Phase relations in stainless steel slags

Transcription

c
°
Katholieke Universiteit Leuven
Faculteit Ingenieurswetenschappen
Arenbergkasteel, B-3001 Heverlee (Leuven), Belgium
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any form, by print, photoprint, microfilm or any other means without
written permission from the publisher.
D/2009/7515/16
ISBN 978-94-6018-033-0
Dankwoord
Acknowledgments
Is er een beter moment dan een koude januarizondag om even terug te
blikken op welke schitterende mensen allemaal mee bijgedragen hebben
aan dit doctoraat? Ik had me alvast altijd al zoiets voorgesteld bij het
schrijven van een voorwoord.
Als eerste wil ik Bart bedanken, die me warm heeft gemaakt voor
het hogetemperatuursveld en me alle kansen heeft gegeven om me in het
domein (en haar inwoners) te verdiepen. Ik hoop dat ik je in de komende
jaren nog af en toe gelukkig mag maken door je aan het werk te zetten.
Ook Patrick, een man die zijn gevoel voor finesse tot ver buiten de keuken
weet aan te wenden, wil ik graag bedanken voor de ondersteuning.
Many thanks to prof. In-Ho Jung and his group for the warm welcome
in Montreal and the fruitful cooperation. Thanks also for crossing the
ocean with two pages of questions. Bedankt aan mijn assessoren, prof.
Vleugels en prof. Elsen, en aan prof. Van Gerven, voor het aandachtig
lezen van mijn tekst en het stellen van geı̈nteresseerde vragen, evenals
aan prof. Sansen, voor zijn gewaardeerde voorzitterschap.
De mensen van ArcelorMittal Stainless Genk wens ik te bedanken voor
de boeiende projecten waaraan we samen hebben gewerkt. Ik vermoed
dat we elkaar nog wel tegen komen, crisis of niet.
Ook de collega’s die bij die projecten betrokken waren wil ik graag bedanken: Dirk, een prima onderzoeker en een blij verwonderde vader; Tom,
met zijn doorzicht in onderzoek, ecologie, metallurgie, de maatschappij
en vooral alles daartussen;
Muxing, thanks for sharing your experimental experience and Chinese culture. Frederik, bedankt voor de productieve tijden in de Belgian Lattice Boltzmann Community, waarvan het
resultaat in deze tekst zich beperkt tot bladzijde P-1 en verder.
Annelies, bedankt om ons bureau op te fleuren en sportief te houden,
and thanks to all the other old and new members of the Thermogroup
and of MTM for the very enjoyable lunch breaks, summer picnics, group
i
weekends, barbecues, house warmings, and so on.
Aan de serieuzere kant wil ik Pieter, Eddy, en Luk bedanken voor
het op punt zetten en houden van wat eerst een stuk wetenschappelijk
erfgoed leek, en Paul, altijd bereid om desnoods een kassei te knippen met
een schaar, en de mannen van de werkplaats, waar ook weinig onmogelijk
is. Joris en Marie-Aline wil ik zeker niet vergeten voor het op-, uit- en
ombouwen van de Gero. Joris, wat dat bouwen betreft zullen we nog
niet meteen mogen stilvallen. Tot slot nog Danny en Thierry-van-Imec
voor de experimenten die de tekst niet gehaald hebben, en alle anderen
die hun steentje bijdragen aan de goede wetenschappelijke, technische, en
administratieve werking van MTM.
Het leven in Leuven zou veel minder plezant geweest zijn zonder familie (in het bijzonder de papa, de mama en de zus), vrienden, ex-kotgenoten
die dit nooit zullen lezen, en de
van het CLT.
Tot slot: dankjewel, liefste An, om de afgelopen twee jaar (en ik
ben er zeker van, ook de volgende 104) een pak gekker, grappiger, sneltreinachtigietser en vooral fijner te maken.
Ik wens iedereen veel succes met het afwerken van studies, het schrijven van doctoraten, het uitbouwen van carrières en/of gezinnen, en op
kortere termijn: veel leesplezier.
Sander
ii
Abstract
Computational thermochemistry is an important research tool for hightemperature materials processing. In stainless steelmaking, it proves to
be a useful tool both for process improvement and slag reutilisation.
Thermodynamic databases allow to calculate phase diagrams, complex
phase equilibria, solidification sequences and much more. Although they
can provide good approximations from a limited amount of data, the
databases can only be as correct as the experimental data they are based
on. Therefore, it remains important to measure phase diagram and thermodynamic data, concurrently with model optimisation.
This work studies the high temperature phase relations of stainless
steel slags and their subsystems. In a first part, the principles of both
modelling and experimental determination of oxide phase diagrams are
discussed. In addition, an overview of the present state of knowledge
is given. The available thermodynamic models for the multicomponent
system CaO-CrOx -MgO-Al2 O3 -SiO2 , which contains the major oxides
present in industrial slags, are reviewed. The experimental studies on
the ternary subsystem CrOx -MgO-SiO2 are summarised as well.
In the second part, new experimental and theoretical work is discussed. First, an experimental method to study liquidus-solidus relations
in the system under investigation is proposed. Equilibration, sampling
and microprobe analysis are the different steps to determine the equilibrium phase compositions. Next, the experimental results in the CaOCrOx -MgO-Al2 O3 -SiO2 system are discussed. Systematic differences between FactSage calculations and experimental data are observed, which
appear to be a result of incomplete ternary descriptions, especially in the
CrOx -MgO-SiO2 system. Therefore, this system is studied experimentally in for oxygen partial pressure levels ranging from air to Cr metal
saturation. Finally, an improved description of the CrOx -MgO-SiO2 system is proposed, based on literature data and new results. Although some
differences remain, the new ternary provides better results in the ternary
system, and, moreover, in the higher order systems.
iii
iv
Beknopte samenvatting
Computationele thermochemie is een belangrijk onderzoeksinstrument voor materiaalverwerking op hoge temperatuur. In het kader van roestvaststaalproductie
helpt ze om processen te verbeteren en slak bruikbaar te maken voor hergebruik. Met thermodynamische databanken kunnen onder meer fasediagrammen, complexe fasenevenwichten, en stolsequenties berekend worden. Alhoewel
ze een realistische schatting kunnen vormen uit een beperkt aantal experimentele gegevens, kunnen de databanken nooit betrouwbaarder zijn dan de gegevens
waarop ze gebaseerd zijn. Daarom blijft het belangrijk om, naast het optimaliseren van de thermodynamische modellen, fasediagrammen en thermodynamische
gegevens ook experimenteel te bepalen.
In dit werk worden de faserelaties op hoge temperatuur voor roestvaststaalslakken en hun deelsystemen bestudeerd. In een eerste deel worden de principes
van zowel de modellering als de experimentele bepaling van oxidische fasediagrammen behandeld. De beschikbare modellen in het CaO-CrOx -MgO-Al2 O3 SiO2 systeem, dat de hoofdbestanddelen van industriële slak bevat, worden besproken. De experimentele studies in het ternaire deelsysteem CrOx -MgO-SiO2
worden eveneens samengevat.
In het tweede deel wordt nieuw experimenteel en theoretisch werk behandeld. Eerst wordt een experimentele methode besproken om de liquidus-solidusrelaties in het onderzochte systeem te observeren. Daarna worden de experimentele resultaten in het CaO-CrOx -MgO-Al2 O3 -SiO2 systeem samengevat. Daarbij
trekken systematische verschillen tussen FactSage-berekeningen en experimenten
de aandacht. Deze blijken het gevolg te zijn van onvolledige beschrijvingen van
de ternaire deelsystemen, in het bijzonder CrOx -MgO-SiO2 . Daarom wordt dit
ternair systeem verder bestudeerd, onder zuurstofdrukken variërend van lucht
tot evenwicht met metallisch chroom.
Tot slot wordt een verbeterde beschrijving van het CrOx -MgO-SiO2 systeem
voorgesteld, gebaseerd op gegevens uit dit werk en uit de literatuur. Hoewel er
verschillen blijven, geeft de nieuwe beschrijving betere resultaten in het ternaire
systeem, en eveneens in het hogereordesysteem.
v
vi
Contents
Dankwoord
i
Abstract
iii
Beknopte samenvatting
v
Contents
vi
List of symbols
xi
1 General introduction
1
I
5
Literature
2 Calculating oxide phase diagrams
2.1 The CALPHAD method . . . . . . . .
2.1.1 Calculating phase diagrams . .
2.1.2 Thermodynamic models . . . .
2.1.3 Assessment . . . . . . . . . . .
2.1.4 Advantages and disadvantages
2.1.5 Software . . . . . . . . . . . . .
2.2 Solution models for liquid oxides . . .
2.2.1 Modified quasichemical model .
2.2.2 Ionic two-sublattice model . . .
2.2.3 Associate liquid model . . . . .
2.2.4 Cell model . . . . . . . . . . .
2.2.5 Other models . . . . . . . . . .
2.2.6 Comparative remarks . . . . .
2.3 Conclusion . . . . . . . . . . . . . . .
vii
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CONTENTS
3 Assessments within CaO-CrOx -MgO-Al2 O3 -SiO2
3.1 Based on quasichemical liquid models . . . . . . .
3.2 Based on ionic liquid models . . . . . . . . . . . .
3.3 Based on associate liquid models . . . . . . . . . .
3.4 Based on cell liquid models . . . . . . . . . . . . .
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . .
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4 Slag phase diagram determination
4.1 Studying oxide phase equilibria . .
4.1.1 Static methods . . . . . . .
4.1.2 Quenching methods . . . .
4.1.3 Dynamic methods . . . . .
4.2 pO2 -dependent systems . . . . . . .
4.2.1 Controlling pO2 . . . . . . .
4.2.2 Containing the sample . . .
4.3 Conclusion . . . . . . . . . . . . .
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5 Experiments on Cr2 O3 -MgO-SiO2
5.1 Liquidus information . . . . . . . . . . . . . . .
5.1.1 Liquidus in air . . . . . . . . . . . . . .
5.1.2 Liquidus in reducing conditions . . . . .
5.1.3 Liquidus in equilibrium with metallic Cr
5.2 Solidus information . . . . . . . . . . . . . . . .
5.3 Subsolidus information . . . . . . . . . . . . . .
5.4 Thermodynamic information . . . . . . . . . .
5.5 Conclusion . . . . . . . . . . . . . . . . . . . .
II
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Research
6 Experimental method
6.1 Equilibration and sampling .
6.2 Analysis . . . . . . . . . . . .
6.3 Microstructure interpretation
6.4 Conclusion . . . . . . . . . .
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7 CaO-CrOx -MgO-Al2 O3 -SiO2 liquidus
7.1 Experimental approach . . . . . . . . . . . . .
7.2 Results . . . . . . . . . . . . . . . . . . . . . .
7.2.1 Liquidus . . . . . . . . . . . . . . . . .
7.2.2 Influence of basicity at MgO/Cr2 O3 =1
7.2.3 Solidus . . . . . . . . . . . . . . . . .
viii
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79
CONTENTS
7.3
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9 Assessment of CrOx -MgO-SiO2
9.1 The binary systems . . . . . . . . . . . . . .
9.1.1 MgO-SiO2 . . . . . . . . . . . . . . .
9.1.2 MgO-Cr2 O3 and MgO-CrO . . . . .
9.1.3 Cr2 O3 -SiO2 and CrO-SiO2 . . . . .
9.2 Extrapolation . . . . . . . . . . . . . . . . .
9.3 Description of solid silicate solution phases
9.3.1 (Mg,Cr)2 SiO4 . . . . . . . . . . . . .
9.3.2 (Mg,Cr)SiO3 . . . . . . . . . . . . .
9.4 Description of the liquid phase . . . . . . .
9.5 Optimised phase diagram description . . . .
9.6 Discussion . . . . . . . . . . . . . . . . . . .
9.7 Multicomponent system . . . . . . . . . . .
9.8 Conclusion . . . . . . . . . . . . . . . . . .
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7.4
Discussion: origin of the differences . . . . .
7.3.1 Eskolaite liquidus in CaO-CrOx -SiO2
7.3.2 Spinel liquidus in CrOx -MgO-SiO2 .
Conclusion . . . . . . . . . . . . . . . . . .
8 Ternary system CrOx -MgO-SiO2
8.1 Liquidus in air . . . . . . . . . . . . . . .
8.2 Liquidus in reducing conditions . . . . . .
8.3 Liquidus in equilibrium with Cr . . . . . .
8.4 Liquidus and solidus as a function of pO2
8.5 Conclusion . . . . . . . . . . . . . . . . .
10 Conclusions
127
10.1 Results and evaluation . . . . . . . . . . . . . . . . . . . . 127
10.2 Suggestions for further work . . . . . . . . . . . . . . . . . 129
References
131
III
143
Appendices
A Experimental data
A-1
B Model parameters
B-1
Nederlandse samenvatting
N-1
List of publications
P-1
ix
CONTENTS
Curriculum vitae
x
CV-1
List of symbols
a, b, c
bi
A,B
∆g
E
GE
Gm
i, j ,k
k, l, m
Li,j:k
NA
P
pi
R
T
W
Xi
yi
Yi
adjustable parameters
coordination factor (quasichemical model)
components
contribution to Gm
interaction energy (cell model)
excess Gibbs energy
molar Gibbs energy of a phase
index of components
exponents
interaction parameter (two-sublattice model)
Avogadro’s number
pressure
partial pressure of i
universal gas constant (8.314472)
temperature
reaction energy (cell model)
molar fraction of component i
site fraction of component i on a sublattice
equivalent fraction of component i (quasichemical model)
α,β
η
²ij
φklm
σij
ξij
ω
ω kl
phases
pair exchange reaction entropy (quasichemical model)
pair bond enthalpy (quasichemical model)
ternary interaction parameter (quasichemical model)
pair bond entropy (quasichemical model)
multicomponent composition variable (quasichemical model)
pair exchange reaction enthalpy (quasichemical model)
binary interaction parameter
xi
Components
A
C
CrOx
K
M
S
Al2 O3
CaO
chromium oxide (CrO or Cr2 O3 , or a combination)
Cr2 O3
MgO
SiO2 (component)
Phases
C2 S
E
MS
M2 S
S
Sp
P
Ca2 SiO4 phase, at high T: α-belite
eskolaite phase, (Cr,Al)2 O3
(Mg,Cr)SiO3 phase (protoenstatite)
(Mg,Cr)2 SiO4 phase (forsterite)
SiO2 phase (cristobalite)
spinel phase, Mg(Al,Cr)2 O4
periclase phase, (Mg,Al2/3 ,Cr2/3 )O
xii
Chapter 1
General introduction
Control over the slag is crucial in stainless steelmaking. The composition
of the slag is the key to limit chromium losses or to enhance the lifetime
of the refractory material. Indeed, adapting the slag composition allows
to increase the activity coefficients of chromium oxide, or to decrease
the solubility of the components in the refractory. In addition, if the
electric arc furnace slag can be foamed, substantial energy can be saved by
shielding the arc, the refractory is protected, and the chromium reduction
is further enhanced.
Apart from the question to improve the performance and decrease the
cost of the steelmaking processes themselves, new questions have risen in
the recent years. Process sustainability receives an increasing attention,
and one of the compelling issues is the need to transform slag from a
waste to a valuable side product. This too can only be attained by control over the slag composition and mineralogy, which in turn influences
the mechanical and chemical properties requested for the reuse of slag in,
for example, construction applications. Relationships between mechanical stability, leaching properties or hardness on the one side, and slag
microstructure on the other side, are being unraveled at a quick pace.
An important research tool, both for process improvement and slag reutilisation, is computational thermochemistry. Thermodynamic databases
allow to calculate phase diagrams, complex phase equilibria, solidification
sequences and much more. Although they can provide good approximations from a limited amount of data, the databases can only be as correct
as the experimental data they are based on. Therefore, it remains important to measure phase diagram and thermodynamic data, apart from, or
better concurrently with, model optimisation.
1
CHAPTER 1. GENERAL INTRODUCTION
Objectives
In one sentence, the objective of this work is to improve the thermodynamic description of stainless steel slag. Concretely, the CaO-CrOx -MgOAl2 O3 -SiO2 system, containing the five major components of stainless
steel slag, is studied from both a modelling and an experimental point
of view. The objective is to spot lacunae in the available description,
by tracking the differences down from the multicomponent system to the
ternary systems. Next, this work will also improve the description for the
ternary system CrOx -MgO-SiO2 , where the most conspicuous discrepancies between modelling and experiments are located. By improving this
ternary description, the general agreement of the multicomponent model
with experimental data is also improved.
Outline
In the first part of this text, the principles and methods of both modelling
and experimental determination of oxide phase diagrams are discussed.
After the more general chapters 2 and 4, specific literature for the systems
under investigation is discussed in the separate chapters 3 and 5.
Chapter 2 discusses the basic principles of thermodynamic phase diagram modelling. A Gibbs energy function, dependent on composition
and temperature, is assigned to every phase, which allows to calculate
stable phase relations solely based on Gibbs energy minimisation. Next,
it gives an overview of the different approaches to model liquid oxides.
These different approaches also lead to different databases, available in
different software packages.
Next, the existing descriptions within the multicomponent system
CaO-CrOx -MgO-Al2 O3 -SiO2 are listed in Chapter 3. The approach using
the modified quasichemical model, used in the slag databases of FactSage,
will appear to provide the most advanced description of the system under
investigation.
The following chapters consider the indispensable experimental side
of oxide phase diagram studies. Chapter 4 provides an overview of experimental methods to determine relevant data for oxide systems. Special
attention is paid to the additional challenges posed by systems which are
dependent on the oxygen partial pressure pO2 .
Subsequently, the experimental investigations conducted in the system
CrOx -MgO-SiO2 are reviewed in Chapter 5. As this system is strongly
pO2 dependent, a fascinating range of phase diagram sections is found at
any temperature.
The second part of the text deals with the research conducted during
2
this thesis. First, the methods applied for the experimental investigations are discussed in Chapter 6. Equilibration, sampling and microprobe analysis are the different steps to determine the equilibrium phase
compositions.
Chapter 7 then summarises the experimental results in the CaO-CrOx MgO-Al2 O3 -SiO2 system, for different temperatures, Al2 O3 contents, and
basicity (CaO/SiO2 ) levels. Systematic differences between FactSage calculations and experimental data are observed, especially at low basicity.
These differences appear to be a result of incomplete ternary descriptions.
Therefore, the ternary system where the largest possible improvements are expected, CrOx -MgO-SiO2 , is studied experimentally in Chapter 8. For pO2 levels ranging from air to Cr metal saturation, new experimental data are compared with calculations and literature data, if
available.
As the FactSage model of CrOx -MgO-SiO2 appears incapable of correctly describing the phase diagram, an improved description is proposed
in Chapter 9. Although some differences remain, the new description provides better results in the ternary system, and, moreover, in the higher
order system.
Finally, in Chapter 10, the results are summarised and suggestions are
made for clarifying experimental work and further model improvement.
3
CHAPTER 1. GENERAL INTRODUCTION
4
Part I
Literature
5
Chapter 2
The Calculation of oxide
phase diagrams
The CALPHAD method is a step-wise approach to create large selfconsistent databases for calculations of multiphase, multicomponent equilibria. The databases contain Gibbs energy parameters for thermodynamic models for the different phases. In this chapter, the CALPHAD
concept will first be discussed. The history, fundamentals and work approach will be dealt with. Second, the different thermodynamic models
for liquid oxides will be compared.
2.1
The CALPHAD method
CALPHAD is short for calculations of phase diagrams or, in an updated
formulation, Computer Coupling of Phase Diagrams and Thermochemistry.
In the late 1960’s, a few people such as Kubaschewski, Hillert and
Kaufman had been studying the link between Gibbs energy and phase
stability. Kaufman had worked on calculations of phase diagrams based
on the concepts of “lattice stabilities” and “competition between phases”
[1]. Lattice stabilities designated the Gibbs energy differences between
different crystal forms of a pure metal. Competition between phases, the
idea that a phase diagram represents the phase combinations with the
lowest Gibbs energy from all possible competing phases, meant a radical
focus shift in a time when most phase stability theories and calculations
were based on the electronic structure of the atoms. The conflicting
concepts lead to animated discussions [2], but together with the increasing
computer power, the Gibbs energy approach meant the emergence of a
7
CHAPTER 2. CALCULATING OXIDE PHASE DIAGRAMS
new research field.
The CALPHAD method originated at a meeting organised by Larry
Kaufman in 1973. Spencer [3] describes how some 13 scientists working
on phase diagram calculations, met and discussed how to coordinate their
activities, and how to make their future calculations consistent and compatible with each others work. Their discussions on re-evaluating pure
element stabilities, on the effect of the choice of a ternary interaction
model, and much more, laid the fundamentals of the CALPHAD method.
Despite the progress since 1973, most of these topics keep returning. Since
then a meeting is held every year, a dedicated journal was started, and
calculations have become indispensable in every thermodynamics group.
At present, the link with quantum-chemistry based calculation methods
(ab initio methods) is increasingly explored [4], and the thermodynamic
descriptions are also used in diffusion and microstructural evolution calculations, e.g. in the Dictra program [5] or the phase field method [6].
Also, the approach is no longer limited to constant atmospheric pressure
but is also applied to geological systems at, e.g., up to 1 GPa [7]. This
work will only consider models at constant atmospheric pressure. A detailed description of the method can be found in the book by Lukas et al.
[8].
2.1.1
Calculating phase diagrams
If, for a certain pressure, the Gibbs energies of every phase are known at
all compositions and temperatures, it is possible to construct the phase
diagram. By minimising the total Gibbs energy for every composition
and temperature, the stable phases at every point are known.
For binary system, the well-known common tangent construction is
exactly this minimisation of Gibbs energy. In this construction, the molar
Gibbs energy Gm of the phases is plotted as a function of composition,
as shown in Figure 2.1. Now the Gibbs energy is minimised by searching
for the phase or phase combination with the lowest energy. The Gibbs
energy of a combination of two phases can be found by a mixing rule,
graphically expressed as a line between two points on the curves of both
phases. For some compositions, the energy of a combination is lower
than the energy of either phase. In that case a two-phase region will be
observed. The equilibrium combination of those phases has the lowest
possible molar Gibbs energy, and is therefore defined by the common
tangent. The equilibrium concentrations of B in the solution phases, xαB
and xβB , are found on the points of tangency of the energy curves.
The necessity of a common tangent is commonly derived from the
8
2.1. THE CALPHAD METHOD
equality of chemical potential of each component in both phases [9]. As
chemical potentials are partial molar Gibbs energies, it can be shown that
they are found at the end points of the tangent to the phase’s Gibbs energy
curve on the pure component axis. Hence, when each component has the
same chemical potential in both phases, both phases have compositions
defined by a common tangent.
Gm
b
a
A
a is stable
xBa
xBb
a+b
is stable
B
b is stable
Figure 2.1: Common tangent construction for finding the equilibrium phases
and phase compositions of two phases α and β at constant T and
p.
For multicomponent calculations, the geometric construction becomes
multidimensional, but the minimisation of Gibbs energy is still valid.
Therefore, efficient computer algorithms have been developed, e.g. [10,
11], which evolved to commercially available software packages, which
will be discussed later.
2.1.2
Thermodynamic models
A model is a description of the Gibbs energy of a phase as a function of
temperature and composition. The (molar) Gibbs energy Gm is relative
to the standard state of the atoms, namely the stable structure at 298.15
K and 1 atm. Certain assumptions are made concerning the behaviour
of atoms in the modelled phase. This leads to Gibbs energy terms with
certain adjustable parameters. For example, a very simple model could
look like:
9
Gm = X1 G1m +X2 G2m +RT(X1 ln X1 +X2 ln X2 )+(A+BT)X1 X2 , (2.1)
in which X1 and X2 are the mole fractions of components 1 and 2
in the mixture, and A and B are adjustable parameters. The first three
terms form an ideal solution, where G1m and G2m are the Gibbs energies
of the pure components. Many assumptions are possible, for example,
it can be assumed that all atoms mix randomly, or that the atoms have
fixed positions in the lattice. This leads to different excess Gibbs energies of mixing. Hence, the available models are diverse and range from
simple regular solution models to complex multi-sublattice models for ordered compounds. Most models are available in all commercial software
packages.
The pure components, as well as solids with low or poorly determined
solubilities, are described as stoichiometric compounds. In that case the
Gibbs energy is solely a function of temperature, with adjustable parameters a, b and c:
Gm = a + bT + cT ln T...,
(2.2)
For some more complex solution models, the Gibbs energy of the solution phase is not explicitly expressed. The phase consists of components
of which the Gibbs energy is defined. For example, some models are
described in terms of atom pairs or of associate molecules. Interaction
terms between the compounds are also explicitly entered. In these models, the composition will have an effect on the type and amount of the
components, which can mostly not be expressed analytically. To obtain
the Gibbs energy of the phase at a certain composition, the amounts of
the different components have to be optimised. Hence, the algorithm performing the Gibbs energy minimisation does not only calculate the set of
phases with the lowest total Gibbs energy, it has also to calculate the set
of components within some solution phases with the lowest energy for the
phase under consideration. Detailed examples of thermodynamic models
will be discussed in Section 2.2.
2.1.3
Assessment
In general, the phase diagram or parts of it are known, and the Gibbs
energies of the phases are not. Before the phase diagram can be calculated from the description, the inverse problem has to be solved. The
10
2.1. THE CALPHAD METHOD
procedure in which it is attempted to find the most suitable Gibbs energy descriptions based on the available experimental data is called an
assessment or optimisation.
The approach is step-wise, which means first of all, the standard state
of pure elements is defined. Next, the binary systems are optimised, after
which ternary and higher order systems can be tackled.
Model selection
The first step in developing a thermodynamic description of a binary
system is the choice of suitable thermodynamic models for all phases.
Schmid-Fetzer et al. [12] discuss the recommended practice for producers
of assessed thermodynamic data. On the one hand, the model should
reflect the arrangement of the atoms in the crystal structure as accurately
as possible. On the other hand, the model should be as simple as possible.
A balance between these two requirements should lead to an optimal
description.
Also, the selected model for phases that form multicomponent solutions should be flexibly extendable to higher order systems. Probably
other subsystems have already been optimised. To be compatible with
the other subsystems, the same model has to be used for the phases that
form higher order solutions. In some cases this may not be the most appropriate model for the considered subsystem. When a different model
is selected, a reoptimisation of the other subsystems would be required
to enable the construction of a multicomponent database. Therefore, the
same model will often be chosen to be compatible with earlier work. However, when the model used in the other subsystems is not suited for the
considered subsystem, the most suitable model should be used.
Experimental data
The next step is gathering all available experimental data, which will be
used to determine the unknown parameters in the last step. It is important that all data is considered, and that the original data are collected.
The use of derived data or compilations of phase diagrams may obscure
the actual conditions of the measurements and their errors.
Generally, the data of interest is divided into two groups: phase diagram data and thermodynamic data. It is considered positive when
enough data is available in both groups, because of their different function in the optimisation process. Phase diagram data is data on phase
boundaries, such as liquidus temperatures, solubilities, or primary phase
regions. They are rather phenomenological, as they show what should be
11
the result of the Gibbs energy minimisation. Thermodynamic data, on
the other hand, can give a more direct view on the variation of the Gibbs
energies as a function of temperature and composition. These data could
be heat capacities, activity coefficients, as well as enthalpies of reaction
or solution.
Optimisation of parameters
The last step in an assessment is the optimisation of the parameters itself.
Mostly this will be preceded by a series of trial-and-error calculations to
decide which Gibbs energy terms and interaction parameters are needed
to qualitatively reproduce the experimental data. At this stage it could
appear that certain data are conflicting with other more reliable sources.
It is possible that those data are disregarded in the further process. When
it is known which parameters are needed and which data sets will be used,
an accuracy is assigned to the experimental data sets. Next, a penalty can
be calculated for every data point, determined by the squared difference
between calculated and experimental data multiplied by a weight factor.
The data sets with higher accuracy will also receive higher weights. The
penalty of all data points is summed, and it is attempted to minimise the
total penalty (least squares) as a function of the unknown parameters,
which is essentially a least squares problem. The set of parameters which
gives the lowest (weighted) deviation from the experimental data, gives
the optimised thermodynamic description. As a result of the uncertainties
on the measurements, sometimes an accuracy of the parameter is calculated. However, for complex systems or models, optimisation software
is not always available, and the parameters can be optimised by manual
iterative adjustments.
Iteration
An important aspect of the CALPHAD method is feedback to earlier
steps. Whereas, up to now, the method was presented as step-wise and
straightforward, in practice iteration is necessary. Often, during the definition of parameters, the selected model will appear to be inappropriate.
Or, the ternary data might throw a new light on conflicting data in the
binary. This might lead to different conclusions and a reoptimisation of
the binary. Another possibility is incompatibility of models for phases in
different binary systems, which appear to form a continuous solution in
the ternary.
12
2.2. SOLUTION MODELS FOR LIQUID OXIDES
2.1.4
Advantages and disadvantages
The advantages of thoroughly assessed thermodynamic descriptions are
numerous. Even when experimental data are limited, the descriptions
provide realistic phase diagrams and thermodynamic functions over the
complete relevant composition and temperature ranges. Moreover, consistent lower order assessments can be combined into larger databases,
which together with specialised software packages, provide good estimations of complex multiphase, multicomponent equilibria.
The major disadvantage is that the models are only as reliable as the
available experimental data. When little data are available, a complete
description might raise the impression that the system has been studied
in detail. When using such a description for predictive calculations, care
has to be taken with the results in regions were no experimental data is
available.
2.1.5
Software
Several software packages for thermodynamic calculations have been developed. The most used programs are Thermo-Calc [13], FactSage [14],
MTDATA [15] and Pandat [16]. Except for MTDATA, all of them also
provide tools for optimising model parameters. The differences between
the software packages are in their user-friendliness, calculation strategy
and implemented models. For instance, only FactSage can fully consider the most recent version of the quasi-chemical model. Thermo-Calc
is mostly operated by command line, and Pandat has the only global
minimisation procedure which is claimed never to give metastable results. Users with own databases can make their choice based on this
kind of arguments. However, most users need a calculation tool with
a suitable database for their application. Therefore, the quality of the
available databases will often be the most important argument. For instance, FactSage is well-known for high temperature metallurgical liquids,
whereas Thermo-Calc would have the most detailed steel alloy databases.
2.2
Solution models for liquid oxides
Liquid oxides need particular models, as the different oxides can behave
quite differently. Especially when silicon oxide is present, the thermodynamic description can become quite complex. Silicon oxide, the major
acid oxide, forms large networks, which break up when basic oxides, such
as CaO or MgO, are added. These basic oxides form metal cations which
13
prefer to be surrounded by silicate anions. Hence, there will be a preference for atoms to have certain neighbouring atoms in certain amounts.
This behaviour is called short-range ordering, and can be described in
various ways. The formation of networks can be described quite directly,
as in the ionic two-sublattice model. The formation of second-nearestneighbour pairs can be described by a reaction, as happens in the modified quasichemical model. Or, complex compounds between the oxides
can be postulated to exist in the liquid, which is the approach of the associate model. Even more approaches are possible, which will be discussed
only briefly, as they are not so commonly used.
A good model needs to capture the short-range order interactions
to approximate the resulting configurational entropy as well as possible,
without excessive detail obstructing efficient calculations. The use of
a certain model is, however, not only related to the most appropriate
physico-chemical description of the liquid. The more prosaic reason is
often the possibility to use a certain model within a commercial software
package, such as FactSage or Thermo-Calc. Also, once lower-order optimisations using a particular model have been performed, higher-order
optimisations will often adopt these descriptions, which requires adopting
the same model. As a result, the larger group of compatible optimisations
will grow more easily.
In the following paragraphs, the basic assumptions of the models will
be discussed. First, the modified quasichemical model will be discussed
in some more detail. Next, the ionic two-sublattice, the associate model,
and the cell model will be summarised. The CaO-SiO2 system will be
used as an example, as, firstly, it contains all the typical challenges for
oxidic liquids. The Gibbs energy of mixing deviates strongly from ideality,
with maximum ordering around the composition 2CaO.SiO2 . There is a
miscibility gap at the SiO2 rich side. Secondly, the system is so important for slags that the phase diagram has been described with numerous
models.
2.2.1
Modified quasichemical model
In the modified quasichemical model, as described by Pelton and Blander
[18], the slag is modelled as a mixture of oxides. The components are
e.g. CaO or SiO2 , and when a metal can have different valencies, different components are considered, e.g. FeO and Fe2 O3 . Short-range order
between the metal atoms (Ca-Ca, Ca-Si) is modelled by pair formation.
Hence, only the order between second-nearest neighbours is taken into account, and the behaviour of oxygen is not explicitly considered. Further
14
Figure 2.2: CaO-SiO2 phase diagram based on experiments. [17].
15
improvements of the model have been described in [19–22].
Binary parameters In the original quasichemical model for a liquid
with components 1 and 2, the interaction is described by defining different pair bond energies ²ij and entropies σij for 1-1, 1-2 and 2-2 pairs.
In the modified quasichemical model, the description is changed by a coordination factor bi to find the maximum order at the right ratio, e.g.
XSiO2 =1/3 and XCaO =2/3. Therefore the number of pairs and the Gibbs
energy are defined in terms of equivalent fractions Yi :
Yi = bi Xi ,
(2.3)
The number of pairs of each kind is determined by the minimisation
of Gibbs free energy. The Gibbs free energy is determined by the configurational entropy, and an excess term GE containing two parameters
that can be adapted to fit experimental data. The first parameter is the
molar enthalpy change of the formation “reaction” of 1-2 pairs from 1-1
and 1-2 pairs:
ω = NA (2²12 − ²11 − ²22 ),
(2.4)
where NA is Avogadro’s number. The second parameter is the nonconfigurational entropy of the reaction η, which is defined analogously:
η = NA (2σ12 − σ11 − σ22 ).
(2.5)
Both parameters form the Gibbs energy of the reaction, ∆g12 =
ω − ηT , and may be expanded as functions of the composition and temperature for more detailed fitting, e.g. to reproduce a miscibility gap.
The composition dependent terms for ω are noted as:
ω=
X
ω kl Y1k Y2l ,
(2.6)
in which k and l are chosen integers, of which mostly one or both are
zero. Although more recent versions of the model also use expansion in
the pair fractions [19]. The minimisation of Gibbs energy, determining
the amounts of each kind of pairs, can be done analytically [18]. By
writing the “equilibrium constant” of the pair formation reaction, the
pair fractions can be expressed and filled out in the Gibbs energy of the
reaction. The resulting excess Gibbs energy with the chosen parameters
is:
16
2Y1 Y2
GE = (ω − ηT ) q
¡
¢
1 + 4Y1 Y2 e2(ω−ηT )/2RT − 1
(2.7)
When ω is very negative, A-B pairs are strongly preferred. For example, in basic CaO-SiO2 slag, Ca-Ca and Ca-Si pairs predominate, and
the amount of Si-Si pairs is approximately zero. For the liquid phase, the
following quasichemical parameters were obtained (with ω in J/mol and
η in J/(mol.K)):
ω = −158218 − 37932 YSiO2 − 90148 Y5SiO2 − 439893 Y7SiO2 (2.8)
η = −19.456 + 133.888 Y7SiO2
(2.9)
The resulting Gibbs energy of mixing shows a strong V-shaped minimum at composition of maximum ordering, as shown in Figure 2.4.
Figure 2.3: CaO-SiO2 phase diagram using a quasichemical liquid model from
Eriksson et al. [23].
Higher order description For ternary or higher order systems, the
description of the model is comparable. An energy is defined for every
pair exchange reaction. This energy is mostly known from the binary
system and needs to be extrapolated to the ternary system, as discussed
17
0
Gibbs energy of mixing (J/mol)
-10000
1600°C
-20000
-30000
-40000
-50000
-60000
-70000
0.0
0.2
0.4
0.6
0.8
1.0
xSiO2
Figure 2.4: Gibbs energy of mixing in the quasichemical CaO-SiO2 liquid after
Pelton and Blander [18].
in the next paragraph. However, the Gibbs energy for a multicomponent
system is no longer an analytical expression which can be calculated a
priori. It is the result of a minimisation of the Gibbs energy for a certain
composition, by adjusting the pair fractions, subject to mass balance
constraints. Therefore, the quasichemical model needs specific procedures
to be programmed in the calculation software.
Extrapolation from binary to ternary systems In order to estimate a ternary diagram when the binary systems have been optimised,
an assumption has to be made to approximate the effect of the binary
parameters in the ternary system. Indeed, the interaction parameters
between a set of two components i and j, ωij and ηij are known in the binary system. To know their influence when a third component is present,
Pelton and Blander [18] suggest two methods. The geometric interpretation of those methods is shown in Figure 2.5. For a certain point in
the ternary system, ωij and ηij are approximated. In the symmetric approximation (also called Kohler model), ωij and ηij are assumed constant
along lines of constant ratios of the equivalent molar fractions, Yi /Yj .
In the asymmetric approximation (also called Kohler-Toop model), the
interactions involving the asymmetric component (component 1 in Figure 2.5) are assumed constant at lines of constant Y1 , while ω23 and η23
are constant at constant Y2 /Y3 .
18
Pelton [24] also considers a third model, the Muggianu model, in which
the interactions are constant along lines of constant Yi −Yj . This is an often used and simple approach to extrapolate Redlich-Kister terms, which
are interactions expressed in (Yi − Yj )k . However, it is not considered
very realistic by Pelton [24], and it is never used with the quasichemical
model.
Symmetric and asymmetric models can give greatly different results.
If the binary excess Gibbs energies are large and the interactions are
clearly asymmetric, not choosing an asymmetric model can lead to problematic ternary diagrams. Pelton [24] gives the following example. Component 1 is chemically different, and component 2 and 3 mix ideally and
have exactly the same negative interactions with 1. One would expect
a constant behaviour when substituting 2 with 3, however, when a symmetric model is used, an incorrect region of immiscibility appears.
When only one acidic component is present in an oxide system, the
best results are indeed obtained by taking it as the asymmetric component. For instance, in the CaO-MgO-SiO2 system, CaO and MgO have
comparable strong interactions with SiO2 . These interactions depend on
the basicity (CaO+MgO)/SiO2 , hence on the amount of SiO2 , rather than
on the ratios CaO/SiO2 and MgO/SiO2 independently.
1
w23 = const.
w23 = const.
1
w 31
=
st.
co n
w12 = const.
w31 = const.
w
12
=c
on
st.
3
2
Symmetric approximation
3
2
Asymmetric approximation
Figure 2.5: Symmetric and asymmetric approximations for estimating ωij in a
ternary system from binary values. The same relations hold for ηij .
The composition coordinates are not mole fractions but equivalent
fractions Y1 , Y2 and Y3 . After Pelton and Blander [18].
Ternary parameters If experimental ternary data are available, the
ternary solution model can be further refined by adding ternary terms to
19
the Gibbs energy expression [18]:
k l m
GE = GE
bin + φklm Y1 Y2 Y3
(2.10)
in which GE
bin is the approximation from the binary terms, and φ is
an adjustable parameter, and k, l and m are chosen positive non-zero
integers. With this formulation, the parameters are zero in the binary
systems, so they do not have an effect on previous lower order work. One
or more of these terms can be added. The binary models should of course
be good enough so that the ternary parameters can be small.
In a more recent version of the model by Pelton and Chartrand [20],
a more complex definition [25] for the ternary terms is used. They are
dependent on the chosen extrapolation approximation. For example, in
a symmetric system, the influence of component 3 on the 1-2 interaction
is written as:
µ
∆g12 =
bin
∆g12
+
φklm
12(3)
Y1
Y1 + Y2
¶k µ
Y2
Y1 + Y2
¶l
Y3m ,
(2.11)
which is essentially a 1-2 interaction multiplied with the m-th power of
the fraction of component 3. If component 1 is an asymmetric component,
this reads:
µ
¶m
Y3
bin
klm
k
l
∆g12 = ∆g12 + φ12(3) Y1 (1 − Y1 )
.
(2.12)
Y3 + Y2
In this case, not the relative fractions of Y1 and Y2 are the main variables, but the absolute fraction Y1 is. The effect of the latter parameter
will extend “parallel” to the concentration of component 1, whereas the
the parameter for a symmetric system will extend towards component 3.
This difference is illustrated schematically in Figure 2.6.
Extrapolation to multicomponent systems In Pelton [24], it is
shown how different binary and ternary parameters can be used in multicomponent systems. Also the different assumptions on the extrapolation
of binary terms in the ternary have to be combined. To that end, another
set of composition variables is defined:
ξij = Yi +
X
Yk
(2.13)
k
The summation is made over all components k in asymmetric i − j − k
systems where j is the asymmetric component. This variable is used in the
20
1
1
w10
w10
f102
12(3)
f102
12(3)
3
2
3
2
Symmetric approximation
Asymmetric approximation
Figure 2.6: Schematic illustration of the region in a ternary diagram where a
10
is active in
ternary parameter is active. The binary parameter ω12
the 1-2 binary, more on the side of component 1. The ternary parameter φ102
12(3) influences the 1-2 interaction on the side of component 3, but the exact location depends on the chosen extrapolation
scheme.
above equations instead of Yi in most, but not all, places. It is clear that
this complicates the model even further, but such a description is needed
to be able to treat any subsystem freely as symmetric or asymmetric.
Essentially, the description in [24] provides a complex but reasonable
summation of parameter contributions from different binary and ternary
system with different descriptions, even with other than quasichemical
interaction parameters.
2.2.2
Ionic two-sublattice model
In the ionic liquid model [26, 27], the components of the slag are ions.
For slags, metal cations (Ca2+ , Fe3+ ), oxygen (O2− ) and silicate anions
2−
(SiO4−
4 and sometimes SiO3 ) are considered. The mixture also contains
0
the neutral SiO2 , which is used to represent the pure liquid silica network.
Sometimes other complex ions are considered for a better description, for
example, AlO−
2 [28, 29]. The cations and anions are divided over two
sublattices, indicating that the components on one sublattice have the
components of the other sublattice as their nearest neighbours. Cations
mix on one sublattice and anions mix on the other. The neutral variants
mix on the same sublattice as the other ions of the same metal. For
0
example, the CaO-SiO2 system is noted as (Ca2+ )p (O2− , SiO4−
4 , SiO2 )q
by Hillert et al. [30]. The indices p and q indicate that the number of
21
sites on both sublattices varies with the composition. Without SiO2 ,
the system is described by (Ca2+ )0.5 (O2− )0.5 . Without CaO, the neutrality condition forces the silicon oxide to be neutral, and only (SiO02 )1
remains. At the composition of maximum ordering, the system will approach (Ca2+ )0.67 (SiO4−
4 )0.33 . Hence, the composition influences the type
of species present, which describes the ordering in this model.
The Gibbs energy of certain combinations, such as the pure liquid oxides and (Ca2+ )2 (SiO4−
4 ), is defined first. For detailed fitting, interactions
Li,j:k can be defined between components i and j on one lattice in the
presence of a certain component k on the other lattice. The influence of
such a term on the Gibbs free energy is:
GE = yi yj yk Li,j:k ,
(2.14)
in which y is the site fraction, i.e. the fraction of the component on
the sublattice. Li,j:k can be temperature and composition dependent.
The model has been updated for improved compatibility with other
models. The version by Sundman [27] is equivalent with a simple substitutional regular solution model for a single sublattice. This means, if only
one sublattice is used, the model and the interaction parameters formally
reduce to the commonly used regular solution model. Moreover, when
composing the sublattice model, interactions of components that reside
on the same sublattice might already be optimised with a regular solution model. These interactions can then be implemented directly into the
two-sublattice model. However, the consideration of the interaction of
components without a second sublattice may only be sensible for neutral
species and not for ions.
In Figure 2.7 the CaO-SiO2 phase diagram from Hillert et al. [30],
updated for rankinite (3CaO.2SiO2 ) [31], is shown. The Gibbs energy of
(Ca2+ )2 (SiO4−
4 ) is expressed as
GLiq
(Ca2+ )
4−
4 (SiO4 )2
Liq
−1
= 2GLiq
CaO + 2GSiO2 − 390979 J mol ,
(2.15)
The excess Gibbs energy in the liquid is given by interaction terms on
the anion sublattice:
´
L + 1 L(yO2− − ySiO02 ) + 2 L(yO2− − ySiO02 )2 (2.16)
´
³
+ 2ySiO4− .ySiO02 . 0 L + 1 L(ySiO4− − ySiO02 ) + 2 L(ySiO4− − ySiO02 )2
GE = yO2− .ySiO02 .
4
22
³
0
4
4
Figure 2.7: CaO-SiO2 phase diagram using an ionic two-sublattice liquid
model from Hillert et al. [31].
23
As there is only one cation on the other sublattice, the third component k from equation 2.14 is not explicitly considered here. The parameters n L are linear functions of temperature (in SI units):
2.2.3
0
L = −37.687 T
1
L = −153124 + 65776 T
2
L = −33772 − 11.132 T
3
L = −39132
(2.17)
Associate liquid model
In the associate liquid model [32], the components in the liquid are not
only the pure oxides, but also compounds between them, the so-called
associates. These compounds mostly correspond to existing solid compounds, but can also be postulated. They contain up to three different
elements and oxygen. All associates are multiplied with a stoichiometry
factor to have exactly 2 non-oxygen atoms, for a consistent “molecular
size”, even if this makes the associates look rather unphysical. This is
noted by adding a colon and the stoichiometry factor after the notation
with integer stoichiometry. As an example, in the CaO-SiO2 system,
Besmann and Spear [33] consider the following components in the liquid: the end-member species Ca2 O2 and Si2 O4 plus the associate species
Ca2 SiO4 :2/3 (i.e. Ca4/3 Si2/3 O8/3 ), Ca3 SiO5 :1/2, and CaSiO3 .
A Gibbs free energy of formation is attributed to the complex components in the liquid. This energy can be experimentally observed, e.g. for
an existing solid compound of which the heat of fusion and the capacity
in the liquid is known, or estimated. Originally, the pure oxides and the
associates were all assumed to mix ideally in the liquid. In the more recent work, detailed fitting of miscibility gaps is performed by defining a
limited number of regular solution terms for positive interactions between
the components. For any composition, the fraction of each component can
be calculated by minimisation of the Gibbs energy. Also here, changes in
compositions lead to changes in the species present, and to the desired
short-range order behaviour.
In Besmann and Spear [33], the Gibbs energy of the associate species
in the CaO-SiO2 system is not given. The excess energy, determined by
“trial and error”, is given by:
GE = X(1 − X) [(141000 − 65T) + (−10000 − 10T)(1 − 2X)] ,
24
(2.18)
in which X is the mole fraction of Si2 O4 . The resulting phase diagram
is shown in Figure 2.8.
Figure 2.8: CaO-SiO2 phase diagram using an associate liquid model from Besmann and Spear [33].
2.2.4
Cell model
The Kapoor-Frohberg cell model [34] describes the liquid as a mixture
of symmetric (i-O-i) and asymmetric cells (i-O-j). For example, in the
CaO-SiO2 system, Ca-O-Ca, Si-O-Si and Ca-O-Si are considered. The
Gibbs free energy of the symmetric cells corresponds to that of the pure
liquid oxides. The Gibbs energy of the asymmetric cells is modified with
an excess term, expressed as a reaction energy term W for the formation
of one mole of cells. W can be dependent on the composition. Although
the formulation is different, the model concept and the resulting Gibbs
energy seem to be quite close to the quasichemical model [35, 36], as the
cell model also describes some kind of reaction from symmetric secondnearest neighbour pairs to asymmetric pairs or cells. Besides the reaction
25
energy W, also an interaction energy E between Si-O-Si and asymmetric
cells is defined.
The model was used by Gaye and Welfringer [37] for the description
of slags in iron and steel production (IRSID model, also called CEQSI)
and applied to inclusion formation [38]. However, the description of the
solid phases in the IRSID model is very basic. The description may be
good for multicomponent slags in equilibrium with iron, but the different
binary and ternary systems do not correspond to experimental data [35].
However, the cell model is also used for qualitative optimisations starting from binary systems. For example, the CaO-SiO2 phase diagram according to Taylor and Dinsdale [39] is given in Figure 2.9. Also, the Gibbs
energy of mixing in the liquid is given in Figure 2.10. The optimised parameters in the liquid phase are (in J/mol):
W = −49953.11 − 6906.437 XSiO2
E = −52244.52 + 106715.81 XSiO2 − 43390.716
2.2.5
(2.19)
X2SiO2
(2.20)
Other models
Different other models have been applied to oxidic liquids. For instance,
Hoch [40] used a polynomial representation of liquid complexes. Kim and
Sanders [41] used a standard regular solution model. The stoichiometricMargules model by Berman and Brown [42] can also be mentioned. However, all of these approaches were limited to one or a few optimisations,
and it is therefore unlikely that they will lead to large multicomponent
databases.
2.2.6
Comparative remarks
As can be seen on CaO-SiO2 phase diagrams in Figures 2.3, 2.7, 2.8, and
2.9, all models are capable of providing a good description for this complicated system. It is also clear from Figures 2.4 and 2.10 that the eventual
shape of the mixing energy in the liquid is rather similar. Only, the description of the miscibility gap in the cell model [39] leads to somewhat
higher demixing temperatures, but, according to the authors, this could
probably be covered by assigning more weight to the miscibility gap data
in the assessment. The short-range order and the miscibility gap can thus
be covered with any of the models. Hence, the question is not whether
the models are suitable for two-component slags. Rather, the results on
26
Figure 2.9: CaO-SiO2 phase diagram using a Kapoor-Frohberg cell liquid
model from Taylor and Dinsdale [39].
27
0
Gibbs energy of mixing (J/mol)
-10000
3000 K
2200 K
-20000
-30000
-40000
-50000
-60000
-70000
0.0
0.2
0.4
0.6
0.8
1.0
xSiO2
Figure 2.10: Gibbs energy of mixing in the cell model CaO-SiO2 liquid after
Taylor and Dinsdale [39].
extension to ternary and multicomponent systems will be a criterion to
evaluate the validity of a model.
The quasichemical model leads to complicated excess energies, but
the ternary interaction terms are mostly limited and not too complicated.
The model was also criticised by Saulov [43], as it can lead to physically
unrealistic pair fractions due to the complex equations. In their reply,
Pelton and Chartrand [44] state these unrealistic solutions can only occur
with unrealistic parameters.
In the two-sublattice model, extension to ternary systems often leads
to miscibility gaps or deviations which are hard to eliminate using ternary
interactions [29, 35].
The associate and cell models have quickly been extended to multicomponent systems, but the quality of the published sections seems to be
inferior to those produced with datasets of the quasichemical and twosublattice models.
Fabrichnaya et al. [35] compared the two-sublattice model with the cell
model for the MgO-Al2 O3 -SiO2 system. They concluded that, whereas in
the binary systems the models yield comparable phase diagrams, extension to the ternary leads to greatly different results. Figure 2.12 shows
a comparison of the liquidus surfaces using both models. The primary
phase fields have irrealistically curved shapes in the two-sublattice model.
When comparing with the accepted experimental diagram in Figure 2.11,
28
2.3. CONCLUSION
it is clear that the cell model is superior in this case. Possibly, the introduction of a new species in the two-sublattice model, e.g. AlO−
2 as
in [28], could have lead to better results. However, this species was not
needed for the binary systems. This means the binary descriptions are
not readily extendable to the ternary for this system. The same system
has been optimised with the quasichemical model by Jung et al. [45], with
satisfying results. The primary phase fields are similar to the calculation
using the cell model, or possibly even closer to the experimental diagram,
as shown in Figure 2.13.
Liq2
Cr
Tr
Ppx
Cord
Mul
Sap
Ol
Sp
Al2O3
Hal
Figure 2.11: Experimental MgO-Al2 O3 -SiO2 liquidus surface. [17] Abbreviations from [35] added for comparison with Figure 2.12-2.13.
2.3
Conclusion
This chapter first discussed the basic principles of thermodynamic phase
diagram modelling. Only with an appropriate model, it is possible to
find a good description of systems exhibiting short range order, such
29
Figure 2.12: Comparison between calculated MgO-Al2 O3 -SiO2 liquidus surfaces using the Kapoor-Frohberg cell model (left) and the twosublattice ionic liquid model (right), from Fabrichnaya et al. [35]
SiO2
Liq2
Cr
Ppx
Tr
Cord
Ol
Sap
Hal
MgO
Mul
Sp
weight percent
Al2O3
Al2O3
Figure 2.13: Calculated MgO-Al2 O3 -SiO2 liquidus surface using the quasichemical model, after Jung et al. [45]
30
2.3. CONCLUSION
as liquid oxides. Therefore, secondly, this chapter discussed the various
approaches to model liquid oxides. The solution model for the liquid
determines the possibility to extend the model to multicomponent systems, and the compatibility of new optimisations into existing databases.
The modified quasichemical model was discussed in most detail, as it
integrates the most versatile extrapolations to multicomponent systems,
and has been proven very suitable to model oxide systems. In the next
chapter, it will appear the most detailed description of the multicomponent system CaO-CrOx -MgO-Al2 O3 -SiO2 has been developed using the
modified quasichemical model.
31
32
Chapter 3
Thermodynamic
assessments within the
CaO-CrOx-MgO-Al2O3-SiO2
system
The CaO-CrOx -MgO-Al2 O3 -SiO2 system consists of the five major components in stainless steel slags. Several CALPHAD-assessments have
been performed in the system under consideration. The larger set fits
within the quasichemical framework and is part of the FACT-databases.
Also using other models, considerable parts have been optimised.
In what follows, the notation “CrOx ” will be used for the concept
“chromium oxide”, be it CrO or Cr2 O3 or a combination of both. Chromium oxide in the liquid solution needs at least two components to be
modelled. However, those components (e.g. CrO and Cr2 O3 ), are never
modelled separately, and an optimisation with chromium oxide should
always contain both valencies to be complete. Therefore, the pO2 dependent system CaO-CrOx -SiO2 will be called a ternary system, although
strictly speaking, four components are needed to describe it.
3.1
Based on quasichemical liquid models
All ten binary systems have been optimised. When there are several
assessments, only the most recent one is given.
The CaO-CrOx and CrOx -Al2 O3 systems were assessed by Degterov
and Pelton [46]. Wu et al. [47] considered the CaO-MgO system. CaOAl2 O3 was taken care of by Eriksson and Pelton [48]. The CaO-SiO2
33
CHAPTER 3. ASSESSMENTS WITHIN CaO-CrOx -MgO-Al2 O3 -SiO2
MgO
Al2O3
CrO
Cr2O3
CaO
MgO
CrO
Cr2O3
CrO
Cr2O3
CaO
Al2O3
SiO2
CaO
CrO
Cr2O3
CaO
Al2O3
SiO2
CaO
MgO
SiO2
MgO
CrO
Cr2O3
Al2O3
Figure 3.1: Approximation assumptions for the optimised ternary systems using the quasichemical model within CaO-CrOx -MgO-Al2 O3 -SiO2 .
Symmetric approximations are indicated by a slanted line, whereas
asymmetric approximations are indicated by a line of constant concentration of the asymmetric component.
system was optimised by Eriksson et al. [23]. The MgO-SiO2 system was
considered by Wu et al. [49]. Degterov and Pelton [50] modelled the CrOx SiO2 system, whereas Eriksson and Pelton [48] modelled SiO2 -Al2 O3 . To
complete the list, both CrOx -MgO and MgO-Al2 O3 were optimised by
Jung et al. [51]. All optimisations with CrOx use the components CrO
and Cr2 O3 , and the interactions between these components are taken
from the description for CrO-Cr2 O3 from Degterov and Pelton [46].
Seven out of ten ternary systems have been optimised. The CaOMgO-SiO2 system was optimised by Jung et al. [52]. Eriksson and Pelton
[48] considered CaO-Al2 O3 -SiO2 , whereas CaO-CrOx -SiO2 was assessed
by Degterov and Pelton [53]. The systems CaO-MgO-Al2 O3 and MgOAl2 O3 -SiO2 were modelled by Jung et al. [45]. An optimisation of SiO2 MgO-Al2 O3 was performed by Degterov and Pelton [50], and finally, the
MgO-CrOx -Al2 O3 system has been considered by Jung et al. [51]. CaOCrOx -MgO, CaO-CrOx -Al2 O3 , and CrOx -MgO-SiO2 have not been optimised to date. The choice of symmetric and asymmetric approximation
assumptions (cfr. section 2.2.1) is shown in Figure 3.1. It is noteworthy
that Al2 O3 is mostly considered as a symmetric component, but is asymmetric in CaO-MgO-Al2 O3 . This is because in the vicinity of only very
basic components such as CaO and MgO, Al2 O3 behaves as an acidic, or
network-forming, component.
All optimisations are compatible, and a coherent multicomponent
database is available within the FactSage database package [54]. For the
non-optimised systems, it is not explicitly published which approximation assumptions are used in the database. However, when no exceptions
34
3.2. BASED ON IONIC LIQUID MODELS
are implemented, SiO2 is considered as an asymmetric component, and
systems without SiO2 are considered symmetric.
3.2
Based on ionic liquid models
For systems containing chromium within the quinary system under consideration, only the Cr-Cr2 O3 and Al2 O3 -Cr2 O3 systems have been optimised using an ionic liquid. Povoden et al. [55] considered Cr-Cr2 O3 using
a (Cr3+ ,Cr2+ )p (O2− ,Vaq− )q description for the liquid. For the Al2 O3 Cr2 O3 system, Saltykov et al. [56] only considered Cr3+ and no Cr2+ in
the liquid. For the remaining quaternary system CaO-SiO2 -MgO-Al2 O3 ,
all 6 binary systems and all 4 ternary systems have been optimised.
The CaO-SiO2 system was optimised by Hillert et al. [31], as shown in
Figure 2.7, and SiO2 -MgO was optimised by Hillert and Wang [57]. Both
systems were slightly modified by Huang et al. [58] based on ternary
information. An optimisation of CaO-MgO was performed by Hillert and
Wang [59]. CaO-Al2 O3 was modelled by Hallstedt [60] and modified by
Mao et al. [61] to include AlO−
2 , as this component was needed for the
ternary system. The MgO-Al2 O3 binary was also optimised by Hallstedt
[62] and updated by Mao et al. [61]. SiO2 -Al2 O3 was studied by Mao
et al. [28].
The ternary system CaO-SiO2 -MgO was assessed by Huang et al. [58].
CaO-MgO-Al2 O3 was optimised by Hallstedt [63]. MgO-Al2 O3 -SiO2 was
studied by Fabrichnaya et al. [35] although the results were better using
the cell model, as shown in Figure 2.12. Finally, Mao et al. [29] modelled
the CaO-SiO2 -Al2 O3 system, including the component AlO−
2 for the first
time.
The optimisations are included in the ionic liquid database for ThermoCalc (ION2 database).
3.3
Based on associate liquid models
The optimisations with associate liquids are mostly aimed at higher order
systems without the traditional stepwise expansion from the binary systems. Initially, the correct prediction of vapour pressures was the main
concern. Hastie and Bonell [64] started with glasses within Na2 O-K2 OCaO-MgO-Al2 O3 -SiO2 and extended the range to Li2 O-Na2 O-K2 O-CaOMgO-Al2 O3 -Fe2 O3 -SiO2 [32]. However, no phase diagrams were calculated as this was not the focus at that time.
In the quinary system under consideration, some binary and ternary
35
CHAPTER 3. ASSESSMENTS WITHIN CaO-CrOx -MgO-Al2 O3 -SiO2
systems have been optimised. Ball et al. [65] modelled the CaO-Al2 O3 SiO2 system as part of the CaO-Al2 O3 -SiO2 -UO2 -ZrO2 system. Also the
Al2 O3 -SiO2 was optimised as part of a large nuclear waste glass system by
Spear et al. [66]. Besmann and Spear [33] optimised the CaO-SiO2 system, as shown in Figure 2.8, and the quaternary Na2 O-Al2 O3 -B2 O3 -SiO2 ,
of which only the Na2 O-Al2 O3 subsystem was calculated. Later, focused
lower order optimisations were performed with the associate model. Besmann and Kulkarni [67] assessed the systems Al2 O3 -Cr2 O3 , Cr2 O3 -SiO2 ,
and Al2 O3 -Cr2 O3 -SiO2 , important for refractory materials, but without
considering other valencies of Cr. Recently, also the Al2 O3 -SiO2 system
was reoptimised in great detail by Yazhenskikh et al. [68].
Large multicomponent databases are available for use with MTDATA.
3.4
Based on cell liquid models
The cell model was applied for a large Fe-containing slag database which
is available in Thermo-Calc (SLAG2 database). The slag phase in this
database contains the 12 elements Al, Ca, Cr, Fe, Mg, Mn, Na, Si, O,
S, P and F [69]. However, the model has not been used for many detailed optimisations of lower order systems. In the considered quinary
system, only a few phase diagram calculations have been published. The
CaO-SiO2 system was optimised by Taylor and Dinsdale [39], as shown
in Figure 2.9. The MgO-Al2 O3 -SiO2 system and its subsystems were
assessed by Fabrichnaya et al. [35]. Zhang et al. [70] considered the CaOAl2 O3 -SiO2 system.
3.5
Conclusion
The quinary system CaO-CrOx -MgO-Al2 O3 -SiO2 contains several important ternary systems, which have been optimised with different models
and from different perspectives. Several multicomponent databases covering the system are available. However, most of them are not based
on detailed optimisations, certainly not for Cr-containing systems. The
FactSage database, on the other hand, does use a solid amount of wellassessed work using the quasichemical model. From the overview in this
chapter, it is clear that this database represents the state of the art thermodynamic slag model for the system under consideration. Therefore, it
will be used as a reference for comparison with the experiments, and a
starting point for further modelling in the final chapter.
36
Chapter 4
Experimental methods for
slag phase diagram
determination
This chapter gives an overview of the methods to determine phase equilibria in slag systems. First, some general remarks are made on possible
static and dynamic experimental techniques. Next, the specific aspects of
studying phase relations in pO2 -dependent oxide systems are discussed.
In Chapter 6, the quenching methods used in this work will be discussed
in more detail.
4.1
Studying oxide phase equilibria
Jak and Hayes [71] discuss the experimental determination of phase equilibria in oxide systems. An overview of experimental methods used in
oxide phase equilibria determination is given in Table 4.1. A first distinction is made between dynamic and static methods.
4.1.1
Static methods
In static methods, a certain property of the sample is measured at high
temperature. For example, in high temperature XRD, an X-ray spectrum
of an equilibrated sample is measured ‘in situ’, or in hot stage microscopy,
the microstructure of the sample is observed at high temperature. In
EMF measurements, the electromotive force over an electrochemical cell
at high temperature is measured. From this quantity, thermodynamic
properties such as activities or Gibbs energies of reaction can be derived.
37
CHAPTER 4. SLAG PHASE DIAGRAM DETERMINATION
Table 4.1: Summary of the principal experimental methods used in phase equilibrium determination in oxide systems, from Jak and Hayes [71].
Methods
STATIC METHODS
Electrochemical
Vapour pressure
X-ray powder diffraction
Hot stage microscopy
Calorimetry
Equilibration/quench/
analysis
DYNAMIC METHODS
Thermogravimetric analysis
Differential thermal analysis
38
Suitability for oxide systems
Thermodynamic properties (e.g., ai , ∆G, ∆S)
Knudsen - low metal vapour pressure,
non-aggressive slags
Reactive gas equilibration - low metal
vapour pressure - pO2 control
Isopiestic (constant p) equilibria high metal vapour pressures
Phase detection/identification
Extensive solid solutions
- lattice parameters at temperatures
Liquidus of low vapour pressure systems,
transparent liquids
Enthalpies, ∆H
- of formation
- of solution
- of phase transition
Liquidus of high viscosity fluids
(e.g. high silica slags)
Solid state phase equilibria
Gas/solid reactions
Gas/liquid reactions
Rapid phase transitions (e.g. melting
point of congruently melting compounds)
Liquidus/solidus of low viscosity liquids
4.1. STUDYING OXIDE PHASE EQUILIBRIA
The advantage of the static approach is that temperature, pressure and
certain activities (such as pO2 ) can be precisely controlled. Also, it is
mostly possible to allow sufficient time to reach complete equilibrium.
However, the time can be limited due to reactions with the vapour phase
or the containment materials.
4.1.2
Quenching methods
The quenching technique can be considered as a static method, as the
sample is equilibrated in controlled conditions. However, the equilibration is followed by rapid cooling, whereafter some properties are measured
or observed at room temperature. If the phases present at high temperature can be conserved at room temperature, quenching methods have a
superior accuracy and convenience as a result of the possibility to perform
the measurements at room temperature. Phase relations and solutions in
the solid state can be studied by this technique, as well as phase relations
involving the liquid, in cases where the liquid can be quenched to a glass
phase, or a well recognisable fine crystalline structure.
In the first studies on oxide phase diagrams, executed by geologists,
the analysis after quenching was performed by petrographic microscopy.
As the phases were distinguished by their optical properties, those properties were often measured for newly encountered phases. Later, also industrially relevant slag systems were examined with this approach. Further
on, X-ray diffraction was used for phase identification and characterization. Possibly the greatest improvement of the quenching technique, however, was the coupling with electron-probe microanalysis (EPMA). Up to
that time, the limits of stability for a certain phase were determined by
its presence or absence in the microstructure. For liquidus determination,
the quenched samples had to be examined for the presence of a precipitated primary phase. Hence, several experiments at closely interspaced
compositions and temperatures had to be performed in order to accurately define the phase boundaries. Moreover, the accuracy was limited
by the ability to detect small quantities of the primary phase. EPMA, on
the other hand, allows to measure the composition of quenched liquids or
solid solutions, thus defining the limits of stability much more precisely.
The difference can be compared to stepping from integer to float numbers, or from raster to vector graphics. Also, possible inaccuracies by
evaporation of volatile metals [72, 73] or weighing errors are eliminated
due to analysis after the experiment. Nevertheless, the approach without
compositional analysis of the liquid is still used [74].
Older, but equivalent techniques can be found in the segregation or
39
saturation techniques, schematically illustrated in Figure 4.1. In the segregation technique, the sample is held below the liquidus, and the primary
phase (or multiple solid phases) are allowed to segregate. After the equilibration, the phases are sampled separately or separated physically or
chemically. The individual phases are then chemically analyzed. In the
saturation technique, the primary phases are added as a pellet or used as
a container material to equilibrate with the liquid. This requires known,
preferably stoichiometric, primary phases. By sampling or by mechanical
means, the saturated liquid can be separated and chemically analyzed.
precipitation
saturation
segregation
by pellet
liquid phase
saturating phase
inert material
by crucible
Figure 4.1: Different experimental set-ups for equilibration of a liquid with one
or more solid phases.
4.1.3
Dynamic methods
Dynamic techniques are based on the measurement of a property change
occurring during a phase transformation in the system. For example,
thermogravimetric analysis measures the weight of a sample as a function
of temperature, and is therefore suited for reactions or phase transformations involving the gas phase. In differential scanning calorimetry (DSC),
the heat input into or output from the sample and a reference sample is
measured during heating and cooling. During phase transformations or
reactions, the enthalpy of reaction or transformation will lead to peaks
in the heat flux. In differential thermal analysis (DTA), the heat flux to
40
4.2. PO2 -DEPENDENT SYSTEMS
the sample and the reference is equal, and the temperature difference is
measured.
The disadvantage to measure equilibrium data with any dynamic technique is that the system is, by definition, in a non-equilibrium state. In
systems with slow phase transformations, dynamic measurements are easily disturbed by kinetic and metastability effects. For example, it can be
difficult to measure an exact transformation temperature using DSC if
the transformation involves solid state diffusion. The maximum enthalpy
release in DSC measurements is to be expected at invariant points, such
as eutectics, where all of the liquid is transformed into solid phases at a
single temperature, or vice versa. If solidus and liquidus temperatures are
differing strongly, solidification or melting will occur over a wide range of
temperatures. Due to the spread release of the heat of transformation in
these cases, the uncertainty about the start and end temperature of the
transformation can be high.
Also, high-silica oxidic liquids are known to exhibit slow nucleation
and growth and easy glass formation. For these reasons, Jak and Hayes
[71] consider dynamic methods not appropriate for liquidus determination
in highly-viscous slags, and only useful for fast reacting systems, such as
some displacive, diffusionless transformations and highly fluidic systems.
However, despite their limitations, dynamic techniques have been used
successfully for silicate systems. For example, Claus et al. [75] determined
the melting temperatures in the Li4 SiO4 -Li2 SiO3 region of the Li2 O-SiO2
system using DTA, and Kolitsch et al. [76] used DSC to measure the
ternary eutectic temperature in Gd2 O3 -Al2 O3 -SiO2 .
4.2
Studying phase relations in pO2 -dependent
systems
Slag systems without metals with multiple valencies can be studied relatively easily in air. Most industrial slag systems, however, contain a
transition metal that is to be reduced. Hence, these systems are dependent on the oxygen partial pressure in the gas phase. Often, the oxides of
the same metal with different valencies behave completely different in the
liquid. To study these systems in conditions that are comparable to those
in industrial processes, the oxygen partial pressure mostly needs to be in
the region where the reduction and hence the rapid changes happen, and
therefore needs to be accurately controlled. Furthermore, the choice of
crucible and support materials can be limited by the chosen atmosphere.
41
4.2.1
Controlling pO2
There are different possibilities to control the oxygen partial pressure. In
earlier experiments, it was sometimes attempted to control the amount of
oxygen and the metal valency in the sample rather directly, by enclosing
the sample in a sealed container. However, this approach is reliable nor
precise. Therefore, the sample is now mostly equilibrated in an atmosphere inducing a certain pO2 . The simplest approach is to use a flow
of gas containing a certain concentration of oxygen, and gases that are
inert or negligible. For example, using air is an easy approach to impose
a pO2 of 0.21 atm. However, the flow of gas, as well as the concentration
of oxygen, need to be abundant, so that the oxygen partial pressure does
not change by reactions with the sample. Therefore, it is not possible
to impose reducing oxygen pressures with this approach. Reactive gases
provide a solution for a large range of oxygen pressures. In this approach,
two reactive gases, such as CO and CO2 , or H2 and H2 O are mixed. At
high temperature, the ratio of the gases leads to a dynamic equilibrium in
the gas phase according to the equilibrium constant of the gases’ reaction,
e.g.:
1
CO + O2 CO2 ,
2
∆G◦ = −281885 + 85.678 T
(4.1)
∆G◦ values are averaged values from Rao [77], detailed values as a
function of temperature can be found in Chase [78].
As the partial pressures of the reactive gases are several orders of
magnitude larger than the partial pressure of oxygen, the oxygen partial
pressure is not affected by the addition of small amounts of oxygen. When
the amounts of reactive gases used are large enough, the reactive gases
can form a buffer providing oxygen or absorbing oxygen from the sample
without notably changing their ratio.
As CO is a highly toxic gas it is sometimes preferred to work with
mixtures of H2 and H2 O:
1
H2 + O2 H2 O,
2
∆G◦ = −247392 + 55.849 T.
(4.2)
In both cases, the oxygen partial pressure can be easily calculated as
a function of the volumetric gas flow ratios:
42
µ
=
−2
Keq
or =
−2
Keq
pO2
µ
¶−2
CO
CO2
(4.3)
H2
H2 O
¶−2
,
(4.4)
when the effect of the reaction itself on the imposed gas ratio is neglected. The respective equilibrium constant Keq is calculated as
Keq = e
−∆G◦
RT
.
(4.5)
It is interesting to note that the equilibrium pO2 is not dependent on
the total pressure of the reactive gases, but only on their ratio. Therefore,
the mixture can be diluted with an inert gas without affecting the pO2 .
As H2 O vapour is difficult to control, another option to avoid the
use of bottled CO gas is to use a mixture of CO2 and H2 . The major
equilibrium will then be:
CO2 + H2 CO + H2 O,
(4.6)
◦
∆G = 34493 − 29.829 T
Here, the initial ratio piH2 /piCO2 will not remain unchanged. The
equilibrium has to be calculated from:
Keq =
=
pCO pH2 O
pCO2 pH2
(piCO2
(4.7)
x2
− x)(piH2 − x)
again neglecting the formation of O2 , and hence with the progress
variable x=pCO =pH2 O . The oxygen pressure can then be derived using
equation 4.3 or 4.4. The resulting oxygen partial pressure is shown in
Figure 4.2. At high H2 /CO2 ratios, the equilibrium of reaction 4.6 is
limited by the amount of CO2 . The resulting amount of H2 O is close to
the initial amount of CO2 , whereas the amount of H2 remains virtually
unchanged. As a result, the H2 /CO2 and H2 /H2 O ratios in the gas are
similar, and the pO2 will approach that of reaction 4.2. At low H2 /CO2
ratios, most of the H2 reacts away and the amount of CO will be similar
43
to the initial amount of H2 . This leads to a pO2 approaching that of
reaction 4.1.
To use reactive gases, the temperature needs to be high enough to
enable the gases to reach the dynamic equilibrium. According to Bolind
[79], there is no reaction in a H2 /H2 O mixture below 400◦ C. At 1300◦ C,
a reducing mixture will equilibrate in less than 1 second. At that temperature, CO/CO2 mixtures still need more than a minute to reach the
equilibrium pO2 . These calculations were based on reaction rate constants
from Glassman [80]. The creation of radicals such as OH and O are rate
limiting steps in the reaction mechanisms.
Figure 4.2: Resulting oxygen partial pressure pO2 as a function of the ratio of
reactive gases at the inlet, for different pairs of gases, at 1600◦ C.
In some cases, only one reactive gas is used. For example, Fahey et al.
[81] used pure CO2 as an atmosphere, leading to a pO2 of
pO2
= (pCO2 /Keq )2/3 ,
(4.8)
with Keq given by 4.1 and 4.5, when neglecting the effect of the formation of O2 on the pressure of CO2 . In this case, the advantage of having
an oxygen buffer is lost, as the amount of CO is not much larger, but
only double the amount of oxygen:
44
pCO2
pO2
= piCO2 − x
= x
pCO = x/2.
(4.9)
(4.10)
(4.11)
Another possibility is the use of a pure metal as an oxygen buffer. For
example, Devilliers and Muan [82] measured the CaO-CrO-Cr2 O3 phase
diagram in equilibrium with solid chromium. In that case, the oxygen
partial pressure is not directly controlled. Instead, the activity of the
metal is imposed and equal to one. Because of the equilibrium between
the metal and the oxide in the slag, also the pO2 is fixed, but unknown.
Of course, the atmosphere has to be an inert gas, so that the pO2 can be
controlled by the sample. The chosen metal has to be part of the slag
system. The approach is also limited to systems where no other metal
can be reduced from the slag by the pure metal, as both metals would
probably form an alloy in which their activity is no longer known.
4.2.2
Containing the sample
To contain the sample, there are essentially two major options. Either an
inert container is used, or a reactive, saturating container is chosen. Apart
from containing the sample, there are possibilities to perform containerless experiments using magnetic levitation. For oxide systems, the set-up
mostly comprises a thin slag layer wetting a metal droplet to generate
enough magnetic force. Controlling the temperature of such a sample is
far from evident. This method is only used when extremely fast quenching is needed or no suitable solid containment material can be found, and
will therefore not be considered further.
Inert containers are mostly metals which retain sufficient strength at
high temperature. Platinum is an interesting material with good formability. However, in reducing conditions, there is a risk of forming an alloy
with a metal from the slag, e.g. Cr or V [83]. Because of low activity
coefficients of these metals in Pt, a considerable amount of metal can be
reduced to the alloy even at moderately reducing conditions. Pt is also
rather expensive. Another often used option is molybdenum, which remains very strong at high temperatures. It can, however, only be used in
reducing conditions, as otherwise a volatile oxide, MoO3 , is formed, and
the container corrodes quickly. The oxide also dissolves in the slag. Another disadvantage is that Mo is difficult to machine, and becomes brittle
after use at high temperature. Also Fe or C containers can be used at
45
sufficiently reducing conditions. The use of iron is limited by its melting
point at 1535◦ C.
Reactive containers can be interesting when studying a liquid saturated in a pure oxide, such as MgO, Al2 O3 or SiO2 . Crucibles made out
of these oxides are commercially available. It is even possible to use e.g. a
Fe foil, which is oxidised to Fe2 O3 to serve as an envelope for the slag [71].
However, care has to be taken that only a limited part of the crucible will
dissolve. Also, the porosity needs to be very low as the liquid oxide wets
oxidic materials well.
The second choice to make is how to support the sample. The sample
can be hung on a wire of inert material, or placed on a support. The
advantage of a hanging set-up in a vertical furnace is that the sample can
be dropped in water to quench it, if the furnace design and the atmosphere
allow that the furnace is opened at the bottom. The advantage of a
supported set-up is that the vertical position of the sample is well known,
and hence, its temperature is well controlled.
4.3
Conclusion
In this chapter, a variety of methods to study equilibria involving a liquid
oxide have been discussed. Static quenching methods are generally rather
robust methods, if certain conditions are fulfilled. The quench should
be fast enough, a suitable containment material has to be found, and
sufficient time is needed for equilibration. For pO2 dependent systems,
also the oxygen activity has to be controlled. Reactive gas mixing and
metal saturation are the most used and most reliable methods to control
this. Therefore, these will also be the methods used in the experimental
work discussed later.
46
Chapter 5
Experimental investigations
of the Cr2O3-MgO-SiO2
system
The system CrOx -MgO-SiO2 contains various interesting materials, from
refractory materials, such as magnesia-chrome bricks [84], to functional
materials, such as the lasing chromium doped forsterite [85]. The elements
O, Mg, and Si are abundant in the earth’s mantle, ranking first, second
and third in average weight percent, and Cr is also estimated to be in the
top ten [86]. Therefore, the system contains various minerals and is part
of extensively studied geological systems [87, 88]. Within metallurgy, it is
an important system to understand the behaviour of Cr in stainless steel
or ferro-alloy making slags, or to understand the reactions between slags
and refractory materials.
In Chapter 3, an overview of the CALPHAD optimisations within the
CaO-CrOx -MgO-Al2 O3 -SiO2 system showed the CrOx -MgO-SiO2 has not
been optimised to date. In Chapters 7 and 8, experiments and calculations will demonstrate that this leads to discrepancies reaching far into the
multicomponent system. Therefore, an overview of literature containing
experimental data on the system will be discussed in this chapter, which
will serve as a basis for the assessment in Chapter 9.
5.1
5.1.1
Liquidus information
Liquidus in air
Keith [89] measured liquidus temperatures in air using equilibration,
quenching and analysis by petrographic microscopy and XRD. The study
47
CHAPTER 5. EXPERIMENTS ON Cr2 O3 -MgO-SiO2
was part of a series of investigations on steelmaking refractory systems.
The liquidus and the investigated compositions are shown in Figure 8.1.
The maximum investigated temperature was 1850◦ C. A large miscibility
gap is indicated, extending from the MgO-SiO2 binary around 1700◦ C to
the complete Cr2 O3 -SiO2 system above 2100◦ C. Only a small area of liquid phase is found at steelmaking temperatures, around the composition
of MgO.SiO2 . The solubility of spinel was also measured by Morita et al.
[90], as indicated in Figure 5.2.
Figure 5.1: Cr2 O3 -MgO-SiO2 liquidus projection in air from Keith [89]. Black
dots are investigated compositions. Above 1850◦ C, the liquidus
lines are assumed. The area with a grey border indicates a miscibility gap in the liquid.
5.1.2
Liquidus in reducing conditions
The solubility of MgO.Cr2 O3 in MgO-SiO2 (-CrOx ) melts was determined
by Morita et al. [91], and reused in [92]. The solubility was determined by
saturation of MgO-SiO2 mixtures with MgO.Cr2 O3 pellets in CO/CO2
48
5.1. LIQUIDUS INFORMATION
atmospheres and chemical analysis of the quenched liquid. The liquidus
is shown in Figure 5.2. A considerable increase in CrOx solubility is noted
as compared to the liquidus in air. The observed high MgO solubility in
the liquid in equilibrium with spinel and M2 S is remarkable. Indeed, in
air and in equilibrium with metallic Cr, the slope of the M2 S liquidus is
flatter, and the M2 S solubility seems not so heavily affected by the CrOx
content in the liquid.
30
70
pO2=2.73x10
L+SiO2
-10
atm
in air
SiO2
40
60
L
wt% MgO
wt% SiO2
50
50
L+MgO.Cr2O3
L+M2S
2MgO.SiO2
60
0
10
20
30
wt% CrOx
Figure 5.2: Solubility of MgO.Cr2 O3 in CrOx -MgO-SiO2 melts at 1600◦ C after
Morita et al. [91].
Morita et al. [91] also measured the total Cr and Cr2+ concentration in
CrOx -MgO-SiO2 melts saturated with MgO.Cr2 O3 and M2 S, as a function
of pO2 . Because of the use of CO/CO2 mixtures, the lowest reachable pO2
is limited by the formation of Cr7 C3 . This pO2 is, however, comparable
to that of pure Cr formation. The amount of Cr2+ was determined by
titration. The observed fraction of Cr2+ is quite low, however, as it
is generally accepted that the majority (>90%) of Cr is Cr2+ at pO2 <
10−11 at 1600◦ C, and Cr2+ /Cr approaches 1 in equilibrium with Cr metal
[46, 93]. It is considered difficult to maintain and determine Cr2+ fractions
correctly, and an improved analytical method has been proposed by Wang
et al. [94].
5.1.3
Liquidus in equilibrium with metallic Cr
The liquidus of CrOx -MgO-SiO2 in equilibrium with metallic Cr was measured by Collins and Muan, following the work of Collins and Muan [95]
for CrOx -SiO2 . The original data of both systems, however, was never
49
9
Total Cr
Cr2+
Cr7C3 satd.
8
7
wt% Cr
6
5
4
3
2
1
0
−14
−12
−10
−8
−6
−4
−2
0
log pO (atm)
2
Figure 5.3: Total Cr and Cr2+ concentration in CrOx -MgO-SiO2 melts saturated with MgO.Cr2 O3 and M2 S at 1600◦ C, after Morita et al.
[91].
published. The liquidus without specific details on experimental set-up
was published in an overview by Muan [96], only giving the experimentally studied compositions, as shown in Figure 5.4. Later, the liquidus
was shown in Muan [97] and [17], without the compositions. Based on
the dotted lines used at high temperature, the maximum studied temperature was around 1700◦ C. The liquid area at 1600◦ C extends from the
MgO-SiO2 to the CrOx -SiO2 binary systems. Also the miscibility gaps in
the systems MgO-SiO2 and CrO-SiO2 are connected.
In the original publications of Muan [96, 97], the composition is indicated as weight percent (wt%) Cr2 O3 . However, the compositions of
the stable or hypothetic solid phases MgCr2 O4 , Cr2 SiO4 and CrSiO3
rather correspond to wt% CrO. In the compilation of Verein Deutscher
Eisenhüttenleute [17], the composition of these phases was corrected to
match with the wt% Cr2 O3 scale, and the liquidus itself was left untouched. However, it is possible that the scale itself was erroneous, and
therefore, the diagram should be interpreted as wt% CrO. As will be
discussed later (Chapter 9), this seems reasonable when comparing the
CrO-SiO2 binary with other ternary systems studied by the group of
Muan.
50
5.1. LIQUIDUS INFORMATION
SiO2
2 liquids
Pro
to
MgSiO3
17
18
Cris
ens
toba
lite
tatit
e
1700
160
0
150
0
00
00
Mg2SiO4
140
Forsterite
(CrSiO3)
0
15
00
16
17
19
00
20
00
24
25
26
27
MgO
00
00
00
Periclase
21
Spinel
00
22
00
00
(Cr2SiO4)
18
00
Eskolaite
19
00
00
23
00
200
00
weight %
0
MgCr2O4
Cr2O3
Figure 5.4: CrOx -MgO-SiO2 liquidus projection in equilibrium with metallic
Cr after Muan [96, 97]. The area with a grey border indicates
a miscibility gap in the liquid. The black dots are experimentally
studied compositions. It is unclear if the compositions scale should
not be interpreted as wt% CrO instead of Cr2 O3 .
51
5.2
Solidus information
The distribution of Cr between forsterite (M2 S) and the melt was studied
by Mass et al. [98], as well as by Dudnikova et al. [99], as a function of pO2 .
As Cr4+ is the active ion in chromium doped forsterite lasers [85, 100],
also the Cr4+ /Cr3+ ratio was studied by Mass et al. [98]. In both studies,
single crystals were grown in melts with 0.01-1 wt% Cr and log pO2 from
-4 to 0. As the data concerns crystal growth, it is not certain that there
is an equilibrium between solid and liquid.
5.3
Subsolidus information
Subsolidus equilibria at high pressures in equilibrium with metallic Cr
capsules were measured by Li et al. [101]. Temperatures ranged from 1100
to 1500◦ C. Samples were equilibrated, quenched and analysed by XRD,
SEM-BSE, and microprobe. The major part of the results is given in
Figure 5.5. Because of the high pressure, no liquid is observed at 1400◦ C,
in contrast to the liquidus by Muan [96] in Figure 5.4. Apart from the
relations with the liquid, the phase relations at atmospheric pressures are
not expected to differ greatly from the observed results. At 1300◦ C, both
MgSiO3 (MS) and Mg2 SiO4 (M2 S) show considerable solubilities for Cr.
This solubility increases at 1400◦ C. The largest difference, however, is
in the phase relations at the chromium rich side. There, the following
reaction occurs when increasing the temperature:
MgCr2 O4 + SiO2 → (Mg, Cr)SiO3 + Cr2 O3 .
5.4
(5.1)
Thermodynamic information
Morita et al. [91] measured the activity of CrO and CrO1.5 by equilibration of M2 S saturated melts with Ni-Cr and Cu-Cr alloys in CO/CO2
atmospheres, and wet chemical analysis of total Cr and Cr2+ content.
The activity coefficients as a function of pO2 are reproduced in Figure 5.6
However, as the Cr2+ concentration measurements, shown in Figure 5.3,
seem unrealistic, the derived activity coefficient data may be unreliable.
5.5
Conclusion
In the review in this chapter, the Cr2 O3 -MgO-SiO2 appeared well-studied
at different temperatures and oxygen partial pressures. The system is
52
5.5. CONCLUSION
Figure 5.5: CrOx -MgO-SiO2 subsolidus phase relations in equilibrium with
metallic Cr from Li et al. [101]. Sp=MgCr2 O4 , Esk=Cr2 O3 ,
Cpx and Opx=(Mg,Cr)SiO3 (clino- and ortho-pyroxene), Qz=SiO2
(quartz), Ol=(Mg,Cr)2 SiO4 (olivine)
53
24
20
gCrO1.5, gCrO
16
12
Cr7C3
satd.
8
gCrO1.5
gCrO
4
0
-13
-11
-9
-7
log pO2 (atm)
Figure 5.6: Activity coefficients γCrO and γCrO1.5 in CrOx -MgO-SiO2 melts
saturated with MgO.Cr2 O3 and M2 S at 1600◦ C, after Morita et al.
[91].
heavily dependent on pO2 , with a very limited CrOx solubility in the
MgO-SiO2 liquid in air, changing to an extensive liquid area up to the
CrO-SiO2 binary system in equilibrium with metallic Cr at 1600◦ C. Apart
from the phase relations with the liquid, also some subsolidus data is
available, albeit at high pressure. These data show extensive solubilities
of Cr in MS and M2 S in reducing conditions. The systems phase relations
are thus reasonably well known. However, not all data appear to be fully
reliable, and not all details on the experimental methods can be retrieved.
Also, thermodynamic data in this ternary system is scarce.
54
Part II
Research
55
Chapter 6
Experimental method
In Chapter 4, it appeared that quenching methods are well suited to
study oxide phase diagrams. Attention was paid to the non-evident issues of selecting a container for the sample and controlling the oxygen
partial pressure for pO2 dependent systems. In this chapter, the experimental method applied for the experiments in the following chapters
is discussed. The method consists of equilibration in a tube furnace,
sampling or quenching, and EPMA analysis. During analysis, a correct
interpretation of the quenched microstructure is important. These steps
will be discussed in the following sections.
6.1
Equilibration and sampling
Synthetic slag samples are prepared by weighing dried oxides CaO, SiO2 ,
MgO, Cr2 O3 , and Al2 O3 . Commercially available purity oxides are used,
except for CaO, which is obtained by calcination of CaCO3 at 1000◦ C for
24 hours. After weighing, the mixtures of 10 to 100 g are dry mixed in a
polyethylene bottle for 16 hours. Before melting, the samples are stored
in a desiccator.
The samples are equilibrated in a vertical tube furnace with MoSi2
heating elements. The furnace temperature is PID controlled within 1◦ C
using a type B (Pt-6%Rh / Pt-30%Rh) thermocouple. The temperature
in the centre of the furnace tube was checked to be within 1◦ C in a 40 mm
zone for the employed setup, leading to an estimation of 3◦ C for the total
accuracy of measurement and control. The difference between control
temperature and the temperature in the constant zone is measured for
every new furnace tube. The experimental set-up is shown in Figure 6.1.
In most cases, the oxygen partial pressure is controlled by mixing
bottled CO and CO2 using mass flow controllers (MFC). The maximum
57
CHAPTER 6. EXPERIMENTAL METHOD
flow rate of the CO and CO2 controllers is 500 ml/min and 100 ml/min,
respectively, and specified flow rate errors are 0.2% of the maximum flow
rate. Flow rates are set to minimum 10 ml/min CO2 to limit the flow
rate errors. The furnace atmosphere is in a slight overpressure to allow
the exit gas to run through a dibuthyl phthalate lock. A zirconia oxygen
sensor (Cambridge-Sensotec Rapidox 2100) is used to check the oxygen
partial pressure. When reactive gases are used, the sensor can only give
an indication of the pO2 at the sensor temperature (650◦ C).
To start a test, a molybdenum crucible with a weighed amount of
powder is inserted into the low temperature zone of the furnace, and the
furnace is gas tightened. After flushing with the CO/CO2 mixture, the
sample is placed into the high temperature zone by lowering a sealed
Mo hook. The molybdenum crucible is placed in a set of two alumina
protection crucibles. The alumina crucibles are supported by an alumina
tube and disc. Cylindrical alumina protection parts are on top of the
protection crucible.
Mo hook
Sampling bars
MFC CO
Ar inlet
MFC CO2
Mo crucible
Slag sample
Oxygen sensor
Tube furnace
Figure 6.1: Set-up for equilibration and sampling.
Samples are taken without breaking the atmosphere, by dipping an
alumina bar and retracting it to the cold zone of the furnace (<250◦ C).
Also alumina tubes can be used for sampling if more volume is needed.
Mostly, bars are used to minimise CO leakage risks. The alumina bars
are sealed at the top flange of the furnace using perforated silicone rubber
stoppers. A welding glass window is provided to facilitate operations. The
58
6.1. EQUILIBRATION AND SAMPLING
sampling technique allows to quench samples in a few seconds. As liquid
oxides tend to wet alumina well, the sample sticks well to the surface
of the bar. Only when the sample undergoes large volume changes on
cooling, as is the case when 2CaO.SiO2 is present in quantities larger
than a few percent, it is difficult to retain the sample on the bar.
For the experiments conducted in air atmosphere or equilibrated with
Cr metal, a Pt or Mo envelope is used, respectively, instead of a Mo
crucible. The envelope is hung in a vertical tube furnace together with a
thermocouple for temperature verification. The samples are quenched in
water after equilibration.
For samples in equilibrium with solid Cr, a 1-2 g mixture is weighed
directly in the envelope. Chromium oxide is added as Cr2 O3 + Cr, to
give the molar composition CrO, and some excess metal is added. This
is based on the method from Devilliers and Muan [82]. For compositions
39 and 40 in Table 8.1, the main part of the SiO2 and MgO is added
as a 60 weight percent (wt%) SiO2 , 40 wt% MgO premelted slag, in
order to facilitate melting and to fit a considerable mass inside the small
containers.
The necessary time for equilibration was determined by comparing
glass matrix compositions for samples taken at different reaction times
in CO/CO2 atmospheres. Mostly, these samples are taken for one preparation test, leading to a curve as shown in Figure 6.2. For the obtained
data, an indicative fit with an exponential shape has been added.
From such a single curve, it can be concluded that 8 hours are a sufficiently long equilibration time, as the increase in concentration between
8 and 24 hours is within the experimental errors. However, it can also be
suspected that the observed change in concentration between 8 and 24
hours, although limited, might be physical, and will occur in all samples,
and more precise results might be obtained after 24 hours. However, after
24 hours, samples at certain compositions can already be reacting with
protection crucibles due to wetting of the Mo crucible. A balance between
reasonable experimental times and a closer approach to equilibrium has
thus to be sought.
Therefore, in the following experiments, mostly a sample was taken
after 8 and 24 hours. This provided a sample at a certainly sufficient, but
sometimes experimentally challenging time (24 hours), and one already
providing an estimation within errors (8 hours). Furthermore, having
multiple samples per experiment allowed for further analysis of the equilibration behaviour.
Figure 6.3 shows the evolution of the chromium concentration in the
liquid as a function of the reaction time. The concentrations have been
59
12
11
wt% Cr2O3 in liquid
10
9
8
7
6
5
experimental data
indicative fit
4
3
0
5
10
15
time (h)
20
25
30
Figure 6.2: Chromium oxide concentration in the liquid as a function of reaction time for a single test.
divided by the maximum observed concentration. It is clear that the
maximum observed concentration is mostly observed after 24 hours. Also,
several samples show a considerable increase in Cr2 O3 concentration after
8 hours. It is assumed that these samples did not reach equilibrium in
the shorter time.
Some samples show a decrease in concentration between 8 and 24
hours. It will appear in section 6.3 that the decreasing concentrations are
artifacts in samples with a too high solid fraction.
6.2
Analysis
After embedding the samples in resin, wet grinding and polishing, and
coating with a carbon layer, the phase compositions are analysed using
electron probe micro-analysis (EPMA, ARL SEMQ 34). Standardised
wavelength dispersive spectroscopy (WDS) is performed on spots and
areas, using pentaerythritol (PET), thallium acid phthalate (TAP), and
lithium fluoride (LiF) crystals. The crystals and standards used for every element are given in Table 6.1. Except for Mo, oxide standards are
selected. Apart from the elements in the system (Ca, Cr, Mg, Al and Si),
also two expected contaminations, Mo and Fe were measured. As Fe was
not found in relevant amounts (<0.1%), it will not be given in the compo60
6.2. ANALYSIS
1
0.95
normalized wt%Cr2O3
0.9
0.85
0.8
0.75
0.7
0.65
0.6
0.55
0.5
0
5
10
15
20
25
30
35
40
time (h)
Figure 6.3: Chromium oxide concentration in the liquid divided by the maximum observed concentration in the set as a function of reaction
time for sets of samples with the same overall composition. In
case of multiple data points on the same coordinate, the area of
the symbol is increased proportionally.
sitions in what follows. Operating conditions comprised an accelerating
voltage of 20kV, and a sample current on willemite of 20 nA.
Suitable standards are also selected for interferences and background
counts. The interference of Al on the Cr peak is measured on the glass
standard, and the interference of Mg on the Mo peak is measured on
the spinel standard. Except for Mo, the background counts on the peak
positions are calculated using Mean Atomic Number (MAN) interpolation
[102], in which the MAN is defined as:
MAN =
X
wfi Zi ,
(6.1)
i
with wfi and Zi the weight fraction and atomic number of element
i. For the interpolation, the counts on the peak positions are measured
on a number of standards spread over a range of mean atomic numbers.
A relation between the mean atomic number and the counts at the peak
position is fitted for every element. Only the standards that do not contain the element or an interfering element are used. Some standards are
added to the set in Table 6.1, as shown in Table 6.2. When measuring
a sample with unknown composition, the compositions and the resulting
61
Table 6.1: Crystals, standards, and elemental concentrations in the standards
for EPMA analysis.
Element
Al
Ca
Cr
Fe
Mg
Mo
Si
Crystal
TAP
PET
LiF
LiF
TAP
PET
PET
Standard
Glass
Glass
Eskolaite
Hematite
Spinel
Molybdenum
Glass
Formula
Si-Ca-Al-O
Si-Ca-Al-O
Cr2 O3
Fe2 O3
MgO.Al2 O3
Mo
Si-Ca-Al-O
El. wt%
8.4
22.1
68.4
69.9
17.1
100.0
24.9
MAN are first estimated. Then the compositions are corrected for the
background, leading to a new MAN, which has to converge by iteration.
For Mo, the background is estimated by off-peak measurements at both
sides of the peak.
Table 6.2: Standards used for background MAN fitting (in order of increasing
MAN).
Standard
Spinel
Glass
Apatite
Eskolaite
Hematite
Willemite
Cobalt
Nickel
Sodium antimonate
Cassiterite
Molybdenum
Anglesite
6.3
Formula
MgAl2 O4
Si-Ca-Al-O
Ca(PO4 )3 F
Cr2 O3
Fe2 O3
(Zn,Mn)2 SiO4
Co
Ni
NaSbO3
SnO2
Mo
PbSO4
MAN
10.6
12.6
14.1
18.9
20.6
21.3
27.0
28.0
35.5
41.1
42.0
59.4
Microstructure interpretation
Two effects of the finite quenching speed are encountered in the microstructures, but appropriate measures can easily be taken. First, the
matrix is often not completely glassy but consists of fine crystalline phases,
frequently containing micron-sized secondary precipitates, as shown in
62
6.3. MICROSTRUCTURE INTERPRETATION
Figures 6.4 and 6.5. Therefore, the matrix composition is measured on
areas in the order of 100 µm2 .
Sp
L
Figure 6.4: BSE image of a slag sample containing liquid and spinel. Due to
the finite cooling speed on quenching, the liquid converted to a
finely structured matrix, in which different crystalline phases have
grown. Some amorphous quenched liquid may also be left.
Second, due to the precipitation reaction during quenching, lower concentrations of the precipitating elements are measured in the neighbourhood of primary precipitates, which can sometimes be visually observed
by the absence of secondary precipitates as in Figure 6.5. As shown in
Figure 6.6, the precipitates sink during equilibration. As a result, different zones with a high and a low precipitate content are frequently
encountered in a single cooled sample on the bar. In those cases, the
low solid content zones are preferred for matrix analysis, as the matrix
composition will be less affected by the presence of primary precipitates.
Since the samples are small, however, it is possible that only a precipitate
rich zone is found. In that case, a small underestimation of the solubility
could be introduced. The underestimation could however be problematic
with high precipitate fractions (>30%), hence samples with such a high
precipitate content are not considered satisfactory and are not used for
63
L
Sp
S
Figure 6.5: BSE image of a slag sample containing liquid, spinel and SiO2
(L+Sp+S) in which major secondary precipitation of SiO2 occurred. Due to the growth of the primary SiO2 precipitates during
quenching, there is a lower concentration of SiO2 around them,
and no secondary precipitates are formed there. Also the spinel
particles act as sites for heterogeneous SiO2 nucleation.
64
6.4. CONCLUSION
L
L+E
Mo crucible
1 mm
Figure 6.6: BSE image of a slag sample containing eskolaite precipitates,
cooled in the crucible. A clear sedimentation of the precipitates
into the lower zone is observed.
further processing.
Third, a small increase of the Al2 O3 concentration is sometimes observed close to the alumina sampling bar. This effect is easily avoided by
measuring at distances larger than 100 µm away from the bar.
6.4
Conclusion
This chapter discussed the experimental techniques employed in the next
two chapters. The method consists of equilibration at high temperature,
sampling or quenching, and subsequent microprobe analysis. The pO2 is
controlled by gas mixtures with a controlled CO/CO2 ratio, and in some
cases by equilibration with air or Cr metal. The analysis was performed
with standardised wavelength dispersive EPMA. As the sampling procedure only leads to a moderately fast quench, the microstructural artifacts
induced in the quenched samples have to be considered.
65
66
Chapter 7
The multicomponent
system: liquidus of
CaO-CrOx-MgO-Al2O3-SiO2
In this chapter, the stainless steel slag system is simplified to its main components CaO, SiO2 , MgO, Al2 O3 , Cr2 O3 and CrO. As before, Cr2 O3 and
CrO will be noted as one component, CrOx . The remaining quinary oxide
system is the minimal system to describe a lime-silica based slag containing MgO.(Al,Cr)2 O3 spinel particles. The phase relations are investigated in the CaO-MgO-SiO2 -CrOx quaternary and the quinary system
with Al2 O3 , at 1500 and 1600◦ C and in reducing atmospheres by quenching and compositional analysis of equilibrated samples, as described in
chapter 6. In the first section, some specific details of the experiments
in this chapter are dealt with. Next, the results will be compared with
calculations based on FactSage databases (version 5.5). Finally, it will
appear logical that the differences originate in two ternary subsystems.
7.1
Experimental approach
Details on the experimental setup can be found in Section 6.1. The phase
relations are studied in CO/CO2 ratios of 20/1 and 50/1. Using FactSage
data, this corresponds to oxygen partial pressures of pO2 =10−9.36 atm at
1600◦ C for 20/1 and pO2 =10−10.16 atm at 1600◦ C and 10−11.04 atm at
1500◦ C for 50/1.
The compositions of the starting powders are given in Table 7.1. The
compositions are grouped for different basicities and Al2 O3 contents. To
see the influence of basicity, two basicities are selected, 0.5 and 1.2. The
67
CHAPTER 7. CaO-CrOx -MgO-Al2 O3 -SiO2 LIQUIDUS
basicity of 1.2 is close to industrial practice. The value of 0.5 is interesting as a large increase in Cr2 O3 solubility is expected. As the relative
precision will increase with higher concentrations, this lower basicity allows to study the influence of basicity with higher accuracy. To study
the influence of Al2 O3 , four different levels (0, 10, 20 and 30 wt%) are
selected. To study the influence of basicity in more detail, five samples
with different CaO/SiO2 =C/S ratios are added. Finally, in every group
a number of MgO and Cr2 O3 compositions are chosen in the expected
hypersaturated liquid area, ranging from the system without MgO to the
system without Cr2 O3 . In the last group, with changing basicities, the
molar ratio MgO/Cr2 O3 is chosen equal to 1.
Table 7.1: Compositions of starting powders
Mixture
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
68
wt% CaO
46.4
46.1
45.4
45.0
43.6
42.2
40.9
41.7
39.2
36.8
37.1
34.9
32.7
32.4
30.6
28.6
26.5
25.8
23.8
21.8
21.1
54.3
48.6
36.8
18.7
12.8
SiO2
38.6
38.4
37.9
37.4
36.3
35.2
34.0
34.7
32.7
30.6
30.9
29.0
27.2
27.0
25.5
23.8
53.0
51.7
47.6
43.7
42.2
36.2
40.4
43.2
53.3
60.2
MgO
0.0
1.0
4.2
6.4
12.5
18.8
25.1
0.0
11.3
22.6
0.0
10.1
20.1
0.0
8.7
17.6
0.0
4.4
18.4
31.6
36.7
2.0
2.3
4.2
5.9
5.6
Cr2 O3
15.0
14.4
12.5
11.2
7.6
3.8
0.0
13.5
6.8
0.0
12.0
6.0
0.0
10.5
5.3
0.0
20.5
18.0
10.3
2.9
0.0
7.5
8.7
15.8
22.1
21.3
Al2 O3
0.0
0.0
0.0
0.0
0.0
0.0
0.0
10.1
10.0
10.0
20.0
20.0
20.0
30.0
29.9
30.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
B=C/S
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
0.5
0.5
0.5
0.5
0.5
1.5
1.2
0.85
0.35
0.21
7.2. RESULTS
7.2
Results
The composition of the equilibrium phases in the selected samples and the
standard deviations on the EPMA measurement are given in Appendix
A, Tables A.1-A.3. The results are also plotted in Figures 7.1-7.10.
The symbols indicate the stable phases, with their mineral names
E=eskolaite, Sp=spinel, P=periclase, and L=liquid for the phases with
extensive solubilities. For silicon oxide (normally cristobalite) S=SiO2 ,
and for the complex silicate phases, C2 S=dicalcium silicate and M2 S=
forsterite, the common abbreviation of the chemical formula is used. Error bars indicate the estimate for the population standard deviation (±1s)
on the EPMA measurements.
7.2.1
Liquidus
The analysis using EPMA gives the composition of both the saturated
liquid and the saturating solids. First, the composition of the liquid,
hence the liquidus surface, is discussed.
Liquidus of CaO-SiO2 -MgO-CrOx
The liquidus results are presented as constant temperature, oxygen partial
pressure, basicity and Al2 O3 content sections in Figures 7.1-7.4. In the
figures, the composition of MgO and CrO+Cr2 O3 in the liquid is plotted.
The total chromium oxide content is given both as total elemental wt%
Cr, and expressed as trivalent oxide (Cr2 O3 ).
Figure 7.1 and 7.2 show the phase diagram at 1600◦ C for B=1.2 for
pO2 =10−10.16 and pO2 =10−9.36 atm respectively. In Figure 7.3, the liquidus at 1600◦ C for the lower basicity B=0.5 at pO2 =10−9.36 atm is presented. Finally, the liquidus for B=0.5 at T=1500◦ C and pO2 =10−11.04
atm is shown in Figure 7.4.
The agreement with the calculations at the higher basicity B=1.2 is
very good. Only one considerable deviation is noted for the measured
eskolaite solubility. The solubility is systematically 2-3% (Cr2 O3 ) lower
than calculated. As a result, in contrast to the calculations predicting
spinel, eskolaite is also observed at 1.4% MgO in Figure 7.1. Hence, the
three-phase equilibrium L+E+Sp should be at the higher MgO contents
than calculated. When Figures 7.1 and 7.2 are compared, it is clear that
an increasing oxygen pressure has a strong decreasing effect on CrOx
solubility.
At low basicity (B=0.5) in Figure 7.3 and 7.4, however, the situation
is different. On the one hand, the results in the ternary subsystems on the
69
L+E
L
+
E
12
L+Sp
L+Sp+C2S+P
L+C2S+P
L+Sp
10
wt% Cr
8
L+Sp+C2S+P
6
4
L
2
L+C2S
0
0
5
10
15
L+C2S+P
20
25
wt% MgO
Figure 7.1: Experimental liquid composition (symbols) compared to calculated phase diagram (solid lines) for CaO-CrOx -MgO-SiO2 .
The phases present in the samples are indicated in the legend.
B=CaO/SiO2 =1.2, pO2 =10−10.16 atm, T=1600◦ C.
L
+
Sp
L +
+ E
E
12
L+E
L+Sp
L+Sp+C2S+P
L+Sp
10
L
+
Sp
+
C2S
wt% Cr
8
L+Sp+C2S+P
6
4
L
2
0
L+C2S
0
5
10
15
L+C2S+P
20
25
wt% MgO
Figure 7.2: Experimental liquid composition (symbols) compared to calculated phase diagram (solid lines) for CaO-CrOx -MgO-SiO2 .
B=C/S=1.2, pO2 =10−9.36 atm, T=1600◦ C.
70
7.2. RESULTS
axes are comparable with the situation at higher basicity. In the system
without CrOx , the M2 S liquidus is in good agreement. In the system
without MgO, the eskolaite solubility is overestimated at low temperature
and low pO2 in Figure 7.4. The points in the quaternary system, on the
other hand, deviate strongly from the calculations. In Figure 7.3, the
spinel liquidus is found at higher CrOx contents than calculated. Also, a
sample was found to be completely liquid, whereas L+Sp, or less likely
L+Sp+M2 S, was expected from the calculations. At lower temperature
the L+Sp+M2 S point is found, but the same underestimation of spinel
solubility is noted. In section 7.3, the possible reasons for the deviations
will be examined.
16
L
+
E
L+E
L+Sp
14
L
L+M2S
12
wt% Cr
10
L
+
Sp
+
M2S
L+Sp
8
6
4
0
L
+
M2S
L
2
0
5
L + SiO2
10
15
20
25
30
35
wt% MgO
Figure 7.3: Experimental liquid composition compared to calculated
phase diagram for CaO-CrOx -MgO-SiO2 with B=C/S=0.5, at
pO2 =10−9.36 atm and T=1600◦ C.
Influence of Al2 O3
Aluminium oxide is soluble in both spinel and eskolaite. Corundum
(Al2 O3 ) forms a complete solid solution with eskolaite (Cr2 O3 ), and magnesia alumina spinel (MgO.Al2 O3 ) exhibits the same phenomenon with
picrochromite spinel (MgO.Cr2 O3 ). Therefore, it could be expected that
adding substantial amounts of Al2 O3 to the slag will promote the precipitation of eskolaite and spinel. This could result in drastic decreases in
the solubility of CrOx . It will become clear, however, that the decrease
71
L+E
L+E
L+Sp
L+Sp+M2S
L+M2S
L+Sp
L
L
+
M2S
L+S
Figure 7.4: Experimental liquid composition compared to calculated
phase diagram for CaO-CrOx -MgO-SiO2 with B=C/S=0.5, at
pO2 =10−11.04 atm and T=1500◦ C.
in solubility is rather limited.
In Figure 7.5, calculated phase diagrams are shown, indicating the
effect of adding 10, 20 and 30 wt% of Al2 O3 to the system in the same
conditions as in Figure 7.2. First, although the effect of those substantial
additions of Al2 O3 is limited, a clear decrease in CrOx solubility is noted,
through promotion of spinel and eskolaite formation. Second, for low
CrOx and high MgO concentrations, the addition of Al2 O3 changes the
primary phase. Whereas at 0% Al2 O3 C2 S was the primary phase in
the system without CrOx , periclase is found at higher concentrations of
Al2 O3 , until the spinel liquidus reaches the MgO axis (0% CrOx ), and
MgO.Al2 O3 spinel precipitates before MgO.
To compare the experimental results with the calculations, diagrams
such as Figure 7.6 can be constructed, in which the phase diagram at
a constant Al2 O3 concentration of 10 wt% is shown for T=1500◦ C and
B=1.2. However, at higher oversaturation and higher Al2 O3 concentrations, these diagrams quickly become unsuitable. Indeed, samples with
the same global Al2 O3 concentration, but different oversaturation cannot
be plotted on the same graph, as the precipitation of phases richer or
poorer in Al2 O3 leads to lower or higher Al2 O3 concentrations in the liquid. Then, the liquid compositions can not be plotted on a section with
constant Al2 O3 concentration. The tie lines between liquid and solids are
72
7.2. RESULTS
L
+
E
L
+
Sp
+
E
10% Al2O3
20% Al2O3
30% Al2O3
L+Sp
L+Sp+P
L
(L+P)
Figure 7.5: Calculated phase diagrams in the five-component system CaOCrOx -MgO-Al2 O3 -SiO2 with B=C/S=1.2 and for 10%, 20% and
30% Al2 O3 (at any point in the diagram), at pO2 =10−9.36 atm and
T=1600◦ C.
also no longer lying in the depicted plane.
Another approach would be to calculate the liquid composition for a
compositional line through the experimental global compositions. Then,
the liquid does not have a constant Al2 O3 concentration, but the calculated composition should be comparable with the experimental composition. This approach could be called “numerical precipitation”. Such
a calculation, in comparison with experimental results, is shown in Figure 7.7 for 1600◦ C, B=1.2 and a global Al2 O3 concentration of 10 and 20
wt%.
To allow a clearer evaluation of the influence of Al2 O3 on the liquidus,
a different perspective is taken in Figures 7.8 and 7.9. These figures show
the solubility of eskolaite and spinel, expressed as Cr solubility, as a function of Al2 O3 concentration in the liquid. For eskolaite, the experiments
without MgO are shown, and the MgO content in the calculation is 0%.
For spinel, the MgO and Cr2 O3 concentrations are diluted by the addition of Al2 O3 , as in the experimental powder compositions in Table 7.1.
In both calculations, as well as for the experiments, the oxygen partial
pressure is 10−9.36 atm and the temperature is 1600◦ C.
From Figure 7.8, it can be seen that the difference between calculated
and experimental eskolaite solubility, which was already noticed before, is
73
12
L
+
Sp
+
E
10
L+E
L+Sp
L+P
wt% Cr
8
L+E
6
L+Sp
4
L+Sp+P
2
L
0
L+P
0
2
4
6
8
10
12
14
16
18
20
wt% MgO
Figure 7.6: Experimental liquid composition compared to calculated phase diagram in the five-component system CaO-CrOx -MgO-Al2 O3 -SiO2
with B=C/S=1.2 and 10% Al2 O3 (at any point in the diagram),
at pO2 =10−11.04 atm and T=1500◦ C.
systematic and appears independent of Al2 O3 concentration. The agreement for spinel in Figure 7.9, however, is very good.
For both phases, the influence of Al2 O3 on the solubility of CrOx is
rather limited. For instance, adding 20% of Al2 O3 to the liquid changes
the CrOx solubility with only 1 or 2%.
Finally, the influence of Al2 O3 in the CaO-MgO-Al2 O3 -SiO2 system is
shown in Figure 7.10 for T=1600◦ C and pO2 =10−9.36 atm. Whereas C2 S
precipitates first when adding MgO to a CaO-Al2 O3 -SiO2 liquid at low
Al2 O3 concentrations, the primary phase changes to periclase and spinel
when adding more Al2 O3 . This evolution is also observed experimentally.
The calculations seem to establish a small underestimation of the MgO
solubility, but due to large errors on the MgO concentrations, no definitive
conclusion can be drawn. The errors are probably due to the formation
of MgO containing crystals.
7.2.2
Influence of basicity at MgO/Cr2 O3 =1
In Figure 7.11 and 7.12, a series of experiments is shown, in which the
influence of the basicity on the CrOx solubility is analysed. In the overall
composition, the molar ratio of MgO/Cr2 O3 (M/K) is kept constant at 1.
74
7.2. RESULTS
experimental 10% Al2O3
experimental 20% Al2O3
L+E
calculated 10% Al2O3
calculated 20% Al2O3
L+Sp
L+P
Figure 7.7: Experimental liquid composition compared to calculated liquid composition in the five-component system CaO-CrOx -MgOAl2 O3 -SiO2 with B=C/S=1.2 when equilibrating a sample with a
global composition of 10% and 20% Al2 O3 , at pO2 =10−9.36 atm
and T=1600◦ C.
75
atm
atm
wt% Cr in liquid
atm
wt% Al2O3 in liquid
Figure 7.8: Measured and calculated eskolaite liquidus (shown as Cr and
(Cr2 O3 ) solubility) as a function of the Al2 O3 content of the liquid
with B=C/S=1.2.
3
atm
atm
2.5
atm
wt% Cr
2
1.5
1
0.5
0
0
5
10
15
20
25
30
wt% Al2O3
Figure 7.9: Measured and calculated spinel liquidus (shown as Cr and (Cr2 O3 )
solubility) as a function of the Al2 O3 content of the liquid, with
B=C/S=1.2. The origin of the Al2 O3 axis has been shifted for
clarity.
76
7.2. RESULTS
30
L+Sp
L+ Sp
L+P
25
L+P+C2S
15
L+P
wt%
Al
2
O
3
20
10
5
L+C2S
0
0
5
10
15
wt% MgO
L+P+C2S
20
25
30
Figure 7.10: Experimental liquid compositions in comparison with lower
Al2 O3 part of calculated CaO-MgO-Al2 O3 -SiO2 liquidus for fixed
B=1.2. T=1600◦ C, pO2 =10−9.36 atm.
77
Therefore, the compositions can be plotted on a ternary diagram CaOSiO2 -MgO.Cr2 O3 , as in Figure 7.11. Notable differences are observed
between the experimental observation and the calculated phase diagram.
Mainly, the precipitation of spinel is calculated, but eskolaite is observed.
Only at the highest basicity of 1.5, spinel is experimentally detected.
Also, at high SiO2 content, a miscibility gap is observed, of which no
experimental evidence was found.
MgO.Cr2O3
L+E
L+E+S
L+Sp+C2S
L+Sp
L1 +
L2+Sp
L1+L2
+Sp+S
L1+L2
L
CaO
L+C2S
L+S
SiO2
Figure 7.11: Experimental observations compared to calculated phase diagram
for CaO-SiO2 -MgO.Cr2 O3 at pO2 =10−9.36 atm and T=1600◦ C.
For the target overall compositions of the powder mixtures,
the observed phase assemblies are indicated. The molar ratio
MgO/Cr2 O3 is equal to 1 in both calculations and experimental
compositions.
When looking at the experimentally observed liquid compositions in
Figure 7.12, the MgO/Cr2 O3 ratio is no longer constant, due to the precipitation of eskolaite. For the sample with the largest eskolaite precipitation, the M/K ratio increased to 1.7. Therefore, a calculated liquidus
line at M/K=2 is added in Figure 7.12. It is however noted that this line
is rather close to the liquidus at M/K=1. Therefore, it is still possible to
78
7.2. RESULTS
compare the experimental info on this diagram, in which the MgO and
Cr2 O3 concentrations are added to form the third coordinate. A clear
observation can be made from this figure: the lower the basicity, the
more the observed (eskolaite) liquidus differs from the calculated (spinel)
liquidus.
MgO+Cr2O3
Exp. L+E
Exp. L+E+S
Calc. M/K=1
Calc. M/K=2
L+Sp
L1 +
L2+Sp
L1+L2
+Sp+S
L1+L2
L
CaO
L+C2S
L+S
SiO2
Figure 7.12: Experimental observations compared to calculated phase diagram
for CaO-SiO2 -Cr2 O3 +MgO at pO2 =10−9.36 atm, T=1600◦ C and
MgO/Cr2 O3 =M/K=1. The observed liquid compositions and
the observed phase assemblies are indicated. As eskolaite precipitates, whereas spinel is calculated, the molar ratio MgO/Cr2 O3
in the observed liquid composition is increased. As shown by
the dotted line for MgO/Cr2 O3 =M/K=2 this does not strongly
influence the calculated diagram.
7.2.3
Solidus
Apart from some limited mutual solubility in C2 S and M2 S, the composition of the solids only deviates from stoichiometry when adding Al2 O3 .
In Figure 7.13, the Al2 O3 content of eskolaite and spinel is plotted as a
function of the Al2 O3 concentration in the liquid. The Al2 O3 content in
79
spinel rises faster than the concentration in the liquid, whereas the Al2 O3
content in eskolaite rises slower. The calculations are in good agreement,
although the experimental points for both phases seem to indicate a more
linear behaviour than predicted by the calculations.
50
experimental Sp
calculated Sp
experimental E
calculated E
45
40
30
2
3
wt% Al O solid
35
25
20
15
10
5
0
0
5
10
15
20
25
30
wt% Al O liquid
2
3
Figure 7.13: Measured and calculated Al2 O3 content of spinel and eskolaite
as a function of the Al2 O3 content of the liquid. T=1600◦ C,
pO2 =10−9.36 atm.
7.3
7.3.1
Discussion: origin of the differences
Eskolaite liquidus in CaO-CrOx -SiO2
Only one major point of deviation has been observed at B=1.2. The
calculated eskolaite solubility is systematically 1-2 wt% Cr higher than
the experimentally determined solubility, or a relative disagreement of
about 20%. This can be noticed in Figures 7.1, 7.2 and 7.6, and in more
detail for 0% MgO and varying Al2 O3 content in Figure 7.8. At lower
basicity, the same error is observed at low temperature and low oxygen
pressure in Figure 7.4.
We believe this error originates in the ternary system CaO-SiO2 -CrOx .
Indeed, for this basicity of 1.2 and at 1500◦ C, a similar difference can be
observed in the optimisation paper by Degterov and Pelton [53] where
the model is compared with ternary data from Pretorius and Muan [103].
80
7.3. DISCUSSION: ORIGIN OF THE DIFFERENCES
This comparison is shown in Figure 7.14. At lower basicities, the difference disappears, as confirmed by the ternary measurement of this work
at B=0.5. At lower oxygen partial pressure, however, the overestimation
of the eskolaite solubility seems to increase, especially for high or very
low basicities.
If the calculated eskolaite liquidus should indeed be corrected to lower
solubilities, and if it is assumed the calculated spinel liquidus is correct,
then a shift of the three-phase equilibrium L+E+Sp to higher MgO contents is expected. This is confirmed by the experiments for the quaternary
system in Figure 7.1, as no spinel is observed at 1.4% MgO.
A partial explanation for the overestimation in the calculation could
be the oxygen deficiency of the eskolaite, which is not modelled by Degterov
and Pelton [53]. This phenomenon was recently modelled by Povoden
et al. [55] for pure Cr2 O3−x . Extension of this model to (Cr,Al)2 O3−x
could provide a stabilisation of eskolaite under reducing atmospheres and,
hence, a lower solubility.
50
this work
-9.36
T=1600°C pO2=10
calculated
Pretorius and Muan 1992
-9.56
T=1500°C pO2=10
calculated
Pretorius and Muan 1992
-12.5
T=1500°C pO2=10
calculated
45
40
35
wt% Cr
30
25
20
15
10
5
0
0
0.2
0.4
0.6
0.8
1
1.2
basicity
Figure 7.14: Overestimation of CrOx solubility at high basicity and low pO2
in FactSage calculations for eskolaite liquidus in CaO-CrOx -SiO2 ,
when compared with data from this work and Pretorius and Muan
[103]. Data from [103] at intermediate pO2 omitted for clarity.
81
7.3.2
Spinel liquidus in CrOx -MgO-SiO2
The differences in calculated and experimental spinel liquidus at low basicities seems to be a problem of extrapolation. The ternary systems
CaO-CrOx -SiO2 and CaO-MgO-SiO2 , on the axes in Figures 7.3-7.4, are
in good agreement. However, the more the composition moves away from
the ternaries into the quaternary, away from the axes, the more deviation
is noted. At higher basicity, the difference is not noted. As discussed
in Chapter 3, the ternary subsystems CrOx -MgO-SiO2 and CaO-CrOx MgO have not been optimised. This means the ternary interaction in
these systems have not been defined. For instance, for the interaction of
MgO and CrOx in the presence of CaO or SiO2 , a simple extrapolation
is used, which might deviate from reality. The deviations occur at low
basicity, i.e., at high SiO2 content. This seems to indicate some missing
or wrong interaction between CrOx and MgO with SiO2 , rather than with
CaO.
In Figures 7.11-7.12, another indication is found that the FactSage
description of the CrOx -MgO-SiO2 system is insufficient. For a constant
molar ratio MgO/Cr2 O3 =1, the calculated liquidus deviates more and
more from the experimental data, and even a completely unphysical miscibility gap appears. Therefore, it is assumed that the largest problems
originate in the CrOx -MgO-SiO2 system. Consequently, this system will
be studied in detail in the next chapter.
7.4
Conclusion
This chapter discussed experimental investigations of the phase relations
in CaO-CrOx -MgO-Al2 O3 -SiO2 at high temperature. The influence of
pO2 , temperature and composition was studied. When comparing the
results with FactSage calculations, some systematic differences are observed. Especially at low basicities, large deviations occur. At higher
basicity, and hence, higher CaO content, good agreement is found. Also
the influence of Al2 O3 is in good agreement. When CaO and Al2 O3
are disregarded, the CrOx -MgO-SiO2 system remains. Because there are
good reasons to assume the interactions in this system are responsible for
a large part of the deviations, this ternary system will be studied in the
next chapters, both experimentally and by thermodynamic modelling.
82
Chapter 8
The ternary system
CrOx-MgO-SiO2
In the previous chapter, considerable differences between calculated and
experimental liquidus compositions were observed for lower basicities in
the multicomponent system CaO-CrOx -MgO-Al2 O3 -SiO2 . This lead to
the assumption that important ternary interactions in the CrOx -MgOSiO2 system are missing in the thermodynamic database. In this chapter,
this assumption will be evaluated. The CrOx -MgO-SiO2 system itself will
be investigated at different oxygen partial pressures. Increasingly reducing conditions are studied, in which the pO2 is controlled by air, CO/CO2
mixtures and equilibrium with metallic Cr. For every set of experiments,
the results will be compared with available literature data and with calculations using the FactSage database (version 5.5). The experimental
approach has been discussed in Chapter 6. The compositions of the starting powders are given in Table 8.1. The equilibrium phase compositions
are listed in Appendix A, Tables A.4-A.5.
8.1
Liquidus in air
In air, the spinel (Sp) liquidus is limited by the cristobalite liquidus (SiO2 ,
S) and the forsterite liquidus (M2 S). Two measurements were conducted
at 1600◦ C to define the location of the two bounding three-phase equilibria L+S+Sp and L+Sp+M2 S. Also the solubility of chromium oxide
(CrOx ) in M2 S was determined. Later it will appear the solubility increases with decreasing pO2 . Even in this oxidising conditions there is
some solubility, albeit only about 0.6 wt% expressed as Cr2 O3 .
The composition of the liquid and of the M2 S phase is plotted in
83
CHAPTER 8. TERNARY SYSTEM CrOx -MgO-SiO2
Table 8.1: Compositions of starting powders
Mixture
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
SiO2
65.2
54.0
56.0
53.0
57.9
38.0
41.9
50.0
57.0
57.0
43.8
41.8
46.3
31.6
42.0
24.2
MgO
28.4
42.0
26.0
31.0
31.9
50.0
46.2
36.0
20.0
14.1
35.9
40.3
31.0
21.2
29.9
40.6
Cr2 O3
6.5
4.0
18.1
16.0
10.1
12.0
11.9
14.0
23.1
29.0
20.3
17.9
12.6
28.6
20.4
17.6
Cr
10.1
18.6
7.7
17.6
Figure 8.1. The results agree well with the diagram drawn by Keith
[89] at 1600◦ C. Also the liquidus data from Morita et al. [90] is in good
agreement, although the extent of the spinel liquidus towards the M2 S
side seems overestimated. In the next paragraph, it will be explained this
could be caused by the saturation technique used by Morita et al. [90].
8.2
Liquidus in reducing conditions
In a first set of experiments in reducing conditions, it was attempted to
reproduce the results of Morita et al. [91]. The same conditions as in
Morita et al. [91] are applied. The ratio of CO/CO2 was 25/1, which
yields a pO2 =10−9.56 atm at 1600◦ C.
In Figure 8.2, and in more detail in Figure 8.3, the results from literature and from the present investigation are compared. A very good
agreement is found at the SiO2 side, and for the liquid saturated in SiO2
and spinel. However, a remarkable high MgO solubility in the liquid in
equilibrium with spinel and M2 S is measured by [91]. Their “spinel liquidus” results at the lower SiO2 side do, however, correspond well to
the tie-line between our liquid and M2 S compositions, both saturated in
spinel. In the case of Morita et al. [91], the solubility was determined
84
8.2. LIQUIDUS IN REDUCING CONDITIONS
20 80
30
70
%
L+Sp+S
60
SiO
wt
L
%
40
wt
Mg
O
L+S
2
L+Sp
50
50
L+Sp+M2S
M2S
60
0
10
20
30
40
40
wt% Cr2O3
L+Sp+S liquidus
L+Sp+M2S liquidus this work
M2S composition
liquidus data from Morita
liquidus from Keith
calculated phase diagram
Figure 8.1: Comparison of experimental observations from this work, from
Morita et al. [90], liquidus from Keith [89] and calculated phase
diagram from FactSage for the constant temperature section of
CrOx -MgO-SiO2 in air, at T=1600◦ C.
85
by saturation of MgO-SiO2 mixtures with MgO.Cr2 O3 pellets, followed
by mechanical separation and chemical analysis of the quenched liquid.
Probably they interpreted high temperature M2 S crystals as part of the
quenched liquid. As a result, the “liquid” at the low SiO2 side could be
a mixture of the quenched liquid and the M2 S phase. This technique was
also used in air by Morita et al. [90], and the same artifacts may therefore
be observed in Figure 8.1.
In this work, it was possible to distinguish large M2 S crystals from
the quenched liquid, as a result of the sampling technique combined with
microprobe analysis. The observed liquid composition should therefore
be quite reliable. Considering the gentle slope of the M2 S liquidus with
increasing CrOx content at other oxygen partial pressures, it is assumed
that the proposed phase diagram is more correct than the one from Morita
et al. [91]. Because of the distinction between the phases by microprobe
analysis, it was also possible to measure the considerable solubility of
chromium oxide (CrOx ) in M2 S (5.2 wt% when expressed as Cr2 O3 ).
This aspect will be discussed in more detail in Section 8.4. Because of
the high solid content in some of the samples, the liquid composition
was affected by quenching and contained a high level of impurities. The
data from these samples was not considered when drawing the proposed
liquidus. However, they do confirm the solubility of CrOx in M2 S and
the M2 S liquidus, and therefore they are indicated in grey on the figures.
In Figure 8.3, the results are also compared with the liquidus calculated with the FactSage databases. The calculated solubility of spinel in
the liquid is much smaller than observed. In the calculations, there is no
possibility for CrOx to dissolve in M2 S (not shown in Figure 8.3).
In a second set of experiments the ratio CO/CO2 was set to 50/1,
leading to a pO2 =10−10.16 atm. The results are plotted in 8.4. Two
samples were completely liquid, and one contained liquid and SiO2 . The
L+Sp+S and L+Sp+M2 S were also observed. When compared with Figure 8.2, a notably higher spinel solubility in the liquid phase at high
SiO2 contents is observed, although it is difficult to reconcile the L+S
and L+S+Sp points in a realistic phase diagram. As the microstructure
of the L+S+Sp point showed some irregularly shaped SiO2 precipitates,
which may indicate some growth of the SiO2 phase during cooling, it is
possible that the actual SiO2 content of the liquid at high temperature is
higher.
86
8.3. LIQUIDUS IN EQUILIBRIUM WITH Cr
SiO2
L+S
L
L+Sp+S
L+M2S
M2S
P+M2S
MgO
L
L+Sp+M2S
+
Sp
L+Sp+E
L+P+M2S
weight percent
Sp
Cr2O3
liquidus data (Morita et al.)
liquidus data (this work)
M2S composition data (this work)
proposed liquidus
proposed phase diagram
Figure 8.2: Compared experimental observations and proposed phase diagram for the constant temperature section of CrOx -MgO-SiO2 at
pO2 =10−9.56 atm and T=1600◦ C. Spinel is schematically drawn
stoichiometric.
87
20 80
30
70
%
60
L
S iO
wt
40
%
wt
Mg
O
L+S
2
50
L+M2S
L+Sp
L+Sp+M2S
M2S
60
0
50
10
20
30
40
40
wt% Cr2O3
L+Sp+S
L+Sp
L+Sp+M2S
data with high solid content
proposed liquidus
calculated liquidus
Figure 8.3: Detailed comparison of experimental observations and calculated
liquidus from FactSage for CrOx -MgO-SiO2 at pO2 =10−9.56 atm,
T=1600◦ C. For part of their data, Morita et al. [91] seem to have
measured the L+M2 S tieline in equilibrium with spinel.
88
SiO2
L+S
L+M2S
L+Sp
M2S
L+Sp+M2S
P+Sp+M2S
MgO
Sp
weight percent
Cr2O3
L+S liquidus
L+Sp+S liquidus
L+Sp liquidus
L+Sp+M2S, liquidus
L+Sp+M2S, M2S composition
calculated liquidus
fully liquid
Figure 8.4: Comparison of experimental observations and calculated liquidus from FactSage for CrOx -MgO-SiO2 at pO2 =10−10.16 atm,
T=1600◦ C.
89
SiO2
L+S
L
L+M2S
Mg2SiO4
L+Sp+M2S
(Cr2SiO4)
L+Sp
P+Sp
P+Sp+M2S
L+E
MgO
weight %
MgCr2O4
Sp
Cr2O3
L+Sp liquidus
L+Sp+M2S, liquidus
P+Sp+M2S, M2S composition
P+Sp+M2S, P composition
liquidus by Muan
Figure 8.5: Comparison of experimental observations of this work and proposed liquidus from Muan [96] for CrOx -MgO-SiO2 in equilibrium
with solid Cr, T=1600◦ C.
90
8.3
Liquidus in equilibrium with metallic Cr
Figure 8.5 gives the results in equilibrium with solid Cr, and compares
them with the liquidus from Muan [96]. The calculated liquidus is shown
in Figure 8.6. The experimental results agree reasonably well with the
diagram by Muan [96]. However, the presence of solid Cr at high temperature could not be confirmed in our samples, which could have led to a
somewhat higher pO2 . This might explain the lower concentration of Cr
for the L+Sp+M2 S liquidus point, compared to Muan’s indication of the
invariant line.
Figure 8.6 shows the calculated phase diagram from FactSage in equilibrium with Cr at 1600◦ C. When it is compared to the experimental and
literature data in Figure 8.5, it can clearly be observed that the present
model is not in agreement. The calculations show a large miscibility gap
between a Cr rich and a Cr poor liquid, which is almost perpendicular to
the demixing tendencies in both MgO-SiO2 and CrO-SiO2 , where a miscibility gap between a SiO2 rich and a SiO2 poor liquid exists above 1700◦ C.
The wrongly calculated miscibility gap extends into the calculations in
the quaternary system studied in Figures 7.11-7.12.
8.4
Liquidus and solidus as a function of pO2
From the previous paragraphs, the strong pO2 dependence of the liquidus
can be noted. In Figures 8.7 and 8.8 this behaviour is studied in more
detail for the ternary points L+M2 S+Sp and L+Sp+S.
Figure 8.7 shows the pO2 dependence of the liquid and M2 S composition in the L+M2 S+Sp equilibrium. The Cr concentration in both phases
increases considerably as the oxygen partial pressure is decreased. The
concentration of Cr in the M2 S+spinel saturated liquid can also be compared to the work of Morita et al. [91] as a function of pO2 and of Muan
[96] in equilibrium with metallic Cr, as shown later in Figure 9.20. The
associated M2 S composition has not been studied before. The solubility
of CrOx in M2 S changes dramatically, from 0.6 wt% (Cr2 O3 ) in air, to
almost 15 wt% (Cr2 O3 ) in equilibrium with metallic Cr. The observed
stoichiometry of the phase indicates the major dissolved chromium oxide
is CrO.
The liquid composition saturated in spinel and SiO2 is depicted in
Figure 8.8. In the studied reducing atmospheres, the Cr solubility increases very sharply. In equilibrium with metallic Cr, there is no L+Sp+S
equilibrium. Due to this sharp rise, a small error in pO2 may lead to a
considerable error on the Cr concentrations. The error bars, however,
91
0.2
0.8
0.1
0.9
SiO2
0.7
0.3
L1+S
0.4
0.6
L1+L2+S
0.5
0.5
L1
L1+L2
L2
0.6
0.4
L1+M2S
L1+Sp
0.8
0.2
0.7
L1+L2+Sp
0.3
L1+M2S+Sp
P+M2S+Sp
0.1
0.9
MgO
L2+E
L2+Sp
0.9
0.8
0.7
0.6
0.5
mass fraction
0.4
0.3
0.2
0.1
L2+Sp+E
Cr2O3
Figure 8.6: Calculated liquidus from FactSage for CrOx -MgO-SiO2 in equilibrium with solid Cr, T=1600◦ C.
92
8.4. LIQUIDUS AND SOLIDUS AS A FUNCTION OF PO2
25
M S composition
2
liquid composition
20
wt% (Cr2O3)
15
10
5
0
-14
-12
-10
-8
-6
log pO (atm)
-4
-2
0
2
Figure 8.7: Experimental observations for the solubility of CrOx in M2 S
in equilibrium with liquid and spinel as a function of pO2 at
T=1600◦ C. Lines are only indicative.
93
only indicate the standard deviations on the EPMA measurements.
Figure 8.8: Experimental observations for the concentration of Cr in the liquid in equilibrium with SiO2 and spinel as a function of pO2 at
T=1600◦ C. The line is only indicative.
8.5
Conclusion
By comparison of new experimental data with available literature data
and calculations, this chapter showed the peculiarities of the ternary system CrOx -MgO-SiO2 . The measured data is generally in good agreement
with literature data. Some experiments in literature need to be reinterpreted, such as the saturation technique used by Morita et al. [91],
which probably lead to a mixture of phases being identified as liquid.
The calculations using the FactSage database deviate heavily when the
oxygen partial pressure is lowered. In the next chapter, an updated thermodynamic description will be proposed, which copes with the largest
deviations, and enlightens some remaining conflicts in the experimental
data.
94
Chapter 9
Thermodynamic assessment
of the CrOx-MgO-SiO2
system
In the previous chapter, the CrOx -MgO-SiO2 system was studied experimentally for a wide range of oxygen partial pressures. It became clear
that the current FactSage description is not suitable to predict the phase
relations in reducing conditions. Therefore, in this chapter, an updated
description will be developed. Starting from the binary systems, an extrapolated phase diagram is calculated. Next, solid solution phases are
added and the description of the liquid is optimised with respect to the
experimental data. Finally, the new description is integrated in a multicomponent database to recalculate some of the diagrams studied earlier,
and an improved agreement is found.
9.1
The binary systems
The first step to optimise the thermodynamic description of a ternary system is checking the binary descriptions. If the ternary experimental data
are not in agreement with the binary description, the ternary data may
be incorrect, or the binary description may be incomplete. For example,
a liquidus surface in the ternary could be drawn up to the binary system,
and not be present in the binary phase diagram description. In such a
case, the experimental evidence used to draw the binary and ternary diagrams has to be compared and one of both diagrams has to be adjusted.
In the studied system, all binary phase diagrams are in agreement with
the ternary data, except for a compositional shift in CrO-SiO2 . However,
95
CHAPTER 9. ASSESSMENT OF CrOx -MgO-SiO2
it was decided not to alter the binary description.
9.1.1
MgO-SiO2
The MgO-SiO2 system, calculated from the description of Wu et al. [49],
is shown in Figure 9.1. The phase diagram is in good agreement with
binary experimental data, as well as with the ternary data in the system
under consideration.
3000
2600
L
T (°C)
2200
L+P
L1+L2
1800
L+M2S
1400
P+M2S
L+MS
L+S
M2S+MS
MS+S
1000
0
.2
.4
.6
.8
1
mole SiO2/(SiO2+MgO)
Figure 9.1: Calculated binary system MgO-SiO2 .
9.1.2
MgO-Cr2 O3 and MgO-CrO
The system MgO-CrOx is dependent on pO2 . Therefore the two extremes
MgO-Cr2 O3 and MgO-CrO are considered. Even these denominations
are not completely correct, as it is impossible to force all chromium into
a trivalent or divalent state. The stoichiometric composition CrO dissociates into Cr and Cr2 O3 or into Cr and a liquid containing some Cr2 O3 .
More correctly, MgO-Cr2 O3 denominates the system in air and MgO-CrO
denominated the system in equilibrium with Cr. The phase diagrams,
which are consistent with ternary data, are depicted in Figure 9.2 and
9.3. In equilibrium with metallic Cr, the spinel solution reaches until the
Cr3 O4 composition around 1650◦ C. The thermodynamic description was
optimised by Jung et al. [51].
96
9.1. THE BINARY SYSTEMS
3000
L
2600
T (°C)
P
Sp
2200
1800
P+Sp
Sp+E
1400
1000
0
.2
.4
.6
mole Cr2O3/(Cr2O3+MgO)
.8
1
p(O2)= 0.21 atm
Figure 9.2: Calculated binary system MgO-Cr2 O3 in air.
3000
L
1852
2600
1851
T (°C)
L
2200
Sp
L+P
P
1800
Sp
1400
P+Sp
Sp+E
1000
0
.2
.4
.6
mole Cr2O3/(Cr2O3+MgO)
.8
1
aCr(s) = 1
Figure 9.3: Calculated binary system MgO-CrO in equilibrium with metallic
Cr.
97
9.1.3
Cr2 O3 -SiO2 and CrO-SiO2
The pO2 dependent boundary system CrOx -SiO2 is studied in somewhat
more detail. In air (Figure 9.4), the calculation is not in conflict with the
ternary data, as the experimental data is limited to temperatures where
the stability domain of the binary liquid is very small. In equilibrium
with metallic Cr, however, the liquid area of Muan [97] is larger than
calculated. Consequently, the original data in the binary is collected.
The work of Healy and Schottmiller [104], which forms the basis of the
optimisation by Degterov and Pelton [50], contains only one point for
which the presence of Cr was confirmed. Therefore, different experimental
investigations of multicomponent systems containing CrO and SiO2 in
equilibrium with metallic Cr are considered. The points on the binary
liquidus, investigated or extrapolated from the liquidus line, are indicated
in Figure 9.5. Data for the systems with MgO [96, 97], with CaO [82, 105]
and with both Al2 O3 and MgO [106] is considered.
In Section 5.1.3, it was noted that the indicated compositions of the
solids in Muan [97] may suggest that the diagram was actually drawn in
wt% CrO instead of Cr2 O3 . If it is assumed that the phase diagram of
Muan [97] is actually drawn for the CrO composition, the points at the
SiO2 side coincide with the liquidus from Devilliers and Muan [82]. As
both studies originate from the same research group, this could confirm
the CrO hypothesis. However, at the CrO side, the points do not coincide.
The set of data seems to indicate a change in the binary is needed,
especially at the CrO side. A possible updated version of the liquid
would then contain the following parameters, as defined in Equation 2.6
(in Joules) [107]:
07
ωCrO−SiO
2
= 552455 − 231.935 T
00
ωCrO−SiO
2
10
ωCrO−SiO
2
= 40413 − 18.636 T
(9.1)
= −20920,
instead of the version by Degterov and Pelton [50] used in FactSage:
07
ωCrO−SiO
2
= 754823 − 325.372 T
(9.2)
The phase diagram calculated with the updated parameters is also
indicated in Figure 9.5. There is a better agreement with the data on
the CrO side, while maintaining the location of the phase boundaries at
the SiO2 side. However, there is almost no data which is really in the
98
9.2. EXTRAPOLATION
binary system. Also, the ternary data at high CrO side is scarce. As a
change in the binary system would have consequences for many ternary
systems in the database, a more solid argumentation would be needed
to insert two extra parameters. This work will therefore build on the
existing description of the binary systems.
3000
L1
L2
L1+L2
2600
2200
T (°C)
L1
L2
L2+E
L1+E
L2+S
1800
E+S
1400
1000
0
.2
.4
.6
mole SiO2/(CrO+SiO2)
.8
1
p(O2)= 0.21 atm
Figure 9.4: Calculated binary system Cr2 O3 -SiO2 in air.
9.2
Extrapolation
After checking the binary systems, an extrapolation of the binary systems
to the ternary system is made. To extrapolate the binary interactions,
SiO2 is treated as an asymmetric component, as is usual within the quasichemical approach. In this case, this leads to results in which the general
features are already more in agreement with experimental data, as compared to the FactSage results. The FactSage database apparently contains
an incorrect interaction parameter. As an example, the isothermal sections at 1600◦ C in equilibrium with metallic Cr and at pO2 =10−9.56 atm
are shown in Figure 9.6-9.7. From the liquidus of Muan [96], arbitrary
points are selected, which do not correspond to actual experiments.
Although the major features are already present, the calculation still
needs considerable improvement. In general, the liquid area is rather
large, so a general positive interaction parameter will be needed. In
99
L+Si
2000
L
1800
L1+L2
L+Sp
1600
T (°C)
L+S
L+E
1400
Eutectic point (Collins and Muan,1982)
Liquid (Xiao and Holappa, 2002)
Liquidus (Healy et al., 1964)
Liquidus extension from:
Muan, 1990
Muan, 1990, if in CrO
Xiao and Holappa, 2002
Kossyrev et al., 1998
de Villiers and Muan, 1992
E+S
1200
1000
0
.2
.4
.6
mole SiO2/(CrO+SiO2)
.8
1
aCr(s) = 1
Figure 9.5: Calculated binary system CrO-SiO2 in equilibrium with metallic Cr using FactSage (dotted line) and adapted model (full line,
Eq. 9.2), in comparison with experimental data from [82, 95, 97,
104–106].
100
9.2. EXTRAPOLATION
This work:
L+M2S+Sp liquidus
L+Sp liquidus
L+M2S+Sp, M2S comp.
spinel+M2S+MgO, M2S comp.
spinel+M2S+MgO, MgO comp.
From Muan, 1983:
liquidus, arbitrary points
liquidus, on univariant lines
0.2
0.8
0.1
0.9
SiO2
0.7
0.5
0.5
0.4
0.6
0.3
L+S
0.6
0.4
L
L+M2S
0.7
0.3
M2S
L+M
S+S
p
L+Sp
0.8
0.2
2
P+M2S+Sp
0.9
0.1
L+Sp+E
E
MgO
P
0.9
0.8
0.7
0.6
0.5
mole fraction
0.4
0.3
0.2
o
Sp
0.1
1600 C, a(Cr(s)) = 1
CrO
Figure 9.6: Extrapolated phase diagram description in equilibrium with solid
Cr.
101
SiO2
S
L+Sp+S
0.1
0.9
L+Sp
0.8
0.3
0.7
0.2
0.4
L+S
0.6
L+Sp+M2S
L+S+Sp
0.5
0.4
2
0.6
L+
M
S
0.5
L
L+Sp
S+Sp+E
M2S
0.8
0.3
0.2
0.7
L+M2S+Sp
0.9
0.1
P+M2S+Sp
E
MgO
P
0.9
0.8
0.7
0.6
0.5
mole fraction
0.4
0.3
Sp
o
0.2
1600 C, p(O2) = 10
0.1
-9.56
atm
CrO
Figure 9.7: Extrapolated phase diagram description in reducing conditions
(pO2 =10−9.56 ).
102
9.3. DESCRIPTION OF SOLID SILICATE SOLUTION PHASES
addition, the solid solubility of the M2 S (and MS) phase needs to be
implemented.
9.3
9.3.1
Description of solid silicate solution phases
(Mg,Cr)2 SiO4
For the description of the M2 S phase, the compound energy formalism
(CEF) is used, which was already used to model other olivine structures,
with Mg and Ca [52] and several other cations [108, 109].
The olivine structure has two different octahedral sites, called M1 and
M2. These sites have different sizes, and therefore, the larger cations will
prefer to be on the larger M2 sites. To capture this behaviour, which
affects the configurational entropy, the phase is described with four sublattices, as:
[Mg2+ , Cr2+ ]M2 [Mg2+ , Cr2+ ]M1 [Si4+ ][O2− ]4 .
(9.3)
The last two sublattices contain only one component and are not considered further, leading to the simpler notation [Mg,Cr]M2 [Mg,Cr]M1 SiO4 .
As in the two-sublattice ionic liquid model, a Gibbs energy needs to be assigned to all combinations. The first combination is [Mg]M2 [Mg]M1 SiO4 ,
which is pure forsterite, for which the Gibbs energy is known from the
binary.
Secondly, [Cr]M2 [Cr]M1 SiO4 is defined. The Gibbs energy Gm (see
equation 2.2) of this hypothetic compound is defined as follows:
2
2
2 SiO4
2 O3
2
GCr
= GCr
+ GCr
+ GSiO
+ Gadd ,
m
m
3 m
3 m
(9.4)
in which the additional energy Gadd is an adjustable parameter. The
value of Gadd =37656 J/mol is determined in the optimisation, based on
the solubility of CrO in M2 S inequilibrium with liquid and spinel, or
periclase and spinel.
For the last two combinations, [Mg]M2 [Cr]M1 SiO4 and its stoichiometric equivalent [Cr]M2 [Mg]M1 SiO4 , an exchange reaction energy α is
defined:
CrM2 MgM1 SiO4 MgM2 CrM1 SiO4 , ∆G = 2α.
(9.5)
The Gibbs energies of the hypothetic compounds are then defined as:
103
Cr
Gm
M2 MgM1 SiO
4
Mg
Gm
M2 CrM1 SiO
4
=
=
1 Mg2 SiO4 1 Cr2 SiO4
Gm
+ Gm
+α
2
2
1 Mg2 SiO4 1 Cr2 SiO4
Gm
−α
+ Gm
2
2
(9.6)
(9.7)
(9.8)
The value of α is determined from the empirical relationship observed
by Jung [108], as shown in Figure 9.8. The cation distribution data by
Ericsson and Filippidis [110] reveals a correlation between the ratio of
ionic radii and the equilibrium distribution between the sites. The cation
distribution constant Kd for the ions A and B is defined similar to an
equilibrium constant for the exchange reaction:
Kd =
M2 y M1
yB
A
,
M2 y M1
yA
B
(9.9)
where yiM1 is the site fraction of component i on sublattice M1.
From the high spin ionic radii in sixfold coordination recommended
by Shannon [111], the ratio rMg2+ /rCr2+ = 0.915. This corresponds to a
distribution constant Kd of 10−1.39 , which in turn leads to an exchange
Gibbs energy α of 18410 J/mol. The resulting behaviour is illustrated in
Figure 9.9, and a preference for Cr on M2 sites is observed as expected.
9.3.2
(Mg,Cr)SiO3
Few data is available on the extent of the (Mg,Cr)SiO3 solution phase.
Therefore, a simple regular solution model is used. The Gibbs energy
of pure MgSiO3 (proto-enstatite) is known from the binary system. As
CrSiO3 is a hypothetic compound, its Gibbs energy is defined with a
similar approach as for Cr2 SiO4 :
1
1
3
2 O3
2
GCrSiO
= GCr
+ GCr
+ GSiO
+ Gadd .
m
m
m
3
3 m
(9.10)
Again, Gadd is the only adjustable parameter for the solid solution. In
this case, Gadd is determined by the MS+M2 S+Sp and MS+Sp+S equilibria solid phase relations, and to a minor extent by the L+MS liquidus.
Because the subsolidus data are only available at high pressures [101], and
the L+MS liquidus data of Muan [96] are scarce, only a rough estimate
was determined here, Gadd =16736 J/mol (or 4000 cal/mol).
104
9.3. DESCRIPTION OF SOLID SILICATE SOLUTION PHASES
3
Mg-Co
1
Mg-Fe
ln Kd
-1
-3
Ca-Mn
-5
Mg-Mn Cr-Mg
Fe-Co
Fe-Mn
Fe-Ni
Ni-Mg
Mn-Co
Ca-Fe
Ca-Mg
-7
-9
Zn-Mg
Fe-Zn
0.65
0.7
Ca-Co
0.75
0.8
rB/rA
0.85
0.9
0.95
1
Figure 9.8: Relationship between the cation distribution constant Kd and the
ratio of ionic radii rB /rA for A-B couples with rB < rA , after
Jung [108]. Closed symbols are experimental data from Ericsson
and Filippidis [110], open circles are modelled by Jung [108]. The
model of this work is indicated by a star.
105
M2
M1
Cr Mg SiO4
Cr2SiO4
MgM2CrM1SiO4
Mg2SiO4
Figure 9.9: Calculated equilibrium site fractions for the (Mg,Cr)SiO4 solution
at 1400◦ C.
9.4
Description of the liquid phase
The liquid slag phase is modelled using the quasichemical model. The
binary parameters are taken from the binary systems, as discussed in
Section 9.1. By trial and error, three parameters are selected for the
ternary interactions in the liquid. No interactions involving Cr2 O3 were
implemented.
φ002
CrO−SiO2 (MgO) = −33472 J/mol
(9.11)
φ011
MgO−SiO2 (CrO)
φ011
SiO2 −MgO(CrO)
= 54392 J/mol
(9.12)
= 29288 J/mol
(9.13)
The Gibbs energy change resulting from such a parameter φ is defined in Equation 2.12. The value of these parameters is determined by
iterative manual phase diagram calculations, with smaller and smaller
parameter modifications, to find the most appropriate values to represent
the experimental data. Once more detailed changes (in practice, modifications of 500 cal/mol) did not have a notable effect, the iteration was
stopped. The conflicts encountered in this process will be discussed later.
106
9.5. OPTIMISED PHASE DIAGRAM DESCRIPTION
The effect of the different parameters is illustrated in 9.10. The phase
diagram in equilibrium with metallic Cr at 1600◦ C is selected as an example, as it shows the effects on a large compositional domain. The regions
where the parameters are active are depicted, similar to the schematic
illustration in Figure 2.6 for a system with an asymmetric component.
First, φ002
CrO−SiO2 (MgO) is a negative parameter with a strong influence
on the M2 S liquidus. In combination with the other positive parameters,
it allows to shift the L+M2 S+Sp equilibrium to lower CrO concentrations.
Second, φ011
MgO−SiO2 (CrO) is a general positive parameter, allowing to
lower the spinel and M2 S solubility. As a side effect, the SiO2 solubility
is raised.
Finally, the positive φ011
SiO2 −MgO(CrO) is more centrally active and lowers the SiO2 solubility as well as M2 S solubility, making the liquid region
more narrow on the left side. In this way it compensates some of the side
effects of the previous parameters. It also suppresses the spinel solubility
at higher pO2 , when the spinel liquidus arrives in its target region. However, it also affects the L+M2 S+Sp equilibrium, thus undoing part of the
effect of the first parameter.
9.5
Optimised phase diagram description
The optimised phase diagram is compared to the experimental results in
Figures 9.11-9.18. An overview of the parameters in the ternary solution
phases is given in Appendix B, Table B.1.
The system in air was left unchanged, as there was no need to define
ternary interactions with Cr2 O3 based on the experimental data. Therefore, the phase diagram in air at 1600◦ C can still be seen in Figure 8.1.
Another section, at 1800◦ C, is represented in Figure 9.11.
The system in intermediately reducing conditions is shown in Figure 9.13, for pO2 =10−9.56 atm, and in Figure 9.14, for pO2 =10−10.16 atm.
Experimental data from this work and determined by Morita et al. [91]
are included.
Finally, the phase diagram in equilibrium with metallic chromium is
depicted in Figures 9.15-9.17. Here, data from this work and from Muan
[96] are indicated. As it appeared possible that the data of Muan [96]
should be recalculated as if the diagram was in CrO instead of Cr2 O3 ,
two versions of his data are plotted. A full liquidus projection is given in
Figure 9.18.
The remaining differences between calculations and experiments, and
the conflicts between different experimental data points, will be discussed
in the next section.
107
f 011
MgO-SiO (CrO)
f 002
CrO-SiO (MgO)
2
2
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.3
0.2
0.4
0.3
0.2
0.1
0.1
0.2
0.1
CrO
MgO
0.9
0.9
0.3
mole fraction
0.8
0.8
0.4
L
0.7
0.7
w00
0.6
0.6
0.5
0.5
0.5
0.6
0.4
0.4
0.7
0.3
0.3
w01
L
0.8
0.2
0.2
0.9
MgO
0.1
0.9
SiO2
0.1
0.9
SiO2
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
mole fraction
0.1
CrO
f 011
SiO -MgO(CrO)
2
extrapolated diagram
diagram with a single parameter
effect of this parameter
0.5
0.5
0.4
L
0.6
0.3
01
MgO
0.9
0.1
0.8
0.2
0.7
w
region where parameter is active
0.4
0.6
0.3
0.7
0.2
0.8
0.1
0.9
SiO2
0.9
0.8
0.7
0.6
0.5
mole fraction
0.4
0.3
0.2
0.1
CrO
Figure 9.10: Effect of the implemented parameters in the liquid on the phase
diagram in equilibrium with metallic Cr at 1600◦ C. The first parameter is negative, the other two are positive.
108
SiO2
0.2
0.8
0.1
0.9
L2
0.3
0.7
L1+L2
0.4
0.6
L1+L2+Sp
L1
0.5
0.4
L1+Sp
0.3
M
S+
Sp
0.8
0.2
2
0.7
L+
0.6
M2S
0.5
L2+Sp+E
0.1
MgO
P
0.9
0.8
0.9
P+M2S+Sp
0.7
0.6
0.5
Sp
mole fraction
0.4
0.3
o
0.2
0.1
1800 C, p(O2) = 0.21 atm
Cr2O3
calculated phase diagram
liquidus (Keith, 1954)
miscibility gap (Keith,1954)
Figure 9.11: Optimised phase diagram description in air at 1800◦ C, in comparison with experimental data from [89].
109
0.1
0.9
SiO2
0.2
0.8
Eskolaite
0.3
0.7
2 liquids
Cristobalite
Protoenstatite
0.6
0.4
00
16 00
17 0
0
00
20
00
0.5
19
0.5
Forsterite
0
220
18
0.4
0.3
0.2
0.1
MgO
0.9
250
0
2 40
0.9
270
0.8
2200
Periclase
2 60
2 liquids
00
0.7
21
0.6
Spinel
23 0 0
0
0
0
0.8
0.7
0.6
0.5
mass fraction
0.4
0.3
0.2
0.1
Cr2O3
Figure 9.12: Calculated liquidus projection in air. The extent of the miscibility
gap linked to the Cr2 O3 -SiO2 system above 2200◦ C has been
omitted for clarity.
110
SiO2
S
L+Sp+S
0.1
0.9
L+Sp
0.3
0.7
0.2
0.8
L+Sp+M2S
0.6
0.4
L+S
L+S+Sp
0.5
2
L+
M
S
L+Sp
0.6
0.4
0.5
L
S+Sp+E
L+M2S+Sp
0.8
0.2
0.7
0.3
M2S
0.9
0.1
P+M2S+Sp
E
MgO
P
0.9
0.8
0.7
0.6
0.5
mole fraction
0.4
0.3
Sp
0.2
0.1
CrO
Figure 9.13: Optimised phase diagram description at pO2 =10−9.56 atm at
1600◦ C, in comparison with experimental data from [91] and Figure 8.3.
111
SiO2
S
L+Sp+S
0.1
0.9
L+S
L+Sp
liquidus data
0.2
0.8
L+Sp+M2S
M2S composition data
0.3
0.7
L only
0.6
0.4
L+S
L+S+Sp
0.5
0.5
L
2
M
L+
S+Sp+E
M2S
0.3
L+M2S+Sp
0.7
0.8
0.2
0.6
0.4
S
L+Sp
MgO
P
0.9
0.1
P+M2S+Sp
0.9
0.8
0.7
0.6
0.5
mole fraction
0.4
0.3
Sp
0.2
0.1
E
CrO
Figure 9.14: Optimised phase diagram description at pO2 =10−10.16 atm at
1600◦ C, in comparison with experimental data from Figure 8.4.
112
L+Sp liquidus
SiO2
L+Sp+M2S, liquidus
S
P+Sp+M2S, M2S composition
0.1
0.9
liquidus by Muan
0.2
0.8
P+Sp+M2S, P composition
liquidus by Muan, if in CrO
0.7
0.5
0.5
0.4
0.6
0.3
L+S
0.6
0.4
L
L+M2S
0.7
0.3
M2S
L+M2S+Sp
0.2
0.8
L+Sp
P+M2S+Sp
0.9
0.1
L+Sp+E
E
MgO
P
0.9
0.8
0.7
0.6
0.5
mole fraction
0.4
0.3
0.2
Sp
0.1
CrO
Figure 9.15: Optimised phase diagram description in equilibrium with solid Cr
at 1600◦ C, in comparison with arbitrary points on the experimental liquidus from [96] and experimental data points from Figure
8.5.
113
1500°C
Muan, 1983
Muan, if in CrO
1700°C
Muan, 1983
Muan, if in CrO
0.2
0.8
0.1
0.9
SiO2
0.7
0.4
0.6
0.3
L+S
0.6
0.4
0.5
0.5
L+MS
0.3
0.7
L+M2S
0.8
0.2
L+E
MgO
0.9
0.1
L+Sp
0.9
0.8
0.7
0.6
0.5
mole fraction
0.4
0.3
0.2
0.1
CrO
Figure 9.16: Optimised phase diagram description in equilibrium with solid Cr
at 1500 and 1700◦ C, in comparison with experimental data from
[96].
114
SiO2
Muan, 1983
Muan, if in CrO
0.4
0.6
0.3
0.7
0.2
0.8
0.1
0.9
S
0.5
0.5
MS+S+Sp
L
0.6
0.4
MS
M2S
0.8
0.2
0.7
0.3
MS+M2S+Sp
0.1
MgO P
0.9
0.8
0.7
0.9
P+M2S+Sp
0.6
0.5
mole fraction
0.4
0.3
0.2
o
Sp
E
0.1
1400 C, a(Cr(s)) = 1
CrO
Figure 9.17: Optimised phase diagram description in equilibrium with solid
Cr at 1400◦ C, in comparison with experimental data from [96].
The equilibria can also be compared to the high pressure data in
Figure 5.5.
115
0.1
0.9
SiO2
0.8
00
0.2
19
2 liquids
0.7
0.3
1800
1700
Protoenstatite
1500
0.6
0
0.5
Cris
toba
0
lite
0.5
150
17
0.4
1600
15 0
16
00
00
0.4
0.6
Forsterite
Eskolaite
0.3
0.7
Spinel
1 180
2 900 0
21 000
00
20
0
23
24 00
00
25
00
0.2
0.1
00
0.9
26
27
0.8
Periclase 2
00
MgO
0.9
0.8
0.7
0.6
0.5
mass fraction
0.4
0.3
0.2
0.1
CrO
Figure 9.18: Calculated liquidus projection in equilibrium with solid Cr.
Above 2300◦ C, a miscibility gap originating in the CrO-SiO2 system has been omitted for clarity.
116
9.6. DISCUSSION
9.6
Discussion
SiO2 liquidus The experimental data on the SiO2 liquidus are somewhat scattered, as illustrated in Figure 9.19. This figure is a summary
of the high SiO2 sides of Figure 9.13, 9.14 and 9.15. The extent of the
liquidus is heavily affected by the pO2 . The calculated liquidus at different pO2 , however, shows the liquidus is extended without a considerable
influence on its location. Therefore, it is expected that also the experimental data would be located on a single curve, which is not the case. The
liquidus line from Muan [96] shows a constant deviation from the calculation, already originating in the binary. As discussed in Section 9.1 on the
binary systems, recalculating the diagram as if it was expressed in CrO
removes the larger part of this error. It has to be noted that Muan [96]
only measured a few data points on the SiO2 side, as shown in Figure 5.4.
However, the data measured at lower temperatures constrain the SiO2 liquidus to a more or less straight line. The L+S point at pO2 =10−10.16
atm is located on this line. The other data, however, suggest a lower
SiO2 solubility in the liquid. A possible explanation is the crystallisation of SiO2 from the liquid on quenching, e.g. in the L+S+Sp sample at
pO2 =10−10.16 atm, which could lead to lower SiO2 concentrations in the
observed quenched liquid.
L+M2 S+spinel equilibrium The composition of the liquid in equilibrium with M2 S and spinel, as well as the composition of M2 S in equilibrium with liquid and spinel, are strongly influenced by pO2 . Figure
9.20 compares the Cr concentration of both phases with the experimental
data from this work and from Morita et al. [91] and Muan [96].
Considering that the pO2 in our experiment with metallic Cr may have
been somewhat higher than intended, the M2 S composition of the new
description agrees very well with our data. Good agreement is also found
with the data of Morita et al. [91]. Their intent was to measure the liquid
composition saturated with M2 S and spinel, but, as explained in Section
8.2, the analysed phase was probably mostly M2 S, in combination with
some liquid.
The modelled liquid composition slightly underestimates the Cr content in our measurements. However, in equilibrium with solid Cr, the
model agrees well with the phase diagram of Muan [96]. If the parameters
are adjusted to move the L+M2 S+Sp equilibrium to higher CrO contents
at intermediate pO2 , the phase diagram in equilibrium with metallic Cr
is also affected, and there also the L+M2 S+Sp point shifts to higher Cr
concentrations.
117
SiO2
pO2=10-9.56 atm:
L+S
pO2=10
0.1
0.9
L+Sp+S (Morita, 1988)
-10.16
atm:
L+Sp+S
0.2
0.8
L+Sp+S
with Cr:
0.6
0.4
0.6
0.4
O
Cr
L
0.5
0.5
L+S
L+S (Muan, if in CrO)
0.3
0.7
L+S (Muan, 1983)
MgO
Figure 9.19: Detailed comparison of SiO2 liquidus data at different pO2 . The
extent, but not the location of the calculated SiO2 liquidus (lines)
is affected by pO2 . The experiments (symbols), on the other hand,
are not located on one single curve.
118
9.6. DISCUSSION
Cr satd.
The reliability of the phase diagram by Muan [96] in Figure 5.4 is
uncertain. His group mostly only used optical microscopy to analyse
the experimental outcome in terms of stable phases, and positioned the
results on the original compositions, which may not have been the final
composition after the experiment. In experiments with metallic Cr, the
oxidation of Cr may lead to a higher CrOx content in the oxidic part
of the sample than originally mixed. It is also uncertain if the presence
of Cr was verified after the experiments, a procedure which could have
eliminated possible results where the actual pO2 was higher than it should
have been. Nevertheless, several experimental points are indicated around
the L+M2 S+Sp equilibrium, and it was therefore decided to fit the data
as well as possible.
Muan, 1983
Muan, if in CrO
Morita et al., 1988
This work, Liquid
This work, M2S
Model, Liquid
Model, M2S
Figure 9.20: Cr concentration of liquid and M2 S in the L+M2S+Sp equilibrium as a function of pO2 . Experimental data from [96], [91] and
Figure 8.7. The data from Morita et al. [91] agrees well with the
composition of M2 S, although their intent was to measure the
liquid composition.
119
Spinel liquidus First, the spinel liquidus in reducing atmospheres is
in good agreement with our data and the data from Morita et al. [91], as
shown in Figure 9.13 and 9.14. However, the slope is not completely correct. This difference is difficult to eliminate, as the compositional domain
is rather small. It would require rather large counteracting parameters
which can lead to miscibility gaps in other parts of the phase diagram.
Second, the spinel liquidus in equilibrium with metallic Cr has a different shape as the one drawn by Muan [96]. This can be observed in
Figure 9.15, where the shape of the experimental liquidus of Muan [96]
is indicated by arbitrary points. However, very few experiments were
conducted in this area, as indicated on the original liquidus projection in
Figure 5.4.
Liquidus at T<1600◦ C At 1400 and 1500◦ C, the calculated liquid
area is considerably smaller than in the phase diagram by Muan [96]. One
part of the explanation is probably the larger liquid area in the binary
CrO-SiO2 assumed by Muan [96]. However, another part of the difference comes from the overall positive parameters needed to fit the data
at higher temperature. It is, of course, possible to define temperature
dependent parameters. In this case, however, a rather large temperature
dependent term would be needed to annihilate the positive parameters
over a few hundred degrees. Moreover, this term would be positive, so the
interaction parameters would become quickly larger at higher temperature. This is a dangerous situation as it creates inverted miscibility gaps
[12]. Instead of the linear a + bT terms, Kaptay [112] proposed to use an
exponential term c · exp(−T/d), which goes to zero at high temperatures.
The use of this kind of parameters has, however, not been implemented
in the quasichemical model.
Miscibility gap in air The major feature in the liquidus projection
by Keith [89] is a large miscibility gap, extending from the MgO-SiO2
binary to the Cr2 O3 -SiO2 binary. This would require the MgO-SiO2 miscibility gap to grow with higher temperatures and higher Cr2 O3 content.
At 1800◦ C, the calculated liquidus shown in Figure 9.11 is in good agreement with the liquidus by Keith [89], except for the extent of the miscibility gap. However, from the experiments by Keith [89] up to 1800◦ C,
as indicated in Figure 5.1, no real evidence for the extent of the miscibility gap can be expected. Therefore, the calculated behaviour, where the
MgO-SiO2 miscibility gap shrinks with increasing temperatures, is considered credible. The calculated liquidus in air is shown in Figure 9.12.
At temperatures around 2100◦ C, lower than the melting point of Cr2 O3 ,
120
9.7. MULTICOMPONENT SYSTEM
an extended Cr2 O3 liquidus is calculated, without miscibility gap. The
Cr2 O3 -SiO2 miscibility gap then only appears at temperatures somewhat
below the melting point of Cr2 O3 .
Conclusions The presented model of the phase diagram CrO-Cr2 O3 MgO-SiO2 provides a large step forward from the FactSage description
and the extrapolation from the binary system. However, some differences
with experimental data remain. Several differences can be attributed to
uncertainties in the experimental data, but certain systematic deviations
are present. These could not be solved without substantially increasing
the complexity of the model.
Also, as ternary interaction parameters can have a temperature dependence, but not a pO2 dependence, they have an effect on all sections
at different pO2 at the same temperature simultaneously. Therefore, it is
difficult to adapt the model to contradicting data at different pO2 . It also
restricts the absolute value of the implemented parameters. If a parameter is mostly active in the partially solid region at higher pO2 , it can still
be very effective fit the liquidus data there. However, it may be active in
the liquid region at very low pO2 , where it can lead to a miscibility gap.
As a result, the remaining differences can probably only be resolved by
other means, e.g. the interaction between CrO and Cr2 O3 , or the Gibbs
energy of spinel. Affecting these would however have a consequence for
several other systems.
9.7
Multicomponent system
In this section, the adapted model for CrO-Cr2 O3 -MgO-SiO2 is integrated
into the multicomponent database with CaO, and the results of this modified database are compared to the experimental results discussed in Chapter 7.
First, a section at B=CaO/SiO2 =0.5 is calculated, as depicted in Figure 9.21. A substantial improvement of the agreement with experimental
data is noted. The agreement is not perfect, however, as this would require an even higher spinel solubility but a lower eskolaite solubility.
Second, a calculation at a higher basicity B=1.2 is performed. As can
be observed on Figure 9.22, the new model systematically overestimates
the experimentally observed solubility. There is no reason to assume
that the new CrOx -MgO-SiO2 interactions are too positive. They are,
however, too positive in the FactSage model, as they lead to a miscibility
gap in the CrOx -MgO-SiO2 , as shown in Figure 8.6. Therefore, it is
assumed that the difference on the CrOx axis in Figure 9.22 now extends
121
16
L
+
E
L+E
L+Sp
L
L+M2S
14
12
FactSage
Our model
wt% Cr
10
L+Sp
L
+
Sp
+
M2S
8
6
4
L
2
0
L
+
M2S
0
5
L + SiO2
10
15
20
25
30
35
wt% MgO
Figure 9.21: Phase diagram calculated with FactSage and updated database
compared to experimental observations for CaO-CrOx -MgO-SiO2
with B=C/S=0.5, at pO2 =10−9.36 atm and T=1600◦ C.
122
9.8. CONCLUSION
over the whole spinel liquidus, whereas it is compensated by uncorrect
CrOx -MgO-SiO2 interactions in the FactSage model. This difference was
discussed in Section 7.3.1, where it was shown to originate in the CaOCrOx -SiO2 system. Therefore, an update of the CaO-CrOx -SiO2 system
to eliminate the differences on the eskolaite liquidus is probably needed
to find a perfect agreement.
12
L
+
E
L
+
Sp
+
E
L+E
L+Sp
L+Sp+C2S+P
FactSage
L+Sp
10
L
+
Sp
+
C2S
wt% Cr
8
Our model
L+Sp+C2S+P
6
4
L
2
0
L+C2S
0
5
10
15
L+C2S+P
20
25
wt% MgO
Figure 9.22: Phase diagram calculated with FactSage and updated database
compared to experimental observations for CaO-CrOx -MgOSiO2 . B=C/S=1.2, pO2 =10−9.36 atm, T=1600◦ C.
Finally, the diagram at varying basicity and constant MgO/Cr2 O3
ratio is recalculated in Figure 9.23. In contrast to the FactSage calculation
in Figure 7.12, the calculated liquidus seems to agree quantitatively with
the experimental data. However, the calculated primary phase is still
spinel, although eskolaite is now also stable in a small area. As the
stabilities of eskolaite and spinel appear to be very close to each other,
and the stability of the liquid seems more or less correct now, it is probably
necessary to adapt the stabilities of the solids.
9.8
Conclusion
Based on the experimental data from literature (Chapter 5) and from
the present investigation (Chapter 7), a new thermodynamic description
123
Exp. L+E
Exp. L+E+S
Calc. M/K=1
Calc. M/K=2
0.6
0.4
0.5
0.5
0.4
0.6
0.3
0.7
0.2
0.8
0.1
0.9
MgO+Cr2O3
0.3
L+S
L
0.2
L+Sp+C2S+E
0.9
0.1
0.8
L+C2S+Sp
0.7
L+Sp+E
+S
Sp
L+
L+Sp
L+C2S
CaO
0.9
0.8
0.7
0.6
0.5
mass fraction
0.4
0.3
0.2
0.1
SiO2
Figure 9.23: Phase diagram calculated with the updated database compared to experimental observations for CaO-SiO2 -Cr2 O3 +MgO
at pO2 =10−9.36 atm, T=1600◦ C and MgO/Cr2 O3 =M/K=1. As
eskolaite precipitates, the molar ratio MgO/Cr2 O3 in the observed liquid composition is increased and lies between 1 and
2. The figure can be compared to the FactSage calculation in
Figure 7.12.
124
9.8. CONCLUSION
of the CrOx -MgO-SiO2 system was developed. The binary systems were
left untouched, as well as the interactions involving Cr2 O3 . Essentially,
three CrO-MgO-SiO2 interaction terms were added in the liquid, and two
solids (Mg2 SiO4 and MgSiO3 ) were extended to solid solutions. The resulting description exhibits a good, although not perfect, agreement with
the experimental data. Certain conflicts and assumptions made in the
literature have been clarified. Sometimes the assumptions could not be
confirmed, such as the assumption of Keith [89] that the miscibility gaps
in MgO-SiO2 and Cr2 O3 -SiO2 would connect in the ternary. A reasonable
compromise was proposed for apparently conflicting experimental data,
such as the shape of the SiO2 liquidus or the position of the L+Sp+M2 S
equilibrium. When the description is integrated in the multicomponent
database, a better agreement with experimental results at low basicity is
found. At higher basicity, the agreement is somewhat worsened. Overall,
the new model provides a better and more consistent description of both
the ternary and the higher order system.
125
126
Chapter 10
Conclusions
The objective of this work was to improve the thermodynamic description
of stainless steel slags, a multicomponent system reduced to CaO-CrOx MgO-Al2 O3 -SiO2 . Combining a modelling and an experimental point
of view, the goal was to spot lacunae in the available thermodynamic
description. Differences observed in the multicomponent system would
be tracked down to the ternary systems. The work would also improve
the description for the ternary system where the most conspicuous discrepancies between modelling and experiments are located, which would
appear to be CrOx -MgO-SiO2 . By improving this ternary description,
the general agreement of the multicomponent model with experimental
data should also be improved.
10.1
Results and evaluation
This text started with an overview of methods for modelling liquid oxide
systems and for determining oxide phase diagram data. On the modelling
side, it appeared that the modified quasichemical model had succeeded in
providing an adequate description of the short range order in oxidic liquid,
and had been applied in the most detailed description of the multicomponent system under study. On the experimental side, it was concluded
that quench methods provide the most robust technique to study oxide
phase relations involving the liquid.
With this background in mind, a method to determine liquidus-solidus
relations in the pO2 system under investigation was proposed. The method
consists of equilibration in a tube furnace, sampling or quenching, and
subsequent analysis of the different quenched phases. The oxygen partial
pressure pO2 was controlled by gas mixtures with a controlled CO/CO2
ratio, and in some cases by equilibration with air or Cr metal. The
127
CHAPTER 10. CONCLUSIONS
analysis was performed with standardised EPMA-WDS. Sampling was
performed with alumina bars, without breaking the atmosphere. This
lead to a moderately fast quench, of which the artifacts induced in the
quenched samples were discussed.
In the multicomponent system CaO-CrOx -MgO-Al2 O3 -SiO2 , phase
diagram sections at different temperatures, Al2 O3 contents, and basicity
(CaO/SiO2 ) levels were measured. The agreement between calculation
and experiments on the influence of temperature, MgO and Al2 O3 on
the CrOx solubility was good. The influence of the basicity was less well
estimated by the calculations. Two sets of systematic differences were
observed:
1. The calculated eskolaite solubility is systematically 1-2 wt% Cr
higher than the experimentally determined solubility. It was shown
that this difference originates in the CaO-CrOx -SiO2 system.
2. The calculated spinel solubility at low basicities is several wt% Cr
lower than experimentally determined. Also this difference seemed
to be a problem of extrapolation from the ternary systems, and
appeared to originate from the system CrOx -MgO-SiO2 .
As the second issue seemed the most problematic, the CrOx -MgOSiO2 system was studied next. In the experiments, a large dependence on
pO2 was found, and the lower the pO2 , the more the FactSage calculations
deviated from the experimental data from this work and from literature.
Also, at lower pO2 , a substantial solubility of Cr in the forsterite (M2 S)
phase was noticed.
To address the discrepancies in the FactSage description of CrOx MgO-SiO2 , a new description was developed. This description is based
on the quasichemical model for the liquid, the compound energy formalism for the solid solution (Mg,Cr)2 SiO4 , and a regular solution for
(Mg,Cr)SiO3 . In the liquid, three ternary interaction parameters were
defined. In the solids, the Gibbs energy of the hypothetic chromium silicate phase was the only adjustable parameter. The reliability of the
experimental data could be assessed during the process of optimising the
description. When the new model is compared with experimental data,
some differences remain, especially at lower temperatures and high CrOx
content in equilibrium with metallic Cr. Overall, the description was
found to be a good compromise, also when integrated in the higher order
database.
128
10.2. SUGGESTIONS FOR FURTHER WORK
10.2
Suggestions for further work
A number of experiments could further clarify the phase relations in the
studied systems:
1. In the CrO-SiO2 binary system, very few data points are really
in equilibrium with metallic Cr. As this is a key system for the
understanding of the behaviour of Cr in silicate slags, a series of
experiments to determine the exact location of the eskolaite and
cristobalite liquidus would be useful.
2. Also the exact location of the spinel liquidus in the CrO-MgO-SiO2
system in equilibrium with metallic Cr has not been studied in
detail. As the new description still deviates in this region, some
additional experiments could help to determine the accuracy of the
description of liquid and spinel.
3. There is no reliable experimental thermodynamic data in the CrOMgO-SiO2 system in equilibrium with metallic Cr. The new description is therefore solely based on the location of phase boundaries. Activity or mixing enthalpy measurements would constrain
the ternary interactions in the liquid in a more direct way.
Also, further modelling efforts could reduce the disagreements between calculations and experimental data:
1. The CrO-MgO-SiO2 system in equilibrium with metallic Cr is still
not perfectly described at temperatures lower than 1600◦ C. Using
temperature dependent interaction terms, this may be resolved, although more experimental evidence would also be helpful.
2. The Gibbs energy of spinel and eskolaite probably need to be slightly
adjusted, as the equilibrium between both phases and the liquid
needs to be shifted to higher Cr concentrations. Possibly the integration of some Cr2+ in Cr2 O3 at low pO2 needs to be modelled.
3. In the new model, the error on the eskolaite liquidus in the system
CaO-CrOx -SiO2 extends further into the quaternary system with
MgO. Therefore, an update of the CaO-CrOx -SiO2 is probably necessary.
129
CHAPTER 10. CONCLUSIONS
130
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REFERENCES
142
Part III
Appendices
143
Appendix A
Experimental data
In the next pages, the experimental results are tabulated. The total chromium oxide is expressed as Cr2 O3 . Standard deviations on the EPMA
measurements are given in italic below the compositions. The sample
names correspond to the initial compositions given in Table 7.1 and 8.1.
A-1
APPENDIX A. EXPERIMENTAL DATA
Table A.1: Experimental results in the CaO-CrOx -MgO-Al2 O3 -SiO2 system.
Sample
T (°C )
phases
1A
L+E
1B
L+E
2
L+E
3
L+Sp
4A
L+Sp
4B
L+Sp
4C
L+Sp
5A
L+Sp
log pO2
phase
time
1600
-9.36 L
24
E
1600 -10.16 L
23.5
1600 -10.16 L
30
1600 -9.36 L
8
Sp
1600
-9.36 L
16.5
Sp
1600
-9.36 L
24
1600 -10.16 L
12
Sp
1600
-9.36 L
14.5
Sp
5B
1600 -10.16 L
L+Sp
8
6A
1600 -9.36 L
L+Sp+P+C2S
8
Sp
P
C2S
6B
1600 -10.16 L
L+Sp+P+C2S
22
Sp
P
7
1600 -10.16 L
L+P+C2S
8
P
C2S
A-2
wt% CaO
SiO2
MgO
Al2O3
Cr2O3
MoO3
St. Dev.
s.d.
s.d.
s.d.
s.d.
s.d.
47.8
1.5
0.7
0.3
46.0
0.8
49.2
0.9
49.3
0.4
2.5
0.1
49.3
0.9
1.8
0.1
48.9
0.4
48.3
1.4
1.5
0.4
47.5
0.5
1.1
1.0
46.8
1.0
44.5
0.6
1.1
0.2
0.3
0.0
58.6
44.8
1.7
0.8
0.0
0.3
42.2
5.9
0.3
0.0
56.1
1.8
43.4
1.5
0.1
0.0
40.9
0.3
41.5
0.7
42.1
0.4
0.1
0.0
39.7
1.1
0.2
0.1
38.6
0.8
41.3
1.6
0.1
0.0
39.8
0.4
0.6
1.0
39.5
0.5
36.4
0.5
0.1
0.0
0.1
0.0
34.6
37.5
0.4
0.2
0.1
0.2
35.8
1.0
0.0
0.0
32.8
0.6
0.32
0.02
0.00
0.00
0.16
0.01
1.39
0.05
3.3
0.1
19.3
0.2
5.0
0.1
19.2
0.2
5.0
0.3
5.3
0.9
19.7
0.2
11.5
0.2
21.1
0.4
11.5
0.1
16.2
0.5
21.1
0.3
83.6
1.9
5.8
16.8
1.0
21.7
0.3
85.3
17.8
5.2
96.9
1.5
5.5
0.3
0.4
0.0
0.2
0.0
0.4
0.0
1.0
0.2
0.7
0.0
0.6
0.0
0.4
0.0
0.4
0.0
0.5
0.0
0.4
0.1
0.5
0.0
0.4
0.0
0.7
0.0
0.3
0.1
0.3
0.1
0.7
0.0
0.1
0.0
0.0
0.5
0.0
0.9
0.1
0.2
0.3
0.2
0.1
0.0
0.0
0.0
8.3
1.1
96.9
0.7
11.8
0.5
10.5
0.5
6.2
0.2
77.9
0.5
3.7
0.7
74.0
0.3
4.5
0.1
5.4
0.5
77.7
1.3
2.2
0.2
76.9
1.5
2.9
0.3
1.0
0.2
74.7
0.8
15.4
0.3
0.3
1.6
0.3
76.3
0.6
16.7
0.01
0.01
0.15
0.06
0.00
0.00
.45
.13
.37
.18
.04
.01
.03
.02
.48
.06
.07
.02
.45
.12
.05
.02
.57
.03
.07
.04
.05
.02
.62
.05
.02
.02
.03
.02
.75
.15
.19
.05
.03
.01
.15
.13
.04
.23
.04
.00
.12
.08
.00
.01
.02
.01
Total
C/S
no. of
points
100.7
1.10
98.3
8
3
99.4
1.12
7
103.5
1.19
6
102.1
1.17
7
100.6
98.6
2
1.24
95.7
6
3
98.2
1.27
6
100.8
1.17
9
99.6
101.9
3
1.19
100.4
18
4
101.2
1.19
8
99.1
1.22
4
97.9
4
99.6
4
99.5
101.3
1.20
100.4
102.7
96.3
1
7
2
1.18
1
12
97.5
3
94.5
5
Table A.2: Experimental results in the CaO-CrOx -MgO-Al2 O3 -SiO2 system
(continued).
Sample
T (°C)
phases
8A
L+E
8B
L+E
9A
L+Sp
9B
L+Sp
9C
L+Sp
10A
L+P
10B
L+P
11
L+E
12
L+Sp
phase
time
1600
-9.36 L
32
E
1500 -11.04 L
23.5
E
1600
-9.36 L
8.5
Sp
1600 -10.16 L
13.5
Sp
1500 -11.04 L
23
Sp
1600
-9.36 L
15
P
1500 -11.04 L
23.5
P
1600
1600
13
1600
L or L+P
14
1600
L+E
15
L+Sp
log pO2
1600
-9.36 L
14
E
-9.36 L
24
Sp
-9.36 L
32
-9.36 L
16
E
-9.36 L
23.5
Sp
wt% CaO
SiO2
MgO
Al2O3
Cr2O3
MoO3
St. Dev.
s.d.
s.d.
s.d.
s.d.
s.d.
44.1
0.3
0.5
0.2
46.1
1.3
1.1
0.2
41.5
0.5
0.6
0.2
40.9
0.7
1.0
0.2
42.7
1.6
1.3
0.2
37.4
1.4
0.2
0.0
38.0
0.5
0.2
0.0
38.8
0.5
1.1
0.1
39.1
0.6
0.9
0.1
31.8
1.2
35.2
0.6
1.0
0.2
35.1
1.7
0.8
0.1
36.8
0.4
0.0
0.0
36.4
0.5
0.1
0.1
35.5
0.4
0.1
0.0
35.0
0.2
0.1
0.0
36.8
0.8
0.2
0.2
29.4
1.0
0.0
0.0
31.8
0.7
0.0
0.0
32.4
1.2
0.1
0.0
30.6
0.6
0.1
0.0
27.0
0.7
27.3
0.7
0.1
0.1
28.9
1.3
0.0
0.0
0.26
0.02
0.00
0.00
0.17
0.02
0.00
0.00
9.4
0.3
22.4
0.3
9.7
0.1
21.9
0.1
9.6
0.5
24.1
0.8
18.7
1.6
99.3
0.9
17.5
0.2
99.9
0.5
0.15
0.02
0.00
0.00
8.0
0.3
23.8
0.1
18.5
1.3
0.10
0.01
0.00
0.00
6.2
0.5
26.4
1.2
11.3
0.1
4.9
0.0
10.8
0.5
5.2
0.6
10.2
0.6
15.9
0.3
10.0
0.3
15.7
0.1
10.3
0.8
20.7
1.9
11.6
0.7
0.9
0.0
11.0
0.3
0.9
0.0
20.8
0.6
10.8
1.7
18.9
0.2
29.2
0.6
19.7
0.6
29.6
0.5
19.2
2.0
28.2
0.9
42.2
1.6
6.9
0.6
93.2
0.4
5.5
0.2
92.9
3.1
2.0
0.4
58.9
0.7
2.6
0.2
57.4
0.3
1.3
0.2
53.2
2.4
0.00
0.00
0.03
0.00
0.06
0.00
0.17
0.01
5.8
0.4
84.5
1.4
1.6
0.2
43.9
0.9
0.06
0.02
5.7
0.5
78.9
1.5
1.6
0.2
31.5
1.2
.21
.02
.11
.05
.03
.01
.14
.09
.33
.03
.02
.02
.05
.02
.06
.02
.03
.02
.04
.02
.61
.08
.02
.01
.04
.02
.01
.01
.16
.02
.08
.08
.30
.02
.05
.01
.37
.05
.14
.02
.15
.12
.17
.02
.03
.02
Total
C/S
no. of
points
99.6
1.20
98.7
99.0
5
1.27
99.4
99.0
1.17
1.17
1.16
1.27
1.19
8
5
1.20
96.5
98.5
8
3
101.3
98.1
15
6
100.5
98.5
9
5
99.6
97.7
11
5
96.1
100.8
7
5
97.9
98.3
9
10
5
1.28
97.9
8
4
97.5
1.18
10
98.0
1.29
6
99.4
100.3
100.9
4
1.22
15
12
A-3
Table A.3: Experimental results in the CaO-CrOx -MgO-Al2 O3 -SiO2 system
(continued).
test
phases
17A
L+E
L
E
18A
19A
L+E
L+Sp
L
L
Sp
20A
21A
L
L+M2S
L
L
M2S
17B
18B
19B
20B
L+E
L+E
L+Sp
L
L
L
L+Sp+M2S L
M2S
21B
L+M2S
L
M2S
22
L+C2S+Sp L
C2 S
23
24
25
26
A-4
L/L+E
L+E
L+E
L+S+E
Total
time
log pO2
s.d.
s.d.
incl. Mo, Al
(h)
(atm)
52.6
0.29
20.4
100.1
23.5
-9.36
1.3
0.01
0.3
phase wt% CaO Cr2O3
present
L
L
L
L
s.d.
s.d.
25.9
0.8
SiO2
MgO
0.7
0.1
0.00
96.2
0.2
0.0
0.00
2.3
27.1
51.2
4.3
16.4
0.1
0.5
0.1
0.1
24.4
47.7
18.0
9.0
0.0
0.6
0.1
0.1
0.7
0.2
21.0
79.9
0.2
0.1
0.2
1.0
22.4
44.2
30.9
2.83
1.0
0.6
1.7
0.06
24.7
42.1
30.6
0.00
1.3
0.1
2.5
0.00
2.5
42.0
55.8
0.00
0.1
0.2
0.7
0.00
28.3
16.2
54.8
0.1
0.4
0.3
0.5
0.0
26.0
15.7
54.6
4.6
0.3
0.2
0.2
0.0
24.4
8.5
50.2
17.5
1.1
0.1
0.8
0.2
26.4
3.0
46.4
24.5
0.7
0.1
0.4
0.7
2.7
1.5
43.5
55.4
0.0
0.1
0.3
0.3
29.4
0.2
43.8
25.2
3.7
0.0
1.1
4.3
3.2
0.2
42.5
54.7
0.1
0.0
0.4
0.5
50.8
6.8
44.8
2.3
1.7
1.0
1.1
0.3
62.1
2.5
36.1
1.0
0.8
1.0
1.0
0.1
48.0
8.2
41.4
2.3
0.4
0.4
0.4
0.2
37.5
10.3
45.2
4.6
0.4
0.7
0.6
0.2
18.7
19.1
56.5
6.0
0.4
0.3
0.8
0.0
15.2
16.4
60.5
6.9
0.6
0.2
0.9
0.3
T
(°C )
1600
Basicity Contami-
# pts
C/S nations
0.49
97.7
12
0.4% MoO 3
3
99.7
24
-9.36
1600
0.53
6
100.1
24
-9.36
1600
0.51
7
102.8
3
101.1
24
-9.36
1600
0.51
9
98.1
23.5
-9.36
1600
0.59
6
100.4
3
100
23.5
-11.04
1500
0.52
15
101.4
23.5
-11.04
1500
0.48
14
101
23.5
-11.04
1500
0.49
8
100.8
21.5
-11.04
1500
0.57
9
103.4
99.4
8
16.5
-11.04
1500
0.67
14
100.8
105.5
7
21
-9.36 1600
1.13
0.6% MoO 3
101.7
4
3
100.4
23.5
-9.36 1600
1.16
98.5
24
-9.36 1600
0.83
13
100.9
23.5
-9.36 1600
0.33
8
99.8
23.5
-9.36 1600
0.25
11
0.4% MoO 3
4
Table A.4: Experimental results in the CrOx -MgO-SiO2 system in air and reducing atmospheres.
test
phases
phase
present
27
28
L+S+Sp
L+M2S+Sp
L
L
M2S
29A
30A
31
32
L+Sp+S
L+Sp
L
L+Sp+M2S
L
L
L
L
M2S
33
L+Sp+M2S
L
M2S
34
L+Sp+M2S
L
M2S
35
36
37
29B
30B
38
L+S
L+S+Sp
L+Sp
L
L
L+M2S+Sp
L
L
L
L
L
L
M2S
Cr2O3
SiO2
MgO
Total
time
log pO2
s.d.
s.d.
s.d.
incl. Mo, Al
(h)
(atm)
1.5
64.2
33.8
0.1
1.2
0.9
1.4
59.0
39.2
0.1
2.5
2.0
0.6
43.5
57.7
0.0
0.6
0.7
16.0
57.7
25.8
0.6
0.3
0.7
13.3
54.9
30.7
1.2
1.0
1.0
12.4
58.9
29.1
1.0
0.6
0.9
9.7
64.0
10.1
0.5
1.0
0.2
4.8
44.4
55.4
1.2
1.4
1.2
9.9
53.0
34.9
1.1
1.0
1.9
4.8
42.5
54.6
0.6
1.4
2.1
11.8
52.5
34.4
0.4
0.5
0.6
5.2
41.1
53.6
0.2
0.3
0.4
20.6
59.0
20.7
0.8
0.9
0.5
31.2
50.7
17.7
1.1
1.4
0.6
15.0
51.9
35.1
1.1
1.4
1.3
17.2
0.0
25.4
0.5
0.0
0.4
15.3
54.1
30.5
2.0
1.6
1.8
15.6
50.3
33.1
1.2
2.7
2.5
6.6
40.3
51.9
0.1
0.3
0.4
T
99.8
20
Air
(°C )
1600
101.1
20
Air
1600
Contami-
# pts
nations
11
10
102.0
10
100.3
16
-9.56
1600
10
100.1
23
-9.56
1600
5
100.8
24
-9.56
1600
8
103.6
22
-9.56
1600
13% CaO
3
6% Al 2O3
105.2
101.4
4
23
-9.56
1600
2.5% CaO
11
1% Al 2O3
102.5
99.9
12
24
-9.56
1600
100.1
10
11
100.6
24
-10.16
1600
10
100.0
20
-10.16
1600
11
102.5
24.5
-10.16
1600
14
100.5
24
-10.16
1600
11
101.0
26
-10.16
1600
10
99.6
20
-10.16
1600
11
99.0
8
A-5
Table A.5: Experimental results in the CrOx -MgO-SiO2 system in equilibrium
with metallic Cr.
test
phases
phase
present
39
L+M2S+Sp
L
40B
41
Total
time
log pO2
s.d.
incl. Mo, Al
(h)
(atm)
49.6
29.2
0.4
0.4
14.1
39.0
46.5
0.4
0.7
1.0
28.9
45.7
27.4
0.7
0.8
0.7
40.2
41.5
22.4
0.8
0.7
1.4
L
48.0
47.0
10.1
L+M2S formed
2.7
1.1
2.6
23.9
39.6
40.8
2.4
1.0
1.9
26.5
1.0
73.6
3.8
0.6
3.9
3.2
41.4
54.6
0.1
0.4
0.3
L+Sp
L+Sp
L
P+M2S+Sp
L
L
M2S
P
M2S
A-6
MgO
s.d.
0.5
on cooling
42
SiO2
s.d.
20.3
M2S
40A
Cr2O3
99.5
20
Cr met.
T
(°C)
1600
Contami-
# pts
nations
10
100.3
8
102.5
20
Cr met.
1600
16
104.6
20
Cr met.
1600
10
106.0
27
Cr met.
1600
10
104.6
101.8
100.1
10
25.5
Cr met.
1600
5
0.7% CaO
8
Appendix B
Model parameters
B-1
APPENDIX B. MODEL PARAMETERS
Table B.1: Model parameters for the adapted phase descriptions in the CrOx MgO-SiO2 system (J/mol and J/mol.K).
Liquid oxide
Stoichiometry: (CrO, CrO1.5 , MgO, SiO2 )
Binary parameters [46, 49–51]
07
ωCrO−CrO
= 48610
1.5
00
ωCrO1.5 −MgO = -16736
07
ωCrO−SiO
= 754823 – 325.372 T
2
00
ωCrO1.5 −SiO2 = 167360
00
ωMgO−SiO
= -86090
2
01
ωMgO−SiO2 = -48974 + 37.656 T
07
ωMgO−SiO
= 328109 – 125.52 T
2
Ternary parameters
φ002
CrO−SiO2 (MgO) = −33472
φ011
MgO−SiO2 (CrO) = 54392
φ011
SiO2 −MgO(CrO) = 29288
Olivine
Stoichiometry: [Mg2+ , Cr2+ ]M2 [Mg2+ , Cr2+ ]M1 SiO4
Mg SiO
GMM = Gm 2 4
Cr2 SiO4 = 2 GCr2 O3 + 2 GCr + GSiO2 + Gadd ,
GKK = Gm
m
3 m
3 m
Gadd = 37656
2 α = GKM - GMK = 36820
GKK + GMM = GKM + GMK
K and M represent Cr and Mg respectively.
M1 and M2 represent different octahedral sites for cations.
Enstatite
Stoichiometry: (Mg,Cr)SiO3
3 = 1 GCr2 O3 + 1 GCr + GSiO2 + Gadd ,
GCrSiO
m
m
3 m
3 m
Gadd = 16736
B-2
Fasediagrammen voor
roestvaststaalslakken
Dit deel is een Nederlandstalige samenvatting van deze doctoraatstekst.
Referenties naar hoofdstukken, figuren, tabellen of formules verwijzen
naar de Engelstalige tekst.
Inhoud van deze samenvatting:
1. Inleiding
2. Literatuur
3. Experimentele methode
4. Experimentele resultaten
5. Modellering
6. Besluit
1. Inleiding
Bij de verwerking van metalen op hoge temperatuur vormen zich naast de
vloeibare metaalfase ook andere fasen, zoals de slakfase, met even cruciale
functies. In de slak verzamelen zich de oxides. Bij het produceren van
roestvast staal beschermt de slak het staal voor oxidatie, zorgt ze voor een
thermische afdekking, en verzamelt ze onzuiverheden. De samenstelling
van de slak is het voorwerp van uitgebreid onderzoek omdat deze een
grote invloed heeft op de levensduur van het refractair materiaal, het
verlies van chroom naar de slak, en de bruikbaarheid van de slak als
secundaire grondstof (bijvoorbeeld als bouwmateriaal) na afkoelen.
In de zoektocht naar verbeterde processen is computationele thermochemie een belangrijk onderzoeksinstrument. Met thermodynamische
N-1
databanken kunnen complexe berekeningen met vele elementen en fasen
uitgevoerd worden. Dit laat toe om onder meer fasediagrammen, complexe fasenevenwichten, en stolsequenties te berekenen. Alhoewel de databanken een realistische schatting kunnen vormen op basis van een beperkt
aantal experimentele gegevens, kunnen de databanken nooit betrouwbaarder zijn dan die gegevens. Daarom blijft het belangrijk om, naast
het optimaliseren van de thermodynamische modellen, fasediagrammen
en thermodynamische gegevens ook experimenteel te bepalen.
Het doel van dit werk is de thermodynamische beschrijving voor roestvaststaalslakken te verbeteren. Concreet wordt het CaO-CrOx -MgOAl2 O3 -SiO2 , dat de vijf belangrijkste componenten van roestvaststaalslak
bevat, experimenteel bestudeerd. Aan de hand van deze resultaten worden enkele lacunes in de beschrijving geı̈dentificeerd. Het ternaire systeem
waar de grootste verschillen tussen de experimenten en de berekeningen
worden teruggevonden CrOx -MgO-SiO2 , wordt vervolgens in detail onderzocht. Gebaseerd op nieuwe experimentele gegevens en gegevens uit
de literatuur wordt een nieuwe beschrijving van dit ternair systeem ontwikkeld.
2. Literatuur
2.1. Thermodynamisch modelleren van oxidesystemen
In Hoofdstuk 2 worden de principes van de modellering van oxidische
fasediagrammen behandeld. Een thermodynamische beschrijving bestaat
uit een uitdrukking voor de Gibbs vrije energie van elke fase, in functie
van de samenstelling en de temperatuur, zoals vergelijking 2.1 aangeeft.
Door het minimaliseren van de totale Gibbs vrije energie, schematisch
getoond in Figuur 2.1, wordt bepaald welke fasen stabiel zijn, en in welke
samenstelling. Voor deze berekening zijn verschillende softwarepakketten
beschikbaar, waarvan FactSage, Thermo-Calc, MTDATA en Pandat de
bekendste zijn.
Een optimalisatie behelst het zoeken naar de beste beschrijving voor
de verschillende fasen in het systeem. De beste beschrijving benadert de
experimentele gegevens zo goed mogelijk, zonder te veel vrije parameters
in de modellen in te bouwen.
Voor oxidische vloeistoffen zijn verschillende oplossingsmodellen ontwikkeld. Deze modellen beschrijven de korteafstandsorde met specifieke
veronderstellingen. Dit leidt telkens tot een sterk samenstellingsafhankelijke Gibbs vrije energie voor de vloeistof.
In het quasichemisch model [18, 19] worden interacties tussen de oxiN-2
des van verschillende metalen beschreven als het vormen van paren. In
vergelijking 2.4 en 2.5 wordt een Gibbs vrije energie gedefinieerd voor de
reactie van gelijke paren (bijv. CaO-CaO) naar ongelijke paren (bijv. CaOSiO2 ). Deze binaire interactietermen leiden tot de V-vormige mengenergie
uit Figuur 2.4. Met specifieke aannames worden de binaire interacties
geëxtrapoleerd naar ternaire systemen. Zo wordt SiO2 behandeld als
een asymmetrische component, wat betekent dat de interacties met SiO2
constant blijven bij een constante SiO2 -fractie in het ternaire systeem
(Figuur 2.5). Er worden eveneens ternaire interactietermen gedefinieerd.
Ten slotte is er een benadering voorzien om alle binaire en ternaire interacties in een multicomponentmodel te verzamelen.
Het ionische subroostermodel Hillert et al. [26], Sundman [27] benadert de vloeistof als een rooster met kationen (Ca2+ , Mg2+ ) en een
0
rooster met anionen (O2− , SiO4−
4 ) en het neutrale SiO2 . Het CaO-SiO2 2+
0
systeem wordt bijvoorbeeld geschreven als (Ca )(O2− , SiO4−
4 , SiO2 ).
Naargelang de samenstelling van de vloeistof veranderen de hoofdcomponenten van de vloeistof. Zuiver CaO wordt (Ca2+ )(O2− ), terwijl zuiver
SiO2 als (SiO02 ) wordt geschreven. Bij de samenstelling met maximale
ordening, benadert de vloeistof (Ca2+ )0.67 (SiO4−
4 )0.33 . Door voor deze
verschillende combinaties van ionen verschillende energieën te definiëren,
wordt de Gibbs vrije energie van de vloeistof samenstellingsafhankelijk.
Ook in dit model kunnen los daarvan extra interactietermen ingevoerd
worden.
In de paragrafen 2.2.3-2.2.5 worden enkele andere modellen besproken. Zo veronderstelt het associate model Hastie and Bonell [32] een
aantal virtuele verbindingen in de vloeistof (bijv. Ca2 SiO4 ) met een specifieke Gibbs vrije energie. Het Kapoor-Frohberg celmodel [34] benadert
de korteafstandsorde als de vorming van cellen, wat tot een vergelijkbare
mengenergie leidt als de vorming van paren in het quasichemisch model.
Uit de vergelijking van de verschillende oplossingsmodellen voor vloeibare oxides blijkt dat het quasichemisch model de meeste uitbreidingsmogelijkheden naar multicomponentsystemen kent. Dit model heeft zijn
geschiktheid ook voor het grootste aantal oxidesystemen bewezen. Hoofdstuk 3 geeft aan in welke mate het CaO-CrOx -MgO-Al2 O3 -SiO2 systeem
reeds werd beschreven met de verschillende modellen. Daarbij blijkt dat
zeven van de tien deelsystemen, aangegeven in Figuur 3.1, reeds geoptimaliseerd werden met het quasichemisch model [45]-[53]. Deze deelsystemen zijn verenigd in het slakmodel van FactSage (FToxid database versie 5.3). De beschikbare modellen met het ionische subroostermodel (in
Thermo-Calc) en het associate model (in MTDATA) zijn op beduidend
minder optimalisaties gebaseerd. Het FactSage-model wordt daarom geN-3
kozen als vergelijkingspunt voor de experimentele gegevens in Hoofdstuk
7 en 8, en voor verbere uitbreiding in Hoofdstuk 9.
2.2. Experimenteel bepalen van oxidische fasediagrammen
Hoofdstuk 4 geeft een overzicht van de experimentele methodes om oxidische fasediagrammen te bepalen. Daarbij wordt een onderscheid gemaakt
tussen statische en dynamische methodes. Bij dynamische methodes
wordt een eigenschap van het materiaal gemeten tijdens een faseverandering. Zo kan de smeltwarmte tijdens het opwarmen van een monster
gedetecteerd worden in bijv. DSC (differentiële scanning calorimetrie).
Het systeem is dan echter niet in evenwicht, en de traagheid van de
meeste reacties in oxidesystemen beperkt vaak de nauwkeurigheid van
deze methodes. Statische methodes, daarentegen, bestuderen de eigenschappen van een materiaal dat lange tijd in dezelfde omstandigheden
wordt gehouden. Als deze eigenschappen behouden worden tijdens het
afschrikken, kunnen ze na het experiment nauwkeurig bestudeerd worden
op kamertemperatuur. Vaak wordt dan de samenstelling van verschillende fasen, die op hoge temperatuur in evenwicht waren, gemeten met
elektronenbundelmicroanalyse (EPMA).
Oxidesystemen waar metalen met meerdere valenties (zoals ijzer of
chroom) in voorkomen zijn afhankelijk van de zuurstofpartieeldruk, pO2 .
Om ze te bestuderen is het vereist de pO2 te controleren. Hiervoor is een
buffer nodig, die ervoor zorgt dat het sample zuurstof kan opnemen of
afgeven zonder dat de pO2 verandert. In lucht is de zuurstofbuffer groot
genoeg. In reducerende omstandigheden moet echter gewerkt worden
met reactieve gassen, of met een hoeveelheid metaal in evenwicht met het
monster. De pO2 die via de reactieve gasmengsels CO/CO2 , H2 /H2 O en
H2 /CO2 bereikt kan worden, wordt weergegeven in Figuur 4.2. In paragraaf 4.2.2 wordt ingegaan op de materiaalkeuze voor de kroes, die zowel
compatibel moet zijn met de zuurstofpartieeldruk als met het monster.
Hoofdstuk 5 vat vervolgens experimentele studies in het ternaire deelsysteem CrOx -MgO-SiO2 samen. Het sterk pO2 -afhankelijke systeem
werd reeds bestudeerd bij verschillende zuurstofdrukken en temperaturen.
Door het ontbreken van experimentele details of door onverenigbaarheid
met andere data lijken niet alle gegevens echter even betrouwbaar.
3. Experimentele methode
In Hoofdstuk 6 wordt een experimentele methode besproken om de liquidus-solidus-relaties in het onderzochte systeem te observeren. Poeders
N-4
van de zuivere oxides worden gemengd en tot evenwicht gebracht in een
Mo-kroes in een verticale buisoven bij 1500◦ C of 1600◦ C, zoals Figuur
6.1 laat zien. Zuurstofpartieeldrukken tussen 10−11.04 en 10−9.36 atm
worden opgelegd via mengsels van CO en CO2 . De samenstelling van
de poeder is zo gekozen dat één of twee vaste fasen in evenwicht met de
vloeistof aanwezig zijn. Na 8 en 24 uur wordt een sample genomen met
behulp van een staaf uit aluminiumoxide. Door de staaf in de koude zone
van de oven te trekken wordt het sample redelijk snel afgeschrikt. Een
zekere kristallisatie in de matrix, en een beperkte groei van de vaste fasen,
kunnen daarbij niet vermeden worden. Dit verhindert een nauwkeurige
meting van de samenstelling echter niet. In sommige gevallen wordt in
evenwicht met lucht of met vast metallisch chroom gewerkt. Daarbij
wordt het monster in een Pt- of Mo-folie in evenwicht gebracht, en wordt
het volledige monster afgeschrikt in water.
De afgeschrikte samples worden met een microsonde met golflengtedispersieve spectroscopie (EPMA-WDS) geanalyseerd. Daarbij worden
de materialen uit Tabel 6.1 als standaard gebruikt.
4. Experimentele resultaten
4.1. CaO-CrOx -MgO-Al2 O3 -SiO2
Hoofdstuk 7 bespreekt de experimentele resultaten in het multicomponentsysteem CaO-CrOx -MgO-Al2 O3 -SiO2 . Er worden secties van het
fasediagram bestudeerd bij verschillende temperatuur, pO2 , en basiciteit
(B=CaO/SiO2 ). Figuur 7.1 en 7.2 geven de resultaten weer bij hogere
basiciteit B=1.2, zonder Al2 O3 . Hierbij staan de symbolen voor de samenstelling van de vloeistof in de experimenten en de lijnen voor het berekende fasediagram. Een goede overeenkomst tussen het FactSage model
en de experimenten wordt gevonden, in het bijzonder voor de spinelliquidus (L+Sp). De berekende eskolaiet-liquidus (L+E, E=(Cr,Al)2 O3 )
ligt echter steeds 1-2 gew% hoger dan experimenteel bepaald. Dit verschil blijft systematisch aanwezig wanneer er Al2 O3 aan het systeem wordt
toegevoegd, zoals uit Figuur 7.8 blijkt. Dit verschil lijkt afkomstig uit het
systeem CrOx -CaO-SiO2 , waar de berekening bij lage zuurstofpartieeldruk afwijkt van experimenten uit de literatuur. Dit wordt weergegeven
in Figuur 7.14.
De overeenkomst voor de spinel-liquidus blijft behouden bij het toevoegen van Al2 O3 , zoals te zien is op Figuur 7.9. Ook de berekende
samenstelling van spinel en eskolaiet in Figuur 7.13, als functie van de
Al2 O3 -concentratie in de vloeistof, stemt goed overeen met de experimenN-5
tele resulaten.
Bij lagere basiciteit B=0.5 worden echter grote verschillen waargenomen in de fasediagramsecties in Figuur 7.3 en 7.4. Terwijl de overeenkomst
op de assen (zonder MgO of zonder CrOx ) even goed is als bij hogere basiciteit, is er een grote afwijking op de spinel-liquidus. Deze blijkt het
gevolg te zijn van een onvolledige beschrijving van het ternaire deelsysteem CrOx -MgO-SiO2 .
4.2. CrOx -MgO-SiO2
Dit systeem wordt daarom verder bestudeerd in Hoofdstuk 8. Voor omstandigheden van zeer oxiderend (in lucht) tot zeer reducerend (in evenwicht met metallisch chroom) wordt het fasediagram bij 1600◦ C bestudeerd. De experimentele resultaten worden vergeleken met experimentele
gegevens uit de literatuur en berekeningen met het FactSage-model.
In lucht (Figuur 8.1) is de overeenkomst redelijk goed. Hoe reducerender de omstandigheden, hoe meer de berekeningen echter afwijken van de
experimentele gegevens. In reducerende omstandigheden, pO2 =10−9.56
en 10−10.16 atm (Figuur 8.3 en 8.4), onderschat de berekening de oplosbaarheid van spinel met de helft. In evenwicht met metallisch chroom
voorspelt de berekening in Figuur 8.6 een ontmengingsgebied, dat volledig
tegenstrijdig is met de experimentele resultaten in Figuur 8.5.
Tussen de experimentele gegevens onderling is de overeenkomst goed,
behalve voor de data van Morita et al. [91] en [90], waar de oplosbaarheid
van Mg2 SiO4 (M2 S) in de vloeistof overschat wordt door hun methode.
Daarin wordt de vloeistof na verzadiging met een blokje spinel geanalyseerd, zonder na te gaan of er geen tweede fase (in dit geval M2 S) gevormd
was in de vloeistof.
In de experimenten wordt een grote oplosbaarheid van Cr in de M2 Sfase vastgesteld, zoals Figuur 8.7 weergeeft. De gemeten stoichiometrie,
en de grote toename van de oplosbaarheid bij afnemende pO2 , wijzen op
een (Mg,Cr)2 SiO4 formule, waarin Mg2+ vervangen wordt door Cr2+ .
5. Modellering
Tot slot wordt in Hoofdstuk 9 een verbeterde beschrijving van het CrOx MgO-SiO2 systeem ontwikkeld, gebaseerd op gegevens uit dit werk en uit
de literatuur. In paragraaf 9.1 wordt eerst gecontroleerd of de bestaande
optimalisaties in overeenstemming zijn met de ternaire gegevens. Voor het
CrO-SiO2 -systeem in evenwicht met metallisch chroom blijkt er een kleine
afwijking te zijn tussen de optimalisatie van Degterov and Pelton [50] en
N-6
het experimentele fasediagram van Muan [96]. De experimentele gegevens
waarop beide fasediagrammen gebaseerd zijn, wegen echter te licht om de
extra binaire parameters uit vergelijking 9.1 te funderen. Daarom wordt
met de bestaande versie verdergewerkt. De ternaire gegevens zijn volledig
consistent met de andere geoptimaliseerde fasediagrammen.
Met de bestaande binaire modellen kan bijgevolg een eerste versie
van het ternaire fasediagram worden berekend. Daarbij wordt, zoals gebruikelijk, een asymmetrische benadering gebruikt met SiO2 als de asymmetrische component. Figuur 9.6 en 9.7 tonen dat dit kwalitatief reeds
een goed resultaat geeft, maar dat de oplosbaarheden sterk overschat
worden.
Vervolgens worden de vaste oplossingen (Mg,Cr)2 SiO4 en (Mg,Cr)SiO3
aan het model toegevoegd. Voor de eerste, M2 S, wordt het Compound Energy Formalism gebruikt, waarbij alle mogelijke verbindingen een Gibbs
vrije energie toegekend krijgen. De olivijnstructuur van M2 S bevat twee
verschillende posities voor de metaalionen, M1 en M2. De fase wordt
daarom voorgesteld als
[Mg2+ , Cr2+ ]M2 [Mg2+ , Cr2+ ]M1 SiO4 .
De Gibbs vrije energie van de verschillende combinaties wordt vastgelegd, waarbij die van Mg2 SiO4 reeds gekend is. De Gibbs vrije energie
van de hypothetische verbinding Cr2 SiO4 bevat een term om de oplosbaarheid van Cr in M2 S te laten overeenkomen met experimentele gegevens
(vergelijking 9.4). De energie van [Cr][Mg]SiO4 en [Mg][Cr]SiO4 is licht
verschillend omdat het Cr-ion de M2-positie verkiest (vergelijking 9.5).
Voor de tweede vaste fase, (Mg,Cr)SiO3 , wordt een eenvoudig idealeoplossingsmodel gebruikt waarbij de Gibbs vrije energie van CrSiO3
opnieuw een aanpasbare term bevat (vergelijking 9.10).
In de vloeistof worden drie interactietermen tussen CrO, MgO en SiO2
bepaald, die de liquidus op verschillende plaatsen corrigeren, zoals Figuur
9.10 aanduidt. Vergelijking 9.11 geeft de parameters weer. Een overzicht
van de parameters in het geoptimaliseerde model wordt in Tabel B.1
gegeven.
Het nieuwe model benadert de fasediagrammen op hoge temperatuur
goed. De resultaten bij verschillende zuurstofpartieeldrukken worden
vergeleken met experimentele gegevens in de reeks figuren 9.11-9.18. Ook
de oplosbaarheid van Cr in M2 S in Figuur 9.20 komt goed overeen met de
experimentele data. In paragraaf 9.6 worden de overblijvende verschilpunten bediscussieerd. Zo komt het model minder goed overeen met het fasediagram van Muan [96] bij 1400 en 1500◦ C. Dit zou kunnen verholpen
N-7
worden door temperatuursafhankelijke interactietermen te definiëren, al
zouden extra experimentele resultaten daarvoor welkom zijn.
Ook in het hogereordesysteem met CaO benadert het nieuwe model
de experimentele resultaten beter dan het FactSage-model. Figuur 9.21
en 9.22 tonen een sterke verbetering bij lage basiciteit. Bij hoge basiciteit lijkt de fout uit het CrOx -CaO-SiO2 -systeem nu een groter effect
te hebben.
5. Besluit
Het doel van dit werk was de thermodynamische beschrijving voor roestvaststaalslakken te verbeteren. In de literatuurstudie werd de basis van
zowel de thermodynamische beschrijving als de experimentele studie van
oxidische fasediagrammen samengevat. Vervolgens werd een methode
ontwikkeld om pO2 -afhankelijke slaksystemen te bestuderen. De studie
van het vijfcomponentsysteem CaO-CrOx -MgO-Al2 O3 -SiO2 wees vervolgens op enkele verschillen, die terug te brengen zijn tot een kleine afwijking in het CrOx -CaO-SiO2 -systeem en een onvolledige beschrijving
van het CrOx -MgO-SiO2 -systeem. In dat laatste systeem werden daarom
gegevens uit de literatuur geverifieerd en aangevuld met nieuwe experimentele gegevens. Op basis van deze data werd de thermodynamische beschrijving van het CrOx -MgO-SiO2 -systeem geoptimaliseerd. Dit
leidde tot een goede benadering van de fasediagrammen in dit ternair
systeem, en in het hogereordesysteem.
N-8
List of publications
Publications in international refereed journals
Published
S. Arnout, F. Verhaeghe, B. Blanpain, P. Wollants
A thermodynamic model of the EAF process for stainless steel
Steel Research International 77 (5) 317-323, 2006.
Lattice Boltzmann modelling of refractory slag interaction
Progress in Computational Fluid Dynamics 7 (2/3/4) 111-117, 2007.
Lattice Boltzmann model for diffusion-controlled indirect dissolution
Computers & Mathematics with Applications, 55 (7) 1377-1391, 2008.
S. Arnout, D. Durinck, M. Guo, B. Blanpain, P. Wollants
Determination of CaO-SiO2 -MgO-Al2 O3 -CrOx liquidus
Journal of the American Ceramic Society, 91(4) 1237-1243, 2008.
F. Verhaeghe, S. Arnout, B. Blanpain, P. Wollants
Lattice Boltzmann model for dissolution of solid structures in multicomponent liquids Physical Review E 72, 036308-2, 2005.
Lattice Boltzmann modeling of dissolution phenomena
Physical Review E 73, 036316-2, 2006.
F. Verhaeghe, J. Liu, M. Guo, S. Arnout, B. Blanpain, P. Wollants
Dissolution and diffusion behavior of Al2 O3 in a CaO-Al2 O3 -SiO2 liquid:
an experimental-numerical approach
Applied Physics Letters 91 (12), 124104, 2007.
P-1
F. Verhaeghe, J. Liu, M. Guo, S. Arnout, B. Blanpain, P. Wollants
Determination of the dissolution mechanism of Al2 O3 in CaO-Al2 O3 -SiO2
liquids using a combined experimental-numerical approach
Journal of Applied Physics 103 (2), 023506, 2008.
D. Durinck, S. Arnout, G. Mertens, E. Boydens, P.T. Jones, J. Elsen,
B. Blanpain, P. Wollants
Borate distribution in stabilised stainless steel slag
Journal of the American Ceramic Society, 91 (2) 548-554, 2008.
D. Durinck, F. Engström, S. Arnout, J. Heulens, P.T. Jones, B. Björkman, B. Blanpain, P. Wollants
Hot stage processing of metallurgical slags
Resources, Conservation & Recycling, 52, 1121-1131, 2008.
Submitted
S. Arnout, M. Guo, I.H. Jung, B. Blanpain, P. Wollants
Experimental determination of CaO-Cr2 O3 -MgO-SiO2 and thermodynamic
modeling of the CrO-Cr2 O3 -MgO-SiO2 system
Journal of the American Ceramic Society, submitted.
Contributions to compendiums
P. Perrot, J. Vrestal, S. Arnout
Evaluation of the ternary system Cu-Fe-O Copper-Iron-Oxygen
Landolt-Börnstein Subseries IV/11 Authored by MSIT, Ternary Alloy
Systems, Subvolume D. Iron Systems, in press.
O. Fabrichnaya, S. Arnout
Evaluation of the ternary system Ca-O-Zr Calcium-Oxygen-Zirconium
Landolt-Börnstein Subseries IV/11 Authored by MSIT, Ternary Alloy
Systems, Subvolume E. Refractory Systems, in review.
Contributions to conference proceedings
Lattice Boltzmann modelling of refractory slag interaction
Proceedings of CFD2005, Trondheim, Norway, June 6-8, 2005.
P-2
Lattice Boltzmann modeling of pyrometallurgical phenomena
Proc. of New Technologies and Achievements in Metallurgy and Material
Engineering, Czestochowa, Poland, June 2-3, 2005.
A thermodynamic model of the EAF process for stainless steel
Proceedings of the European Metallurgical Conference EMC2005, p. 13251337, Dresden, Germany, September 18-21, 2005.
Lattice Boltzmann model for refractory wear
Proceedings of UNITECR ’05, p. 227-231, Orlando, Florida, U.S.A.,
November 8-11, 2005.
Lattice-Boltzmann model for dissolution phenomena,
PAMM, Proceedings in Applied Mathematics and Mechanics 7, 11407011140702, 2007.
S. Arnout, M. Guo, D. Durinck, P.T. Jones, B. Blanpain, P. Wollants
Proceedings of EMC2007, p. 1931-1946, Düsseldorf, Germany, June 1114, 2007.
D. Durinck, P.T. Jones, M. Guo, S. Arnout, J. Heulens, P. Wollants,
B. Blanpain
How to improve slag valorisation by hot stage processing: an example of
industrial ecology in steelmaking
Proceedings of the third Baosteel biennial academic conference, p. L1-L7,
Shanghai, China, September 26-28, 2008.
D. Durinck, S. Arnout, M. Guo, P.T. Jones, B. Blanpain, P. Wollants
Stainless steel slags: processing, microstructure and utilization
Proceedings of the Sano Symposium, Tokyo, Japan, October 2-3, 2008.
D. Durinck, S. Arnout, P.T. Jones, B. Blanpain, P. Wollants
Analysis of the air-cooling process of basic metallurgical slags
Proceedings of Molten Slags, Fluxes and Salts 2009, Santiago, Chili, Jan
2009, in press.
P-3
S. Arnout, D. Durinck, M. Guo, P.T. Jones, B. Blanpain, J. Van Dyck
Solidification, stabilisation and phase relations studies for reuse of stainless steel slags
Proceedings of EMC2009, June 28 - July 1, 2009, in preparation.
Presentations at international conferences
Oral presentations
Diffusion controlled dissolution of porous media
ICMMES, Hong Kong, China, July 26-29, 2005.
Lattice Boltzmann model for refractory wear
UNITECR ’05, Orlando, Florida, U.S.A., November 8-11, 2005.
EMC2007, Düsseldorf, Germany, June 11-14, 2007.
S. Arnout, D. Durinck, M. Guo, P.T. Jones, B. Blanpain, P. Wollants
Modelling and experiments for stainless steel slag valorisation
GTT-Technologies workshop, Aachen, Germany, 21 June, 2007.
Poster presentations
S. Arnout
Presented at GRC High Temperature Materials, Processes and Diagnostics, Waterville, Maine, U.S.A., July 16-20, 2006.
Presented at High Temperature Materials Chemistry, Vienna, Austria,
September 18-22, 2006.
Presented at Euromat, Nürnberg, Germany, September 9-13, 2007.
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Curriculum vitae
Personal data
Sander Arnout
Date and place of birth: September 20, 1981, Kortrijk, Belgium
Nationality: Belgian
Home address: Milseweg 22, 3001 Heverlee, Belgium
Work address: Katholieke Universiteit Leuven
Department of Metallurgy and Materials Engineering
Kasteelpark Arenberg 44 - box 2450, 3001 Heverlee, Belgium
Tel: +32 16 321 279
Fax: +32 16 321 991
E-mail: [email protected]
Education
2004-Present
Doctoral student at the Department of Metallurgy and Materials Engineering, research assistant on IWT-projects 030880 and 050715 in cooperation with Ugine & ALZ Belgium Genk (ArcelorMittal).
2001-2004
Burgerlijk materiaalkundig ingenieur, K.U.Leuven (Belgium)
1999-2001
Kandidaat burgerlijk ingenieur, K.U.Leuven (Belgium)
CV-1

Phase relations in stainless steel slags

Transcription

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