildings, houses and pavements. At the same time an increasing population and industrialization leads to a larger consumption of land at the expense of nature, environment and wildlife, with one of the consequences being a more rapid increase of carbon dioxide (CO 2 ) emissions [2]. To accommodate for larger cities and an expanding infrastructure demand, one of the most important materials is concrete, which is one of the most consumed resources on the planet [3]. Some even say it’s the most used material of today [4, 5]. Concrete is used to construct buildings, bridges, to establish tunnel networks and create pavement and road foundations. All these different infrastructures are essential for our modern and highly populated society [3, 6]. Additionally, with an increase in wealth and indus- trial evolution in many developing countries, the consumption of concrete increases even more, mainly due to a higher demand of reliable infrastructure. An example is Mozambique where the annual cement (main ingredient in concrete) consumption in 2012 was less than 50kg per capita and had the projection to grow 35% each year [7]. Several countries in Africa experience the same situation as Mozambique and in recent years Africa as a region has seen an increase from around 40kg to 112kg per capita in cement consumption [8]. Considering that the global average in 2018 was 521 kg per capita, it is clear that the African market demand will be potentially huge in the near future [9].

Concrete is created by a mixture of gravel/pebbles and cement where the cement acts like an adhesive or binder. Unfortunately, the production of cement is asso- ciated with large CO ₂ emissions. Depending on the fuel efficiency in production, the amount of CO ₂ released is between 0.84-1.15 kg per kg clinker, a pre-product of cement [5]. About 62% of the CO ₂ emissions are process emissions, resulting from the calcining process of limestone, while the rest comes from the fuel used in the heating process[10, 11]. An increase in the demand of cement ultimately leads to even more CO 2 emission. Therefore, the cement and concrete industry are finding new production techniques to minimize their environmental impact [5, 12, 13].

Another industry that relies on the calcining process of limestone and is related to the cement industry is the quicklime industry. They also face the problem with increasing CO 2 emissions. Companies involved with either cement or quicklime in Sweden have an interest in reducing their CO 2 emissions and are therefore interested in finding modern and more environmental friendly production techniques. These new techniques need evaluation as well. During evaluation it is essential to analyze the raw material before and after the production process of cement and quicklime.

This is done to check the characteristics and quality of the cement or quicklime in

order to assess, develop and improve a specific production technique. The largest

companies in Sweden working within the cement and quicklime industry are Cementa

AB, Nordkalk AB and SMA Mineral AB and the main materials of interest are

limestone, clinker and quicklime. The methods used currently for analyzing mineral

content and internal structure are chemical analysis, X-ray diffraction (XRD), X-ray

fluorescence (XRF) and microscopy techniques such as scanning electron microscopy

(SEM) and optical microscopy. However, material characteristics related to porosity,

microstructure and the distribution of these within the sample have previously only

1 INTRODUCTION

been partly assessed by SEM and occasionally by utilizing Archimedes principle.

Therefore, there is an incentive to complement already existing analytical methods and to produce a more complete analysis of these characteristics since they impact the final product quality. One method that might fill the gap is the use of X-ray microtomography (XRT).

Nowadays XRT is used within several fields of science and for numerous applica- tions, including detection of lung cancer [14], studying tissue and cell organelles [15]

and in geoscience [16]. The application of XRT in geoscience has emerged thanks to the usage of X-rays with higher energy. With higher energy, objects with higher density can be scanned. The entry of XRT in geoscience has enabled a new way of analyzing compositions and structures of rocks and many studies are conducted on limestone and sandstone. The primary objective of using XRT in geoscience is to determine pore structure [17, 18, 19], porosity [20, 21], grain analysis and min- eral compositions [16]. Researchers have used high-resolution XRT to study micro- structures and cracks over time when pressurizing limestone samples to determine deformation and fracture toughness [22]. In addition, synchrotron-based XRT is also used for more detailed studies of the geological structure within rocks [23]. One geological structure of special interest is porosity. Porosity and pore sizes can for example help to understand permeability and fluid flow through rocks [20, 24]. A better understanding of the relation between porosity and fluid flow gives insight to engineering and technical applications of rocks and also how the structures of sedi- mentary rocks in nature change over the course of time. In fact, the non-destructive benefit of XRT enables analysis of rocks under certain conditions over time. An example is to expose wet sandstone to SO 2 to follow the change in porosity in an effort to simulate the natural weathering of sandstone [25].

XRT has been used to distinguish between calcite (CaCO 3 ) and dolomite

(MgCa(CO ₃ ) ₂ ) in limestone samples. It was also used to characterize fractures within heated limestone samples. Images were then taken before and after the heating process to determine the amount of fracturing occurring during the heat treatment. The detection of dolomite was inconclusive but the ability to detect fracturing was successful [26]. By using a synchrotron X-ray source, the increase in resolution might make it possible to detect areas of different materials, such as calcite and dolomite.

With XRT it is possible to study dual porosity rocks. Dual porosity means that there exists two distinct distributions of pore sizes and individual pores can range from nanometers to millimeters [27]. Using XRT to examine pore structure throughout a large range in pore sizes at the same time is efficient and gives struc- tural information across a broad spectra. The pore structure can be divided into networks, where one network is called the main pore network and the other is called residual pore network. The difference is that pores in the main network are con- nected while residual pore are cut off and isolated. This can be examined by using a watershed algorithm [19].

A collaboration between Nordkalk AB and Umeå university started with the

purpose to investigate the potential usage of XRT when analyzing materials in the

cement and quicklime industries. Characterization of porosity and microstructure

in limestone, clinker and quicklime can give insight to a more efficient use of raw

materials and optimized production. In the end, an optimized production can lead

to reduced CO 2 emissions from the industries. As a part of this ongoing project,

1 INTRODUCTION

this master’s thesis project was developed. The aim of this master’s thesis project is

to determine if XRT, including synchrotron-based XRT, is a reliable method when

determining overall porosity, pore structure and internal distributions of pores, cav-

ities and pyrite grains (FeS ₂ ) in limestone. A reliable porosity measurement should

be a single value without ambiguity, and/or with a narrow interval that defines if a

rock is low-porous or high-porous. The structure and internal distributions should

be displayed in such a way that variations are clearly visible and can be linked to

material properties. Additionally, the aim includes determining if XRT can be used

to resolve material variations, fine-grained and larger crystals in limestone. Crys-

tals and material compositions should be visually distinguished just as when using

optical microscopy and SEM. Determining the material composition as done with

XRD might not be possible at an equivalent level but seeing areas and distributions

of distinct materials inside the sample is more plausible. The performed XRT was

done at two different facilities with a difference in resolution and therefore the aim

also includes a brief comparison between the two methods. This project is of interest

to Cementa AB and SMA Mineral AB in addition to Nordkalk AB since they work

together on reducing their CO ₂ emissions.

2 METHOD

2 Method

The work within this project consisted of several phases, starting with a pilot study where research regarding tomography and tomography applications in geology was done. The workflow and phases that have passed during the project are seen in figure (fig.) 1. Much work has been put into getting familiar with the software and finding suitable software tools appropriate for the aims of the project. Major phases (coloured in green) are seen together with related minor objectives (coloured in red).

Figure 1: An illustration of the workflow throughout the project. The project started with a pilot study to get familiar with the topic. Arrows indicate the direction of flow between the major phases (green).

Objectives associated to the major phases are coloured in red.

2.1 X-ray tomography

X-ray tomography (XRT), also known as computed tomography (CT), was devel- oped with the intention to enable more precise imaging than traditional and old- fashioned X-ray scanning. XRT has led to the possibility of rendering 3D structures of the object at hand. One advantage compared to traditional X-ray scanning is that XRT eliminates the problem of superimposing the structure of the sample onto a 2D image [28].

During the early 1980s, XRT developed further with more precise apparatus that

minimized the diffraction of the X-rays which led to sharper images and higher res-

olution. This refinement was called X-ray microtomography (also denoted XRT), or

micro-CT, since the resolution was at micrometer scale. XRT enabled a more de-

tailed analysis of structures within the sample. The resolution today reaches down

to sub-micron level [16]. The resolution can even reach down to 50 nm for certain

laboratory scanners [29]. There also exists research focusing on image processing

algorithms to specifically enhance fine-scale features of the samples that are in the

same order of magnitude as the voxels (volume pixels). This means that the reso-

lution can appear to be sharper[30]. The high resolution increases the power and

versatility of XRT.

2.1 X-ray tomography 2 METHOD

In fig. 2 a XRT schematic shows the setup inside the hutch at beamline 8.3.2 at the synchrotron facility Advanced Light Source, Lawrence Berkeley National Lab- oratory in Berkeley, California (ALS) [31]. The X-rays penetrate the sample while the sample rotates. The sample is thereby scanned from multiple angles between 0 ^◦ and 180 ^◦ . The remaining X-ray intensities are recorded for all angles and 2D projec- tion images are created and each projection image corresponds to a specific angle.

The 2D projection images are then recombined back together with the inclusion of filtering and noise reduction techniques. The result is a stack of 2D images (or 2D slices), and these can be combined to create a 3D representation of the sample. The corresponding pixel for the 3D representation is referred to as a voxel. The length scale of a feature in the sample is related to the number of voxels that the feature occupies. The X-ray energy can be tuned which increases the variety in materials that can be investigated.

Figure 2: Image showing the working principle and setup of X-ray tomography inside the synchrotron facility Advanced Light Source in Berkeley, California. The X-rays (1) penetrate the sample (2) which is mounted on a rotating table (3). The resulting X-ray intensity is passed through a scintillator (4) and is redirected and focused through a mirror (5) and lenses (6). A CCD camera (7) records the intensity as 2D projections images. Each projection image corresponds to a specific angle. In this schematic 720 images are recorded over angles between 0-180 ^◦ with increments of 0.25 ^◦ . The projected images are combined/transformed (with linear algebra algorithms) into a stack of 2D images (bottom right). The stack is then assembled into a 3D representation consisting of voxels (volume pixels). Image reprinted with permission from McElrone et.al. [31].

In the 3D representation the internal structure, such as cavities or heterogeneous

areas, is visible without having to interfere or dissect the sample. Here one benefit

of using XRT as an investigation and imaging technique shows itself; it is a so-called

non-invasive/non-destructive method [14, 27, 28]. Another benefit is that sample

preparations are relatively simple. When using other imaging techniques like opti-

cal microscopy, atomic force microscopes (AFM) and scanning electron microscope

(SEM) samples need to be dissected and are often treated in several ways to enable

high resolution images [32]. These types of preparations do not occur for XRT. By

2.2 Material 2 METHOD

having a large range in resolution, tomography methods can complement or replace methods such as optical microscopy and SEM. Optical microscopy lies in a lower resolution range while SEM operates at a higher resolution. Still, XRT can cover both cases.

2.1.1 Synchrotron X-ray microtomography

Synchrotron-based XRT uses a synchrotron radiation source instead of traditional X-ray tubes and X-rays generated by point sources. The radiation from synchrotrons comes from relativistic charged particles orbiting in storage rings [33]. To increase the intensity of the radiation alternating magnetic fields are sometimes used [34].

The radiation from the charged particles in the storage ring also has a broad and wide energy spectrum and the radiation beam is very colinear with low divergence [35]. Due to the high intensity, or high X-ray flux, researchers in XRT are some- times utilizing synchrotron radiation sources instead of using lab-based equipment.

Synchrotron radiation is used especially when requiring images to be taken with specific wavelengths, with a reduction in noise and if a sample is in need of a shorter exposure time [36]. To select a specific wavelength (or a very narrow range of wave- lengths) in synchrotron-based XRT, a monochromator is often used. A narrow range of wavelengths decreases the diffraction of the X-rays. The low diffraction together with a focused beam reduces the artifacts in the tomographic images and enables high resolution [23]. The resolution can reach sub-micron scale [36].

2.2 Material

There were ten limestone samples serving as a basis for the analysis, five from Nordkalk AB and five from SMA Mineral AB. The samples from Nordkalk AB were labeled NK1 to NK5. The samples from SMA Mineral AB were labeled SMA1- 1, SMA1-2, SMA1-3, SMA2-1 and SMA2-2. The SMA1 samples originate from a common larger piece of rock. The same applies for the SMA2 samples which also originate from a common rock, however not the same as SMA1. The five NK samples were scanned by Luleå University of Technology (LTU) and all ten samples were scanned by ALS in Berkeley. The samples in this study have been drill cores with a diameter of 6-7 mm. To the left in fig. 3 a picture of the sample NK2 is seen together with some drill cores. To the right in the same image a 3D reconstruction of a drill core in the Avizo software is seen.

These samples have previously been well analysed with; Inductively Coupled Plasma Mass Spectrometry (ICP) and XRF spectroscopy to determine the elemental composition and powder XRD with a Bruker AXS D8 Advance X-ray diffractometer CuKα-radiation for identification and semi-quantification of crystalline compounds (not in this study). A complete table with XRD data for the limestone samples can be found in table A.1 in Appendix A.

The samples have previously also been through SEM analysis performed with a

variable-pressure scanning electron microscopy (VP-SEM). A Carl Zeiss Evo LS-15

was used with a back-scattered electron detector at an accelerating voltage of 15

kV and probe current of 300-400 pA for morphological investigation. Together with

the SEM-analysis, an energy-dispersive X-ray spectrometer (EDS) with an Oxford

Instruments X-Max 80 mm ² was used for quantifying the elemental composition of

2.3 Experimental setup 2 METHOD

(a) The sample NK2 together with some drill cores.

(b) Example of a reconstruction of the NK2 drill core sample. The reconstruction is done in Avizo.

Figure 3: A real world sample with drill cores is seen to the left and a corresponding reconstruction of a drill core to the right.

the samples at different locations (not in this study). SEM images were used to help evaluate tomography data.

The porosity of NK1 and NK3 has been measured with a method based on Archimedes principle and the resulting porosity was 15% and 1.4% respectively (not in this study).

2.3 Experimental setup

Regarding the experimental setup, XRT relies on relatively simple theory; X-rays are absorbed more when penetrating materials with higher densities, and the result- ing intensity after penetration can be measured. In practice however, fine-tuning equipment and building high precision laboratory setups requires a sophisticated approach. Minimizing diffraction of X-rays and using optics when recording the intensity are examples of actions to increase the resolution. Another example of fine-tuning equipment is that samples need to be centered properly before the scan- ning starts. Due to the rotation of the sample any misalignment around the center axis creates blur and artifacts in the images.

With high resolution the field of view (FOV) is often decreased. This means that only a smaller portion can be scanned even if one were to fit a larger sample.

High resolution might be wanted on larger samples by increasing the FOV. However,

performing XRT scans takes up a lot of data storage. Performing high resolution

images of large samples creates a significant amount of data that quickly becomes

inconvenient. For example, a stack of images from ALS (one sample) in this study

consists of roughly 30 GB. If the FOV is doubled but with the same resolution, that

same stack would take up 240 GB of storage. Very few computers can handle and

access that amount of data at once. Therefore researchers often have to compromise

between sample size, FOV and resolution when using XRT [37].

2.4 Analysis of X-ray tomography data 2 METHOD

2.3.1 Setup at ALS

For the microtomography scans, ALS used an X-ray energy range from 20-50 keV.

The exposure time was 75 ms and 2625 angles were recorded over 180 ^◦ . The effective pixel size was 0.65 µm for the scans. The horizontal FOV was 1.664 mm (2560 pixels) and the vertical FOV was 1.404 mm (2160 pixels). For detection a LuAG:Ce scintillator, a PCO.edge sCMOS detector and a 10x optical lens was used.

2.3.2 Setup at LTU

The setup used at LTU for the microtomography scans consisted of X-rays generated at 100 kV with a total power of 9 W. An LE3 X-ray source filter (Edmund optics) was applied. The exposure time was 1.5 s and 3201 projections were recorded over 180 ^◦ . The effective pixel size was 2.00 µm (lower resolution than at ALS). The distance between the X-ray source and the sample was 10.3 mm and the distance to the detector from the sample was 24.5 mm. The FOV was 2.02 mm and the instrument used was a Zeiss Xradia 510 Versa with a 4x optical lens.

A larger scan of NK3 was also done at LTU by the same instrument, but with a 0.4x optical lens. This setup used X-rays generated at 70 kV with a total power of 9 W. An LE4 X-ray source filter (Edmund optics) was applied. The exposure time was 6.0 s and 1601 projections were recorded over 180 ^◦ . The effective pixel size was 7.5 µm and the FOV was 7.7 mm. The distance between the X-ray source and sample was 14.0 mm and the distance to the detector from the sample was 112.7 mm.

2.4 Analysis of X-ray tomography data

What features the 2D image has and how to find them can require multiple process- ing operations, some which are easy to perform and some which are not. It is within this area that a researcher needs to be creative about which operations to use and to learn from other studies where the same features and materials are examined. Note however that there are limitations to what characteristics can be visualized. Even if one knows beforehand what features are of interest, they might be hard to detect (due to e.g. low resolution, no distinct differences in density within the sample).

2.4.1 Image and analysis difficulties

Problems that occur related to the visualization of the sample are called artifacts.

Some of the most common artifacts in the images are noise, motion of the sample, ring artifacts [29], beam hardening and aliasing [38]. Noise is often reduced by filters and by different transform operations of the images, whilst motion and rings are related to the experimental setup and can often be fixed by simple means.

Aliasing results in having radial lines penetrating the image and is a result of under-

sampling, which can be fixed relatively simple as well. However, beam hardening is

more difficult to troubleshoot. Beam hardening is a result of that X-rays of different

wavelengths are absorbed to different extents. Often, absorption is assumed to

be linear but in reality, it is not. Beam hardening affects the image by creating

darker areas, called streaks, between dense points within the sample. There are two

common approaches to deal with beam hardening: using metal filters in the setup

2.4 Analysis of X-ray tomography data 2 METHOD

that eliminate all lower energy wavelengths before entering the sample or utilizing a synchrotron X-ray source which can produce very monochromatic X-rays [29].

Depending on the resolution of the performed XRT scans the result of total porosity and pore sizes may be inaccurate due to that sub-micron pores smaller than the resolution are missed. Pores below a certain size are neglected by low resolution.

Such small-scale pores are not negligible and may therefore distort the pore size distribution. The average pore size is often overestimated while the total porosity is underestimated. Determining the pore size of connected pores in a larger pore network also becomes troublesome since the pore continues, in a sense, throughout the sample [17]. Thus, it is important to understand how resolution affects the results of measuring porosity.

2.4.2 Specific software used

The two main softwares that have been used in this project are Avizo and ImageJ.

ImageJ was used to crop some of the images. This was done to eliminate artifacts (especially rings artifacts) at the edge of the samples and to remove the outer back- ground of some samples. After these pre-image treatments Avizo v.9.2.0 was used for analysis of porosity, texture interpretation and label analysis. Final image editing to include scales and sample info was done with in-house Windows programs.

2.4.3 Imaging operations in this study

The 2D images were reconstructed by ALS and LTU. Therefore, operations to re- duce noise and artifacts had already been done on site for all samples. No image processing techniques, except for image cropping, were applied beyond the analysis done in Avizo. The image cropping was done to exclude the surrounding outside of the sample (air) and to reduce blur and rings artifacts at the edge of samples.

When investigating pore structure of limestone samples, thresholding techiques is often used to quantify the porosity [27, 39]. Interactive thresholding (manually selected thresholds) is used for examining the pore structure [17]. Interactive thresh- olding selects a part of the grayscale that the images consists of. The marked part of the grayscale can correspond to either pores or pyrite grains. Interactive thresh- olding sets a lower and an upper bound on the grayscale. The voxels containing the shades of grey in that range are included, the rest are excluded. After selecting the number of voxels that are considered pores or pyrite grains these voxels can be expressed as a ratio of the total number of voxels in the sample. The total number of voxels are all voxels in the sample, both material and pores. This gives a volume fraction that represents the porosity or the pyrite content as a ratio. The chosen voxels create a new data set that can be used for further analysis. An operation similar to interactive thresholding is image segmentation. With segmentation it is possible to determine both internal microstructures and porosity in limestone [18].

Image segmentation is used to distinguish multiple areas in the sample, for example by using multiple thresholds to divide the grayscale into several regions.

Label analysis is used to mark individual pores. The marked pores can then be ranked in size by calculating their equivalent diameter. The equivalent diameter (EqD) is calculated as

EqD = p ³

6V /π, (1)

2.4 Analysis of X-ray tomography data 2 METHOD

where V is the volume of the connected voxels representing the pore in the 3D recon-

struction. The diameter for all pores can then be plotted in a histogram showing the

distribution of pores and grains inside a sample with respect to equivalent diameter.

3 RESULTS & DISCUSSION

3 Results & Discussion

3.1 Porosity

To determine the porosity, interactive thresholding was mostly used. Due to homo- geneous samples and that different forms of limestone (calcite/dolomite) in general have similar densities, the attenuation of X-rays is similar as well. The grayscale histogram was hard to separate into several regions with segmentation. The lower limit when using interactive thresholding was chosen so that the largest cavities (i.e.

cavities of darkest shade) were included and there was no particular problem in de- termining the lower limit. However, when the upper limit was chosen there was an ambiguity. Since the grayscale spectrum is continuous there is not a definite cut-off value for pores. This means that a certain upper limit will include too few pores or include some material parts into the pores, unless the limit is set at the equilibrium just between pores and material. Due to scattering of X-rays and small variations in the X-ray absorption throughout the sample an equilibrium limit is most likely not possible to find. Therefore, calculating porosity by setting one specific value as an upper limit is not the best choice. A small range of the upper limit should be used instead, resulting in that the porosity also falls into a range. This is a more realistic estimation and includes an error margin. However, a single value for the porosity does work well if the same sample were to be examined again with the same equipment. At that point, the porosity can be compared between measurements and by using the same threshold values any potential bias is eliminated. In fig. 4 the same sample (SMA2-2) is marked with interactive thresholding but with four sepa- rate upper limits. The resulting porosity varies between 2.3% and 7.0% throughout the images. Fig. 4 illustrates the difficulty of how to determine the upper threshold limit. In some images large areas of a darker shade are seen but they are not marked by the threshold. These areas are larger cavities with newly-formed material inside and lie between pores and brighter material (calcite) in the grayscale histogram (see section 3.2.2 and 3.2.3). Therefore, these larger "pores" are not marked as pores.

Where the limit should be is a matter of visual interpretation. The images from ALS are taken with X-rays from a synchrotron. The high X-ray flux and focused beam leads to small measurement variations over time. Therefore, the grayscale for each scanned sample is very similar which makes it possible to compare all the samples and determine a common upper limit when using a thresholding technique.

The grayscale in the images from ALS had a range of values between 0-255. By comparing several samples an upper threshold limit at 105 was selected as a divider between pores and material. However, even if this threshold was functioning for most samples there were situations where that limit could have been moved up or down along the grayscale with the marking still being reasonable. This yet again hints that an interval for the porosity is preferable over a single value. Fig. 5 shows the visual difference when marking different samples with the same threshold limits.

Most samples were evaluated with interactive thresholding and the resulting porosity

is seen in table 1, both as a range and when marked with the common single upper

limit at 105. The lower and upper limit was set at 20-105 by visual inspection. Also

note the porosity range is set individually for each sample. The values for NK5 in

the table are absent due to poor image quality (blur and artifacts). Regarding the

scans from LTU the grayscale in those images is not as consistent as from ALS and

therefore each sample needed its own specific threshold limits. Thus, the threshold

3.1 Porosity 3 RESULTS & DISCUSSION

(a) The marking corresponds to a porosity of 2.3%. (b) The marking corresponds to a porosity of 3.8%.

(c) The marking corresponds to a porosity of 5.6%. (d) The marking corresponds to a porosity of 7.0%.

Figure 4: Same sample (SMA2-2) illustrating the visual appearance of different thresholds. The porosity varies between 2.3% (a) and 7.0% (d). Note that c) and d) are quite heavily marked to illustrate the visual difference.

limits for the LTU images were not comparable with ALS and are not included in the table.

The porosity for NK1 and NK3 from previous measurements were 15% and 1.4%.

Comparing to the values in table 1 the porosity for NK3 matches fairly well but not for NK1. To receive a porosity of 15% for NK1 with the XRT images used in this study the sample would have been severely over-marked. The reason for this discrepancy is unclear since NK3 seemed to match well in porosity. One possible explanation is that NK1 has very many micropores with sizes below the resolution.

In that case such small micropores would have been missed and the porosity would in

reality be higher than the result from XRT analysis. The effect that micropores are

missed due to insufficient resolution has been seen previously [17]. Overall, XRT is

a suitable and easy method for measuring porosity, but depending on the setup used

it might be more expensive to perform, especially when utilizing synchrotron-based

XRT.

3.2 Texture and structure 3 RESULTS & DISCUSSION

Table 1: Table showing the results from measuring porosity with interactive thresholding. A single value and a range for the porosity in seen. The porosity range is individually set for each sample. One sample is absent due to poor image quality and artifacts. Some samples have very low porosity and the common upper threshold limit was in some cases under-marking pores (visually marking too few pores).

The porosity range was determined by altering the upper threshold limit, the lower was fixed. The results are based on XRT images taken by ALS.

Sample Porosity, common

upper limit (%) Porosity range (%) Notes Threshold limits: 20-105

NK1 0.86 0.86-4.02 105 was the lowest upper limit

NK2 4.17 2.16-5.60

NK3 0.86 0.662-1.18

NK4 0.32 0.32-1.55 105 was the lowest upper limit

NK5 - - Bad image quality/artifacts

SMA1-1 0.05 0.05-0.15 Low porosity

SMA1-2 0.006 0.006-0.30 Low porosity/under-marked

SMA1-3 0.003 0.003-0.31 Low porosity/under-marked

SMA2-1 0.28 0.28-1.88 105 was the lowest upper limit

SMA2-2 1.76 1.35-3.80

3.2 Texture and structure

3.2.1 Texture variations

XRT makes it possible to easily see texture and structural variations in a sample, and examples are seen in fig. 6. Samples exhibit smaller cracks, cavities, darker areas of other material and widespread porous areas. With XRT all these types of variations are found. Porosity can be measured and the length of cracks can be measured but unfortunately, it is hard to quantify the portion of darker areas. The grayscale of the brighter and darker areas overlap, and any specific area is hard to isolate with interactive thresholding or segmentation. An example of two images with darker areas is shown in fig. 7. Still, the visual interpretation is valuable in many cases.

Just as with porosity, the analysis is very biased to the researcher who looks

at the samples (visual interpretation). Therefore certain features might have been

overlooked or missed. Previous experience and knowledge with limestone analysis

helps in finding areas of importance. In addition, further work that aims to relate the

visual analysis of limestone to material characteristics is needed. The relationship

between material analysis and improvement in the production process is vital. Thus,

there lies important work ahead to establish the connection between XRT analysis

and production.

3.2 Texture and structure 3 RESULTS & DISCUSSION

(a) The common threshold is well suited for NK2. (b) The common threshold is also well suited for NK3.

(c) The common threshold is slightly low for NK4. (d) The common threshold is slightly low for SMA2-1.

Figure 5: Several different samples marked with the same threshold. This picture shows that it possible to compare a threshold between samples. Still, it does not guarantee the best marking for an individual sample.

3.2.2 Grains and crystals

Larger grains and crystal structures have been hard to resolve with the scans from

both LTU and ALS when the resolution has been at and below 2 µm. Larger grains

are considered being in the order of 800-2000 µm. However, LTU has made scans

of a larger piece of sample NK3, with a resolution of 7.5 µm. Due to the lower

resolution, the FOV was around 7.7 mm (the whole sample was scanned) instead

of 1.6-2 mm which was the case for the high resolution scans (ALS and LTU). In

the larger sample larger grains are more visible than in the smaller samples. Larger

grains are so big that it is likely the smaller samples consist of only one grain, or

perhaps an intersection between 2-3 grains. Because of this it is hard to see the

big picture regarding larger grains and crystals. When interested in larger grains

and crystal structures a larger sample, with a decrease in resolution, should be

considered. Sample size and resolution should be chosen based on the scale of the

characteristics in focus.

3.2 Texture and structure 3 RESULTS & DISCUSSION

(a) Example of a crack and some pores. (b) Example of a widespread area with many pores.

(c) Example of a typical limestone sample with some cracks.

Figure 6: Images showing the variety of textures occurring for limestone. Both cracks, porous areas and some smaller darker areas are seen.

Smaller grains and crystals have also been hard to resolve. The resolution of the images is probably not sufficient to distinguish small grain/crystal boundaries.

Together with smaller internal fractures and that grains/crystals are positioned very

dense, it becomes hard to draw conclusions regarding the shape and composition of

individual grains/crystals. One exception is the formation of newer crystals inside

larger cavities. Individual crystals are still hard to resolve but areas of more recent

formed crystals are possible to find. The material inside the cavities can be of the

same material as the rest of the sample but also from a different material. An

example is spotting areas of calcite with varying Mg percentage or dolomite. These

areas often appear darker in the images. The reason can be that pores partly shade

3.2 Texture and structure 3 RESULTS & DISCUSSION

the area or that another lighter material is present. A lighter material absorbs less radiation than the surrounding heavier material. That area would then visually appear darker just as a cavity with newly formed crystals does. Therefore it can be hard to determine what the reason is. In fig. 7 two images with darker areas are seen, one from NK2 and one from NK3. Both samples are homogeneous in material composition (see Appendix A for XRD data) and therefore the darker areas are most likely newly formed crystals of the same material (see comparison with SEM regarding NK2).

(a) (b)

Figure 7: Two examples of darker areas within a sample. The darker areas in NK2 (left image) are newly-formed crystals. The darker areas in NK3 (right image) might be newly-formed crystals as well.

3.2.3 Comparison with SEM imaging

As a help to interpret the texture of the samples in the XRT images, SEM images has been available for some samples. In fig. 8 a comparison between the two methods is visible for the sample NK2. The darker areas in the XRT images are the same type of microstructures as seen in the SEM image. This particular sample consists mainly of dolomite (see XRD data in Appendix A) and therefore the difference in texture within the sample is probably due to formation of crystals at different times.

The more rhombic crystals might have been formed later inside the larger cavity and

thus appear visually different. The newer crystals have possibly had more space to

grow in and therefore the edges are seen more clearly than older crystals. However,

in the XRT images only darker areas are seen and not individual crystals (see section

Grains and crystals above).

3.3 Comparison between ALS and LTU 3 RESULTS & DISCUSSION

(a) Texture of NK2 sample when scanned by ALS. (b) SEM image of NK2 sample.

Figure 8: Comparison between the texture of NK2 when images are produced by X-ray microtomography (left) and SEM (right). A darker area in the X-ray microtomography image, marked by a yellow circle, corresponds to the cavity with rhombic crystals in the SEM image.

3.3 Comparison between ALS and LTU

One difference between images from ALS and LTU is the resolution. The resolu- tion from ALS is 0.65 µm and 2 µm from LTU. In fig. 9 one image from ALS and one image from LTU are shown. Both images show larger regenerated cracks and areas/patches with different grayscale value but boundaries and micropores are sharper and clearer when using the higher resolution from ALS. This is probably due to that the scale of the boundaries and pores is roughly at or below the LTU resolution of 2 µm. Features up to a scale of 5-6 µm such as cracks, boundaries and pores can be hard to resolve with a resolution of 2 µm (a more realistic resolution is often said to be roughly 3x pixel/voxel size).

(a) Sample image of NK3 from ALS. (b) Sample image of NK3 from LTU.

Figure 9: Texture comparison between images from ALS (left) and LTU (right). The sharpness of the boundaries is increased with higher resolution (ALS images) while larger patches with a different grey value are still visible.

A comparison of histograms between ALS and LTU is done in fig. 10 and 11.

3.3 Comparison between ALS and LTU 3 RESULTS & DISCUSSION

The histograms show pore diameter for NK2 scanned by ALS and LTU respectively.

They are based on the same porosity, i.e. interactive thresholding was used to obtain the same porosity for both samples. It is clear that the histogram based on the ALS data, fig. 10, is more dense at small diameters and very few pores are larger than 40 µm in diameter. Conversely, fig. 11 shows that there exists more pores with larger diameter when the data is from LTU, and the pore diameter size is more uniformly spread out. As pointed out in a study by Peng, lower resolution often overestimates pore sizes [17]. This is likely to be connected with boundary scales being at a resolution of roughly 2 µm. Therefore two distinct pores might seem to be connected due to lower resolution at LTU, while the two pores are distinguished by a boundary when the sample is scanned by ALS. When regarding the complete sample multiple pores will then be connected to each other and the average pore size will be slightly increased. Naturally, this is also affected by the smallest pore diameter that can be resolved which is equal to the voxel size for each setup (0.65 vs 2 µm).

Figure 10: Histogram over the equivalent diameter of individual pores in NK2. The data is based on

scans by ALS. Note that the y-axis consists of a logarithmic scale.

3.4 Internal distributions 3 RESULTS & DISCUSSION

Figure 11: Histogram over the equivalent diameter of individual pores in NK2. This data is based on scans by LTU. Note that the y-axis consists of a logarithmic scale.

It should be noted that even if the XRT images taken from ALS show a smaller average pore size there still exists micropores smaller than the resolution of 0.65 µm. Therefore, the average pore size might be even smaller than seen in fig. 10 and the porosity might be higher. Any conclusion can only be drawn between these two specific setups and cannot be related to other setups without further comparison.

Another comparison between the two different setups is to investigate how a porosity measurement is affected by the resolution. In the above comparison the porosity was measured equal as a starting point. But it is perhaps of more interest to see if the porosity differs for a sample that has been through XRT at both ALS and LTU. The sample could be marked similarly by visual inspection and a difference in porosity might be found. Such a comparison gives further insight regarding which XRT facility is the most suitable for a specific aim.

3.4 Internal distributions

Combining the 2D images with the marked voxels create volumes throughout the sample. This makes it possible to see and measure the volumes and how they are distributed internally. When investigating pore structure the distribution of the pore network can be examined in addition to measuring the total porosity. In fig.

12 two images of the distribution of pores are visible. The left and right images show pores that are larger and smaller than 20 µm in equivalent diameter respectively.

It is easier to distinguish the density of pores throughout the sample when looking

at the larger pores because the smaller pores clutter the image. Additionally, it is

possible to calculate the amount of pores within a certain size. These pores can be

summed up and expressed as a fraction, just as the total porosity.

3.4 Internal distributions 3 RESULTS & DISCUSSION

(a) Internal distribution of pores larger than 20 µm. (b) Internal distribution of pores smaller than 20 µm.

Figure 12: The figures show internal pore distribution of the NK3 sample. To the left, pores larger than 20 µm are visible, while to the right only pores smaller than 20 µm are visible. The data is based on scans from LTU.

3.4.1 Pyrite distribution

At the other end of the grayscale spectrum it is possible to find pieces of iron compounds, mainly in form of pyrite (FeS ₂ ). Instead of selecting a threshold that targets the porosity the selected threshold can cover the pyrite grains. Just like with porosity, a distribution of pyrite can then be obtained in a visual representation. In fig. 13 grains of pyrite are visible as bright white spots on the left image. In the right image of fig. 13 the pyrite grains are marked with interactive thresholding.

Additionally, the amount of pyrite in a sample can be calculated as both a ratio and a total volume but when analyzing mineral contents XRD and XRF offers analysis that takes multiple minerals into account at the same time and is thus preferable if several minerals are of interest and not pyrite solely. Also, the pyrite content is roughly measured and not as quantitatively as with XRD or XRF.

The distribution of pyrite within NK4 is shown in a 3D image in fig. 14. Here

it is clearly visible that the distribution of pyrite is relatively dense on the left side

but sparse on the right. The benefit of using XRT for 3D analysis of samples is

clear. The histogram over the equivalent diameter of the same pyrite grains from

the 3D distribution in NK4 is seen in fig. 15. The histogram resembles the shape of

the histograms plotted for the porosity measurements. This shows that measuring

pyrite grains is very similar to measuring porosity and could be considered to have

the same reliability. Any error made when measuring pyrite is likely to be roughly

equal to the error made in a porosity measurement, since the analysis of pyrite and

pores consist of the same approach.

3.4 Internal distributions 3 RESULTS & DISCUSSION

(a) Pyrite grains within NK4. The grains are visible as

bright white areas. (b) Pyrite grains within NK4 marked by interactive thresholding.

Figure 13: Pyrite grains from NK4 are visible in the left picture. In the right picture the same pyrite grains are seen, but now marked with interactive thresholding.

Figure 14: 3D distribution of pyrite grains within NK4. Similar to selecting pores but with a threshold

targeting the brighter pyrite regions within the grayscale of the images.

3.4 Internal distributions 3 RESULTS & DISCUSSION

Figure 15: Histogram over the equivalent diameter of pyrite grains in NK4. The histogram has a similar shape to porosity measurements. Note that the y-axis consists of a logarithmic scale.

3.4.2 Variations in distributions

Another interesting aspect is if the pore size differs in two samples that have the same porosity. When comparing images from ALS and LTU there was a clear difference in the average pore size due to the difference in resolution and possibly there lies a discrepancy within a single setup as well. Two samples, SMA1-1 and SMA1-3 (same original stone), were marked in such a way that the resulting porosity was equal.

The histogram over the equivalent diameter of the pores for SMA1-1 and SMA1-3 is shown in fig. 16. Overall, the two histograms are very similar in appearance.

The yellow line is set at 8 µm and the number of pores at that size were 26 vs 24 for the two samples confirming their similarity. It should be noted that SMA1- 1 and SMA1-3 originate from the same larger rock sample and therefore it is not certain that distributions are alike at the same porosity. Two more distinct limestone samples should be considered instead and a difference might occur in that case.

Another approach is to visually mark the samples equally and then compare the

pore size distribution. By forcing the samples to the same porosity pores might have

been missed and material might have been included in the threshold. Therefore an

independent visual marking for each sample could be considered more natural, but

any difference in pore size distribution could then be related to the overall porosity

and/or internal variations. With an equal porosity any difference is isolated to an

internal variation.

3.4 Internal distributions 3 RESULTS & DISCUSSION

(a) Histograms over equivalent pore diameter for SMA1-1 at a porosity of 1.4%.

(b) Histograms over equivalent pore diameter for SMA1-3 at a porosity of 1.4%.

Figure 16: Comparison of equivalent pore diameter between SMA1-1 and SMA1-3. Both samples have the same total porosity and data is based on scans from ALS. Note that the y-axis in each histogram consists of a logarithmic scale. The two histograms are very similar and no significant variation is found.

However, the two samples originate from the same piece of larger rock and no conclusion regarding pore

size variations can be drawn.

4 CONCLUSION

4 Conclusion

4.1 Porosity

XRT is a suitable tool for measuring porosity, but using specific setups (e.g. synchrotron- based XRT) can be expensive and time-consuming. The measurement in Avizo is fast and simple when using interactive thresholding to mark the pores. An interval for the porosity is preferable over a single value since the marking is slightly biased by the investigator. Samples scanned at ALS can be compared to each other and reduces the bias. An interval includes the low and high markings of a sample and therefore most researchers would agree that the porosity lies within the estimated range, but with a single value researchers might not consent on that specific porosity.

The results show that the limestone samples in this study overall are low porosity rocks, but still with some samples being more porous.

4.2 Texture interpretation

The use of XRT is suitable for detecting and inspecting structural variations. In this project extended regions with pores and larger cavities were found. Multiple cavities with newly-formed crystals and several internal cracks could also be found.

However, the comparison between XRT and SEM showed that the visual appearance of individual newly formed crystals was clearer with SEM. With XRT it is easy to move around within the image reconstruction and throughout the whole stack of images. Finding areas of interest is done quickly and with ease.

4.3 Resolution dependence

Several limestone samples were scanned with two different resolutions, 0.65 µm at ALS and 2 µm at LTU. The higher resolution at ALS was preferable for the objectives studied in this project. Many texture boundaries lie at the limit of the resolution from LTU and features were easier to resolve with the higher resolution from ALS.

The average pore size was over-estimated with lower resolution and micropores were overlooked compared to the higher resolution images from ALS.

4.4 When X-ray tomography shines

What stands out with XRT is that a sample is reconstructed in 3D. XRD, SEM and

microscopy can be used to calculate material percentages in a sample and visually

evaluate texture and structure but none gives insight to the internal 3D structure

and distribution within the sample. With XRT an overall porosity or pyrite con-

tent is complemented with a distribution that makes it possible to locate regions

with higher/lower density of pores and grains. Regions with more cracks and/or

limestone/dolomite regeneration can also be examined by visually interpreting the

internal distribution.

5 FUTURE WORK

5 Future work

Limestone is a material of interest for both the cement and quicklime industry.

This study shows that some characteristics of limestone can be examined well with XRT. Some aspects could however be investigated further regarding limestone. For instance the amount of open and closed pores, including the micropores could be calculated by a watershed algorithm [19]. Another aspect is how resolution and experiment setup affects the porosity. A comparison between ALS and LTU was made regarding the equivalent diameter of the pores at the same porosity but not how the setups differ when calculating porosity. This could be investigated by visually marking the same amount of the pores and comparing the overall resulting porosity. It might be hard to mark pores in a consistent manner (visually) but porosity measurements might be subject to the resolution and equipment on site.

Two other materials that were not examined here are clinker and quicklime, both of which are very important for the cement and quicklime industry respectively.

Techniques used to investigate porosity are possibly suitable for these materials as well. A visual texture/structure analysis is also desirable since clinker and quicklime both have undergone a calcination process and several minerals have been formed.

Therefore, using XRT as a method is an interesting starting point for future work with these materials. Other software operations/tools that were not tested here might be of interest and can complement the already tested operations from this study. This can increase the usefulness of the XRT compared to other existing methods (XRD, SEM, optical microscopy).

Further work should be done with the intention of relating texture and structure

within the sample to material properties. It is important to bridge the gap between

XRT analysis and the effect of material properties in the production process. There-

fore, work should be done to understand how the results seen from the XRT analysis,

such as texture and structure variations, translates into to useful information out in

the industry.

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A XRD DATA OF LIMESTONE SAMPLES

A XRD data of limestone samples

All limestone samples used in this study have been put through XRD analysis. The specific XRD analysis used is called Rietveld refinement which has been adapted to work with X-rays. Table A.1 shows the composition of the samples in weight percentage. Note that SMA1-1 to SMA1-3 are from a larger piece of limestone labeled SMA-1 in the table. The same applies for SMA-2 which served as a basis for the two samples SMA1-4 to SMA1-5.

Table A.1: Table showing the data from XRD analysis for all limestone samples. Note that SMA-1 and SMA-2 in the table corresponds to the samples SMA1-1 to SMA1-3 and SMA1-4 to SMA1-5 respectively.

NK-1 NK-2 NK-3 NK-4 NK-5 SMA-1 SMA-2

Formula Name wt-% wt-% wt-% wt-% wt-% wt-% wt-%

CaCO 3 Calcite 86.6

(Mg _0.04 Ca _0.96 )CO ₃ Calcite 3-6% Mg 99.87 94.9 96.55 99.9 100

SiO 2 Quartz 0.13 0.16 0.16 0.99 0.01 0.1

MgCa(CO 3 ) 2 Dolomite 99.28 13.3

CaAl 2 Si 2 O 8 (H 2 O) 4 Gismondine 0.56

Ca 2 MgSiO 2 Åkermanite 4.94 2.46

Sum 100 100 100 100 99.91 100 100