Characterization of phases in

IN

DEGREE PROJECT TECHNOLOGY, FIRST CYCLE, 15 CREDITS

STOCKHOLM SWEDEN 2021,

Characterization of phases in

Argon Oxygen Decarburization slag

EMIL ROSQVIST THEODORE VASSI

KTH ROYAL INSTITUTE OF TECHNOLOGY

Abstract

Slag is an important part of steelmaking with the AOD (Argon Oxygen Decarburization) process.

In this work the focus was on developing a methodology for characterizing phases in slag samples obtained after decarburization, reduction and desulphurization. Six samples from two heats, or batches, (heat A and B) were prepared by baking in Bakelite and polishing. These were analysed in SEM (Scanning Electron Microscope), with BSE (Backscattered Electrons) and EDS (Energy Dispersive X­ray Spectroscopy). Images from BSE were then processed in ImageJ with a denoise method for advanced fraction analysis. Average composition for each noticed phase analysed with EDS is presented in element tables. A systematic portraying of the cross section was performed on samples from heat B. This gave a more in­depth composition and fraction analysis. Due to the nature of slag, scratches were often induced during polishing.

The negative effect of these scratches could be reduced with the denoise method in the fraction analysis. There are three main phases in each stage of the AOD process with similar composition and structure between the two heats. Results showed the importance of measuring different zones of the slag due to its heterogeneity. More specifically, at least four random images from the cross section were required for accurate fraction analysis of samples after decarburization.

Overall, the methodology for characterization was sufficient for samples after decarburization and desulphurization.

Sammanfattning

Slagg är en viktig del av ståltillverkning med AOD­processen (Argon Oxygen Decarburization).

Fokus i detta arbete var att utveckla en metod för att karakterisera faser i slaggprover erhållna efter avkolning, reduktion och avsvavling. Sex prover från två batcher (batch A och B) förbereddes genom bakning i bakelit och polering. Dessa prover analyserades i SEM (Svepelektronmikroskop), med BSE (Backscattered Electrons) och EDS (Energy Dispersive X­ray Spectroscopy). Bilder från BSE bearbetades sedan i ImageJ med en denoise­metod för avancerad fraktionsanalys. Genomsnittlig sammansättning för varje fas analyserad med EDS presenteras i elementtabeller. En systematisk undersökning av heterogenitet hos slagg utfördes på prover från batch B. Detta gav en mer noggrann komposition och fraktionsanalys. På grund av slaggens karaktär uppkom ofta repor under poleringen. Den negativa effekten av dessa repor kunde minskas med denoise­metoden i fraktionsanalysen. Det finns tre huvudfaser i varje steg i AOD­processen med liknande sammansättning och struktur för de två batcherna. Resultaten visade betydelsen av att mäta slaggprovet i olika zoner på grund av dess heterogenitet. Mer specifikt krävdes minst fyra slumpmässiga bilder från tvärsnittet för noggrann fraktionsanalys av prover efter avkolning. Sammantaget var metoden för karaterisering av slagger tillräcklig för prover efter avkolning och avsvavling.

Authors

Emil Rosqvist emilrosq@kth.se Theodore Vassi tvassi@kth.se

Material Science and Engineering Unit of Processes KTH Royal Institute of Technology

Place for Project

Brinellvägen 23 Stockholm, Sweden

Material Science and Engineering Unit of Processes

Examiner

Anders Eliasson anderse@kth.se Brinellvägen 23 Stockholm, Sweden

Material Science and Engineering Education Material Science KTH Royal Institute of Technology

Supervisor

Andrey Karasev karasev@kth.se Brinellvägen 23 Stockholm, Sweden

Material Science and Engineering Unit of Processes KTH Royal Institute of Technology

Contents

1 Introduction 1

1.1 Problem . . . 1

1.2 Purpose . . . 1

1.3 Goal . . . 1

1.4 Ethics and Sustainability . . . 2

2 The Argon Oxygen Decarburization process 3 2.1 AOD Slag . . . 3

2.2 Previous characterization methods . . . 4

3 Methodologies and Methods 5 3.1 Samples . . . 5

3.1.1 Preparation of samples . . . 5

3.2 SEM . . . 6

3.2.1 SEM operations . . . 7

3.3 Fraction analysis . . . 8

3.3.1 Threshold analysis . . . 8

3.3.2 Denoise methodology . . . 8

3.3.3 Number of images required . . . 9

4 Results 10 4.1 Methods . . . 10

4.1.1 Sample preparation . . . 10

4.1.2 EDS method . . . 11

4.1.3 Image analysis . . . 12

4.2 Composition analysis . . . 14

4.2.1 After decarburization . . . 14

4.2.2 After reduction and desulphurization . . . 16

4.3 Results of fraction analysis . . . 19

4.4 Distance dependency . . . 21

5 Discussion 23 5.1 Characterization after decarburization . . . 23

5.2 After reduction and desulphurization . . . 23

5.4 The value of measurements in heterogeneous slag . . . 24 5.5 Optimization of operation . . . 25

6 Conclusions 27

6.1 Future Work . . . 28

7 Acknowledgements 29

8 References 30

Appendices I

Appendix A: Number of images needed I

Appendix B: Area analysis in ImageJ IJ1 Macro III

Appendix C: Visualisation of covered area V

1 Introduction

In today’s society the awareness of global warming is well spread, at least in Sweden. When some companies develop fossil free processes for production of steel, it puts pressure on other to reduce their emissions too. This awareness has given rise to the Vinnova project ”Kvävestyr”

which focuses on the nitrogen control in production of stainless steel [1]. This report and work is a part of the Vinnova project. Their ultimate goal is to gain better understanding of the fluctuating nitrogen content in the AOD (Argon Oxygen Decarburization) process and develop tools to predict this important parameter. Development of these tools requires measurement data from both steel melt and slag in order to compare with thermodynamic models under development.

An AOD converter is an effective tool in stainless steel making and its main purpose is to reduce the amount of carbon present in the liquid steel while maintaining as much chromium as possible.

The slag is of great importance for the interactions in the AOD process and is therefore of interest to investigate further in order to gain a wholesome understanding of the AOD­converter.

1.1 Problem

The industrial way of sampling slag in an AOD­converter consists of obtaining a slag sample from the converter, let it cool and then crush it. With this method the total composition of the slag can be obtained. However, this method gives no further information about the different phases.

To develop more advanced thermodynamic models of the AOD­converter, a more detailed characterisation of the phases in the slag is of interest. Therefore, this thesis will investigate what additional data can be obtained, when analysing slag samples in the solidified state.

1.2 Purpose

To perform a small scale analysis of slag samples from the three main stages of the AOD process. By doing this also trying out effective ways of preparing samples and analysing the micro structure in scanning electron microscope (SEM). Performing the experiments in two steps and analyse what part of the process can be improved and what gives sufficient results for this type of small scale experiment. Gain knowledge of some of the difficulties with analysing slag samples and discuss what can be done for future research in the area.

1.3 Goal

Develop a methodology for sample preparation and characterization of phases in slag samples

1.4 Ethics and Sustainability

This study is part of the Kvävestyr­project which has the ultimate goal to reduce the energy usage in the production of stainless steel and thereby reducing the cost and emissions of the process by developing models for prediction the nitrogen content in the melt. The development of a methodology for characterization of the AOD­slag will not give any direct impact on the society nor increase emissions. However, positive impact on society and the environment starts when the data is used in the Kvävestyr­project and will therefore not be discussed further in this theses.

2 The Argon Oxygen Decarburization process

The AOD (Argon Oxygen Decarburization) converter is an important step in producing stainless steel, and comes after the melting of scrap and other raw materials in the electric arc furnace. As of 2017, 75% of the world production of stainless steel is by AOD conversion due to its efficiency [2]. The main purpose of the process is to reduce the amount of carbon present in the steel melt, while maintaining a high amount of chromium in the material. AOD conversion starts with injection of a mixture of oxygen and argon or nitrogen gas, which lowers the activity of carbon monoxide in the bath. Nitrogen gas is used to decrease the amount of needed argon gas and therefore reduce production costs [2]. Nitrogen is also an important alloying element in some stainless steels as it is cheaper than for example nickel, and can sometimes enhance toughness.

However, the control of nitrogen content is of high importance to avoid excess nitrogen in the melt as it can have detrimental effects on the material properties [3].

There are three main steps in the process: Decarburization, reduction and desulphurization. If only considering argon gas as the inert gas, the ratio between oxygen and argon gas is 5:1 [2].

This ratio is then lowered in steps during the process to promote different kind of reactions.

During decarburization, oxygen blowing promotes the reduction of both iron and chromium oxides, which exist in the steel melt, due to their reaction with the dissolved carbon [4]. A specific reduction process, with a reducing agent such as FeSi, then takes place to reduce chromium oxides as well as other important oxides which exists in the slag. In this way they are brought back from the slag to the melt. The last main step of the AOD process is the sulphur refining (desulphurization), which is promoted by having a highly basic slag by addition of CaO, and a low oxygen activity in the bath [2].

2.1 AOD Slag

The slag is an important part of the AOD process as it interacts with the steel melt and atmosphere around it. By introducing gas in the melt, adding new elements and by stirring, a precise handling of the slag will lead to a high exchange rate of elements between the melt and the slag. Removing unwanted elements in the melt such as carbon, while increasing wanted elements such as chromium [4]. There are many examples of measurements from previous studies of slag composition. Both common slag elements as well as commonly seen oxides in the AOD slag [5] [6]. A study by P. Ternstedt et.al, has examined the phases in solid slag sampled from after decarburization in the AOD process [7]. Here the slag was found to contain four phases, with the first one being a metal phase. Phase 2 was characterized as

CaO*Cr₂O₃ with a ratio of approximately Cr/Ca = 2/1, phase 3 as 3CaO*2SiO₂, and phase 4 as 3CaO*Cr₂O₃*3SiO₂. Important to note is that some differences were found in amount of Ca and Cr between measurements and stoichiometric calculations, but these were small enough to be considered in good agreement for industrial samples.

2.2 Previous characterization methods

There were few studies found examining the method of slag characterization. However, the same study by P. Ternstedt et.al, examined methods for characterization of solid slag samples [7]. Here the samples where roughly polished to gain a flat surface. They where then baked into embedment powder containing graphite and polished with an automatic grinding machine using four different polishing agents. Phases were analysed with SEM and EDS (Energy Dispersive X­ray Spectroscopy) measurements were taken. Images from SEM showing measurements were then edited onto images of the microstructure from LOM (Light Optical Microscope), and then analysed.

3 Methodologies and Methods

To characterize the different phases in slag samples a method of using scanning electron microscope (SEM) to obtain images with backscattered electrons (BSE) for fraction analysis in ImageJ and composition analysis with the built in energy­dispersive X­ray spectroscopy (EDS) were conducted on six samples [8].

3.1 Samples

The materials used in this study are slag samples taken from two different heats, or batches, during refining of stainless steel from a steelmaking company. Each heat contains three steps where each step contains several slag samples which were obtained. These three steps represent the main steps of the AOD process. Samples named 30 are from after decarburization, plus one additional sample from heat A named 31 which is also from after decarburization. Samples named 40 are from after reduction, and samples named 50 are from after desulphurization. In this report, the heats are called heat A and heat B. In text, figures and tables, the samples are refereed to as, for example, A30, A31, A40, B30, etc. When describing the phases of the samples discovered from EDS measurements and fraction analysis, they are refereed to as, for example, A30_1, A30_2, A30_3, etc.

3.1.1 Preparation of samples

From each heat and step in the process, a fitting slag sample was chosen based on if its cross section contained several interesting cooling sections. Two examples are samples A40 from figure 3.1a and A50 from figure 3.1b. These show differing color and structure across their vertical cross section. Another criteria was that the sample needed to be small enough to fit into the Bakelite machine which has a diameter of approximately two centimeters, figure 3.1c.

Due to the brittleness of slag samples it was hard to cut them into the right size. Most of the samples where baked into Bakelite directly with heating up to 180 Celsius, held for ten minutes, and then cooled down for three minutes. Afterwards they were polished with polishing paper with decreasing roughness. For all samples the order of papers were 250 grit, 400 grit, 600 grit and 1200 grit. All samples polished are presented in table 3.1. Sample B50 was polished without being baked at all. Two samples of B40 were prepared, one without being baked at all (B40 (2)), one baked and then polished (B40 (1)). Two samples of A50 were also prepared, one baked directly in Bakelite and then polished (A50 (2)), the other one was polished to obtain a flat surface and then baked, followed by a final polishing of the surface (A50 (1)). All samples

were polished without water to avoid potential chemical reactions of the slag due to contact with water. Especially sensitive oxides commonly seen in slags are calcium oxide (CaO) and magnesium oxide (MgO) which are highly reactive with water.

(a) Slag from A40 (b) Slag from A50 (c) Four baked samples

Figure 3.1: (a), (b) Slag samples of A40, A50 as obtained directly from the company. (c) Example of samples that were baked in Bakelite and polished. Scale in centimeters.

Table 3.1: Codename of all samples polished from different heats and steps in the AOD process.

Samples After decarburization After reduction After desulphurization

Heat A A30 A40 A50 (1)

A31 A50 (2)

Heat B B30 B40 (1) B50

B40 (2)

3.2 SEM

The SEM model S­3700N Hitachi was used for all observations in SEM. This model have a built in systems for EDS and BSE. BSE uses the fact that the weight of each element is different.

When bombarding a surface with electrons some will be deflected from the surface by getting catapulted around the nuclei, like an asteroid around the Earth. This principle is illustrated in figure 3.2a. Heavier elements will catapult more electrons and will give rise to a brighter appearance on the BSE­image compared to a lighter element [9].

EDS uses the fact that every element has unique energy steps between the orbitals. When an electron from SEM knocks out an electron from an atom on the surface of the sample, the electrons from higher orbitals will move to the lower orbital. When they do, they emit radiation with a specific energy that is proportional to the energy levels between the orbitals.

After detecting spikes in the emitted radiation, the composition of the sample can be determined [9].

3.2.1 SEM operations

The procedure started with capturing of BSE­photographs at the minimum magnification to obtain an overview of the sample. Then gradually increasing the magnification to x250 where, with exception of sample A40 where a magnification of x3000 was used, the different phases could easily be distinguished as different shades of gray. By increasing the magnification further to between x3000­10,000, a composition analysis could be acquired with EDS for all phases.

The composition analysis were conducted on several locations of the sample. Both point and area analysis were done on the same place for sample A30, A31, A40 and A50 as seen in figure 3.3.

For sample B30 and B40 however, only point analysis were done. For heat A 3­8 composition analysis were done per phase and 4­12 for heat B. This includes the double measurements on the same phase and location done with point and area for heat A. The magnification of the image used for composition analysis differ depending on the coarseness of the structures in the sample.

(a) BSE (b) EDS

Figure 3.2: Illustrations of the path the electrons in the SEM, (a) backscattered electrons and in (b) the X­rays [10].

(a) Sample A31 (b) Sample A40 (c) Sample A50

Figure 3.3: Example of how the composition measurements were selected on heat A, where the green points and rectangles represents where the point respectively area analysis were done. (a) is one location in sample A31, (b) a location in sample A40 and (c) a location in sample A50.

3.3 Fraction analysis

The fraction analysis was done on BSE­images in ImageJ. ImageJ is a open source software for image analysis [11]. Scripts written in IJ1 Macro were used to automate parts of the analysis to ensure that the procedure was conducted with consistency and to increase the productivity.

3.3.1 Threshold analysis

A set of BSE­images with the same magnification were selected for each sample. The number of phases as well as the appearance of each phase were concluded from the EDS results. Each image were duplicated in ImageJ to the number of phases in that image. Then an interval of threshold for one phase was isolated manually in each duplicate so that all the phases were included and pores and other artefacts were excluded. For each duplicate one area measurement was conducted on the isolated threshold. The unit in ImageJ will by default be inch². However, only the relation between the phases are of interest. The area results and the images of the threshold were saved. All the area results from ImageJ were compiled to calculate the average area fractions for each phase in each sample. The threshold­images were colored and put back together in order to validate what areas that were analysed.

3.3.2 Denoise methodology

Due to overlap in threshold for phases with maximum close to each other, varying degree of noise is present in the nearby phase when they are separated with threshold. Other sources for noise is scratches and artefacts. This noise may lead to inaccurate results in the fraction analysis when pixels from other phases and/or scratches are included. Therefore, a denoise method were used in order to reduce the noise.

After the threshold of one phase was isolated the denoise method were applied. By first using

Remove Outliers­command in ImageJ with a set radius on the dark area in order to clear up the noise particles that were created by the isolated phase. Then use Remove Outliers­command on the bright area with the same radius as for the dark area in order to fill out the holes in the threshold mask that were a result of noise. Then the procedure was repeated on all phases.

The radius used in Remove Outliers­command was changed according to how coarse the main structure appeared in the image.

3.3.3 Number of images required

This analysis were conducted on the results from the threshold analysis in Matlab. When systematically analysing phase fractions of samples it is of interest to know how many random images that are needed in order to achieve an accurate average. This was investigated on B30 with one edge image and eight images on a straight line portraying the cross section of the sample. From the nine images a set of random images were included in an average calculation for each phase. The number of combinations when the order does not matter and no repetition is allowed are governed by equation (1)

r!

n!(r− n)! (1)

where r in this case is the total number of images and n is the set of random images. When the amount of images included in the average increases, the number of combinations of randomly selected images increases until r/2. To truly analyse how many random images are needed in order to be certain of a specific degree of accuracy, all the combinations must be accounted for.

This is possible to do when the number of images are as few as nine, however the number of combinations quickly increases to absurd amounts and may therefore not be accounted for in larger projects.

When all combinations of averages are plotted against n, the combinations of averages converges toward the total average of all images with increasing n. Then the minimum amount of images that achieve the required accuracy can be found in the plot.

4 Results

There are six samples which have been studied in SEM and further analysed with ImageJ. These samples are A30, A31, A40, A50 (1), B30 and B40 (1), table 3.1. There were also other samples polished, including B50, to explore different techniques of polishing. These samples were not further analysed, and are therefore not mentioned explicitly in this section.

4.1 Methods

All measurements on samples from heat A are from random zones and often just covers one part of the sample. Most of the focus was on finding visually interesting phase structures to see how the composition might differ depending on the surrounding structure. All calculations for tables are done in google sheets.

4.1.1 Sample preparation

Generally the samples became more brittle after being baked in Bakelite compared to polishing of the surface directly. This might be because of the heating of slag while baking. For samples 30 and 40 this resulted in small parts of the surface sometimes breaking off and getting stuck in the polishing paper, as can be seen in figure 4.1a. Continued polishing on the same zone of the paper led to scratches on the surface of the sample, figure 4.1c. However most of these surface remained relatively intact and the more samples polished led to less of a risk of obtaining scratches. For Sample A50 almost all of its surface fell of when polishing with the roughest paper, figure 4.1b. A new slag sample was then polished until it had a clear surface and then baked in. Afterwards it was polished with the second roughest paper (400 grit) very carefully.

Some parts still broke of but a part of the surface still remained which could be studied in SEM.

A large amount of artefacts where present in sample A40, figure 4.1d but this was easily avoided for future samples by cleaning them with ethanol after polishing.

(a) Mostly intact slag baked in bakelite (b) Slag surfaces broken of by polishing

(c) Scratch on sample A30 surface from polishing (d) Artefacts and unique phase on sample A40 surface Figure 4.1: (a) Baked sample with some missing pieces of surface highlighted with yellow arrows. (b) Baked samples were the majority of the sample had been crushed during polishing. (c) Micro structure of sample A30 with sharp scratch highlighted with yellow arrows. (d) Micro structure of sample A40 with artefacts, some of them highlighted with yellow arrows. An unique phase highlighted with a red arrow.

This phase is not seen anywhere else in the sample and is therefore ignored in the results.

4.1.2 EDS method

Samples from heat A have EDS measurements of both point analysis and area analysis.

Measurements of three out of four phases in sample A31 are shown in table 4.1. The three phases are seen in figure 4.2a. For phase A31_1 there are two point analysis measurements and two area analysis measurements. For phase A31_2 and A31_4 there are three or more measurements of each. Samples A30 and A50 show similar results as A31. In almost all cases, each point analysis has a matching area analysis at the same spot. Only areas with one phase existing where considered. Some area measurements contains two phases which were measured separately with point analysis, figure 4.2b.

(a) Sample A31, three out of four phases (b) Sample A40

Figure 4.2: (a) Sample A31. Phases A31_1, A31_2 and A31_4 which were used for calculations of difference between point and area analysis. (b) Point and area analysis measurements from EDS on sample A40. Area analysis are from yellow boxes and point analysis are from yellow crosses.

Table 4.1: EDS measurements with both point analysis and area analysis for three of the phases seen in sample A31. The average of all point measurements are compared with the average of all area measurements taken for that phase. Also standard deviation is calculated for these averages. All values are in weight percent.

A31 elements wt% Al Si Ca Cr Mn Fe Ni Mo

A31_1 Avg. Point 0.2 0.2 0.8 23.2 1.2 63.1 3.5 1.6

StDev. Point 0.1 0.1 0.6 1.4 0.8 1.4 0.1 0.6

Avg. Area 0.3 0.2 0.8 23.0 1.0 62.5 3.5 1.7

StDev. Area 0.0 0.2 0.5 1.9 0.2 1.8 0.1 0.5

Mg Al Si Ca V Cr Mn Fe

A31_2 Avg. Point 0.5 0.6 0.0 21.1 0.4 50.2 0.2 0.0

StDev. Point 0.2 0.2 0.0 1.1 0.2 1.9 0.1 0.0

Avg. Area 0.5 0.6 0.0 20.4 0.3 51.1 0.2 0.0

StDev. Area 0.3 0.3 0.0 1.0 0.2 1.6 0.1 0.0

Mg Al Si Ca V Cr Mn Fe

A31_4 Avg. Point 0.1 0.8 16.7 50.8 0.0 1.1 0.0 0.0

StDev. Point 0.1 0.2 0.5 1.5 0.0 0.2 0.0 0.0

Avg. Area 0.2 0.8 16.6 51.5 0.0 1.3 0.0 0.4

StDev. Area 0.1 0.2 0.8 1.7 0.0 0.3 0.0 0.2

4.1.3 Image analysis

The method of using ImageJ for separation of phases with threshold proved to be a smooth process. A large part of the analysis could be automated to decrease the time for each image significantly. By using the same radius for the noise reduction for all phases in one image, the smaller phases suffered greater losses in area relative to the original area of the phase compared to the larger phases.

When conducting fraction analysis on a magnification of x250 with structures on the scale of

<2 µm in the smallest dimension, the uncertainty in the result increases due to the impact of scratches and noise. When the structures in the image have the same size as noise, they are inevitably removed by the denoise method even on the smallest setting (when ignoring floats) as seen in figure 4.3.

(a) BSE­photograph of B40 (b) Raw threshold (c) Denoise threshold Figure 4.3: Visualisation of the area covered without denoise method, (b), and with denoise method, (c), done on a image from B40, (a). B40_1 = red, B40_2 = yellow, B40_3 = magenta and black is not included. (a) is captured with x250 magnification.

On larger structures the settings on the denoise method can be increased to remove larger noise particles and scratches as seen in figure 4.4 where an image from A50 is analysed.

(a) BSE­photograph of A50 (b) Raw threshold (c) Denoise threshold Figure 4.4: Visualisation of the area covered without denoise method, (b), and with denoise method, (c), done on a image from A50, (a). A50_1 = red, A50_2 = yellow, A50_3 = magenta and black is not included. (a) is captured with x250 magnification.

4.2 Composition analysis

This section is a compilation of results from EDS measurements and characterization of phases typically seen in the samples from each part of the AOD process. Images showing the characteristic phases are described as well as element tables with the average values of elements in weight percent. These characteristic phases are visually similar and can be seen in multiple samples from the same part of the AOD process. Each table shows several characteristic phases where phases from specific samples are highlighted with their phase­code. All calculations for tables are done in google sheets.

4.2.1 After decarburization

In all samples obtained after the decarburization process three characteristic phases can be seen.

A metallic phase, a grain phase, and an intermediate phase. The metallic phase usually exists as droplets, figure 4.5b, but can also be mixed with the characteristic grain phase, figure 4.5a.

The grain phase always has the brightest color except the metallic phase, and usually looks like some sort of grain. For example, phase B30_2 in figure 4.5b or phase A30_2 in figure 4.5d.

One exception is sample A31, figure 4.5c, which contains two grain phases, phase two and three. A31_3 was measured in one part of the sample and average values are based on three data points. Its composition differs from A31_2, which can be seen in table 4.2. This phase exists in all areas that were measured. The intermediate phase is the darkest phase and exists where ever the metallic and grain phase does not. In sample A30 one lighter and one darker intermediate phase can be seen, phase A30_3 and A30_4, figure 4.5d. A30_3 is seen in some areas of the sample while A30_4 is seen everywhere. In table 4.2 all noted phases are presented. Also, amount of oxides which each phase contain is presented in wt%. Oxides chosen to calculate are based on commonly seen oxides in AOD slags from the literature. Calculations are based on stoichiometric relations between the elements measured from EDS and the chosen oxides. The choice of included oxides for each phase is based on the amount of various elements which the phase contains. The values are then normalized so that each phase contains a total of 100 wt%

oxides.

(a) Sample A30 main phases (b) Sample B30 phases

(c) Sample A31, two grain phases (d) Sample A30, two intermediate phases

Figure 4.5: (a) Main phases in sample A30. The metal phase exists here as both droplets and mixed with the grain phase. (b) Phases in sample B30. B30­1 is the metal phase, B30­2 is the grain phase, B30­3 is the intermediate phase. (c) Three out of four phases in sample A31. Two grain phases which differ in composition (A31­2 and A31­3) and the intermediate phase (A31­4). (d) Three out of four phases in sample A30. One grain phase (A30­2) and two intermediate phases (A30­3 and A30­4).

Table 4.2: Average values and their standard deviation of elements seen in characteristic phases formed after decarburization. The metal phase is seen as metal droplets. The grain phase is seen as primary precipitates. The IM phase is the intermediate phase. Also includes calculated amount of oxides which are presumed to be present in the phases. All values are in wt%.

metal phase Al Si Ca Cr Mn Fe Ni Mo

A30_1 Avg. 0.0 0.0 0.2 17.9 0.0 69.1 4.3 3.8

A31_1 Avg. 0.2 0.2 0.8 23.1 1.1 62.8 3.5 1.6

B30_1 Avg. 0.0 0.0 0.6 6.4 0.0 77.5 5.9 2.2

grain phase Mg Al Si Ca V Cr Mn Fe

A30_2 Avg. 5.4 0.9 0.0 1.3 0.0 51.1 6.4 2.6

A31_2 Avg. 0.5 0.6 0.0 20.9 0.3 50.5 0.2 0.0

A31_3 Avg. 6.7 0.8 0.1 3.0 0.4 58.8 0.0 1.6

B30_2 Avg. 1.3 0.2 1.1 24.6 0.0 44.6 0.2 3.6

IM phase Mg Al Si Ca Ti Cr Mn Fe

A30_3 Avg. 0.0 0.4 17.8 51.9 0.0 1.5 0.0 0.0

A30_4 Avg. 0.3 4.4 19.1 38.9 1.1 4.5 0.0 0.0

A31_4 Avg. 0.2 0.8 16.7 51.1 0.0 1.2 0.0 0.4

B30_3 Avg. 0.4 0.5 16.5 51.7 0.0 1.5 0.7 0.9

grain phase MgO CaO Cr2O3 MnO FeO

A30_2 Avg. 9.7 0.0 81.3 8.9 0.0

A31_2 Avg. 0.0 28.3 71.7 0.0 0.0

A31_3 Avg. 11.0 4.1 84.8 0.0 0.0

B30_2 Avg. 0.0 33.0 62.6 0.0 4.4

IM phase MgO CaO Cr2O3 SiO2 Al2O3

A30_3 Avg. 0.0 65.6 0.0 34.4 0.0

A30_4 Avg. 0.0 49.4 6.0 37.0 7.5

A31_4 Avg. 0.0 66.7 0.0 33.3 0.0

B30_3 Avg. 0.0 67.2 0.0 32.8 0.0

4.2.2 After reduction and desulphurization

In the two samples obtained after the reduction process three characteristic phases can be seen.

A grain phase, an intermediate phase and a dark phase which look different depending on which sample is studied. Generally the grain phase in these samples has a different shape and is smaller than the grain phase after decarburization. Examples of this phase can be seen in figure 4.6a and figure 4.6b. Measurements from A40 comes from one zone of the sample. Notice the higher standard deviation values of almost all element measurements from the B40 sample in table 4.3. Sample A50 is from after the desulphurization process. Similar to the samples from after reduction the three phases are called the grain phase A50_1, the intermediate phase A50_2 and

the dark dendritic phase A50_3, which can be seen in figure 4.6c. Shape and size differs between phases in reduction samples and sample A50, figure 4.6d. Compositon between the production steps is quite similar for the grain and intermediate phase, but differs a lot for the dark phase.

In table 4.3 all noted phases are presented. Oxides are presented in this table as well. A similar operation like the one done for phases after decarburization was performed to select relevant oxides and calculate their values for each phase.

(a) Sample A40 phases (b) Sample B40 phases

(c) Sample A50 phases (d) Sample A50 shape and size of phases

Figure 4.6: (a) All three phases in sample A40. A40­1 is the grain phase. A40­2 is the intermediate phase. A40­3 is the dark­dot phase highlighted with the yellow arrow (b) All three phases in sample B40.

B40­1 is the grain phase. B40­2 is the intermediate phase highlighted with the yellow arrow. B40­3 is the dark­dot phase highlighted with the red arrow. (c) All three phases in sample A50. A50­1 is the grain phase. A50­2 is the intermediate phase. A50­3 is the dark­dot phase. (d) Image of sample A50 with magnification of x250 showing the typical size and shape of the three phases.

Table 4.3: Average values and their standard deviation of elements seen in characteristic phases formed after reduction and desulphurization. The grain phase is seen as the primary precipitate. The IM phase is the intermediate phase. The dark phase is seen as small dark dots or dendrites growing close to the grain phase in samples after reduction. Composition, shape and size changes for the dark phase after desulphurization. Also includes calculated amount of oxides which are presumed to be present in the phases. All values are in wt%.

Reduc. grain phase Mg Al Si Ca Ti Cr Mn

A40_1 Avg. 0.8 1.9 16.7 49.8 0.0 0.0 0.0

StDev 0.4 0.7 1.3 0.2 0.0 0.0 0.0

B40_1 Avg. 1.1 3.4 15.1 49.3 1.5 0.7 0.0

StDev 0.5 3.1 1.8 1.9 0.4 0.4 0

Reduc. IM phase Mg Al Si Ca Ti Cr Mn

A40_2 Avg. 2.1 21.8 4.1 39.0 0.0 0.7 0.2

StDev 0.1 2.6 1.1 1.2 0.0 0.4 0.1

B40_2 Avg. 2.2 18.7 4.8 38.6 0.6 0.3 0.0

StDev 1.5 5.3 2.7 4.3 0.2 0.2 0.0

Reduc. dark phase Mg Al Si Ca Ti Cr Mn

A40_3 Avg. 36.8 8.0 2.5 17.7 0.0 2.1 1.3

StDev 1.6 1.2 0.2 0.2 0.0 0.0 0.2

B40_3 Avg. 36.1 3.7 3.6 19.9 0.0 1.3 0.7

StDev 10.4 3.0 2.8 8.9 0.0 0.7 0.3

Desulf. phases Mg Al Si Ca Cr Mn Fe

A­50_1 Avg. 0.7 1.8 11.2 57.1 0.0 0.0 0.0

A­50_2 Avg. 1.5 13.1 4.5 48.9 0.0 0.0 0.0

A­50_3 Avg. 60.7 0.1 0.0 1.6 1.1 0.6 1.3

Reduc. grain phase MgO Al2O3 SiO2 CaO

A40_1 Avg. 0.0 3.2 32.8 64.0

B40_1 Avg. 0.0 6.1 29.9 64.0

Reduc. IM phase MgO Al2O3 SiO2 CaO

A40_2 Avg. 0.0 39.4 8.4 52.2

B40_2 Avg. 0.0 35.4 10.3 54.3

Reduc. dark phase MgO Al2O3 SiO2 CaO

A40_3 Avg. 57.5 14.2 4.9 23.3

B40_3 Avg. 58.5 6.8 7.5 27.3

Desulf. phases MgO Al2O3 SiO2 CaO

A50_1 Avg. 1.1 3.1 22.1 73.7

A50_2 Avg. 2.4 23.5 9.2 64.9

A50_3 Avg. 97.7 0.2 0.0 2.1

4.3 Results of fraction analysis

Most samples had a set of photographs for calculation of phase fractions at a magnification of x250 with exception of sample A40 which had two images with x3000 magnification. The phase fractions in each sample can be seen in table 4.4. On some locations in sample A30 there were a dendritic structure (A30_3) in the otherwise only present intermediate phase (A30_4). Where A30_3 were present the ratio between it and A30_4 was 35.9 % ± 1.2 % and 64.1 % ± 1.2

% respectively with denoise applied and 38.6 % ± 0.5 and 61.4 % ± 0.5 with raw threshold analysis.

Table 4.4: Average phase fractions for each sample on the set magnification with the set number of images, where f0is calculated without denoise method and f1is with.

Phase Nr. A30 A31 A40 A50 B30 B40

Magnification x250 x250 x3000 x250 x250 x250

Nr. of Images 5 5 2 6 9 4

1

f0 (%) 8.6 14.3 44.5 37.8 2.4 43.7

Std0 1.0 2.2 0.3 4.6 1.5 1.8

f1 (%) 8.1 16.7 44.1 37.6 2.2 45.6

Std1 1.0 3.3 0.2 4.9 1.5 1.2

2

f0 (%) 49.6 62.3^∗∗ 49.9 45.2 72.5 47.7

Std0 1.3 4.1 0.7 5.8 8.9 0.2

f1 (%) 53.3 62.3^∗∗ 50.5 45.8 76.0 48.1

Std1 2.4 4.6 0.7 6.5 8.1 0.2

3

f0 (%) 41.8^∗ 23.3 5.6 16.9 25.1 8.6

Std0 0.9 1.8 0.5 9.9 4.9 1.9

f₁ (%) 38.6^∗ 21.0 5.4 16.6 21.8 6.2

Std1 1.8 1.8 0.5 10.5 5.9 1.4

* The total fraction of A30_3 and A30_4 combined, the two intermediate phases.

** The total fraction of A31_2a and A30_2b, the two grain phases.

The analysis of the number of images needed to require an acceptable error were conducted on the images of B30. All combinations of averages for each number of included images in the calculation were plotted. The procedure was done for each phase. In figure 4.7 all the included images in the analysis can be seen. The images 1­9 are captured from one end of the sample to another, illustrating a cross section of B30.

The result of the different combinations of averages were calculated on data modified with the denoise method and can be seen in figure 4.8. The black line that each plot converges to is the average of all nine images. The dashed lines display deviations from the total average with varying amounts of standard deviations, σ. The blue line represents the maximum and minimum

Figure 4.7: Images of the cross section of B30 in order from one side to another side of the sample following a straight line between image 2­9.

value of the combinations. The intersection of the blue line and the dashed line representing

±σ represents where all combinations of averages are within the standard deviation of all nine images. For this analysis the numbers from the denoise was used. The minimum number of random images needed in order to be certain of getting an average within the standard deviation was four.

0 2 4 6 8

Random images, [n]

0 1 2 3 4 5 6

Area fraction, [%]

2

-

(a) B30_1

0 2 4 6 8

Random images, [n]

50 60 70 80 90 100

Area fraction, [%]

2

- -2

(b) B30_2

0 2 4 6 8

Random images, [n]

10 15 20 25 30 35

Area fraction, [%]

2

- -2

(c) B30_3

Figure 4.8: All combinations of averages for a set number of random selected images for each phase in B30 except B30_4. The black line is the average of all nine images. The black dashed line is deviation from average with σ and the red dashed line represents deviation with 2σ from the average of all images.

4.4 Distance dependency

An attempt at measuring distance dependency of slag composition was performed by making phase measurements in four zones spread out in the sample. These zones are shown as red boxes in figure 4.9 and are approximate places measured in millimeters from the left of the image.

Figure 4.9: Images of the cross section of B40 in order from one side to another side of the sample.

Consists of three merged images. Red boxes show each zone of the sample where measurements took place. The whole visible area is measured as 6,35mm and individual points are measured at a) 0,51mm;

and 1,92mm; b) 3,39mm; c) 5,95mm.

Phase B40_1 had three measurements from each zone except at the bottom zone with two, figure 4.10a and figure 4.10d. Phase B40_2 and B40_3 had one or two measurements per zone. In the third zone at 3,39mm phase B40_2 was not found, figure 4.10b and figure 4.10e. All phases are split up into ”elements, small amounts” and ”elements, large amounts” for visual clarity of the elements which the phase contains small amounts of.

0 2 4 6 Length [mm]

0 2 4 6 8 10

Elements [wt%]

Mg Al Cr

(a) B40_1 elements, small amounts

0 2 4 6

Length [mm]

0 2 4 6 8

Elements [wt%]

Mg Si Cr

(b) B40_2 elements, small amounts

0 2 4 6

Length [mm]

0 2 4 6 8

Elements [wt%]

Al Si Cr Mn

(c) B40_3 elements, small amounts

0 2 4 6

Length [mm]

10 20 30 40 50

Elements [wt%]

Si Ca

(d) B40_1 elements, large amounts

0 2 4 6

Length [mm]

15 20 25 30 35 40 45

Elements [wt%]

Al Ca

(e) B40_2 elements, large amounts

0 2 4 6

Length [mm]

15 20 25 30 35 40

Elements [wt%]

Mg Ca

(f) B40_3 elements, large amounts Figure 4.10: Sample B40. Average element values in weight percent for each phase split up in two figures per phase. There are four data points for each phase except B40_2 where there are three. The x­axis is the distance measured in millimeters from the left of the sample in figure 4.9.

The structure in A40 coarsens from one side of the sample to the other as seen in figure 4.11. On the coarse side, crystals of A40_1 and A40_3 have formed in a dendritic structure, figure 4.11c.

In the central part finer dendrites of what can be observed in figure 4.11c can be seen along with one abnormal growth of A40_3, figure 4.11b. The finer structure on the other side displays a uniform structure that contains the composition of all phases, figure 4.11a.

(a) Sample A40, edge (b) Sample A40, middle (c) Sample A40, other side Figure 4.11: Images displaying the cross section of A40. (a) is the side with finer structure, (b) is in the central part and (c) is the coarser side.

5 Discussion

5.1 Characterization after decarburization

The Cr content in the different metal phases increases in order of B30, A30 and A31. With a total difference of 17wt%. Conversely, the Fe content in samples decreases in the same order.

With a total difference of 15wt%. These differences are quite large compared to most other phases noticed. It can be assumed that the samples of heats A and B were taken by production of different steel grades having various contents of alloying elements. Locally seen grain phase A31_3 is similar to grain phase A30_2 in composition. These two grain phases are quite different from the other grain phases. Differences in composition could be seen between the intermediate phases. Phase A30_3, which has been observed in only one zone, fits well with compositions of the intermediate phases in the other samples. A30_4 however exists everywhere, but differs in amount of Al, Ca and Cr, compared to other intermediate phases. For heat A, A30_2 and A31_2 are quite different in terms of shape. A31_2 has a more rod­like structure altered with grains with round edges while A30_2 consists of a grain structure with sharp edges. B30_2 has the same structure as A31_2. However, the structure in B30 have more defined areas where either rods or grains are dominating with slightly larger areas containing grains.

Similar phases are found by comparing results from the study by P. Ternstedt et al., and this work.

The second phase there consists of mostly Cr₂O₃ and CaO just like some of the grain phases found here. From the previous study, element values obtained by EDS are shown in atomic percent so its hard to compare. However, the ratio between Cr and Ca in the second phase matches well with the ratio between Cr and Ca in the grain phase. Phase 3 in previous study contain CaO and SiO₂just like the intermediate phase. Because of the mentioned uncertainty in CaO measurements from the previous study, it is hard to draw any conclusions about exact ratios between Ca and other elements. Still, the similar phases found in this study after decarburization gives some added reassurance about the accuracy of the results obtained.

5.2 After reduction and desulphurization

Samples after reduction show characteristic phases which have similar structures on both heats.

On the coarse side of A40, the solidification may have occurred under higher temperature to enable crystals of A40_1 and A40_3 to form and grow. The finer structure on the other side may be a result of faster solidification with lower mobility. B40 on the other hand, has a more complicated structural behavior through the cross section. The two edges have similar structures

in terms of size and that dendrites of B40_1 and B40_3 is present. The middle of sample B40 had different color from the rest of the sample. However, the center was crushed during polishing and could not be studied.

Average values of elements are very similar for the two samples after reduction. The higher standard deviation values in sample B40 are noticeable for elements like Mg, Al, Si and Ca.

A reason for these results might be that A40 is measured in only one zone while B40 is more systematically measured in different zones where the micro structure looks vastly different. Due to the heterogeneity of slags a larger error might be expected from B40 but it is interesting that they show such similar average values.

The structure of phases in A50 becomes an order of magnitude coarser compared to samples after reduction and the main structure is no longer dendritic. The structure consists of primary solidification of A50_1 in the form of flakes, secondary precipitation of A50_3 on the surface of A50_1 and an intermediate phase of A50_2.

5.3 Optimization of sample preparation

Time versus size of obtained slag area varied greatly depending on if the samples were polished without Bakelite first or polished after being baked into Bakelite. If samples were baked directly they only required polishing with each paper for around six minutes. This method gave a good surface without many scratches if small pieces did not fall of during the process. However, the resulting size of the surface often became much smaller than the surface of samples polished without Bakelite first. Roughness of the slag surface in an unpolished state is the reason for only some parts of the slag being visible when baked. Once in Bakelite, two to three hours were spent trying to polish with the roughest paper in order to obtain a larger visible slag surface with almost no results. Moreover, continued polishing for an extended time led to an increased risk of inducing raw scratches on the sample surface, as described previously in the results section.

Conversely, when polishing without baking first a large flat surface could be obtained much quicker. The problem with this method was the increased difficulty to hold the slag sample steady and at the same parallel angle towards the polishing paper.

5.4 The value of measurements in heterogeneous slag

According to obtained results four images with x250 magnification are required in order to obtain an accurate average result for each phase, except for B30_4 and A30_3b which are not present through the whole sample and has to be characterized separately. Due to the vast difference in

size of the structure after reduction compared to the other stages, the magnification needs to be increased to easily separate the different phases with threshold. Due to the different coarseness in structure in A40 depending on the distance from each side, further understanding of how the composition changes through the cross section could decrease the locations needed for fraction analysis to only the coarse side if the composition is consistent.

The number of random images required for fraction analysis may differ for each stage in the AOD­process due to the varying coarseness and heterogeneity’s in the structures in different zones of the slag samples. Therefore a similar investigation of the number of images required from each stage with a specific magnification would be needed. If the required amount of images after decarburization are needed after reduction, the data for A40 would be insufficient for a more accurate result.

Temperature gradients in the slag samples led to different cooling conditions which led to structural differences in the sample. The varying cooling may also affect the composition of different zones. Structural differences could clearly be seen in some samples. Varying compositions could also clearly be seen in B40 between each zone of phase measurements.

It is hard to understand the value of measurements when the composition can differ throughout the material but calculations of average phase compositions can show almost identical values to average composition of sample A40, which only had measurements from one zone of the sample.

It is also hard to draw any conclusions when not all zones had three or more measurements each.

5.5 Optimization of operation

Point and area analysis almost always gave similar average values of elements as well as similar standard deviations. Most of the time the deviations were bellow 1 wt%. Therefore, when analysing B30 and B40, only point analysis was conducted to save time and give opportunity to make more measurements and look at other interesting areas in the samples. One flaw of point analysis is when the phases are very small, like in sample A40 and B40. To get accurate results with point analysis a certain fraction of the phase in question should exist around the measurement point. This requires larger magnification and therefore higher demands on the polishing.

Scratches and artefacts on the surface have a negative impact on the fraction analysis due to contamination of the threshold for some phase. Artefacts have an impact on heavier elements such as the metal phase due to their light threshold. While scratches often become darker than

the phase they are present in, they will affect itself and the phases with darker threshold. The effect of these impurities can be reduced by removal of these areas from the fraction analysis with a noise reduction procedure. It is hard to prove numerically that the denoise method yields a more accurate result when the difference in area only can be compared to the original threshold.

However, it is clear that with usage of a denoise method, the visualisation of the area covered have less contamination in what clearly is other phases. To take advantage of the possibility of post­processing of the BSE­images in ImageJ to reduce the noise of other phases and impurities on the surface after sample preparation, a more sophisticated procedure for reduction of noise would be required. This method needs to take into account which phase it is and customize the procedure. By obtaining a better tool for reduction of noise, the importance of the final polishing is reduced.

6 Conclusions

This study has focused mostly on the methodological aspect of sample preparation and methods for characterizing of phases in AOD slag. However, some conclusions regarding the characteristic phases in each stage of the AOD process were done. The tried methodology for sample preparation worked well for samples after decarburization and reduction while the method for analysis of composition and phase fractions worked well for samples after decarburization and desulphurization. More specifically, the following conclusions could be drawn:

• The safest method for preparing the samples which gave the highest success rate were to bake the slag from the beginning and use time available to obtain a large surface. Slag samples should be polished without water to avoid reactions with CaO and MgO, which are present in the slag.

• A magnification of x250 should be used on BSE­images that are used for fraction analysis for slag after decarburization and desulphurization. Higher magnification is needed for samples after reduction.

• For samples after decarburization, not less than four BSE­photographs on the same magnification should be used for fraction analysis.

• ImageJ analysis can successfully be applied for determination of fractions of different phases on BSE­photographs due to that the different colors correspond to different compositions. However, scratches and artefacts affect the fraction analysis negatively and therefore the samples should be prepared in a more meticulous manner.

• Microstructures and phase compositions in different zones of slag samples have significant differences due to different solidification and cooling rates of slag layers during sampling.

• Quality of polishing and fraction analysis method that were used is sufficient for samples after decarburization and desulphurization due to similar scale in microstructure. The methodology for composition analysis used for heat B is sufficient for future analysis.

• There are three main phases in each sample from every step of the AOD process.

Metal droplets exist in samples after decarburization but disappear later. A new dark phase appears after reduction, which changes in size, shape and composition after desulphurization.

6.1 Future Work

Data from samples after desulphurization on a different heat would be of interest to analyse in order to do similar comparisons as was done between the heats for samples after decarburization.

The samples after desulphurization become more brittle when baked in Bakelite and therefore an alternative mounting mechanism would have to be used if the samples were to be polished without Bakelite and then analysed in SEM.

Samples after reduction had significantly finer structure than the samples after decarburization and desulphurization and therefore further research on the methodology is required in order to establish a methodology that yields valid results both for composition and fraction analysis.

7 Acknowledgements

We would like to thank our supervisor Andrey Karasev, at the department of Material Science and Engineering at the Unit of Processes at the Royal Institute of Technology (KTH) in Stockholm, for all the time spent on guiding our study with continuous support through the whole project and also for operating the SEM.

8 References

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Appendices

Appendix A: Number of images needed

1 %% Number of images needed

2 % This code plots all combinations of averages that can be calculated from

3 % the data in the columns on one row without repitition and order dose not

4 % matter. This is tested for tsv−files and might need modification when

5 % alternative formats are imported. The formating in the imported files

6 % should be that all data that will be used in the same calculation will be

7 % on the same row.

8 clear all, close all, clc

9 DataSeriesName = 'Name'; % Name to save as, enter string

10 NOI = importdata('File.tsv'); %import .tvs−file with data

11 phases = size(NOI.data,1);

12 images = size(NOI.data,2);

13 for p = 1:phases

14 Amax = [];

15 Amin = [];

16 figure(p)

17 hold on

18 set(gca,'FontSize',18)

19 box off

20 xlabel('Random images, [n]')

21 ylabel('Area fraction, [%]')

22 for i = 1:images

23 noi = strcat('A',num2str(p),num2str(i));

24 noimax = strcat('A',num2str(p),num2str(i),'max');

25 noimin = strcat('A',num2str(p),num2str(i),'min');

26 variable.(noi) = sum(nchoosek(NOI.data(p,1:images),i),2)/i;

27 variable.(noimax) = max(variable.(noi),[],'all');

28 variable.(noimin) = min(variable.(noi),[],'all');

29 Amax = [Amax,variable.(noimax)];

30 Amin = [Amin,variable.(noimin)];

31 plot(ones(length(variable.(noi)),1)*i,variable.(noi),'k+','MarkerSize',3)

32 end

33 plot(0:images,ones(images+1,1)*variable.(noi),'k')

34 if (variable.(noi)+std(NOI.data(p,1:images),0,'all')) < 100

35 plot(0:images,ones(images+1,1)*(variable.(noi)+std(NOI.data(p,1:images) ,0,'all')),'k−−')

36 text(images,(variable.(noi)+std(NOI.data(p,1:images),0,'all')),'\sigma',' VerticalAlignment','bottom','HorizontalAlignment','right','FontSize' ,18)

37 end

38 if (variable.(noi)+2*std(NOI.data(p,1:images),0,'all')) < 100

39 plot(0:images,ones(images+1,1)*(variable.(noi)+2*std(NOI.data(p,1:images) ,0,'all')),'r−−')

40 text(images,(variable.(noi)+2*std(NOI.data(p,1:images),0,'all')),'2\sigma ','VerticalAlignment','bottom','HorizontalAlignment','right','

FontSize',18)

41 end

42 if (variable.(noi)−std(NOI.data(p,1:images),0,'all')) > 0

43 plot(0:images,ones(images+1,1)*(variable.(noi)−std(NOI.data(p,1:images) ,0,'all')),'k−−')

44 text(images,(variable.(noi)−std(NOI.data(p,1:images),0,'all')),'−\sigma', 'VerticalAlignment','bottom','HorizontalAlignment','right','FontSize' ,18)

45 end

46 if (variable.(noi)−2*std(NOI.data(p,1:images),0,'all')) > 0

47 plot(0:images,ones(images+1,1)*(variable.(noi)−2*std(NOI.data(p,1:images) ,0,'all')),'r−−')

48 text(images,(variable.(noi)−2*std(NOI.data(p,1:images),0,'all')),'−2\

sigma','VerticalAlignment','bottom','HorizontalAlignment','right',' FontSize',18)

49 end

50 plot(1:images,Amin,'b')

51 plot(1:images,Amax,'b')

52 xlim([0 images])

53 saveas(figure(p),strcat(DataSeriesName,num2str(p)),'epsc')

54 end