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Profitability = f(G)
Computational Thermodynamics, Materials Design and Process Optimization
David Dilner
Doctoral Thesis in Engineering Materials Science Stockholm 2016
KTH Royal Institute of Technology School of Industrial Engineering and Management Department of Materials Science and Engineering Unit of Structures SE-100 44 Stockholm, Sweden ISBN: 978-91-7729-084-1 © David Dilner, 2016 Akademisk avhandling som med tillstånd av Kungliga Tekniska högskolan i Stockholm framlägges till offentlig granskning för avläggande av doktorsexamen fredagen den 23 september 2016 kl 10:00 i sal B3, Brinellvägen 23, Kungliga Tekniska högskolan, Stockholm. This thesis is available in electronic format at kth.diva-prtal.org Printed by Universitetsservice US-AB, Stockholm, Sweden
Abstract
The thesis starts by giving a motivation to materials modeling as a way to increase
profitability but also a possibility decrease the environmental impact. Fundamental concepts
of relevance for this work are introduced, this include the materials genome, ICME and of
course the CALPHAD method. As a demonstration promising results obtained by an ICME
approach using genetic algorithms and CALPHAD on the vacuum degassing process are
presented. In order to make good predictive calculations and process models it is important to
have good thermodynamic descriptions. Thus most part of the work has concerned the
thermodynamic assessments of systems of importance for steelmaking, corrosion and similar
processes. The main focus has been the assessment of sulfur-containing systems and
thermodynamic descriptions of the Fe-Mn-Ca-Mg-S, Fe-Ca-O-S, Fe-Mg-O and Mg-Mn-O
systems are presented. In addition, heat capacity measurements of relevance for the Mg-Mn-O
system have been performed. To summarize the efforts some application examples
concerning thermodynamic calculations related to steelmaking and inclusion formation are
shown.
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Contents List of publications ........................................................................................................................... 5 Acknowledgements ........................................................................................................................... 7 Populärvetenskaplig sammanfattning (Swedish) .............................................................................. 9 1. Background ................................................................................................................................. 13 2. Materials and process design ...................................................................................................... 17
2.1 Materials Genome ................................................................................................................. 18 2.2 ICME .................................................................................................................................... 18 2.3 Process modeling .................................................................................................................. 19 2.4 Process optimization using genetic algorithms ..................................................................... 20
3. Computational thermodynamics ................................................................................................. 25 3.1 Thermodynamic principles and Gibbs energy ...................................................................... 25
3.1.1 Probability and entropy .................................................................................................. 25 3.1.2 State functions and Gibbs energy ................................................................................... 27 3.1.3 Regular solutions ........................................................................................................... 29 3.1.4 Thermoeconomics .......................................................................................................... 30
3.2 CALPHAD ............................................................................................................................ 31 3.2.1 Compound energy formalism......................................................................................... 32 3.2.2 Liquid modeling and the ionic two-sublattice liquid model .......................................... 33 3.2.3 Spinel modeling ............................................................................................................. 35
4. Thermodynamic descriptions ...................................................................................................... 37 4.1 TCOX database ..................................................................................................................... 37 4.2 Fe-Mn-Ca-Mg-S ................................................................................................................... 38 4.3 Fe-Mg-O and Mg-Mn-O ....................................................................................................... 44 4.4 Fe-Ca-O-S ............................................................................................................................. 49
5 Applications ................................................................................................................................. 51 5.1 Applications of TCOX in its present state ............................................................................ 51 5.2 Application of sulfide descriptions ....................................................................................... 53 5.3 Sulfur in steelmaking ............................................................................................................ 54
6 Conclusions and future work ....................................................................................................... 57 References ....................................................................................................................................... 59
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List of publications
This PhD project, the COMPASS project (Computational thermodynamics for steel and slag
equilibria), was carried out in collaboration with the companies Ovako, Outokumpu, SSAB EMEA
and Thermo-Calc Software. Most of the work was performed at Department of Materials Science and
Engineering at KTH Royal Institute of Technology in Sweden while some parts of the work were
performed at TU Delft in the Netherlands and TU Bergakademie Freiberg in Germany. Here the
publications included in this thesis and the contributions by the author are listed.
Paper 1: Process-time Optimisation of Vacuum Degassing using a Genetic Alloy Design Approach
D. Dilner, Q. Lu, H. Mao, W. Xu , S. van der Zwaag and M. Selleby, Materials 7 (2014) 7997-8011.
Contribution: Most of the modeling work and most of the writing.
Paper 2: Thermodynamic Assessment of the Mn-S and Fe-Mn-S Systems
D. Dilner, H. Mao, M. Selleby CALPHAD 48 (2015) 95-105.
Contribution: Most of the assessment work and most of the writing.
Paper 3: Thermodynamic Assessment of the Fe-Ca-S, Fe-Mg-O and Fe-Mg-S Systems
D. Dilner, L. Kjellqvist, M. Selleby, Journal of Phase Equilibria and Diffusion 37 (2016) 277-292
Contribution: Most of the assessment work of the Fe-Ca-S and Fe-Mg-S systems, some of the
assessment work on the Fe-Mg-O system and large part of the writing.
Paper 4: Thermodynamic Description of the Fe-Mn-Ca-Mg-S System
D. Dilner CALPHAD 53 (2016) 55-61
Contribution: Sole author.
Paper 5: Thermodynamics of the Mg-Mn-O System – Modelling and Heat Capacity Measurements
D. Dilner, D. Pavlyuchkov, T. Zienert, L. Kjellqvist and O. Fabrichnaya, 2016, Submitted to Journal
of American Ceramic Society for publication.
Contribution: Experimental planning, most of the assessment work and most of the writing.
Paper 6: Thermodynamic Description of the Fe-Ca-O-S system
D. Dilner, M. Selleby, 2016, In manuscript.
Contribution: Most of the assessment work and most of the writing.
Paper 7: Improving Steel and Steelmaking – Computational Thermodynamics using a Sulphide and
Oxide database
D. Dilner, L. Kjellqvist, H. Mao, M. Selleby, 2016, In manuscript.
Contribution: Large part of the calculations and most of the writing.
In addition to the papers included in the thesis, the following papers have been published during the
course of the PhD studies:
The influence of carbon vacancies on thermodynamic properties in TiZrC mixed carbides: ab initio
study
V.I. Razumovskiy, A.V. Ruban , J. Odqvist, D. Dilner and P.A. Korzhavyi, CALPHAD 46 (2014) 87–
91.
Phase equilibria in the ZrO2-MgO-MnOx system
D. Pavlyuchkov, D. Dilner, G. Savinykh and O. Fabrichnaya, 2016, Journal of American Ceramic
Society (2016).
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Acknowledgements
I gratefully acknowledge my main supervisor Malin for all her support, many useful
discussions and also for giving me the possibility to have large influence on the project. I
would also like to thank my co-supervisor Mao for his support and many useful discussions
about modeling. My co-author Lina at Thermo-Calc Software is acknowledged for her
support and many discussions about the implementation of my research in their database.
Many thanks to all my fellow PhD students, postdocs and senior researchers at KTH for many
interesting discussions and joyful moments.
I would like to thank Sybrand for inviting me to TU Delft and thank all people there for
being friendly and welcoming. I also would like to thank Olga for inviting me to TU
Bergakademie Freiberg and for all support I got from her and other people conducting
experimental work and drinking tee. I would also like to thank Tor-Björn at SSAB for
introducing me to the world of steel.
I also acknowledge my friends and relatives for encouraging me over the course of my
academic studies. A great thank to my mother Margareta for always encouraging me to seek
knowledge. Finally, I would like to acknowledge my wife Annika for all her support and
understanding during these five years.
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Populärvetenskaplig sammanfattning (Swedish)
Stål bygger upp det moderna samhället både symboliskt och bokstavligt. Stålets och
bergsbrukets historia är ofta nära sammankopplad med vår historia. Den som är intresserad av
att lära sig mer om de historiska kopplingarna i Sverige kan läsa boken ”Bergsbruk: gruvor
och metallframställning” [1]. Även om stål fortsätter att vara en förutsättning för mycket av
det vi tar för givet är det inte helt oproblematiskt att tillverka stål. Stålföretag brottas med
dålig lönsamhet, hård konkurrens och ibland svårigheter att få tag på råvaror. Detta samtidigt
som omvärlden ställer högre krav på miljöhänsyn beträffande alla delar av produktionen. Hur
ska det gå ihop? Svaret är ständig utveckling av nya produkter och processer som
överensstämmer med såväl lönsamhet som ansvarstagande. Men detta är lättare sagt än gjort
med en stram budget och det är här som modellering kommer in som en attraktiv lösning. Allt
snabbare datorer tillsammans med mer sofistikerade och verklighetstrogna modeller gör att
detta ofta är mycket billigare än att utföra experiment.
När man tillverkar stål så använder man sig av en slagg, bestående av flytande oxider, för
att skydda och rengöra det flytande stålet. Man kan jämföra stål och slagg med en
salladsdressing där slaggen (olivoljan) flyter ovanpå stålet (vinägern). Olika ämnen löser sig i
de olika vätskorna, exempelvis löser sig salt väl i vinäger medan många smak- och färgämnen
löser sig bättre i olivolja. För den som vill ha mer information om ståltillverkning
rekommenderas avsnittet om processer på Jernkontorets hemsida [2], där det även finns annan
information om stål och stålindustrin. Vid ståltillverkning så vill man att föroreningar ska lösa
sig i slaggen medan, ofta dyrbara, legeringsämnen ska lösa sig i stålet. Syftet med
legeringsämnen är att förbättra någon egenskap i stålet, exempelvis korrosionsmotståndet eller
hårdheten. Många föroreningar, t ex syre och svavel, löser sig i slaggen medan exempelvis
nickel stannar i stålet. Det är dock inte alltid så enkelt, exempelvis så trivs koppar, som ofta
betraktas som en förorening, bättre i stålet medan legeringsämnet krom gärna löser sig i
slaggen. Det bör också påpekas att både koppar och svavel kan vara önskvärda i vissa
stålsorter beroende på tillämpningsområde. Även om ståltillverkning inte sker under
jämviktsförhållanden så spelar jämvikter en stor roll för förståelse av dessa fenomen. När det
gäller stål så handlar jämvikt om var atomerna vill befinna sig men jämvikt kan lika gärna
handla om mekanisk jämvikt, exempelvis att en boll hellre ligger i en dal än uppe på en
bergstopp. Då marken är ojämn så hindras ofta bollen att av sig själv rulla ner från
bergstoppen utan man måste tillföra någon form av aktiveringsenergi för att den ska hamna
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nere i dalen, exempelvis genom att någon sparkar på den. I atomernas värld så är värme och
rörelseenergi synonymt varför hög temperatur ger hög rörelseenergi vilket betyder att
aktiveringsenergin för förflyttning av atomer uppnås. Då det är termodynamiken som styr
jämvikten så kan man använda sig av termodynamisk modellering, närmare bestämt den s.k.
CALPHAD-metoden, för att kunna göra beräkningar relaterat till ståltillverkning. CALPHAD
står för ”beräkning av fasdiagram”. Ett välkänt fasdiagram är det för vatten, där man kan
utläsa vid vilka temperaturer och tryck som vatten återfinns som vätska, ånga eller is. I
CALPHAD-metoden så använder man sig av Gibbs energi som är en termodynamisk funktion
vars minimum är liktydigt med jämvikt vid konstant tryck och temperatur. Det ska dock
påpekas att CALPHAD-metoden även kan användas till mycket mer än bara beräkningar av
fasdiagram. För att man ska kunna utföra termodynamisk modellering så behöver man
databaser med termodynamiska beskrivningar av de olika ämnena. Sedan tidigare finns det
termodynamiska beskrivningar av de viktigaste legerings- och slaggsystemen. En stor del av
det här doktorandprojektet har syftat till att lägga till svavel i beskrivningen, mer specifikt har
järn i närvaro av svavel tillsammans med mangan, kalcium och magnesium samt järn i
närvaro av svavel, syre och kalcium undersökts. Man säger att systemen Fe-Mn-Ca-Mg-S
(järn-mangan-kalcium-magnesium-svavel) och Fe-Ca-O-S (järn-kalcium-syre-svavel) har
utvärderats termodynamiskt. Det tidigare systemet är viktigt för att kunna beskriva bildning
av sulfidinneslutningar, små svavelpartiklar i det färdiga stålet som ofta har en negativ effekt
på stålets egenskaper, medan det senare är viktigt för att kunna beskriva svavelrening,
processen för att minska svavelhalten i det flytande stålet. För en mer detaljerad genomgång
av sulfidinneslutningar i stål på svenska finns en artikel av Löfqvist, 1937 [2], som ger en bra
översikt även om de senaste årens framsteg naturligtvis inte finns med. Förutom de
svavelinnehållande systemen har Fe-Mg-O (järn-magnesium-syre) och Mg-Mn-O
(magnesium-mangan-syre) systemen utvärderats termodynamiskt. Dessa system är också
viktiga för att kunna beskriva ståltillverkning. Det primära syftet med att undersöka Mg-Mn-
O var dock att det är av intresse för zirkonia-förstärkta metallkompositer. Zirkonia (ZrO2) är
ett väldigt hårt ämne men har även andra likheter med diamant vilket är en av anledningarna
till att det ofta används som fuskdiamanter. Förutom modellering har även experiment utförts
relaterade till Mg-Mn-O systemet vilka används i modelleringen av detsamma.
Något som börjar få ökad spridning på senare år är flerskalig materialmodellering, ofta
benämnd ICME (integrerad materialberäkningsteknik). Termodynamik och kinetik är vitalt
för den typen av modellering och därför lanserade den amerikanska regeringen 2011
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materialgenominitiativet vilket syftar till att kartlägga materialegenskaperna på ett liknande
sätt som i det mänskliga genomprojektet. Då liknande idéer redan har funnits en tid inom
forskarvärlden så har konceptet snabbt spridits bland forskningsinstitutioner världen över.
ICME har framförallt används för materialutveckling och inte så mycket för
processutveckling. Därför har en del av doktorandprojektet handlat om att använda
termodynamisk modellering för att optimera vakuumreningen. Detta är en viktig del i
ståltillverkningen och innebär att man med hjälp av lågt tryck och kraftig omrörning
påskyndar jämviktsreaktionerna mellan stål och slagg men även avlägsnar flyktiga
föroreningar som kväve och väte. Det visas att man med hjälp av så kallade genetiska
algoritmer kan räkna fram optimala parametrar för vakuumrening vilket minimerar
tidsåtgången och således kostnaden för att slutföra processen. Med det sagt så kan
sammanfattningen avrundas med att förklara titeln som på svenska blir ”Lönsamhet som
funktion av Gibbs energi”. Detta då Gibbs energi är grunden för dessa beräkningar och de kan
användas för att utveckla bättre och billigare produkter. Därav är Gibbs energi, tillsammans
med andra tekniska parametrar samt sociologiska faktorer, en parameter som avgör
lönsamheten vid materialtillverkning.
Svenska referenser [1] Jan af Geijerstam och Marie Nisser (red.), Bergsbruk: gruvor och metallframställning, Sveriges
Nationalatlas, Stockholm, 2011, ISBN: 9789187760587 [2] Jernkontoret, Tillverkning, användning, återvinning – Processer, 2015-05-11, Åtkomst: 2016-
08-21, URL: http://www.jernkontoret.se/sv/stalindustrin/tillverkning-anvandning-atervinning/processer/ [3] Helge Löfquist, Sulfidinneslutningar i järn och stål ur jämviktssynpunkt, Teknisk Tidskrift –
Bergsvetenskap, 67 (1937) 37–44, Åtkomst: 2016-08-21, URL: http://runeberg.org/tektid/1937b/0039.html
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1. Background
Steel has been one of the foundations of modern society both literally and symbolically
since the industrial revolution. It is the backbone in our trucks, skyscrapers, bridges, aircraft
carriers and sometimes it is even part of our bodies. Not surprisingly steel is an important part
of the world economy. This is particularly true for the Swedish economy, with several of its
largest companies being either steel producers or having a large part of their purchase or sales
related to steel.
Given the importance of steel one could believe that steelmaking is a lucrative business
but this is however generally not the case. Even before the financial crisis in 2008 several
steel companies were struggling with profitability problems. The financial crash led to a
dramatic decrease in the steel price, as can be seen in Figure 1 and it still remains at the same
low level, about 300 USD/tonne, August 2016. Low prices together with tougher competition
on the market mean that steel companies always must think about reducing costs, preferably
without decreasing the quality. The steel companies do not only compete about customers but
also about raw materials, mostly alloying elements, slag formers and coal. The supply of
many, for steel making important, raw materials is lower than the demand. Not only are the
raw materials expensive, but the supply is in many cases controlled due to geopolitical reason.
Many mineral deposits are located at sites with civil unrest, human rights problems or even
armed conflicts. This makes the need to reduce the use of certain raw materials even larger. In
some cases it is even desirable to replace one raw material with another. Raw material
consumption is also related to several environmental problems. Most of them require large
amounts of energy to be produced. Mining as well as recycling of several elements are
problematic since they are hazardous to living organisms. From an environmental perspective
this makes the interest to reduce the use, of at least some, raw materials significant. In
addition, legislations due to health and environmental concerns may even cause some
elements to be partly or completely banned in the future. For this reason it is beneficial or
even crucial to be able to replace some raw materials. Companies that succeed to replace raw
materials before they get banned will have an advantage.
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Figure 1 Steel price development since 2008 at London Metal Exchange [1].
Meeting competition could also be done by other means than reducing cost, e.g. by
improving product quality and performance. In some cases this makes it possible to get a
higher profit while sometimes it is simply a matter of survival of the company. Better product
quality, e.g. corrosion resistance or higher strength, in many cases mean longer lifetime of the
materials or lower weight and material need and thus less environmental impact. Another way
to meet competition is to start producing more specialized products. This is already done in
Sweden were no steel company produce steel products in the cheapest segments. By doing
this it is possible to get higher margins but it also makes the need to be ahead of competitors
more important. Making customized products makes it possible to get a higher profit and
simultaneously satisfying specific customer needs. Of course this might be a difficult task,
particularly if the customer demands higher performance than existing products.
Research and development is vital no matter if the ambition is developing a better product,
implementing a cheaper process, replacing a raw material or designing a customized product.
For a company that wants to take a lead position on the market, research and development is a
key area but also a major cost. However, it is not only about cost but also about the time to
develop a new product. In particular experimental work may be very expensive and time
consuming. In order to save time and money modeling is an important tool in the
development process. Several modeling tools are used today where the finite element method
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(FEM) and computational fluid dynamics (CFD) are the two most well-known. In materials
development, computational thermodynamics has become more important over the last
decades since the birth of the CALPHAD method [2]. This may be used alone or combined
with other models, like diffusion calculations or more specific calculations, concerned with
for example bainite or martensite transformation. In its simplest form it can actually be used
to calculate cost directly, based only on equilibrium calculation and raw material prices, as
shown in Figure 2. Although, it should be emphasized that this is a very crude estimation
neglecting all other factors influencing the cost. With that said in its simplicity it really
demonstrates usability of the CALPHAD method for materials and process development.
Lately, other methods like density functional theory (DFT) [3], molecular dynamics [4],
Monte Carlo [5] and phase field [6] have gained more attention in materials development. It is
also possible to combine several models in order to make calculations with the aim of
designing a specific material or process. This thesis aims to describe how materials design can
be used to reduce cost but also to describe computational thermodynamics, which is the key
component upon which this type of holistic modeling is based. The research has been
focusing on describing the thermodynamics of steel and slag, particularly related to sulfur,
and demonstrating how this type of modeling can be utilized to design processes and
materials.
Figure 2 Equilibrium calculation using Thermo-Calc and the TCFE database [7] to calculate the cost of
producing a duplex stainless steel with 50 % austenite with 20 % Cr and variable Mn and Ni contents. The red line
indicates that the detrimental sigma phase is stable.
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2. Materials and process design
The classic way to develop new materials is first to look at the processing and then at what
microstructure that is obtained. A certain microstructure gives certain properties which give
the performance of the final product. However, this approach is time consuming and might
not lead to materials that can meet the challenges of tomorrow. Thus it is desirable to look
from the opposite direction, how can we produce a material that meets specific demands in
terms of performance? The idea is illustrated in Figure 3, based on Ref. [8] which is inspired
by the reciprocity as suggested by Cohen [9]. The red arrow indicates the classic approach
and the black arrow indicates the so-called materials by design approach.
Figure 3 The red arrow is the classic approach where a certain process yields a structure which has some
properties that gives some performance. The black arrow shows the performance driven materials by design
approach. The small arrows indicate which profession that is most involved in each step.
This approach will likely increase the profitability in several ways, for example:
The development cost of new materials will be reduced.
Decreased development time gives competitive advantage.
A tailored alloy does not need to overshoot in performance; it could thus be
designed to minimize the use of expensive raw materials.
The possibility of designing alloys for specific demands opens new markets.
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Of course, as these ideas get more widespread they might turn into a necessity.
Furthermore, if futuristic ideas, like a space elevator to replace costly launch vehicles to carry
payload, should become reality, approaches like this is a requirement and not only a way to
increase the profitability.
2.1 Materials Genome
For the reasons described in the introduction to this chapter several nations have launched
programs aiming to stimulate the development of alloy design methods. Most well-known is
the Materials Genome Initiative (MGI) [10], which was launched by the US government in
2011. The ambition is to shorten materials development times from 10-20 years to 3-5 years.
In order to do so the idea is nothing less than to mimic the successful Human Genome Project.
The original definition of the Materials Genome Initiative was viewed as too vague by
Kaufman and Ågren [11] and they proposed that CALPHAD can be viewed as the materials
genome, since both equilibria and diffusion data are crucial for materials modeling. It is
apparent that CALPHAD is the backbone of the materials genome. Details about the
CALPHAD method are given in Section 3.2. In the US, national institute of standards and
technology (NIST) have taken the role to organize the efforts to collect thermodynamic and
kinetic data, see Ref. [12] for details.
2.2 ICME
Indeed, these ideas have lately started to spread outside the computational materials
science community. However, systematic ideas on alloy design have been around for over 20
years. Researchers at Northwestern University were the first to suggest and use such an
approach. Their first efforts using this so called ‘Materials by Design’ approach was
summarized in a paper by Olson in 1997 [8]. Despite the fact that most real materials are far
from equilibrium, thermodynamic calculation using CALPHAD databases were the most
important part of the design model. Already from the start the materials design philosophy
was included in the teaching at Northwestern University. A good overview of the Integrated
Computational Materials Engineering (ICME) and its relation to the Materials Genome can be
found summarized in Ref. [13] and in more detail in Ref. [14]. Further on, in a paper by
Xiong and Olson [15] the user level of materials design, integrated computational materials
design (iCMD), is reviewed. In these papers Ferrium S53, the first ICME steel to obtain
Accelerated Insertion of Materials (AIM) qualification is discussed. The total development
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time was 8.5 years which is better than standard development times. The next alloy to be
qualified was Ferrium M54 and this time it only took 6 years in total [15] and the time to
market is thus approaching the objective of the MGI. A complete description of how these
ideas are implemented is found in a paper by Campbell and Olson [16]. It starts by translating
desired performance of a high performance stainless steel into properties. These properties are
then related to different process steps and these are connected with various models which can
be used to calculate the properties. Finally, conditions to meet each optimization criterion are
checked to obtain an alloy with the desired properties. Later, other researchers have employed
genetic algorithms to optimize materials properties [17,18]. Researchers at TU Delft
combined genetic algorithms with CALPHAD modeling [19]. The basic idea in their work is
the same as that at Northwestern University. The contrast between these works is that the
latter involves human interaction to evaluate the optimization criteria in the design process.
Using fully automatic optimization procedures, as employed at TU Delft among others, the
human interaction will only be part of setting up the system and analyzing the results. Human
interaction has the advantage that the user will obtain a better understanding along the way
and also that problems are more easily found. On the other hand, a fully automatic optimizing
procedure has the advantage of the possibility to search a large space of parameters and that it
is in principle doing much of the work for you. The research group at TU Delft has also been
utilizing their method to optimize the cost and performance of a ultra-high strength stainless
steel [20].
In this context the book “Materials Selection for Mechanical Design” by Ashby [21] must
be mentioned. It serves as a guide for students in mechanical engineering as well as materials
science on materials selection. However, it is not true materials design in the sense that it only
concerns optimizing performance by using existing materials with desirable properties.
2.3 Process modeling
Although processing is an essential part of ICME, see e.g. [16,19,20], the steelmaking
process is payed little or no attention. However, several modeling methods related to
secondary steelmaking exist, which are reviewed by Du [22]. Among these is an approach to
combine computational fluid dynamics and thermodynamic models [23]. By analyzing the
various conditions during the vacuum degassing it was possible to obtain increased
understanding about the effect of the different process parameters. However, no efforts to
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optimize the process systematically were made. Recently, researchers at École Polytechnique
de Montréal have been implementing mesh-adaptive direct search to make optimization
related to different process steps, including the blast furnace [24]. Materials development
generally aims to create materials with as good properties as possible while keeping down the
cost. Process development on the other hand generally aims to meet specifications, on
composition and inclusions, to as low cost as possible. It should be mentioned that steel plants
generally have quite good experience on how to meet these demands. However, one should
realize that minor improvement could have an impact on the cost. For example lowering the
loss of manganese by 10 kg per 100 ton heat would reduce cost by 200 000 USD per year for
a steelmaker with an annual production of 1 000 000 tons. Further on, assuming full
production, if the time in vacuum degassing would be reduced by 1 minute from 20 minutes
this would mean 5 % increased capacity on existing equipment. As steelmaking is an
investment heavy sector this could have a huge impact on the profitability. Thus
implementing the ICME in the steelmaking process, or for that matter, processing of
nonferrous alloys, has the possibility to greatly increase the profit to an almost neglectable
cost. It should also be mentioned that the process route of completely new alloys might be
unknown and thus be an obstacle to ICME designed alloys, which could be overcome by
process design. Further on, while it might take time to get new alloys qualified, there are in
many cases few external regulations that limit the possibilities to improve the processing.
2.4 Process optimization using genetic algorithms
As could be realized from the previous section, the advantages with implementing an
ICME approach on the steelmaking process are huge. This led to the idea to utilize the
approach presented by Xu et al. [19] on the steelmaking process in a joint effort by KTH
Royal Institute of Technology and TU Delft. It was decided to use the vacuum degassing
process of a low alloyed steel as a demonstration, with the results presented in Paper I [25].
The aim with the vacuum degassing process is to reduce the content of impurity elements and
inclusions. This is done by extensive stirring under low pressure with the aim to let nitrogen
and hydrogen be removed by the gas flow while inclusions and sulfur are dissolved in the
slag. It should be mentioned that the ambition at this stage was not to improve vacuum
degassing but rather to confirm that years of industrial experience could be reproduced to
show the possibilities with this approach.
21
As was mentioned in Section 2.2 the research group at TU Delft uses a genetic algorithm
to design alloys. The principle behind the algorithm is quite simple. The different
optimization parameters resemble genes which can take different expressions, combinations
of 0 and 1 instead of A, C, G and T. In every iteration, a number of genomes, containing one
gene for each parameter, are generated. During these iterations the genes can mutate and the
fittest solutions are most likely to give an offspring, which will survive until the next iteration.
The process models are embedded in the optimization algorithm.
Figure 4 Flowchart of the optimization model showing which properties that are calculated and which constraints
that are used.
As in earlier works, see e.g. Refs. [8,16,19,20], CALPHAD is the most important
modeling tool. Given the complexity of the steelmaking process, which in principle has to be
modeled for each steel plant individually, it is decided to use a simple model for the kinetics.
As mentioned in the previous section, the objective of the steelmaking process is to produce
steel with the correct composition to as low a cost as possible. However, estimating the cost
of a process is not trivial as it not only involves raw materials and energy costs but also costs
22
related to for example staff and investments. For this reason it was decided to use process
time as the optimization criterion. Reducing the process time would mean that existing
equipment is used more efficiently. As with many optimization problems several constraints
will limit which solutions will be allowed. Neither viscosity of the slag nor the foaming height
can be too high. In order to ensure sufficient mass transfer between the steel and the slag the
later should be mostly liquid. The most important constraint is of course that the composition
should fall within an allowed range when the degassing is completed. In order to calculate
these constraints, different empirical models are used. In addition, a model is needed to
calculate the process time, which is done by using an analytical expression [26] combined
with the equilibrium composition calculated by computational thermodynamics. For more
details about the models used see Paper I [25] or the original references [26–32]. The
thermodynamic calculations were performed using Thermo-Calc [33] and a combination of
the TCFE6 [7], SLAG3 [34] and SSUB4 [35] databases. A flowchart showing which models
and constraints that are used is given in Figure 4.
Each optimization parameter could obtain 8 different values within its limit which means
that over 16 million solutions would be possible. However, using genetic algorithms, less than
10000 iterations were needed to reach the optimal set-up. The results, which are in good
agreement with industrial practice, are presented in Table 1. In particular the optimal solution
obtained at 50 Pa pressure is in good agreement. The model seems to optimize the sulfur and
nitrogen contents simultaneously. In Figure 5 the optimal solutions are tested at varying
pressures. It can be seen that the intersections where the nitrogen removal becomes limiting
are close to the pressure at which the solution was found. It can also be noted that the nitrogen
removal is completely dominating at 200 Pa which means that the obtained solution will give
much higher sulfur content in the steel, than would be possible if nitrogen was not considered,
without significantly decreasing the process time. The reason for this is that the time rather
than the sulfur content is the optimization variable.
The fact that the model managed to reproduce industrial experience is promising. Given
the rather crude empirical models it is not certain that the current model setup would give
reliable results in more extreme cases than vacuum degassing of low alloy steels. Thus to
fully demonstrate the usefulness of the approach it needs to be tested using plant specific
process models and full scale testing. The ideas are not restricted to vacuum degassing but can
in principle be used for any process. A possible next step would be to calculate the cost using
both raw material prices and a cost estimate for the time in vacuum degassing.
23
Table 1 Obtained optimal solutions at different pressures and normal industrial values in the bottom row. †Indicates normal process time, i.e. longer than the minimum time.
Pressure
(Pa)
Time
(s)
Al
(mass%)
Ca
(mass%)
Si
(mass%)
Slag
(kg)
Al2O3
(mass%)
MgO
(mass%)
SiO2
(mass%)
Temp.
(K)
50 429 0.010 0.005 0.243 1571 25.7 7.14 5.00 1922
75 479 0.019 0.005 0.243 1143 22.9 7.86 7.14 1964
100 562 0.023 0.005 0.243 1000 20.0 9.29 11.43 1973
200 1002 0.036 0.005 0.243 1286 20.0 8.57 15.71 1973
100 900-1200† 0.020-0.050 0-0.0010 0.20-0.30 1000 25.0-30.0 5.0-10.0 8.0-12.0 1950
Figure 5 Process time versus pressure in Pa for the optimal solutions found at P=50, 75, 100 and 200. Optimal
solutions, where all constraints are fulfilled, can be found at 50, 75, 100 and 200 Pa (red dots). The black and red lines
indicate the time needed for sulfur and nitrogen removal, respectively.
50 75 100 2006
8
10
12
14
16
18
Tim
e n
ee
de
d (
min
)
Pressure (Pa)
5075
100
200
S, P = 50
S, P = 75
S, P = 100
S, P = 200
N, P = 50
N, P = 75
N, P = 100
N, P = 200
24
25
3. Computational thermodynamics
As mentioned in the previous chapter, computational thermodynamics is the key
component of ICME. Not only can it be used to gain information about equilibria, it can also
be an important part of diffusion calculations, phase field modeling and other models related
to phase transformations. There are different methods to calculate equilibria. For reasons that
will be described below minimizing Gibbs energy is the most common and used within the
CALPHAD approach which is today widespread. This method will also be described in this
chapter, as will the so-called ionic two-sublattice liquid model and compound energy model
for spinel phases.
3.1 Thermodynamic principles and Gibbs energy
In order to understand CALPHAD and computational thermodynamics some
thermodynamic basis is needed. In some sense all engineers have some knowledge about
thermodynamics. Something which might strike you is how differently thermodynamics is
taught in different majors. Students in mechanical engineering are focusing on the Carnot
cycle, i.e. engines and heat pumps, and physics students are focusing on statistical mechanics,
i.e. the probability of different states, and students in materials science and chemistry are
focusing on Gibbs energy, although from slightly different angles. It should be emphasized
that it is of course the same thermodynamics but just different focus and sometimes different
representation. Before describing Gibbs energy some thermodynamic principles will be
described.
3.1.1 Probability and entropy
If you are rolling two pair of dice, the chance of getting 7 is much greater than the chance
of getting 2 or 12, i.e. two ones or two sixes. However, the probability of getting 3 on one die
and 4 on the other is equal to that of getting 2 or 12 but there are many other ways to get 7
which give a higher probability to get that number. If you had a large number of dice the
average value would be close to 3.5, which is shown in Figure 6.
26
Figure 6 Average value as function of the number of dice rolled for ten different random sequences.
In a crystal consisting of A and B atoms there is a large number of possible ways the
atoms can arrange themselves. Neglecting the interaction between the atoms it turns out that
the probability of the atoms separating or ordering themselves is negligible. Just like the
probability of getting an average of 6 or 1 if you roll a large number of dice. From
probabilistic principles it is found that the number of possible states, W, for a mixture of A
and B atoms can be calculated as:
𝑊 = 𝑁!/(𝑛𝐴! 𝑛𝐵!)
where N is the total number of atoms, nA and nB are the number of A and B atoms
respectively. By using the number of states the entropy is defined as:
𝑆 = 𝑘𝐵𝑙𝑛𝑊
where kB is Boltzmann’s constant. Now we can calculate the entropy of mixing for the
crystal of A and B atoms using the Stirling approximation:
𝑆 ≈ −𝑘𝐵𝑁(𝑥𝐴𝑙𝑛𝑥𝐴 + 𝑥𝐵𝑙𝑛𝑥𝐵)
27
where xA and xB is the atomic fraction of A and B and N is the total number of atoms.
Using one mole of atoms N=NA, Avogadro’s number, and since the gas constant is defined as
expressed as R=NAkB the molar entropy of mixing becomes:
𝑆𝑀 ≈ −𝑅(𝑥𝐴𝑙𝑛𝑥𝐴 + 𝑥𝐵𝑙𝑛𝑥𝐵)
It is easily seen that the entropy of mixing reaches its maximum when xA=xB=0.5. From
this it can also be seen that it is almost impossible to get a completely pure metal as any
impurity will give a drastic increase in entropy. In fact, in any isolated system, a spontaneous
reaction will always lead to increased entropy, or at least constant entropy in the case of a
reversible process. This is the second law of thermodynamics. It should be mentioned that the
entropy can be much more than just entropy of mixing. A simplified way to see it is that the
disorder in the universe always increases in some way, e.g. we can produce very pure metals
but it requires a lot of energy which will lead to increased entropy. In this case we also have
to consider the reaction in the power plant, e.g. the entropy increase caused by the use of
fossil fuels which forms forming carbon dioxide, water vapor and cooling. If we instead use
solar energy, were wind, water and bioenergy may be considered as indirect solar energy, the
fusion reactions in the sun cause the entropy increase. These are called renewable energy
sources, which is reasonable as we lack the possibility to control the reactions in the sun and
given the lifetime of a star. Even fossil fuels can be considered as indirect solar energy, which
has been stored for millions of years.
3.1.2 State functions and Gibbs energy
The entropy is a so called state function that describes the equilibrium state of a system.
As stated in the previous section, the entropy change of a spontaneous reaction in an isolated
system will always be larger than or equal to zero. Thus maximizing the entropy will tell us
which reactions will occur. The classical way to define the entropy, assuming only pressure-
volume work is performed, is from the differential, dS, as follows:
𝑑𝑆 = (1/𝑇)𝑑𝑈 + (𝑃/𝑇)𝑑𝑉 − ∑(𝜇𝑖/𝑇)𝑑𝑁𝑖
where P is the pressure, V is the volume, μi is the chemical potential of element i and Ni is
the number of atoms of element i. However, if we are not speaking about a so called closed
system the entropy increase of the reaction in principle refers to all connected reactions in the
28
universe. A closed system would require constant internal energy, constant volume and
constant number of atoms. For the practical case, e.g. planning an experiment or
understanding a metallurgical process, such conditions are hard to achieve and thus this
approach becomes impractical. For this reason some other state function would be more
suitable. By defining a function F=U-TS one obtains a state function which describes the
system at constant volume and temperature. F is the so called Helmholtz energy, again
assuming that only pressure-volume work is performed, and the differential is written as:
𝑑𝐹 = −𝑆𝑑𝑇 − 𝑃𝑑𝑉
As Helmholtz energy is a state function at constant volume, it is suitable to relate to so-
called first principles calculations, like DFT. However, it turns out that it is quite hard to
achieve constant volume experimentally. Pressure, unlike volume, is relatively easy to control
experimentally. Thus the state function enthalpy defined as H=U+PV is suitable. The change
in enthalpy can be measured in a straight forward manner seen as change in heat due to a
reaction. However, the enthalpy requires that the entropy of the system is kept constant. If we
instead define a function G=U+PV-TS=H-TS we get a state function which defines the
system at constant pressure and temperature. This function is called Gibbs energy and its
differential is written as:
𝑑𝐺 = 𝑉𝑑𝑃 − 𝑆𝑑𝑇 + ∑(𝜇𝑖/𝑇)𝑑𝑁𝑖
In contrast to the entropy the Gibbs energy is minimized when equilibrium is reached.
Any other thermodynamic quantities can be calculated from Gibbs energy, e.g. the entropy,
enthalpy and pressure, but also the chemical potential, and heat capacity, CP.
𝑆 = −(𝜕𝐺/𝜕𝑇)𝑝,𝑁𝑖
𝐻 = 𝐺 + 𝑇𝑆 = 𝐺 − 𝑇(𝜕𝐺/𝜕𝑇)𝑝,𝑁𝑖
𝑉 = (𝜕𝐺/𝜕𝑃)𝑇,𝑁𝑖
𝜇𝑖 = (𝜕𝐺/𝜕𝑁𝑖)𝑝,𝑁𝑗≠𝑖
𝐶𝑃 = −𝑇(𝜕 𝐺2 /𝜕𝑇2)𝑝,𝑁𝑖
29
Although Gibbs energy cannot be measured directly it is apparently a useful
thermodynamic quantity. This is the reason why it is so frequently used in materials science
and chemistry and to some extent in other fields as well. And it is the reason why it is
probably the most suitable quantity to use in computational thermodynamics.
3.1.3 Regular solutions
In the previous subsection it was stated that equilibrium is obtained by minimizing Gibbs
energy for a system at constant pressure and temperature. When dealing with reactions, like in
chemistry, the Gibbs energy of formation is enough to establish if a reaction will occur or not,
depending on whether ΔG is negative or positive. However, materials science often deals with
alloys, i.e. solutions, in liquid and solid state. A common way to describe Gibbs energy of
solutions is by using the well-known regular solution model. For a system which contains A
and B atoms their partial Gibbs energies, °GA and °GB, will define the baseline of the system.
As described in the subsection about entropy, intermixing two species will increase the
entropy. This is enough to describe so-called ideal solutions:
𝐺𝑚 = 𝑥𝐴°𝐺𝐴 + 𝑥𝐵°𝐺𝐵 − 𝑇𝑆 = 𝑥𝐴°𝐺𝐴 + 𝑥𝐵°𝐺𝐵 + 𝑅𝑇(𝑥𝐴𝑙𝑛𝑥𝐴 + 𝑥𝐵𝑙𝑛𝑥𝐵)
For some type of systems this is actually enough to describe the molar Gibbs energy. In
order for a system to be ideal the atoms must be very similar. The Hume-Rothery rules [36]
gives an idea on the conditions which need to be fulfilled in order for the system to be
reasonably ideal. This means that the atoms need to be similar in size and electronegativity
and have the same crystal structure and valance. It should be noted that fulfilling these rules
does not mean that the system will be ideal but rather that it cannot be ideal if they are not
fulfilled. If the system is not ideal one has to handle the interaction energy, i.e. excess molar
Gibbs energy, GE
m, in some way. The easiest way to describe the excess Gibbs energy is by
setting GE
m=xAxBL. One thus has the regular solution model:
𝐺𝑚 = 𝑥𝐴°𝐺𝐴 + 𝑥𝐵°𝐺𝐵 − 𝑇𝑆 + 𝐺𝑚𝐸 = 𝑥𝐴°𝐺𝐴 + 𝑥𝐵°𝐺𝐵 + 𝑅𝑇(𝑥𝐴𝑙𝑛𝑥𝐴 + 𝑥𝐵𝑙𝑛𝑥𝐵) + 𝑥𝐴𝑥𝐵𝐿
30
For simple solution phases this works well in many cases. However, it might happen that
the excess Gibbs energy cannot accurately be described using only a symmetric interaction
parameter. For this reason Redlich-Kister polynomials [37] are widely used. Thus the
interaction parameter for A and B will be defined in the following way:
𝐿𝐴,𝐵 = ∑(𝑥𝐴 − 𝑥𝐵)𝑣 ∙ 𝐿𝑣𝐴,𝐵
In principle by using many polynomials it is possible to describe any behavior of the
Gibbs energy. However, if more than first or possibly second order polynomials are needed it
is generally an indication that a more advanced model is needed. These models will be
described in the section about CALPHAD.
3.1.4 Thermoeconomics
Given the title of this thesis the concept thermoeconomics [38,39] has to be mentioned. In
principle there is a price on energy and generally the more energy that is needed to produce a
raw material or product the higher the price. As an example this is done on the relating
financial terms to thermodynamics in the energy sector [40]. It should be emphasized that this
is not thermoeconomics but instead computational thermodynamics, which is a tool that can
be used for product and process development. The problem is that one also has to take
sociological factors into account, i.e. supply and demand. How can oil price vary if it is
related to a thermodynamic quantity and how can one explain the value of brands using
thermodynamics? This can be compared with diffusion calculation where the Gibbs energy
and mobility are used to model diffusivity, which by itself contains too little information. The
difference is that sociologic factors are probably far more complicated to model than mobility,
even though the latter is all but trivial. Thus one cannot say that profitability is a function of
only Gibbs energy as other factors must be considered as well. Apart from the sociological
factors this of course also includes other technical factors, like time and reliability of the
equipment, as well as phenomenological factors, like mobility and heat transfer. Overall the
title Profitability = f(G) suggests that this work is focusing on the Gibbs energy and how it
can be used to increase profitability. But who knows, perhaps someday ICME will also
include sociological models?
31
3.2 CALPHAD
As mentioned in the chapter about ICME, the CALPHAD method is an essential part of
alloy design. It was first introduced in 1970 by Kaufman and Bernstein [2], and the meaning
was simply “CALculation of PHAse Diagrams”. As the Gibbs energy can be used to calculate
much more than just phase diagrams the meaning of the acronym was later changed to
“Computer coupling of phase diagram and thermochemistry”, which is used in the full title of
the CALPHAD journal. The calculation of the Fe-Ni phase diagram was published already in
1956 by Kaufman and Cohen [41] and can be considered to be the first CALPHAD
assessment. It should be emphasized that CALPHAD is not a simulation method which can be
used to obtain results by itself, like DFT or Monte Carlo. Nor is it an empirical model, at least
not in the classical sense. Empirical models are often very limited and in principle anything
can be fitted using the right polynomials. That does not mean that an empirical model cannot
be good, it just means that they are only reliable within a defined range. CALPHAD do use
experimental data to fit parameters but the parameters used are based on models which should
be physically correct. Generally this means that one should avoid using too many parameters
as that is usually a sign that the model is incorrect.
One of the main advantages with CALPHAD is that close to everyone within the
community uses the same references for unary systems. In 1991 Dinsdale [42] published the
unary descriptions established by the SGTE group. This means that higher order systems will
be compatible under the condition that also lower order systems are compatible. However, a
drawback with this is that all higher order systems must be re-assessed if the lower order
systems were to be redefined. At present there is an effort to re-assess the unary descriptions
with more physically correct models [43], both to get more accurate results but also to be able
to make use of ab initio data to a larger extent. The first element to be re-assessed was Fe by
Chen and Sundman [44]. However, as several elements of interest to this work are yet to be
re-assessed the old unary descriptions are used. This is a disadvantage but as the application
areas of the work are at higher temperatures this will probably not be a large problem in the
near future.
32
3.2.1 Compound energy formalism
The compound energy formalism, at the time called the sub-lattice model, was first
presented by Hillert and Staffansson in 1970 [45] as a model to be used for reciprocal
systems. This subsection will present the general features about the compound energy
formalism while modeling of ionic liquids will be discussed in further detail in the next
subsection. In a more recent publication, Hillert [46] reviews the model now called the
compound energy formalism. In fact the compound energy formalism is used to model
solution phases with few exceptions. Having the regular solution in mind (Subsection 3.1.3)
the idea is rather simple, to extend the regular solution model to more than one sublattice. For
simplicity most of the discussion will focus on two sublattices, i.e. a (A,B)a(C,D)b model. This
could for example represent a substitutional and an interstitial sublattice in an alloy or a cation
and an anion sublattice in a salt. An important part of the model is the end-members defining
the baseplane of the system, the so called surface of reference. The compound energies of
these end-members have given the name to the model. It should be noted that while these end-
members may exist experimentally there is no need for them to; in fact they might be
impossible to obtain due to for example electroneutrality in some ionic phases. Secondly, just
like in the regular solution model, a simple ideal configurational entropy is assumed. Further
on, the excess Gibbs energy usually needs to be described to model the system. The general
term description of molar Gibbs energy, Gm, is given as:
𝐺𝑚 = 𝐺𝑠𝑟𝑓
𝑚 − 𝑇 𝑆𝑐𝑓𝑛
𝑚 + 𝐺𝑝ℎ𝑦𝑠
𝑚 + 𝐺𝐸𝑚
where the srf
Gm is the surface of reference, cfn
Sm the configurational entropy, phys
Gm the
physical contribution and EGm the excess Gibb energy. The physical contribution is usually
the magnetic part of Gibbs energy. The excess Gibbs energy is described using interaction
parameters using Redlich-Kister polynomials as in the regular solution model but for
interaction on the different sublattices. The surface of reference and the configurational
entropy are expressed as [46]:
𝐺𝑠𝑟𝑓
𝑚 = ∑ °𝐺𝑒𝑛𝑑 ∏ 𝑦𝑖𝑠
𝑆𝑒𝑛𝑑
𝑆𝑐𝑓𝑛
𝑚 = −𝑅 ∑ ∑ 𝑛𝑠𝑦𝑖𝑠ln (𝑦𝑖
𝑠)
𝑖𝑠
33
where 𝑦𝑖𝑠 denotes site fraction of species i on sublattice s, °𝐺𝑒𝑛𝑑 denotes the end-member
energy and 𝑛𝑠 denotes the number of sites on every sublattice. At first this looks intimidating
but one should be aware that it is in principle just the regular solution model. For the simplest
system (A,B)(C,D) this means that the Gibbs energy description can be written as:
𝐺𝑚 = 𝑦𝐴𝑦𝐶°𝐺𝐴:𝐶 + 𝑦𝐴𝑦𝐷°𝐺𝐴:𝐷 + 𝑦𝐵𝑦𝐶°𝐺𝐴:𝐷 + 𝑦𝐵𝑦𝐷°𝐺𝐵:𝐷
+ 𝑅𝑇(𝑦𝐴𝑙𝑛𝑦𝐴 + 𝑦𝐵𝑙𝑛𝑦𝐵 + 𝑦𝐶𝑙𝑛𝑦𝐶 + 𝑦𝐷𝑙𝑛𝑦𝐷) + 𝑦𝐴𝑦𝐵𝑦𝐶𝐿𝐴,𝐵:𝐶
+ 𝑦𝐴𝑦𝐵𝑦𝐷𝐿𝐴,𝐵:𝐷 + 𝑦𝐴𝑦𝐶𝑦𝐷𝐿𝐴:𝐶,𝐷 + 𝑦𝐵𝑦𝐶𝑦𝐷𝐿𝐵:𝐶,𝐷 + 𝑦𝐴𝑦𝐵𝑦𝐶𝑦𝐷𝐿𝐴,𝐵:𝐶,𝐷
where LA,B:C,D is the reciprocal parameter. The next subsection will discuss the liquid
model in further detail while Subsection 3.2.3 will discuss modeling of the spinel phase. As
stated in the overview of the compound energy formalism [46] it can be used to model
ordering in alloys. For further examples on how the compound energy formalism can be used
more applications can be found in a paper by Frisk and Selleby [47].
3.2.2 Liquid modeling and the ionic two-sublattice liquid model
As described in the previous section, the compound energy formalism (CEF) is commonly
used to describe solid solution phases within the CALPHAD community. However, when it
comes to liquids different models are also used. The simplest way to model liquids is to
assume that they behave as a regular solution, which works well for metallic liquids.
However, the regular solution model cannot handle short range order. This can be addressed
by adding associates, i.e. molecules or hypothetical molecules, to the regular substitutional
solution in order to model short range order in liquids. This model is called the associate
model [48] and it is used in for example an description of the Cu-Fe-S system [49]. Another
way to model short range order in liquids is by considering the bonds between different
species. This is done in the modified quasichemical model [50]. This model is widely used by
the FACT group to model different ionic systems, commonly for materials processing
applications. Yet another way to handle short range order in liquids is the Cell Model [51],
which is used in the SLAG database [34], in which one considers mixtures of cells consisting
of cations and anions. In some sense this model can be considered as a mixture between the
modified quasichemical model and the associate model. In the present work the ionic two-
sublattice liquid model is used which was originally developed as a purely mathematical
34
formalism [45], which is today known as the compound energy formalism. The ionic two-
sublattice liquid model has been developed further since then. The idea behind this model
follows the suggestion by Temkin [52] that one could consider an ionic liquid as having a
cationic sublattice and an anionic sublattice. For ionic systems, this feels intuitively correct as
it is reasonable that a positively charged ion wants to surround itself with negatively charged
ions and vice versa. In its original form the ionic two-sublattice liquid model was used in
thermodynamic assessments of for example the Fe-FeS [53], Mn-MnS [54] and Fe-Mn-S [55]
systems. To model the complete Fe-S system Guillermet et al. [56] introduced charged
vacancies on both sublattices. It was later concluded that the model becomes more self-
consistent by restricting the vacancies to the anionic sublattice and having variable number of
sites on the two sublattices [57]. In the same paper the model was compared with the associate
model and it was concluded that the two are identical for binary systems while different for
higher order systems. In fact the associate model needs more parameters in higher order
systems. The excess Gibbs energy of the ionic two-sublattice liquid were then slightly
modified by Sundman in 1991 [58] in order to be able to directly use the regular solution
description of metallic systems to the ionic liquid model and vice versa. The ionic two-
sublattice liquid model is expressed as [57,58]:
(Civi)P(A
vi,Va-Q
,B0)Q
where the site fractions P and Q are the average valence on the opposite sublattice,
calculated using the following expressions:
𝑃 = ∑(−𝑣𝑖)𝑦𝐴𝑖+ 𝑄𝑦𝑉𝑎
𝑄 = ∑ 𝑣𝑖𝑦𝐶𝑖
The molar Gibbs energy and molar excess Gibbs energy for the ionic two-sublattice liquid
model are written as [58]:
𝐺𝑚 = ∑ ∑ 𝑦𝐶𝑖𝑦𝐴𝑗
°𝐺𝐶𝑖:𝐴𝑗𝑗𝑖 + 𝑄𝑦𝑉𝑎 ∑ 𝑦𝐶𝑖°𝐺𝐶𝑖𝑖 + 𝑄 ∑ 𝑦𝐵𝑘
°𝐺𝐵𝑘𝑘 + 𝑅𝑇 (𝑃 ∑ 𝑦𝐶𝑖𝑖 𝑙𝑛𝑦𝐶𝑖+
𝑄 (∑ 𝑦𝐴𝑗𝑗 𝑙𝑛𝑦𝐴𝑗+ 𝑦𝑉𝑎𝑙𝑛𝑦𝑉𝑎 + ∑ 𝑦𝐵𝑘𝑘 𝑙𝑛𝑦𝐵𝑘
)) + 𝐺𝑚𝐸
35
𝐺𝑚 = ∑ ∑ ∑ 𝑦𝐶𝑖1𝑦𝐶𝑖2
𝑦𝐴𝑗𝐿𝐶𝑖1 ,𝐶𝑖2:𝐴𝑗𝑘𝑖2>𝑖1𝑖1
𝐸 + ∑ ∑ ∑ 𝑦𝐶𝑖𝑦𝐴𝑗1
𝑦𝐴𝑗2𝐿𝐶𝑖:𝐴𝑗1 ,𝐴𝑗2𝑗2>𝑗1𝑗1𝑖 +
∑ ∑ ∑ 𝑦𝐶𝑖𝑦𝐴𝑗
𝑦𝐵𝑘𝐿𝐶𝑖:𝐴𝑗,𝐵𝑘𝑘𝑗𝑖 + 𝑦𝑉𝑎 ∑ ∑ 𝑦𝐶𝑖
𝑦𝐴𝑗𝐿𝐶𝑖:𝐴𝑗,𝑉𝑎𝑗𝑖 +
𝑄𝑦𝑉𝑎 ∑ ∑ 𝑦𝐶𝑖1𝑦𝐶𝑖2
𝐿𝐶𝑖1 ,𝐶𝑖2:𝑉𝑎𝑖2>𝑖1𝑖1+ 𝑄𝑦𝑉𝑎 ∑ ∑ 𝑦𝐶𝑖
𝑦𝐵𝑘𝐿𝐶𝑖:𝑉𝑎,𝐵𝑘𝑘𝑖 +
𝑄 ∑ ∑ 𝑦𝐵𝑘1𝑦𝐵𝑘2
𝐿𝐵𝑘1 ,𝐵𝑘2𝑘2>𝑖1𝑘1
It should be noted that in the limit where ΔGC:A= GC:A-(GB+GC) becomes zero the ionic
liquid becomes identical to the regular solution of the C-A system [57] but where the
interaction is between charged vacancies and neutral species instead of between the atoms
directly. Moreover, it is identical to the associate model in the simple binary system [57].
However, it is not identical to the associate model for ternary systems. As stated earlier using
the modifications by Sundman [58] the model also becomes identical to the regular solution
model when yVa=1, i.e. for pure metallic systems.
3.2.3 Spinel modeling
In this work two phases with spinel structures are modeled. They are also modeled using
the compound energy formalism but as in the case with the ionic liquid model their modeling
can be discussed in more detail. The spinel phase is a complex oxide mineral with cubic
symmetry and the chemical formula MgAl2O4. The Mg+2
-ions are primarily dissolved on
tetragonal sites and the Al+3
-ions primarily on the octahedral sites. This is referred to as the
normal spinel with the arrangement (Mg+2
)1(Al+3
)2(O-2
)4. As temperature increases some
Mg+2
-ions and Al+3
-ions exchange sites with each other toward an inverse spinel which would
have the arrangement (Al+3
)1(Mg+2
,Al+3
)2(O-2
)4. In the assessment of the MgAl2O4-spinel
phase by Hallstedt [59] an additional octahedral sublattice was introduce to represent the
vacant octahedral sites. By using this sublattice it is possible to model oxygen deficiency in
the spinel and the complete model used by Hallstedt [59] is:
(Mg+2
,Al+3
)1(Al+3
,Mg+2
,Va)2(Va,Al+3
,Mg+2
)2(O-2
)4
In this work aluminum has not been considered and for this reason neither has MgAl2O4.
However, the complex oxide phases with spinel structures exist in several systems including
the Fe-O system [60], the Mn-O and Fe-Mn-O systems [61] as well as the Fe-Mg-O and Mg-
Mn-O systems which are assessed in Paper 3 [62] and Paper 5. Details about these systems
36
will be given in the next chapter. The phase with the spinel crystal structure in all these
systems can be modeled using the same model. In the assessment of spinel phases, the Gibbs
energy of different reciprocal reactions is used to describe the end-members. However, when
combining different systems one needs to consider that each system uses one end-member as
reference and these may be have been chosen differently in different assessments which needs
to be handled [63]. Commonly, the definition GFe+2:Fe+3:Va:O-2-GFe+3:Fe+2:Va:O-2=0 as suggested
by Sundman [60] is used a reference. In the assessment of a spinel phase the degree of
inversion is an important parameter. The degree of inversion, ξ, is related to the site fractions
and when considering only (Mg+2
,Al+3
)1(Al+3
,Mg+2
)2(O-2
)4 the relations to the site fractions
become ξ=y’Al and ξ=2-y’’Mg. In addition to the standard (cubic) spinel, a tetragonal spinel is
present at lower temperatures in Mn-containing systems like Mn-O [61], Fe-Mn-O [61], Mn-
Ni-O [64] and Mg-Mn-O which is described in Paper 5. In the Mn-O system the cubic spinel
is referred to as β-Mn3O4 while the low temperature tetragonal spinel is referred to as α-
Mn3O4. The β-Mn3O4 most likely has a distribution of manganese cations with different
valances similar to that in other cubic spinels [61,65]. However, the tetragonal α-Mn3O4
probably only has Mn+2
-ions on the tetrahedral sites and Mn+2
, Mn+3
and Mn+4
on the
octahedral sites. Thus a slightly different model is used and it can be argued whether the term
degree of inversion can be used for this model as the manganese would not only need to
change sublattice but also change oxidation state.
37
4. Thermodynamic descriptions
The focus of this work has been has been computational thermodynamics related to
steelmaking and phenomena like corrosion. As was demonstrated in Section 2.4 process
optimization is a suitable method to tailor a process to make a certain steel grade to as low
cost as possible. In order to really be able to make good predictions the thermodynamic
databases, just like the models used, should be as accurate as possible. The SLAG3 [34]
database used has the advantage of using relatively simple models and is thus very
comprehensive. Using more physically correct models would be more accurate but the
development becomes more complicated and time-consuming. The TCOX database [66] is
such a database utilizing the ionic two-sublattice model [57,58] for the liquid and other
sublattice models for complex oxides. As a result of the more complicated models the
database was lacking elements of importance for steelmaking as this work started. The major
part of this work has been to describe the most important sulfur-containing system with the
aim of extending the TCOX database with sulfur.
4.1 TCOX database
When the COMPASS project started the TCOX database contained descriptions of the
most important alloying elements (Fe, C, Cr, Ni and Mn) and slag components (Al2O3, CaO,
MgO and SiO2). The thermodynamic descriptions in the TCOX database are based on
extensive assessment work. A large part of this work have previously been performed at KTH
Royal Institute of Technology, of which much can be found summarized in the PhD theses by
Selleby [67], Jonsson [68], Hallstedt [69], Mao [70] and Kjellqvist [71].
Simultaneously with this project the Thermo-Calc Software company has made efforts
along with other partners to include Y and Zr, in order to be able to perform calculations
related to thermal barrier coatings, which are included in the current version. In addition,
efforts are also being made to add F, Cu and Nb to the description. Fluorine is an element of
great importance in slags, not at least in stainless steel production. In parallel to the
development of TCOX, research is being conducted at KTH Royal Institute of Technology to
describe vanadium-containing slags [72], which can be included in the database in the future.
Further on, some improvements of the existing descriptions have been made. This includes
the finalization of the assessment of the Fe-Mg-O system [62], which will be described further
detail in Section 4.3.
38
4.2 Fe-Mn-Ca-Mg-S
In steels, it is important to predict sulfide formation as sulfides have a large impact on the
properties. They are usually undesirable as they have a negative impact on the mechanical
properties, in particular the toughness, and they can also give rise to pitting corrosion in
stainless steels. However, in some cases sulfur is added on purpose to improve the
machinability of certain steel grades. A lot of research has been done to investigate sulfide
formation in steel, see e.g. [73–75]. For low-alloy steels, and in to some extent even stainless
steels, the Fe-Mn-Ca-Mg-S system is the most important metal-sulfur system. Although it is
obvious that iron is important in steel it should be mentioned that FeS, if formed, gives rise to
hot-shortness due to its low melting temperature. Early steelmakers started using manganese
to avoid formation of FeS. For several reasons manganese is still today a common alloying
element and thus MnS is found in many steels. To obtain better mechanical properties, in
particular toughness, calcium can be added to the steel to form CaS instead of MnS. Many
steel plants use MgO linings in their ladles and considering that MgS has a complete mutual
solubility with MnS, magnesium should be included in a description of sulfides. Of the binary
metal-sulfur sub-systems the Fe-S [53,56] and Mn-S [54,76,77] systems have been assessed
using the ionic two-sublattice model prior to this work. Additionally, the Ca-S [78], Fe-S [79]
and Mn-S [80] systems have been assessed using the modified quasi-chemical model. Of the
ternary sub-systems only the Fe-Mn-S [55,76,77,80] system has been assessed using the ionic
two-sublattice liquid model prior to this work. Besides the Fe-S system, which was accepted
from Lee et al. [49], all sulfur sub-systems have been assessed as part of this work. The stable
FeS-sulfide has the NiAs-structure and its mineral name is pyrrhotite. Paper 2 [81] includes
the assessment of the Mn-S system and Paper 3 [62] includes the assessments of Ca-S and
Mg-S. MnS, CaS and MgS all have the NaCl-structure and is referred to as alabandite which
is the mineral name of MnS. The MnS-alabandite was assessed taking heat content and heat
capacity measurements [82–85] into consideration while CaS- and MgS-alabandite were
assessed using the Neumann-Kopp approximation due to lack of high temperature heat
capacity data. The Mn-S system was optimized using experimental data with the exception of
the liquid phase at sulfur contents over 50 at%, were the liquid was assumed to behave similar
as in the Fe-S system [49]. However, the liquid in Ca-S and Mg-S system were approximated
using parameters from the Ca-O [86] and Mg-O [87] systems respectively. The calculated
phases diagram of the binary metal-sulfur systems are shown in Figure 7.
39
Figure 7 Binary metal-sulfur systems, a) Fe-S calculated using parameters from Ref. [49], b) Mn-S from Paper 2
[81], c) Ca-S from Paper 3 [62] and d) Mg-S from Paper 3 [62].
In sulfide systems, just like for oxide, carbide and nitride systems, a good way to represent
a system is pseudobinary phase diagrams. In these the different equilibria are plotted along a
fixed sulfur content or activity. They are commonly used in handbooks, such as the Slag Atlas
[88]. In this work all pseudobinary phase diagrams for the Fe-Mn-Ca-Mg-S system have been
assessed at fixed sulfur content. This includes the FeS-MnS from Paper 2 [81], FeS-CaS and
FeS-MgS from Paper 3 [62] and CaS-MnS, CaS-MnS and MgS-MnS from Paper 4 [89]. In
addition, the FeS-MnS pseudobinary has also been assessed in equilibrium with iron, in
principle a fixed sulfur activity. The pseudobinary phase diagrams with fixed sulfur content
and fixed sulfur activity assessed in this work are shown in Figure 8 and Figure 9,
respectively.
40
Figure 8 Calculated pseudobinary phase diagrams of the a) FeS-MnS from Paper 2 with experimental data
[90,91] b) FeS-CaS from Paper 3 with experimental data [92–94] c) FeS-MgS from Paper 3 with experimental data
[94,95] d) CaS-MgS from Paper 4 with experimental data [94] e) CaS-MnS from Paper 4 with experimental data
[94,96,97] and f) MgS-MnS from Paper 4.
41
Figure 9 Calculated FeS-MnS pseudobinary with excess iron with experimental data [91,94,98–101].
When thermochemical data are available for a system it is a great advantage since this can
make the description more accurate. For the Fe-Mn-S system activity data for different parts
of the system is found in the literature [101–104]. Additionally, activity measurements have
been reported in the CaS-MnS pseudobinary system [105]. The calculated activity in that
pseudobinary section from the assessment in Paper 4 is shown together with experimental
data in Figure 10.
42
Figure 10 Activity of MnS, using alabandite as reference, in CaS-MnS pseudobinary calculated in Paper 4 [89]
together with experimental data [105].
Experimental data for isothermal sections in the ternaries are only found for the Fe-Mn-S
system. Due to the absence of experimental information in the remaining systems no values
are set for reciprocal liquid parameters in these systems. The calculated isothermal sections at
steelmaking temperature (1600°C) are shown in Figure 11 using results from
Papers 2, 3 and 4.
Just like with pseudobinary sections, pseudoternary sections offer a great way to represent
sulfide systems. Skinner and Luce [94] reports experimental data for several isothermal
pseudoternary sections for the Fe-Mn-Ca-Mg-S system. These are used for the assessment
work in Paper 4 [89] and presented in Figure 12. Only a few parameters were needed to fit
these systems as the interpolation of the low order systems generally give quite good results.
43
Figure 11 Isothermal section at 1600°C for the a) Fe-Mn-S, b) Fe-Ca-S, c) Fe-Mg-S, d) Ca-Mn-S, e) Ca-Mg-S and
f) Mn-Mg-S systems.
44
Figure 12 Calculated pseudoternary isothermal sections from Paper 4 [89] of the a) CaS-FeS-MgS at 800°C, b)
CaS-FeS-MnS at 800°C, c) CaS-MgS-MnS at 600-1000°C and d) FeS-MnS-MgS at 900-1100°C with experimental data
[94].
4.3 Fe-Mg-O and Mg-Mn-O
Given the fact that MgO is a common material used for lining in ladles the Fe-Mg-O
system is of great importance for calculations related to steelmaking. This system was already
included in the TCOX database but during this project it was fully assessed and published in
Paper 3 [62]. The major challenge in this system is the spinel phase which is discussed in
Section 3.2.3. The degree of inversion of the MgFe2O4 spinel fitted using experimental data
which shown Figure 13. It can be seen that the spinel has an inverse structure at room
temperature and gradually transforms toward a normal structure as the temperature increases.
Several thermochemical data were used in this assessment together with phase diagram
data. In Figure 14 are experimental phase diagram data are shown together with the calculated
45
phase diagram in air. In addition, the FeO-MgO pseudobinary and the isothermal section at
1600°C are shown in Figure 15 and Figure 16, respectively. The agreement with the
experimental data is generally good for the Fe-Mg-O system.
Figure 13 Degree of inversion in MgFe2O4-spinel calculated using the description in Paper 3 [62] together with
experimental data [106–112].
46
Figure 14 Calculated MgO-FeOx phase diagram in air from Paper 3 [62] with experimental data [113–116]. The
dashed lines represent the MgO-Fe2O3 phase diagram calculated by setting the oxygen activity to a very high value.
Figure 15 Calculated MgO-FeO pseudobinary from Paper 3 [62] with experimental data [117–121].
47
Figure 16 Calculated isothermal MgO-Fe2O3-FeO section at 1600°C from Paper 3 [62] with experimental data
[122,123].
A part of the PhD studies were performed at TU Bergakademie Freiberg with the ambition
to investigate the thermodynamics of Mg-Mn-Zr-O system. This system is of great
importance for the ZrO2-reinforced metal-matrix composite steel, which are proposed by
Biermann et al. [124]. In Paper 5 a thermodynamic description of the Mg-Mn-O system and
experimental heat capacity of MgMn2O4 and Mg6MnO8 are presented. Like in the Fe-Mg-O
system the largest challenge in the assessment of the Mg-Mn-O is modeling the spinel phase.
However, in this system two spinels are present, the normal cubic spinel at high temperatures
and a tetragonal spinel at low temperatures. In this work the heat capacities of the tetragonal
MgMn2O4-spinel and Mg6MnO8 were measured as that had not been done previously. The
measured and calculated heat capacity is shown in Figure 17. As for the FeMg2O4-spinel the
degree of inversion at different temperatures for the tetragonal MgMn2O4-spinel is used in the
assessment, which is shown in Figure 18 with experimental data Refs. [125–127]. The phase
diagram data presented in a separate publication by the group at TU Bergakademie Freiberg
[128] as well as other phase diagram data [129–132] are used in the assessment which is
shown in Figure 19 displaying the phase diagram in air. For the equilibria between halite and
cubic spinel it should be mentioned that it is chosen to trust the results which suggests a
higher Mg solubility despite that earlier studies report a lower Mg solubility in the spinel. The
48
reason for this decision is that x-ray diffraction (XRD) showed that the samples with lower
Mg solubility were not cubic. Overall, the work in Paper 5 is an important step toward a larger
thermodynamic description related to ZrO2-reinforced metal matrix composites.
Figure 17 Calculated and measured heat capacity from Paper 5 for a) MgMn2O4 spinel and b) Mg6MnO8.
Figure 18 Calculated degree of inversion versus temperature together with experimental data [125–127].
49
Figure 19 MgO-MnOx phase diagram in from Paper 5 with experimental data [128–131].
4.4 Fe-Ca-O-S
The Fe-Ca-O-S system is essential to describe desulfurization of steel. The sub-system Fe-
Ca-O has previously been assessed [86] and the sub-system Fe-Ca-S has been assessed as part
of this work and is presented in Paper 3 [62]. Assessments of the Fe-O-S and Ca-O-S systems
are presented in in Paper 6. For the Fe-O-S system several experimental studies are found
while the experimental information in the Ca-O-S system is limited. In Figure 20 the
calculated pseudobinaries CaO-CaS and FeO-FeS are shown. The information in the Ca-O-S
system is limited to the eutectic point reported by Ref. [133]. However, due to the relative
similar degree of ionization the liquid can probably be assumed to be ideal. In the Fe-O-S
system some studies, see e.g. [134–137], report phase diagram data. Additionally, a lot of
activity data is found for this system, see e.g. [137–145]. One type of activity data is the
potential phase diagram data obtained at P(SO2)=1 at different temperatures [138–141,145].
The calculated potential diagrams for both the Fe-O-S and the Ca-O-S systems are presented
50
in Figure 21. It should be noted that no ternary interaction parameter was needed for the liquid
in the Fe-O-S system which demonstrates the usefulness of the ionic two-sublattice liquid
model. Moreover, it demonstrates one of the true strength in CALPHAD that a good model
and reliable descriptions of low order systems should give good extrapolation in higher order
systems.
Figure 20 Calculated pseudobinaries of the a) FeO-FeS system with experimental data [134,135] and b) CaO-CaS
with experimental data [133,146].
Figure 21 Calculated potential phase diagram at aSO2=1 for the a) Fe-O-S system with experimental data [138–
141,145] and b) Ca-O-S system.
51
5 Applications
In this chapter several application examples will be given to demonstrate the usability of
the TCOX database and the results obtained in this study. Moreover, this will give an idea of
what kind of equilibrium calculations that is possible to perform related to steelmaking and
sulfide formation. It should be noted that these examples concern equilibria and not multi-
scale modeling of the type discussed in Chapter 2. However, as mentioned in the discussion
about ICME it should be emphasized that equilibrium calculations are the basis for more
advanced models. The results presented here summarize the results in Paper 7.
5.1 Applications of TCOX in its present state
As mentioned in Section 4.1 the TCOX database contains the most important oxide
systems for steelmaking applications. To demonstrate the use of the database some are
presented in this section. It is important to be able to predict the oxygen content in the liquid
steel. In an experimental study the oxygen content in pure iron is measured after it has been
equilibrated with MgAl2O4 spinel for 30 minutes at 1600°C [147]. In Figure 22 the calculated
oxygen and magnesium content in liquid steel is shown together with experimental results.
One thing of great interest in stainless steel production is chromium recovery from the slag. It
is measured with different SiO2 additions [148] and in addition the slag melting temperature is
measured, the results are shown in Figure 23 and Figure 24, respectively.
Figure 22 The calculated and experimental oxygen (red) and magnesium (black) content in liquid steel in
equilibrium with MgOAl2O3 spinel using a) Al2O3 crucible and b) MgO crucible.
52
Figure 23 Calculated chromium recovery as function of SiO2 content together with experimental data [148].
Figure 24 Calculated slag melting temperature as function of SiO2 together with experimental data [148].
53
5.2 Application of sulfide descriptions
As a large part of the work has been focusing on describing sulfide systems and therefore
some calculations related to sulfide formation are performed. As much attention has been
payed to the Fe-Mn-Ca-Mg-S system in this work it is natural to make a calculation related to
sulfide formation in low alloy steels. Not many papers which report equilibration trials
concerning sulfide formation in steels are found. A study performed related to MnS formation
in Si-steel [149] is used to compare the results for low alloy steels with experimental results,
as can be seen in Figure 25. In stainless steels sulfides can also be of importance and for this
reason some calculations related to them are made as well. Since Cr and Ni are major alloying
elements in stainless steels preliminary descriptions were made to include these elements in
the sulfide database. In many cases parameters from the Fe-Me-S systems could likely give a
good estimate for these systems. For example, Oikawa et al. [75] suggest that one could
approximate the Cr-Mn-S system based on the Fe-Mn-S system. The calculated chromium
content in MnS in a stainless steel with 13 % Cr and 0.3 % S is shown in Figure 26 together
with experimental data [150]. The sulfur descriptions in their current state can be used for
calculations related to sulfides in both low alloy and stainless steels.
Figure 25 Calculated mass fraction MnS in a Si-steel a) without Ca and b) with Ca. The solid vertical line
indicates the highest temperature where MnS is observed and the dotted vertical line the lowest temperature without
any MnS observation from the experimental study of this steel [149].
54
Figure 26 Calculated chromium content in MnS as function of Mn content at two different temperatures together
with experimental results [150].
5.3 Sulfur in steelmaking
The ambition of this work has been to include sulfur in the TCOX database. For this
reason the sulfur descriptions are combined with the TCOX database. At this stage only a few
parameters are estimated, in principle missing sulfide end-members, in order to be able to
combine the descriptions. In a study [151] the sulphur content in a steel in equilibrium with
different slags is measured at different sulphur partial pressures. As can be seen in Figure 27
the agreement with the experimental results is quite good. Another study [152] investigates
the sulphur solubility in the CaO-Al2O3-CaF2 system. The calculations shown in Figure 28 are
in good agreement with experimental results. Given that few parameters have been set in
order to combine the TCOX database with the sulfide descriptions the results are really good.
This does not only demonstrate the usability of the descriptions but also demonstrates that the
ionic two-sublattice liquid model is indeed powerful when it comes to extrapolating to higher
order system.
55
Figure 27 Calculated sulphur content at different sulphur partial pressure for four different slags, obtained at
log(PO2)=-10.28.
Figure 28 Calculated (solid lines) and experimental (dotted lines) sulphur solubility in the CaO-Al2O3-CaF2
system.
56
57
6 Conclusions and future work
Modeling of materials is a powerful tool in order to improve the profitability at
steelmaking companies. Already today the ICME approach and the materials genome are
showing their usefulness with real applications. It will most likely have even more impact in
the future. The core of the materials genome, and thus ICME, is the CALPHAD method. As
part of this work the ICME approach has been applied on the vacuum degassing process
combining CALPHAD and genetic algorithms. In that model the process time is optimized
since is it closely related to the cost. The results are really promising but it would be very
interesting to try the methodology at a steel plant. However, the ideas do not necessarily have
to involve the vacuum degassing but could equally well be used on another process, for
example argon oxygen decarburization (AOD) or electric arc furnace (EAF).
Given the importance of having good thermodynamic databases a major part of this work
has involved assessment of sulfur-containing systems of importance for steels. The Fe-Mn-
Ca-Mg-S system has been described fully. Moreover, the approximate descriptions of other
metal-sulfur systems have been added to this description. Finally, the Fe-Ca-O-S system has
been described fully. Generally, the thermodynamic descriptions fit well with experimental
data. However, in some cases experimental data is lacking and efforts should be made to get
more information about these systems. In addition to the sulfur-containing systems, the Fe-
Mg-O and Mg-Mn-O systems have been assessed during this work. Having reliable
descriptions of these systems is important for the usability of the TCOX database.
The sulfur description done in this work is validated using experimental results. In
addition, calculations using the current description in TCOX are compared with experimental
results. On top of this, the sulfur descriptions are combined with the TCOX database to obtain
a preliminary description containing both oxygen and sulfur. The results of the sulfide and
oxide calculations agree well with experimental results. Combining the sulfur descriptions
with the TCOX database also gives good agreement with experimental results. Thanks to the
efforts in this work the next release of TCOX database will include sulfur. Additionally, it
will also include fluorine, niobium and cupper, thanks to parallel efforts. Moreover, efforts are
made to add vanadium as well. The natural next step is to add nitrogen as it is an important
element to consider in the steelmaking process. Since it does not dissolve in the slag it would
probably be relatively easy. In addition, phosphorus should be added as this is also an
58
important element in the steelmaking process but that will probably be more complicated
considering the different oxidation states of phosphorus. Of course, minor alloying elements
like titanium and molybdenum should also be included in the description.
To conclude, CALPHAD is an important modeling tool for materials development and it
is one of the cornerstones in ICME. Using this approach it is possible to develop better
materials and processes faster which is a key to profitability. Thus one can say that
profitability is indeed a function of Gibbs energy. Of course other factors have to be involved
as well of which some can be handled using ICME. Finally, it must be emphasized that it is
up to the steel producers to use the ideas as well as the results presented in this thesis and
other sources to increase their profitability and to make a better world. This would benefit
their stock owners and customers but also the rest of society.
59
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