1. business and industrial
2. chemicals industry
3. plastics and polymers

Thermodynamic investigation of systems related
to TWIP steels
Bonnie Lindahl
Doctoral Thesis in Materials Science and Engineering
Stockholm 2015
KTH Royal Institute of Technology
School of Industrial Engineering and Management
Department of Materials Science and Engineering
Division of Computational Thermodynamics
SE-100 44 Stockholm, Sweden
ISBN 978-91-7595-516-2
c Bonnie Lindahl, 2015
Akademisk avhandling som med tillst˚
and av Kungliga Tekniska H¨ogskolan i
Stockholm framl¨
agges till offentlig granskning f¨or avl¨aggande av doktorsexamen
fredag den 22 maj 2015 kl 10:00 i sal B2, Brinellv¨agen 23, Kungliga Tekniska
H¨
ogskolan, Stockholm.
This thesis is available in electronic format at kth.diva-portal.org
Printed by Universitetsservice US-AB, Stockholm, Sweden
To my loving family who has always been there for me.
Education is not the learning of facts, but the training of the mind
to think.
- Albert Einstein
Abstract
The world is facing serious challenges regarding environmental issues. Carbon
dioxide levels increase every day. In an attempt to decrease carbon emissions the
automotive industry searches for lighter, stronger materials. TWinning Induced
Plasticity (TWIP) steels show an impressive combination of strength and ductility. The possibility of adding high amounts of aluminum that decreases the
density while maintaining the mechanical properties makes this type of steel
very interesting for use in automotive applications. The only thing keeping
the TWIP steels from being used in the automotive industry is that the Yield
Strength (YS) is too low. The TWIP steels usually have a YS around 400 MPa.
For them to be useful in automotive applications YS around 600-700 MPa is
necessary. One of the most promising ways of improving the YS is by precipitation hardening. This work has been performed within a European Research
Fund for Coal and Steel (RFCS) project called Precipitation in High Manganese
steels (PrecHiMn). As the name of the project suggests, the goal of this project
has been to study the precipitation in TWIP steels. The precipitation hardening is achieved through the addition of carbide and carbonitride formers such
as Nb, Ti and V. In order to build advanced models to simulate precipitation it
is important to have a good understanding of the thermodynamics of systems
related to TWIP steels.
The goal of this work has been to study the thermodynamic properties of
systems related to TWIP steels, more specifically the system forming the matrix
phases of TWIP steels. Therefore the Al-C-Fe-Mn system has been studied
as well as the Al-Ti-V system. Complete thermodynamic descriptions that
reproduce the experimental data well have been produced including descriptions
of order-disorder transformations.
Sammandrag
V¨
arlden st˚
ar inf¨
or stora utmaningar n¨ar det g¨aller milj¨ofr˚
agor. Koldioxidniv˚
aerna ¨
okar varje dag. I ett f¨ors¨ok att minska koldioxidutsl¨appen s¨oker bilindustrin efter l¨
attare och starkare material. TWinning Induced Plasticity (TWIP)
st˚
al uppvisar en imponerande kombination av h˚
allfasthet och duktilitet. M¨ojligheten
att tills¨
atta h¨
oga halter av aluminium som minskar densiteten med bibeh˚
allna
mekaniska egenskaper g¨
or denna typ av st˚
al mycket intressanta f¨or anv¨andning i
fordonstill¨
ampningar. Det enda som hindrar TWIP st˚
al fr˚
an att anv¨andas inom
fordonsindustrin ¨
ar att str¨
ackgr¨ansen ¨ar f¨or l˚
ag. TWIP st˚
al har vanligtvis en
str¨
ackgr¨
ans runt 400 MPa. F¨or att de ska vara anv¨andbara i biltill¨ampningar
kr¨
avs en str¨
ackr¨
ans omkring 600-700 MPa. Ett av de mest lovande s¨atten att
f¨
orb¨
attra str¨
ackgr¨
ansen ¨
ar genom utskiljningsh¨ardning. Detta arbete har utf¨orts
inom en europeisk forskningsfond f¨or kol och st˚
al (RFCS) projekt kallat Precipitation in High Manganese steels (PrecHiMn). Som namnet p˚
a projektet
antyder, har m˚
alet med projektet varit att studera utskiljning i TWIP st˚
al.
Utskiljningsh¨
ardning uppn˚
as genom tillsats av karbid- och karbonitridbildare
s˚
asom Nb, Ti och V. F¨
or att bygga avancerade modeller f¨or simulering av utskiljning ¨
ar det viktigt att ha en god f¨orst˚
aelse f¨or termodynamiken i system
relaterade till TWIP st˚
al.
M˚
alet med detta arbete har varit att studera de termodynamiska egenskaperna hos system med anknytning till TWIP st˚
al. Mer specifikt har systemet
som bildar matrisfaserna i TWIP st˚
al. Drfr har Al-C-Fe-Mn-systemet studerats liksom Al-Ti-V-systemet. Fullst¨andiga termodynamiska beskrivningar som
˚
aterger experimentella data v¨al har producerats inklusive beskrivningar av ordningsomvandlingar.
Contents
1 Background/Introduction
1.1 TWIP steels . . . . . . . . . . . . . . . . . . . .
1.1.1 History of TWIP steels . . . . . . . . .
1.1.2 Twinning vs. -martensite formation . .
1.1.3 Stacking Fault Energy (SFE) . . . . . .
1.1.4 Plasticity mechanisms . . . . . . . . . .
1.1.5 Twin formation . . . . . . . . . . . . . .
1.1.6 Improvement of the Yield Stress (YS) .
1.2 Thermodynamic modeling (CALPHAD) . . . .
1.2.1 Phase models . . . . . . . . . . . . . . .
1.2.2 Extrapolation into higher order systems
1.2.3 Data evaluation . . . . . . . . . . . . . .
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1
1
2
3
3
4
5
6
7
7
11
12
2 Assessed systems
14
2.1 Binary systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 Ternary systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3 Applications of the database
30
3.1 Experimental investigation . . . . . . . . . . . . . . . . . . . . . . 33
4 Conclusions and Future work
38
4.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5 Appended papers
49
i
Preface
If there is one thing I’ve learned in my PhD studies it’s that the more you know
about something the more you realize that you don’t understand it. Thermodynamics is a very tricky subject and during these past 5 years I’ve found
myself going back to the very basics more than once. Two steps forward, one
step back. Modeling the thermodynamic properties of materials is an iterative
process. Your results can always be improved and it is very hard to say that
something is finished.
The biggest challenge for me during this period has been to let go. Letting
other people read my texts and see my work before I think it’s perfect. Which
is a good thing, because I don’t ever think anything I do is perfect. I would
have gladly spent several more years perfecting this work, but now that task
will fall on someone else.
CALPHAD modeling is something in between physics and mathematics. We
use models that are based on thermodynamic properties and physical phenomena and add parameters that do not always have much physical meaning in
order to be able to reproduce the properties of the system we are looking at.
This usually means that physicists think that it’s not really a science at all. On
the other hand people in industry sometimes think that it is too complicated
and they would rather stick to what they are used to. But I have learned that
with the right models, the CALPHAD method can be an incredibly powerful
tool. I hope that this work will be useful, both for my industry partners to
develop new materials but also for new Calphadians just starting their journey.
Bonnie Lindahl 2015-04-20
ii
List of appended papers
I Bonnie Lindahl, Malin Selleby “The Al-Fe-Mn system revisited: an updated
description using the most recent binaries”, CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry, 43 (2013) 86-93. doi:
10.1016/j.calphad.2013.05.001
Contribution Statement: Bonnie Lindahl performed the thermodynamic
modeling and prepared the draft manuscript.
II Bonnie Lindahl, Benjamin Burton, Malin Selleby, “Ordering in ternary BCC
alloys applied to the Al-Fe-Mn system”, Submitted to CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry
Contribution Statement: Bonnie Lindahl performed the thermodynamic
modeling and prepared the draft manuscript.
III Bonnie Lindahl, Xuan Liu, Zi-kui Liu, Malin Selleby, “A thermodynamic
re-assessment of Al-V toward an assessment of the ternary Al-Ti-V system”, Submitted to CALPHAD: Computer Coupling of Phase Diagrams
and Thermochemistry
Contribution Statement: Bonnie Lindahl performed the thermodynamic
modeling and prepared the draft manuscript together with Xuan Liu.
IV Bonnie Lindahl, Navid Kangouei, Malin Selleby, “A thermodynamic investigation of the Al-C-Fe-Mn system”
Contribution Statement: Bonnie Lindahl performed the thermodynamic
modeling, designed the experiments and prepared the draft manuscript.
V Zuazo, I., Hallstedt, B., Lindahl, B., Selleby, M., Soler, M., Etienne, A., Perlade, A., Hasenpouth, D., Massardier-Jourdan, V., Cazottes, S., Kleber,
X.. “Low-Density Steels: Complex Metallurgy for Automotive Applications”, JOM, 66 (9) (2014) 1747-1758.
Contribution Statement: Bonnie Lindahl performed thermodynamic
calculations, produced some of the images and helped prepare the manuscript.
Other contributions
A Xuan L Liu, Thomas Gheno, Bonnie Lindahl, Greta Lindwall, Brian Gleeson, Zi-Kui Liu, “First-principles calculations, experimental study, and
thermodynamic modeling of the Al-Co-Cr system”, PLOS ONE, 10 (4)
(2015) e0121386.
B M. Palumbo, B. Burton, A. Costa e Silva, B. Fultz, B. Grabowski, G. Grimvall, B. Hallstedt, O. Hellman, B. Lindahl, A. Schneider, P. E. A. Turchi
and W. Xiong, “Thermodynamic modelling of crystalline unary phases”,
pss, 251 (1) (2014) 14-32
iii
Acknowledgments
First of all I would like to thank my wonderful family, ˚
Asa, Thomas and Fanny
for always being there for me, no matter what. Without you I would have
given up before I even started. I would also like to thank my supervisor Malin.
You have been so much more than just a supervisor. You have been my workmom, my role model and my friend. Working with you has been a privilege and
an honor. I would like to acknowledge my wonderful boyfriend Philip. Your
patience and love has kept me going through the last few months of hard work.
A big thanks to my fellow PhD students Bartek, David, Sedi, Thomas, C-M,
and everyone else for making the long hard days more bearable and never saying
no to yet another discussion, regardless of the topic. Thank you Lars for all the
help with computer stuff and for always having an inappropriate on hand.
I would like to acknowledge all my wonderful project partners. It has been
a pleasure getting to know you all and I hope to work with you in the future.
Last of all I would like to thank my amazing friends, Beatrice, Jenny, Aron,
Kalle, Ida, Lisa, Mikaela. You are the very best in the world, and you mean
everything to me.
iv
Nomenclature
FCC – Face Centered Cubic
BCC – Body Centered Cubic
HCP – Hexagonal Close-Packed
CEF – Compound Energy Formalism
SFE – Stacking Fault Energy
2SL – two sublattice
4SL – four sublattice
DSA – Dynamic Strain Ageing
R-K – Redlich-Kister
BWG – Bragg-William-Gorsky
LOM – Light Optical Microscopy
SEM – Scanning Electron Microscopy
XRD – X-Ray Diffraction
DFT – Density Functional Theory
v
Chapter 1
Background/Introduction
This work has been performed within a European Research Fund for Coal and
Steel (RFCS) project called Precipitation in High Manganese steels. The goal
of this project has, as the title of the project suggests, been to study the precipitation in high manganese steels by means of experimental investigation and
modeling work. In order to model the kinetics of precipitation it is important
to have reliable thermodynamic descriptions. It was therefore part of this work
to develop a thermodynamic database containing the most relevant elements for
alloying these steels [1]. The database developed features the elements: Al, C,
Fe, Mn, N, Nb, Si, Ti and V. Nb, Ti and V are carbide and nitride formers and
Al-C-Fe-Mn forms the basis of the steel. In this work the Al-C-Fe-Mn system
has been studied extensively with the addition of the ternary Al-Ti-V system.
The thesis is divided into three parts. In chapter 1 some main features of TWIP
steels as well as thermodynamic modeling using the Calphad approach are discussed. In chapter 2 thermodynamics of all the systems is discussed including all
the subsystems. In chapter 3 some features of the database for the Al-C-Fe-Mn
system are shown and compared to the previous description. Finally chapter 4
concludes the work and gives some suggestions on future work in this area.
1.1
TWIP steels
Steels with Twinning Induced Plasticity (TWIP) have in the past years become
very interesting engineering materials due to the combination of high strength
and high ductility. A special interest has been shown by the automotive industry. The formation of twins when the alloy is deformed is a perfect fit for parts
on a car intended to absorb energy on impact. In the automotive industry there
are always efforts to make lighter cars in order to decrease fuel consumption.
Therefore the possibility to alloy the steel with high amounts of aluminum making L-IP steels, Lightweight steels with Induced Plasticity, has been explored.
Some TWIP alloys are already in use in industry but for some applications the
yield strength of these alloys is still far too low. Several ways to improve the
1
yield strength in these alloys have been explored. One of the improvements that
seems the most promising is precipitation hardening by the addition of carbide
and nitride formers such as Ti, Nb and V.
In recent years TWIP steels have attracted a lot of attention and the number
of publications in the last decade is very large compared to previous years [2].
The main interest for these steels comes from the automotive industry where
the aim is increased passenger safety. Reduction of CO2 emissions due to weight
reduction is also a very attractive point for these materials. The TWIP steels
are similar to the TRIP-steels (TRansformation Induced Plasticity) in that they
undergo microstructural changes during deformation. In the case of the TRIP
steels, they go through a phase transition under plastic deformation to form
martensite whereas the TWIP-steels form twins. The definition of what constitutes a TWIP steel is not always clear, one reason being that it is quite common
that a single grade can exhibit both twinning and formation of -martensite on
deformation. Most authors agree that the definition should be linked to the
Stacking Fault Energy (SFE). According to Sato et al. [3] the γ → transformation will be the dominating mechanism for alloys having SFEs lower than 20
mJ/m2 . The microstructure of TWIP steels is usually austenitic since it is in
the FCC-phase the twins can form. There are efforts being made to produce
duplex grades as well where the twins would only form in parts of the material
making it even more flexible. There are several types of TWIP steels, they are
generally divided into two main categories; High and low carbon steels. The
high carbon steels are usually referred to as Hadfield steels and the low carbon
variants can be e.g. shape memory alloys.
1.1.1
History of TWIP steels
The TWIP steels were originally called High Manganese steels since this is the
type of steel that this kind of twinning-effect was first found in. The forefather
of the High manganese steels is the so-called Hadfield steel, discovered by Sir
Robert Hadfield in 1888 [4]. This steel, high in both manganese and carbon,
exhibited an interesting combination of properties. It had very high strength but
was also very tough. At this time there was no knowledge on the mechanisms
behind these properties or even the microstructure, which was first described by
Hall [5] and Krivobok [6] in 1929. They found that the material was austenitic,
and so the limits for fully austenitic steels were studied by Tofaute and Linden
in 1936 [7]. By this time it was still unclear why the material had the properties
it did and it was not until 1935 that Ch´evenard made the assumption that a
hard phase was formed during straining [8]. Troiano and McGuire suggested
that there were two types of martensite, α and , one formed from rapid cooling
and the other formed under deformation [9]. The hexagonal martensite was
discovered by Schmidt [10] and was determined to be the source of the unusual
properties of the manganese steels. During the 1950s, materials were discovered
that displayed the high work hardening observed in Hadfield steels without
containing any martensite, and the idea of twins was formulated, see e.g. [11].
A while after this, the twins were formally confirmed by TEM studies, see e.g.
2
[12].
1.1.2
Twinning vs. -martensite formation
One of the main phenomena being studied in the literature is the determining
factor deciding whether the deformation of the material will be by martensite
formation or twinning. There seem to be several different factors determining
which will be the dominant deformation mechanism, which will be discussed
further in the next section. One of the main factors regarding the twinning
effect vs. -martensite is the Stacking Fault Energy (SFE). According to Sato
[3], additions of Al to Fe-Mn alloys strongly suppress the nucleation of martensite hence making it easier to form twins. However it also makes it easier to
form α-martensite, wherefore the best approach to achieve TWIP steels is to
have high contents of manganese and small amounts of aluminum. Since manganese also suppresses the martensite transformation Bouaziz and co-workers
[2] claim that the alloys which do not form -martensite also do not form αmartensite. Some authors have claimed that there exists a critical stress that
must be overcome in order to form either mechanical twins or -martensite, e.g.
Bracke [13]. Some authors attribute the kind of deformation mechanism to the
type of Stacking Fault (SF), extrinsic or intrinsic. Idrissi et al. [14] found in their
work that the formation of intrinsic SFs in the sample deformed at 160 ◦ C seems
to agree with the mechanisms based on deviation, which predict the creation of
intrinsic SFs prior to mechanical twinning. Furthermore, these models require
the activation of multiple glide planes as observed in the present case. The
authors conclude that their results indicate that there is a relationship between
the type of stacking fault in the material and the deformation mechanism, extrinsic SFs for the formation of -martensite and intrinsic SFs for the formation
of mechanical twins.
1.1.3
Stacking Fault Energy (SFE)
When a perfect dislocation dissociates into two Shockley partials it is separated
by a stacking fault. The SFE in a material is linked to the separation distance
between the two Shockley partials, the lower the SFE the larger the distance
[15]. There are different ways to estimate or predict the SFE, one experimental
method and two calculation methods [16]. The SFE can be measured using TEM
investigations observing the inscribed dislocation node radius [17]. The SFE can
also be predicted using a model based on thermodynamics [18]. Lastly the SFE
can be calculated using ab-initio methods [15, 19]. Adler et al. [20] proposed
an equation for calculating the SFE in FCC-metals based on thermodynamic
considerations:
SF Eintrinsic = 2ρ∆Gγ→ + 2σ γ/
(1.1)
This equation was revised by Saeed-Akbari et al. [16] to take the effect of grain
size into account.
SF Eintrinsic = 2ρ∆Gγ→ + 2σ γ/ + 2ρ∆Gex
3
(1.2)
where 2ρ∆Gex is the contribution to the SFE due to grain size. Aluminum
increases the SFE of FCC-alloys. Decreasing the grain size will also increase
the SFE. Hedstr¨
om [21] stated that the grain boundaries will act as barriers for
the growth of martensite laths, therefore the reduction of grain size will result in
less strain induced martensite. Saeed-Akbari et al. [16] have studied the effect
of temperature, alloying elements and grain size on the SFE. They showed that
the effects of temperature and aluminum content are greater than that of the
grain size. The sensitivity to temperature changes decreases with the amount of
Mn. It seems like a low SFE is essential for the formation of mechanical twins,
however, according to some authors, this is not the only trigger. Bouaziz et
al. [22] have previously reported that alloys with similar SFE exhibit different
deformation mechanisms depending on the carbon content in the material. The
dissociation of perfect dislocations because of the low SFE makes it harder for
other perfect dislocations to cross slip and therefore makes the glide of perfect
dislocations mainly planar.
1.1.4
Plasticity mechanisms
Materials usually deform by deformation glide but mechanical twinning and martensite formation are competitive mechanisms for deformation [2]. There are
several different explanations for the interesting combination of flow stress and
ductility that the high manganese steels exhibit. The property most attributed
to the interesting qualities that the TWIP steels exhibit is a very high work
hardening effect. The main explanations are an atypical Dynamic Strain Aging
(DSA) and deformation mechanisms besides dislocation glide, e.g. twinning.
The DSA is noticeable due to serrated stress-strain curves and negative strain
rate sensitivity. Due to the fact that this phenomenon only occurs in alloys
containing carbon, it is thought to be the result of the dynamic interaction
between the mobile carbon atoms and dislocations. It has been described in
terms of Portevin-LeChatelier (PLC) effect. The DSA leads to the formation
of PLC (Portevin-LeChatelier) bands. The PLC bands are caused by localized
strain and are similar to neck formation in that the PLC bands form in an angle
to the straining direction. The cause of the high work hardening in the high
manganese steels is cause for controversy in the literature, where some authors
claim that it is caused mostly by the mechanical twins [23] and others say that
the main cause is the DSA mechanism. Bouaziz et al. [2] claim that it is only
the appearance of mechanical twins (or strain induced -martensite) that can
account for all the features during the work hardening. Kim et al. stated in
their work [24] that the DSA probably is a result of the dynamic interaction
between mobile obstacles, such as interstitial atoms, and dislocations during
deformation. The authors claim that this theory is further strengthened by
the fact that the serrations in the stress-strain curve do not seem to appear
in carbon-free alloys see e.g [25]. During deformation parts of the dislocation
can be temporarily arrested at obstacles, such as forest junctions. The longer
the arrest time the more it will contribute to the stress. The movement of the
mobile dislocations is interrupted by forest dislocations or solute atoms during
4
the waiting time. The interstitial solutes, such as carbon, diffuse toward the
arrested mobile dislocation during the aging time and immobilize them. The
activation energy of carbon diffusion is too high at room temperature to be able
to account for the room-temperature DSA in FCC alloys. The activation energy
for the diffusion of a complex vacancy such as Snoek locking is theoretically low
enough to be possible. Although the DSA leads to higher strain hardening it may
also cause an unwanted lowering of the ductility. The other theory is that the
work hardening mainly can be attributed to the formation of mechanical twins
during deformation. Bouaziz et al. [2] state that TWIP steels have excellent
strain-hardening properties because of a reduction in the mean free path for
dislocation glide due to deformation twinning. Adler and co-workers [20] also
claim that twinning is the main explanation for the strengthening in TWIP
steels. They are of the opinion that the hardening in Hadfield steels can almost
entirely be attributed to the formation of twins during deformation. However
some special properties compared to other materials exhibiting twins can be
attributed to pseudo twins or some unknown interaction between the Mn and
C atoms. Carbon atoms in the octahedral sites will become trapped in the
tetrahedral sites inside the twinned regions, if the energy barrier for diffusion is
too high, contributing to the hardening of these materials.
1.1.5
Twin formation
There are also some different theories on how the formation of twins in these
materials takes place. In a recent review Idrissi [26] explains that there are
mainly three theories on how the twins form. The theories are based on the
different mechanisms dominating the actual formation and the type of SF and
they are: (1) pole mechanism which produces perfect twins without SF, (2)
deviation process which produce intrinsic SF together with the nucleation of
Frank or stair-rod sessile dislocations and (3) extrinsic stacking faults (models
based on the interaction between extrinsic SF).
(1) Venables [27] proposed that prismatic glide sources would dissociate under
stress into a Frank partial dislocation (pole dislocation) and a Shockley
twinning partial. The created Shockley partial would then move away
from the sessile Frank partial leaving behind a large intrinsic stacking
fault. When the Shockley partial has created a semicircle it will wind
down to the underlying close packed plane. If this process is repeated on
every plane, a twin structure is created. Hirth [28] proposed a similar kind
of pole dislocation but with different types of dislocations.
(2) The most common theories based on deviation processes are that of Cohen
and Weertman [29] and that of Mori and Fujita [30]. Cohen and Weertman [29] proposed that a perfect dislocation would dissociate into a sessile
Frank partial screw dislocation and a glissile Shockley partial when converging with a Lomer-Cottrel barrier. The deformation twinning would
occur on the conjugate plane. For each Shockley partial emitted a sessile
5
Frank partial is created. Mori and Fujita [30] suggested the dissociation of
a Shockley partial dislocation gliding in the primary plane into a stair-rod
sessile dislocation at the intersection of the primary and conjugate plane.
This phenomenon is also known as the stair-rod cross-slip. Both of these
models require both multiple glide planes and high stress concentrations
to happen in order to get dislocation dissociation in the twinning plane.
(3) The last type of model, the one based on the presence of an extrinsic
stacking fault is dominated by the theory by Mahajan and Chin [31].
It describes two perfect dislocations on the same plane turning into three
Shockley partial on three consecutive adjacent close-packed planes. This
would result in an extrinsic stacking fault configuration that acts as a
three-layer nucleus for twinning. A macro twin would form if several of
these twin nuclei grew into each other.
There have also been models which specifically describe the formation of twins in
the Hadfield-type TWIP-steels. One of the most commonly referred to of these
is the MTN-model proposed by Miura, Takamura and Narita [32]. Idrissi’s study
showed that it is only possible that the Pole mechanism with deviation and the
MTN-model could describe the formation of twins in these steels.
1.1.6
Improvement of the Yield Stress (YS)
The main characteristic of the TWIP steels is the unusual and very interesting
combination of Ultimate Tensile Strength (UTS) and ductility. The main problem with these alloys however is that they generally have to low values on the
Yield Strength (YS) which is a very important factor in most applications and
for automotive applications specifically. Several different routes to improve the
YS of these steels have been investigated in the literature. The most promising
ways seem to be: grain refinement, pre-straining by rolling and precipitation
strengthening. In the automotive industry, a reasonable YS would be 600-700
MPa but most TWIP-alloys have a YS around about 400 MPa. With grain
refinement it is possible to reach a YS of 600-700 MPa if the grain size is reduced to approximately 1 µm. Unfortunately the smallest grain size achievable
in the industrial processes is about 2.5 µm. With pre-straining by rolling, it
is possible to achieve great improvements in the YS and still keep much of the
ductility in the material. However this method gives the material an instantaneous reduction of the strain hardening coefficient. The pre-straining will also
introduce a substantial anisotropy into the material. To prevent the anisotropy
and to regain some of the strain hardening it is possible to perform recovery and
partial recrystallization of the material. It has been found that this might be
an interesting route to take and the best results are achieved after the largest
cold rolling reduction and the lower temperature limit [33]. Last but not least
there is the method of precipitation strengthening which is currently being thoroughly investigated. It is important to be careful when it comes to precipitation
strengthening since most of the precipitates are unwanted. They are unwanted
6
for two reasons; firstly most of the precipitates are carbides which are very
brittle and secondly it will tie up most of the carbon which will minimize the
strain-hardening. It seems like some alloying elements will have positive effects
on the mechanical properties of the material. The most promising elements are
Nb and V but also Ti and W seem to have some interesting influences. So far,
improvements of up to 400 MPa on the YS have been achieved. The influence
of interstitial alloying elements on the strength of the material is not as great as
in ferritic alloys for these materials. However it can be seen that the influence
on the dislocation glide is quite large at lower temperatures. If the temperature
is increased it will however reach a critical value at which a plateau will be
reached. Glide in these alloys is thermally activated at low temperatures.
1.2
Thermodynamic modeling (CALPHAD)
The Calphad technique is a method for describing the thermodynamic properties of alloy systems. In this method the Gibbs energy for each phase is described
by a mathematical expression containing adjustable model parameters that can
be optimized to reproduce experimental or ab initio data on thermodynamic
properties or phase diagram data. CALPHAD is an acronym meaning CALculation of PHase Diagrams but the approach has expanded and can do much
more than just calculate phase diagrams. These days CALPHAD is often said
to mean Computational coupling of thermochemistry and phase diagrams.
1.2.1
Phase models
Pure elements
The descriptions of all unary systems in this work are taken from [34]. Efforts
are presently being made to describe the unary systems using more physics
based models but since the present work has been focused on building a multicomponent database, it is based on the old unaries. The Gibbs energy of each
phase is described by a polynomial in temperature
◦
Gθi − H SER = a + bT + cT lnT + dT 2 + eT 3 + f T −1
SER
(1.3)
where H
is the reference state, usually in thermodynamic databases the
reference used is the enthalpy of the stable configuration of the pure element
at room temperature, i.e. 298 K or 25 ◦ C. The a-term represents enthalpy, b
can be evaluated using information regarding entropy and the rest of the terms
represent the heat capacity (Cp ). The Gibbs energy can also be described as a
function of pressure but this has not been considered in the present work.
7
Compound Energy Formalism
All phase models can be said to be based on the Compound Energy Formalism
(CEF) developed by Hillert [35, 36, 37, 38, 39].
srf
θ
Gθm − H SER = srf Gθm + cnf Sm
· T + E Gθm + phys Gθm
Gθm
where
is the surface of reference,
and E Gθm is the excess Gibbs energy.
srf
Gθm =
X
cnf
θ
Sm
(1.4)
is the configurational entropy
PI0 (Y )◦ GθI0
(1.5)
I0
cnf
E
θ
Sm
= −R
Gθm =
X
n
X
s=1
as
X
(s)
(s)
(1.6)
PI2 (Y )LθI2 + · · ·
(1.7)
yi lnyi
i
PI1 (Y )LθI1 +
I1
X
I2
where I defines a constituent array containing the combination of all the
species being considered. If the constituent array is of the zero:th order all the
end-member compounds are described by PI0 (Y ). ◦ GθI0 represents a nonmagnetic compound energy. R is the gas constant and as is the number of sites for
sublattice s. I1 forms an array with all possible combinations with mixing on
one sublattice and I2 contains mixing on two. LθI1 is an interaction parameter
describing the deviation from ideal mixing when there is interaction on one sublattice and similarly LθI2 describes the deviation from ideal mixing when there is
simultaneous mixing on two sublattices. phys Gθm in eq. 1.4 is the contribution to
the Gibbs energy due to physical phenomena such as magnetism. The magnetic
contribution was described by Hillert and Jarl [40]
mag
Gθm = nRT f (τ )ln(β + 1)
(1.8)
where τ = TTC , T is the thermodynamic temperature and TC is the Curie
temperature. β is the average magnetic moment.
Substitutional solutions
The simplest form of the CEF is the substitutional solution model. The substitutional solution model assumes that atoms mix randomly on a single lattice.
This is often true for melts and terminal phases such as FCC, BCC and HCP
when it comes to metallic elements. The mathematical expression for the sub-
8
stitutional solution model is:
Gθm − H SER =
X
xi ◦ Gθi + RT
i
XX
i
X
xi lnxi +
(1.9)
i
θ
xi xj Ii,j
j
+
XXX
i
j
θ
xi xj xk Ii,j,k
+
phys
Gθm
k
where xi is the mole fraction of element i, ◦ Gθi is the non-magnetic lattice
θ
stability of θ for pure i. Ii,j
is the binary interaction parameter describing
the deviation from non-ideality in the mixing between i and j. The composition
dependence of the interaction parameter can be described using a Redlich-Kister
(R-K) polynomial [41]
θ
Ii,j
=
n
X
v=0
v
Li,j (xi − xj )v
(1.10)
where v Li,j is the interaction parameter of v:th order and can be expanded
according to
v
Li,j = A + B · T
(1.11)
where A and B are model parameters to be optimized to reproduce experimental data. If necessary, it is possible to add more parameters. The contributions to the Gibbs energy from the different parameters are shown in Fig.
1.1.
Stoichiometric compounds and phases with limited solubility
Some phases only exist at a single composition. They are then described as
stoichiometric compounds which can be described similarly to the pure elements
according to equation 1.3. If there is no available information on Cp the energy
of the phase can be described using the Neumann-Kopp approximation which
means that the Cp is taken as the weighted average of the pure elements. The
Gibbs energy of the compound In Jm is thus described by
◦ β
∆GIfn Jm = GIn Jm − n◦ Gα
I − m GJ = ∆Hf − T ∆Sf
(1.12)
◦ β
where ◦ Gα
I resp. GJ is the Gibbs energy of the stable configuration of pure
I and J respectively, at ambient temperature and pressure. ∆Hf is the enthalpy
of formation and ∆Sf is the entropy of formation.
There are many cases when compound phases show some deviation from
ideal stoichiometry, this can be accounted for by introducing defects. Anti-site
9
100
‫ܮ‬,
džĐĞƐƐ'ŝďďƐ ĞŶĞƌŐLJ ΀:ͬŵŽů΁
50
0
‫ܮ‬,
-50
-100
-150
-200
-250
0
0.1
0.2
0.3
0.4
0.5
‫ܮ‬,
0.6
0.7
0.8
0.9
1
DŽůĞ ĨƌĂĐƚŝŽŶ ũ
Figure 1.1: Graphical representation of the addition to Gibbs energy due to
interaction parameters, here the interaction parameters all have the value -1000.
defects can be introduced by allowing an element to occupy the sublattice of
another element, e.g. (A)n (A,B)m . The Gibbs energy will then be described by
GAn Bm − H SER =
0 00 ◦ An Bm
0 00 ◦ An Bm
+ yA
yB GA:B +
yA
yA GA
00
00
mRT (yA
lnyA
+
00
00
yB
lnyB
)
+
(1.13)
0 00 00
yA
yA yB IA,B
n Bm
where yis is the site fraction [38] of i on sublattice s, ◦ GA
is the latA
n Bm
is
the
formation
energy
of the
tice stability of An Bm for pure A and ◦ GA
A:B
compound An Bm from the pure elements.
It is also possible to add vacancy defects in a similar way.
Ordered phases
Ordered compounds can also be described using the CEF. All elements are then
allowed to occupy all sublattices i.e. (A,B)m (A,B)n . There are several ordered
compounds that can be regarded as superstructures to the terminal phases FCC,
BCC and HCP. Depending on the number of sublattices used, a different number
of ordered compounds can be described. In this work, the FCC, BCC and κ
phases have been described using models with four sublattices (4SL) for the
substitutional elements. The phases were described using the partitioning model
(also known as the split CEF) in which the chemical ordering is described as an
10
addition to the Gibbs energy in a similar way as is done for magnetism
Gphase = Gdis + ∆Gord
(s)
ord
(s)
∆Gord = Gord (yi ) − Gord (yi
(1.14)
= xi )
(1.15)
where G
is calculated twice so that the contribution becomes zero if the
phase is disordered i.e. yi0 = yi00 = yi000 = yi0000 = xi .
Using a 4 SL model for the substitutional elements creates many end-member
compounds whose energies need to be determined. In order to limit the internal
degrees of freedom and improve extrapolations into higher order systems the
Bragg-William-Gorsky (BWG) approximation [42, 43] has been implemented in
this work.
Ordering in BCC alloys using a 4SL model is discussed further in paper II.
1.2.2
Extrapolation into higher order systems
The mathematical functions for each phase are stored in a database. Using this
database many different thermodynamic equilibria and thermodynamic properties can be calculated.
Once the binary systems are evaluated they can be combined and used to
extrapolate into higher order systems. There are several methods for conducting
these extrapolations. Illustration of some of the available methods are shown
in Fig. 1.2. The composition from which the binary values will be taken are
evaluated in different ways. The first two methods, the Kohler method and
the Muggianu method are symmetrical methods, where the compositions are
evaluated in a similar manor for all the binaries and the last , the Toop method,
is an asymmetrical method. In this work, the Muggianu extrapolations have
been used for all systems.
1.0
1.0
0.9
0.8
0.9
0.8
0.7
0.8
0.7
0.6
0.7
0.6
0.5
0.6
0.5
0.4
0.5
0.4
0.3
0.4
0.3
0.2
0.3
0.2
0.1
0.2
0.1
0
0.1
0
0
1.0
0.9
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mole fraction B
(a) Kohler
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mole fraction B
(b) Muggianu
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mole fraction B
(c) Toop
Figure 1.2: Illustrations for evaluating the binary composition from which the
energy value will be taken.
The interaction parameters become less relevant the more elements that are
involved. Therefore the highest order systems that are usually evaluated are the
11
30
10
ďĐĐ
ĨĐĐ
5
ŚĐƉ
ďĐĐ
ĨĐĐ
25
Enthalpy of formation [kJ/mol]
Enthalpy of formation [kJ/mol]
15
0
-5
-10
-15
20
ŚĐƉ
15
10
5
0
-5
-10
-15
-20
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mole fraction V
Mole fraction V
(a) Calphad
(b) DFT
Figure 1.3: Enthalpy of formation of BCC (#), FCC (4) and HCP (), a) at
298 K according to the current description and b) calculated with DFT at 0 K.
ternary systems.
Because of the relatively simple mathematics involved it is possible to describe the thermodynamic properties of multicomponent alloys. When building
thermodynamic databases it is necessary to use the same descriptions for the
lower order systems for the higher order descriptions to be compatible. Therefore it happens that ternary or higher order systems have to be reassessed even
though good evaluations of those particular systems are available, if the lower
order systems are improved.
1.2.3
Data evaluation
One of the most important stages of the thermodynamic assessment process
and probably the most time consuming one is critically assessing the available
experimental data. Choosing the “correct” set of data to fit to is crucial in order
to get good extrapolations into higher order systems.
In the cases when thermochemical data is missing, a good approximation
can often be to use data calculated using ab initio methods such as Density
Functional Theory (DFT). It is important to be careful when using ab initio
calculated data. The lattice stabilities in Calphad and DFT do not always
match. With some elements such as FCC vanadium, the mismatch is very
large, making it almost impossible to use some types of data at all directly.
Fig. 1.3 shows the enthalpy of formation calculated with Calphad and DFT
respectively across the entire composition range in the Al-V system.
As can be seen, the enthalpy for the different phases matches well on the
Al-side, but on the V-side the mismatch is quite large. This means that this
data cannot be used directly, specifically near the V-side. It is possible however
12
to look at the trends. In the case shown in Fig. 1.3 the enthalpy of formation
for FCC and HCP phases has been optimized to reproduce the trend so that
the curves for FCC, BCC and HCP cross at the point that they do according
to the DFT data.
The assessment process is an iterative process. Even if binary experimental
data are reproduced with a thermodynamic description it can sometimes prove
to extrapolate badly into higher order systems. This is usually due to lack of
thermochemical data. In general, as few and as small parameters as possible are
desired. If it is necessary to use many large parameters in higher order systems,
it is usually a sign that one or several of the lower order systems need to be
reassessed.
13
Chapter 2
Assessed systems
Within the PrecHiMn project a database containing the elements Al, C, Fe, Mn,
Ti, V, N, Nb, Si has been developed. My work has been to assess some of the
subsystems, the Al-C-Fe-Mn system and its subsystems as well as the Al-Ti-V
system and its subsystems. Table 2.1 shows a summary of all the binary and
ternary systems used within this work. Table 2.2 shows all of the phases in
the Al-C-Fe-Mn system and table 2.3 all the phases in the Al-Ti-V system. In
the following, the available thermodynamic assessments of all the systems dealt
with in this work are discussed. In the cases when there were no satisfactory
descriptions, new thermodynamic assessments have been performed.
Table 2.1: Descriptions of binary systems used in this work.
Al-C
Al-Fe
Al-Mn
Al-Ti
Al-V
C-Fe
C-Mn
Fe-Mn
Ti-V
2.1
Binary systems
Connetable et al. [44]
Sundman et al. [45]
Du et al. [46]
Witusiewicz et al. [47]
Lindahl et al. [paper III]
Gustafsson [48]
Djurovic et al. [49]
Djurovic et al. [50]
Saunders [51]
Al-C-Fe
Al-C-Mn
Al-Fe-Mn
Al-Ti-V
Ternary systems
Connetable et al. [44]
Lindahl et al. [paper IV]
Lindahl et al. [paper I]
Lindahl et al. [paper III]
Binary systems
In order to have accurate thermodynamic descriptions of multicomponent alloys,
it is very important to have sound descriptions of the lower order systems. In
the following, the available binary systems are discussed. It was found that
there are sufficient available thermodynamic assessments for all binary systems
14
Table 2.2: Phases in the Al-C-Fe-Mn system.
Phase
Strukturbericht
Terminal phases
Liquid
FCC
A1
BCC
A2
HCP
A3
α-Mn
A12
β-Mn
A13
Carbides
Al4 C3
M23 C6
cementite
M 5 C2
M 7 C3
Graphite
Alumnides
Al8 Fe5
D82
Al2 Fe
Al5 Fe2
Al13 Fe4
Al12 Mn
Al6 Mn
D2h
R-Al4 Mn
U-Al4 Mn
LT Al11 Mn4 HT Al11 Mn4 Al8 Mn5
D810
Metastable Carbides
M2 C
-
Space group
Pearson symbol
Model
Fm¯
3m
Im¯
3m
P63 /mmc
I¯
43m
P41 32
cF4
cI2
hP2
cI58
cP20
(Al,C,Fe,Mn)1
(Al,Fe,Mn)1 (C,Va)1
(Al,Fe,Mn)1 (C,Va)3
(Al,Fe,Mn)1 (C,Va)0.5
(Al,Fe,Mn)1 (C,Va)1
(Al,Fe,Mn)1 (C,Va)1
¯
R3m
Fm¯
3m
Pnma
C2/c
Pnma
P63 /mmc
hR21
cF116
oP16
mS28
oP40
hP4
(Al)4 (C)3
(Fe,Mn)20 (Fe,Mn)3 (C)6
(Fe,Mn)3 (C)1
(Fe,Mn)5 (C)2
(Fe,Mn)7 (C)3
(C)1
I4¯
3m
P1
oC?
C2/m
Im3
Cmcm
P63 /m
P63 /mmc
P¯
1
Pn21 a
R3m
hR26
aP18
Cmcm
mC102
cI26
oC28
hP586
hP574
aP15
oP156
cI52
(Al,Fe)8 (Al,Fe)5
(Al)2 (Fe,Mn)1
(Al)5 (Fe,Mn)2
(Al)0.6275 (Fe,Mn)0.235 (Al,Va)0.1375
(Al)12 (Fe,Mn)1
(Al)6 (Fe,Mn)1
(Al)461 (Mn)107
(Al)4 (Fe,Mn)1
(Al)11 (Mn)4
(Al,Mn)29 (Mn)10
(Al)12 (Mn)5 (Al,Fe,Mn)9
Pnnm
oP6
except for the Al-V system. A summary of the binary systems used in this work
is shown in table 2.1.
Al-C
The Al-C system was first assessed by Gr¨obner [52]. In his description he
only included the stable phases in this system i.e. liquid, FCC (Al), graphite
(C) and the intermetallic compound Al4 C3 . In 2008 Connetable et al. [44] reassessed the system adding a very slight solubility of carbon in FCC (Al) and
descriptions of the metastable phases BCC and κ where also added. The phase
diagrams according to the different sets of parameters are shown in Fig. 2.1.
The description by Connetable et al. [44] is used in this work.
15
Table 2.3: Phases in the Al-Ti-V system.
Phases
Strukturbericht
Terminal phases
Liquid
FCC
A1
BCC
A2
HCP
A3
Compounds
BCC
B2
AlTi3
D019
AlTi
L10
Al2 Ti
Al5 Ti2
Al3 M
D022
L Al3 Ti Al8 V5
D82
Stoichiometric phases
Al5 Ti3
Al23 V4
Al45 V7
Al21 V2
-
Space group
Pearson symbol
Model
¯
Fm3m
Im¯3m
P63 /mmc
cF4
cI2
hP2
(Al,Ti)1
(Al,Ti)1 (Va)1
(Al,Ti)1 (Va)3
(Al,Ti)1 (Va)0.5
Pm¯3m
P63 /mmc
P4/mmm
I41 /amd
P4/mmm
I4/mmm
I4/mmm
I4¯
3m
cI2
hP8
tP4
tI24
tP28
tI8
tI32
cI52
(Al,Ti)0.5 (Al,Ti)0.5 (Va)3
(Al,Ti)3 (Al,Ti)1
(Al,Ti)1 (Al,Ti)1
(Al,Ti)2 (Al,Ti)1
(Al,Ti)5 (Al,Ti)2
(Al,Ti,V)3 (Al,Ti,V)1
(Al,Ti)3 (Al,Ti)1
(Al)6 (Al,V)2 (Al,V)3 (V)2
P4/mbm
P63 /mmc
C2/m
Fd¯
3m
tP32
hP54
mC104
cF184
(Al)5 (Ti)3
(Al)23 (V)4
(Al)45 (V)7
(Al)21 (V)2
5000
5000
4500
4500
>ŝƋƵŝĚ
'ƌĂƉŚŝƚĞ
3000
2500
1500
3500
'ƌĂƉŚŝƚĞ
3000
2500
2000
ůϰϯ
Temperature [K]
3500
2000
>ŝƋƵŝĚ
4000
ůϰϯ
Temperature [K]
4000
1500
1000
1000
ĨĐĐ
500
ĨĐĐ
500
0
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0
Mole fraction C
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mole fraction C
(a) Gr¨
obner [52]
(b) Connetable et al. [44]
Figure 2.1: Binary phase diagram for the Al-C system.
Al-Fe
The first complete thermodynamic assessment of the Al-Fe system was performed by Saunders [53]. In 1993 Kattner and Burton [54] reviewed the experimental data and the published diagram. They published the generally accepted
16
diagram along with experimental data. Not all of the parameters were published though since the models at that time weren’t sophisticated enough to
deal with the D03 phase. Seiersten [55] made the first complete thermodynamic
assessment of the system with a complete set of parameters. The BCC phase
was modeled with a 2SL model. This was later published as a part of the COST
507 project [56]. In 2008 Du et al. [57] modified Seiersten’s assessment to fit
new experimental data on the congruent melting of Al13 Fe4 . The same year
Connetable et al. [44] reassessed the Al-C-Fe system including reassessments
of the binary Al-Fe and Al-C systems. Jacobs and Schmid-Fetzer [58] made a
thermodynamic assessment of the system based on the assessment of Seiersten
but introduced vacancy defects into the models for BCC and FeAl3 . Sundman
et al. [45] assessed the entire system, this assessment was also based on the one
by Seiersten with the changes made by Du et al. [57], but a 4SL model was
used for the BCC phase in order to describe the ordered D03 phase. The new
experimental information since the assessment of Seiersten was reviewed in this
work. Phase diagrams calculated with descriptions with available thermodynamic model parameters are shown in Fig. 2.2. The description by Sundman
et al. [45] has been used in this work.
Al-Mn
The Al-Mn system has been assessed a number of times in the literature. Due
to vague experimental results, especially concerning the Al8 Mn5 phase and it’s
disordering into the BCC phase, the assessments have given quite different results. Kaufman & Nesor [59] performed an initial assessment of the Al-Mn
system. Their calculated diagram was quite different from the experimental
phase diagram. In 1992 Jansson [60] reassessed the system. The BCC phase in
the middle of the system was ignored in this description.
Later, in 1999, Liu et al. [61] again reassessed the Al-Mn system, this time
including the phase region of BCC in the middle of the phase diagram. They also
used a 2SL model for the BCC phase in order to describe the second order phase
transition from A2 to B2 in that same phase region according to experimental
data from [62].
Ohno et al. [63] slightly adjusted the description by Liu et al. [61] making
the Al11 Mn4 phase stable down to room temperature and also slightly adjusted
the two phase region between Al8 Mn5 and β-Mn.
The latest description of the Al-Mn system was by Du et al. [46]. They
included two more phases in the high-Al region (RAl4 Mn and Al11 Mn4 (HT))
and disregarded the ordering in BCC. The solubility of Al in α-Mn was also
drastically decreased compared to previous versions. The phase diagrams from
the different descriptions are shown in Fig. 2.3. In this work the description by
Du et al. has been used together with information on the ordering in the BCC
phase from Djurovic [64].
17
2000
2000
>ŝƋƵŝĚ
1000
ϱ
ů &Ğ
ďĐĐ
Ϯ
600
ϰ
ϭϯ
ůϴ&Ğϱ
1200
ů &Ğ
ů &Ğ
Ϯ
1400
1000
800
ďĐĐ
600
400
Ϯ
ů &Ğ
Temperature [K]
ůϴ&Ğϱ
1200
ů &Ğ
Temperature [K]
ĨĐĐ
1600
1400
800
>ŝƋƵŝĚ
1800
ĨĐĐ
1600
Ϯ
ϱ
ů &Ğ
1800
ϰ
ϭϯ
400
200
200
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mole fraction Al
Mole fraction Al
(a) Seiersten [55]
(b) Jacobs and Schmid-Fetzer [58]
2000
>ŝƋƵŝĚ
1800
ĨĐĐ
1400
Ϯ;ƉŵͿ
ůϴ&Ğϱ
ů &Ğ
1200
1000
Ϯ
Ϯ;ĨŵͿ
600
400
Ϯ
ϱ
ů &Ğ
800
Ϯ
ů &Ğ
Temperature [K]
1600
ϰ
ϯ
ϭ
Kϯ
200
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mole fraction Al
(c) Sundman et al. [45]
Figure 2.2: Binary phase diagram for the Al-Fe system.
Al-Ti
The Al-Ti system is an important system and has therefore been studied several
times in the literature. The system is a complex one, with many intermetallic
phases. Some regions in the phase diagram have been proven to be very difficult
to determine experimentally wherefore different results have been achieved by
different assessors. The first attempt of a thermodynamic assessment of this system was carried out by Kaufman and Nesor [65] in their binary phase diagram
compilation from 1978. They treated all the intermetallic phases as stoichiometric compounds. In 1988 Murray [66] improved the assessment by adding
a solubility range to the TiAl(L10 )-phase and also treated the order-disorder
transformations for BCC, FCC and HCP using the Bragg-William approximation. The same year Gros et al. [67] published a thermodynamic description
for the Ti-rich side of the phase diagram including only phase equilibria for
18
1800
1800
>ŝƋƵŝĚ
ɴͲDŶ
ďĐĐ
ŚĐƉ
1200
1000
800
ɲͲDŶ
600
400
ĨĐĐ
ůϴDŶϱ
ůϴDŶϱ
ĨĐĐ
1400
ůϭϮDŶ
ůϲDŶ
ůϰDŶ
ůϭϭDŶϰ
600
Temperature [K]
1200
800
ďĐĐ
ďĐĐ
ŚĐƉ
1000
>ŝƋƵŝĚ
1600
1400
ůϭϮDŶ
ůϲDŶ
ůϰDŶ
ůϭϭDŶϰ
Temperature [K]
1600
ɴͲDŶ
ɲͲDŶ
400
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mole fraction Mn
Mole fraction Mn
(a) Jansson [60]
(b) Liu et al [61]
1800
>ŝƋƵŝĚ
ďĐĐ
,důϭϭDŶϰ
1400
ŚĐƉ
ďĐĐ
1200
1000
ůϭϮDŶ
800
600
ůϴDŶϱ
hůϰDŶ
>důϭϭDŶϰ
ĨĐĐ
ů DŶ
Temperature [K]
1600
ɴͲDŶ
ϲ
ɲͲDŶ
400
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mole fraction Mn
(c) Du et al. [46]
Figure 2.3: Binary phase diagram for the Al-Mn system.
the BCC, HCP, Liquid and Ti3 Al(D019 ) phases. In 1992 Kattner et al. [68]
re-assessed the Al-Ti system and added descriptions of two more stoichiometric
phases (Al2 Ti and Al5 Ti2 ). This assessment also treats the order-disorder transformations and accepts a different reaction for the formation of α-Ti, namely:
Liquid + β − T i → α − T i
Instead of the reaction accepted by Murray:
β − T i + T iAl(L10 ) → α − T i
Because of experimental information from McCulloogh et al. [69]. Kattner et
al. also added a solubility range to the TiAl3 (D019 )-phase. The assessment by
Kattner et al. was in 1997 modified by Zhang et al. [70] to better fit data on
intrinsic defect concentration in AlTi(L10 ). However, not many changes were
19
made to the stable phase diagram. Because previous assessments had described
the ordered and disordered phases with the same primitive structure using independent expressions of the Gibbs energy Ohnuma et al. [71] re-evaluated the
Gibbs energies of the FCC, BCC, HCP phases and their ordered counterparts
in 2000. They included a stable A2/B2 transformation and based their evaluation on their own experiments carried out while carefully controlling the oxygen
contamination. In 2008 Witusiewicz et al. [47] reassessed the system putting
more focus on the Al-rich side of the phase diagram. They improved the fit
to the experimental data compared to previous assessments. The work determined that the melting behavior of the BCC-phase is congruent and included
the order-disorder phenomenon in the BCC-phase. The nature of the formation
of the AlTi3 (D019 ) is dependent on whether the A2-B2 ordering is considered
or not. The Al5 Ti3 phase is considered to be stable since it doesn’t interfere
with the rest of the system. The field in the middle of the phase diagram is
modeled as AlTi (L10 ) and ζ (Ti2+x Al5−x ). The most recent assessment was
carried out by Wang et al. [72] in 2012. The most important contribution of
this work is the addition of anti-site defects which will not be considered in the
present work. The phase diagrams calculated from the parameters published by
Ohnuma et al. [71] and Witusiewicz et al. [47] are shown in Fig. 2.4.
2000
2000
ĨĐĐ
ŚĐƉ
Ϭϭϵ
1000
800
ϯ
Ϯ
ĨĐĐ
600
Ϯ
1400
ů dŝ;,dͿ
ů dŝ
1200
1600
ϱ
>ϭϬ
ů dŝ
1400
ďĐĐ;ϮͿ
1200
ŚĐƉ
1000
ϯ
Ϭϭϵ
800
600
Ϯ
ϯ
ϱ
ů dŝ;>dͿ
>ϭϬ
>ŝƋƵŝĚ
ůϱdŝϮ
1800
Ϯ
ů dŝ
Ϯ
ů dŝ
Temperature [K]
1600
ů dŝ
ďĐĐ;ϮͿ
Temperature [K]
1800
>ŝƋƵŝĚ
ϯ
ĨĐĐ
400
400
200
200
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mole fraction Al
Mole fraction Al
(a) Ohnuma et al. [71]
(b) Witusiewicz et al. [47]
Figure 2.4: Binary phase diagrams for the Al-Ti system.
The assessment of Witusiewicz et al. [47] has been used in the present work.
Al-V
Okamoto [73, 74] has reviewed the phase diagram information available for the
Al-V system. The first assessment of the available experimental data of this
system was performed by Murray [75]. Her assessment was mainly based on
experimental information from Bailey et al. [76] on invariant reactions and information from Willey [77] and Eremenko et al. [78] on dilute liquids. The
20
system contains three solution phases, Liquid, FCC (Al) with a very narrow
solubility range of vanadium (0-0.3%V) and BCC (V) with an extensive solubility range (0-50% Al). The system also contains 5 compound phases: Al21 V2 ,
Al45 V7 , Al23 V4 , Al3 V (D022 ) and Al8 V5 modeled as stoichiometric phases due
to lack of experimental information in the assessment by Murray. During the
COST 507 project Saunders [79] assessed the Al-V system. Complete expressions for the Gibbs energy were published to describe all the phases. All the
intermetallic compounds were described as stoichiometric. The phase Al45 V7
was described as Al7 V and the Al21 V2 as Al10 V. The temperatures of the invariant reactions are similar to those published by Murray [66]. In the year 2000
Richter and Ipser [80] re-investigated the Al-V phase diagram experimentally
on the Al-rich side i.e. up to 50% V. They found the same intermetallic compounds as had been reported earlier but the invariant points for the formation
of Al8 V5 and Al3 V varied considerably from earlier reported values. They were
1681 K and 1543 K respectively compared to the values used by Murray (and
Saunders) 1943 (1932.7) K and 1633 (1640.1) K. The most recent assessment
for this system and the one used in the present work is due to Gong et al. [81].
Their assessment puts a higher weight on the more recent experimental results
from Richter and Ipster [80] and puts more focus on the development of a crystallographically correct model for the Al8 V5 phase. The parameters for this
phase were developed in steps starting with a stoichiometric model and then
using those parameters as starting values for the increasingly complex model
until arriving at the model (Al)6/13 (Al,V)2/13 (Al,V)3/13 (V)2/13 . The solution
phases i.e. liquid, FCC and BCC were modeled with Redlich-Kister polynomials based on the unaries published by SGTE [34] and the remaining compound
phases mentioned earlier were modeled as stoichiometric. The phase diagrams
produced from the parameters from Saunders [79] and Gong et al. [81] are shown
in Fig. 2.5.
2200
2200
>ŝƋƵŝĚ
800
600
Ϯ
ϭ
Ϯ
ĨĐĐ
1400
1200
1000
800
600
400
ďĐĐ
ϯ
ůϰϱsϳ
Ϯ
ϭϮ
ϰ
ϯϮ
ů s
ďĐĐ
1600
ů s
ϰ
ϯ
Ϯ
ϯ
ů s
1000
1800
ů s
ůϰϱsϳ
ϱ
ϴ
Temperature [K]
ů s
1200
ĨĐĐ
ů s
1400
ů s
Temperature [K]
1800
1600
>ŝƋƵŝĚ
2000
ů s
2000
ϱ
ϴ
400
200
200
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0
Mole fraction V
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mole fraction V
(a) Saunders [79]
(b) Gong et al. [81]
Figure 2.5: Binary phase diagram for the Al-V system.
21
None of the available descriptions describe the thermodynamic properties
and the phase diagram data well enough. The assessment by Saunders [79] was
published before the experimental data by Richter and Ipser [80] was available
and the description by Gong et al. [81] extrapolates poorly. The Al-V system
have been reassessed in this work.
Details on the thermodynamic assessment of the Al-V system can be found
in paper III. The thermochemical properties of the Al-V system has been studied by Kubaschewski and Heymer [82], Meschel and Kleppa [83], Neckel and
Nowotny [84] and Samokhval et al. [85]. The results of the different studies are
shown in Fig. 2.6.
-10
Enthalpy of formation [kJ/mol]
-15
-20
-25
-30
-35
-40
-45
-50
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mole fraction V
Figure 2.6: Measured enthalpies of formation from [82] (#), [83] (4), [84] ()
and [85] (–)
The values differ quite drastically. The data from Kubaschewski and Heymer
[82] suggest that there should be a minimum at xV = 0.2 while the other data
suggest that the minimum should be around xV = 0.4. In paper III both the
data from Meschel and Kleppa [83] Kubaschewski and Heymer [82] were used
in two different optimization procedures. The produced sets of parameters were
used to extrapolate into the ternary Al-Ti-V system and it was found that the
data from Kubaschewski and Heymer [82] were more reasonable. The produced
Al-V phase diagram is shown in Fig. 2.7.
C-Fe
The thermodynamic properties of the C-Fe system have been investigated several times in the past [88, 36, 89, 90]. The most widely used assessment was
made by Gustafson [48]. He based his description on the one by ˚
Agren [90]
but used a substitutional solution model with a single sublattice for the liquid
phase so that the phase diagram could be calculated across the entire composition range. Later, Franke [91] reevaluated the parameters by Gustafson and
22
2400
1100
2100
>ŝƋƵŝĚ
1050
>ŝƋƵŝĚ
900
800
750
700
600
650
300
ůϮϯsϰ
ĨĐĐ
850
ůϰϱsϳ
900
950
ůϮϭsϮ
1200
Temperature [K]
1500
ůϴsϱ
Temperature [K]
ďĐĐ
ůϯs
1000
1800
600
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0
Mole fraction V
0.05
0.10
0.15
0.20
0.25
0.30
Mole fraction V
(a)
(b)
Figure 2.7: Phase diagram after final optimization together with experimental
data from [80] (#), [86] (4) and [87] ().
removed an inverse miscibility gap in the liquid at high temperatures. Hallstedt
et al. [92] reevaluated the thermodynamic properties of the cementite phase and
found that the Kopp-Neuman rule wasn’t adequate. Djurovic et al. [50] used ab
initio calculations to establish the enthalpies of formation of the metastable iron
carbides. Recently Naraghi et al [93] reassessed the entire C-Fe system using
new descriptions of the unaries. In this work, the description by Gustafson [48]
with the additions by Hallstedt et al. [92] and Djurovic et al. [50] is used.
C-Mn
The C-Mn system has been described 3 times in the literature. The first assessment was done by Lee [94] before the standardization of the descriptions of
the pure elements [34]. The second assessment was performed by Huang [95] at
approximately the same time. Later Djurovic et al. [49] improved the description by Huang including new experimental data and used ab initio calculated
enthalpies for the carbides. The phase diagrams for the two most recent descriptions are shown in Fig. 2.9. The description by Djurovic [49] has been used in
this work.
Fe-Mn
The Fe-Mn system was first assessed by Kaufman [59]. Huang [96], Reassessed
the entire system using the sub-regular solution model for all phases. The magnetic model by Hillert and Jarl [40] was also implemented for the BCC/FCC
equilibria. Later, Huang [97] reassessed the system again based on a new model
for pure Mn, including a magnetic model. Some new experimental information
was also taken under consideration. A description for the metastable HCP phase
23
2500
2500
ƐƚĂďůĞ
ŵĞƚĂƐƚĂďůĞ
>ŝƋƵŝĚ
2000
ĐĞŵ
ĨĐĐ
ĨĐĐ
1000
Dϳϯ
1000
1500
ĐĞŵ
1500
DϱϮ
Temperature [K]
2000
Temperature [K]
ƐƚĂďůĞ
ŵĞƚĂƐƚĂďůĞ
>ŝƋƵŝĚ
500
500
0
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
0
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
Mole fraction C
Mole fraction C
(a) Gustafson [48]
(b) Djurovic et al. [50]
2500
ƐƚĂďůĞ
ŵĞƚĂƐƚĂďůĞ
>ŝƋƵŝĚ
ĨĐĐ
DϱϮ
1500
ĐĞŵ
Temperature [K]
2000
DϮ
1000
500
0
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
Mole fraction C
(c) Naraghi et al. [93]
Figure 2.8: Binary phase diagram for the C-Fe system.
was also added. Lee and Lee [94] presented a new version of the Fe-Mn system.
It was reassessed because of a conflict in selection of model for pure Mn with [96].
The metastable HCP phase was not included in this assessment. Witusiewicz
et al. [98] made a new assessment of the Fe-Mn system based on new experimental results on the enthalpy of mixing for liquid Fe-Mn alloys and enthalpy
of formation of solid FCC and BCC alloys. A new description of the magnetic
contribution to the heat capacity was proposed but not implemented since the
current Thermo-Calc version did not support it. Nakano and Jacques [99] evaluated the influence of Mn on the SFE using the thermodynamic description of
the Fe-Mn system evaluated by Huang [97] with reevaluated Gibbs energy functions for the HCP phase. Djurovic et al. [50] also reassessed the parameters for
the HCP phase to better fit experimental information on the -martensite from
Cotes et al. [100]. The remaining Gibbs energy functions were taken from the
assessment by Huang [97] since the authors are of the opinion that the revision
24
2000
ɴͲDŶ
800
DϱϮ
1000
ɲͲDŶ
Dϳϯ
1200
ďĐĐ
ŚĐƉ
1400
ŐƌĂƉŚŝƚĞ
ĨĐĐ
1200
1000
800
DϱϮ
ŐƌĂƉŚŝƚĞ
ĨĐĐ
Temperature [K]
ŚĐƉ
1400
ĐĞŵĞŶƚŝƚĞ
1600
ďĐĐ
DϮϯϲ
Temperature [K]
1600
>ŝƋƵŝĚ
1800
ĐĞŵĞŶƚŝƚĞ
ɲͲDŶ ɴͲDŶ
Dϳϯ
>ŝƋƵŝĚ
1800
DϮϯϲ
2000
600
600
400
400
ŚĐƉ
200
200
0
0
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
Mole fraction C
Mole fraction C
(a) Huang [95]
(b) Djurovic et al. [49]
Figure 2.9: Binary phase diagram for the C-Mn system.
of the HCP phase by Nakano and Jacques [99] resulted in unacceptable values
for the Gibbs energy at high Mn compositions and a miscibility gap that has
not been seen in experiments. Furthermore the extension of the Gibbs energies
for the FCC and BCC phases to high Mn values seems more reasonable in the
assessment by Huang [97] than in the more recent assessment by Witusiewicz et
al. [98]. The phase diagrams produced with the different descriptions are shown
in Fig. 2.10. The description by Huang [97] together with the parameters for
the HCP phase by Djurovic et al. [50] has been used in this work.
2000
2000
>ŝƋƵŝĚ
1800
1600
ďĐĐ
1400
1200
ɴͲDŶ
ĨĐĐ
1000
800
ɲͲDŶ
600
400
Temperature [K]
Temperature [K]
>ŝƋƵŝĚ
1800
1600
ďĐĐ
1400
1200
ɴͲDŶ
ĨĐĐ
1000
800
ɲͲDŶ
600
400
ďĐĐ
200
ďĐĐ
200
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0
Mole fraction Mn
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mole fraction Mn
(a) Huang [97]
(b) Witusiewicz et al. [98]
Figure 2.10: Binary phase diagrams for the Fe-Mn system.
25
Ti-V
The experimental information on the Ti-V system available before 1993 has been
reviewed by Okamoto [101]. His review was mainly based on information from
Murray [102]. The system contains only terminal phases, HCP (Ti), BCC and
liquid. A thermodynamic description of this system was published by Saunders
in the COST 507 project [51] and has been used in this work.
2.2
Ternary systems
Al-C-Fe
The most extensive experimental studies of the Al-C-Fe system were performed
by Palm and Inden [103] and Oden [104]. Using this experimental information
Ohtani et al. [105] assessed the Al-C-Fe system with the aid of ab initio calculations. Connetable et al. [44] reassessed the system using a more complex
model for the κ-phase. Recently Phan et al. [106] reassessed the system and
performed new experiments. The experiments agreed well with the previous
studies. This assessment used the simpler model for the κ-phase and was therefore disregarded in the present work. Instead the description by Connetable et
al. [44] has been used in this work.
According to the experimental investigation by Palm et al. [103] The solubility of Carbon in BCC seemed to decrease with temperature. This seems
unlikely and therefore we decided to investigate this more closely. Measuring
carbon contents is very difficult. Since it is a light element composition measurements using e.g. Energy Dispersive X-ray Spectroscopy (EDS) can only be
made in a qualitative manor. The more accurate Wavelength Dispersive Spectroscopy (WDS) can be used for quantitative measurements of light elements.
However very good reference samples are needed to get accurate values. In this
work another route was taken. Two samples were prepared with different carbon contents, one that would be in the BCC one phase region according to the
experimental investigation by [103] and the other that would be in the BCC
+ κ two phase region. The two samples were prepared by Arcelor Mittal with
compositions 18 mass-% Al 0.05 mass-% C and 18 mass-% Al 0.1 mass-% C.
The samples were heat treated at 1100 ◦ C for 200 h in evacuated silica tubes
and quenched in brine. After quenching the samples were ground and polished
and etched in 4% nital for 1 min and investigated with Light Optical Microscopy
(LOM). The microstructures are shown in Fig. 2.11.
As can be seen in Fig. 2.11b a second phase has precipitated. Examining
this sample with X-Ray Diffraction (XRD) confirms that the second phase is
the κ-phase. The shape of the κ-phase precipitates suggests that the phase
might have formed during cooling and not during the heat treatment or that
the sample had not reached equilibrium. Longer heat treatment is needed to
clarify this.
26
(a) Low C sample.
(b) High C sample.
Figure 2.11: LOM images of Al-C-Fe samples heat treated at 1100 ◦ C for 200
h in evacuated silica tubes and quenched in brine.
Al-C-Mn
The phase equilibria in the Al-C-Mn system are not well determined. Most of
the studies conducted for this system were focused on the magnetic metastable
τ -phase [107, 108, 109]. The Al-C-Mn system has only been assessed once in
the literature by Chin et al. [110]. This assessment was based on the binary
systems Gr¨
obner [52] (Al-C), Jansson [60] (Al-Mn) and Huang [95] (C-Mn) and
used a simplified model for the κ-phase. In the present work a new assessment
has been performed of the Al-C-Mn system describing the κ-phase with the 5
SL model. Details on this assessment can be found in paper IV.
Al-Fe-Mn
The Al-Fe-Mn system has been studied quite extensively in the literature and the
phase equilibria are well determined, at least in the iron rich part of the system.
The first thermodynamic assessment of this system was by Jansson [111], using
the binary systems by Seiersten [55] (Al-Fe), Jansson [60] (Al-Mn) and Huang
[97] (Fe-Mn). Liu et al. [112] re-assessed the Fe-rich part of the Al-Fe-Mn system
including the FCC, BCC, β-Mn and liquid phases. The parameters for the
binary systems were taken from Huang [97] (Fe-Mn), Jansson [60] (Al-Mn) and
the parameters for Al-Fe were newly optimized. The magnetism was described
using the model proposed by Nishisawa [113]. In 2006, Umino reassessed the
Al-Fe-Mn system using a 2SL model for the BCC phase in order to be able to
describe the second order phase transition into the ordered B2 compound. The
assessment was based on the binary systems by Ohnuma et al. [114] (Al-Fe), Liu
et al. [61] (Al-Mn) and Huang [97] (Fe-Mn). In the present work the Al-Fe-Mn
system was reassessed. The binary systems used are the ones shown in table
2.1. The details of this assessment can be found in paper I.
In paper I the order-disorder transformation in the BCC phase is modeled
using a 2SL model. This makes it possible to describe the transition into the
27
ordered B2 configuration. As reported by [115] another ordered configuration
of the BCC phase, D03 also appears in the Al-Fe-Mn system. In order to be
able to describe the D03 ordering it is necessary to use a 4SL model. In paper
II the evaluation of the parameters for a 4SL model for the ternary Al-Fe-Mn
system is reported.
Al-Ti-V
As mentioned in the introduction precipitation hardening is one of the most
promising ways to increase the yield strength of TWIP alloys. The precipitation is achieved by the addition of carbide and nitride formers to the alloys.
The most common carbide and nitride formers are Nb, Ti and V. In order to
fully understand this system properly, evaluations of the thermodynamics of all
the lower order systems are necessary. It was found that no thermodynamic
assessment of the Al-Ti-V system was available in the literature. The Al-Ti-V
system is also important since it contains the most widely used titanium alloy
Ti-6Al-4V.
Combining the previously available binary descriptions, Al-Ti (Witusiewicz
et al. [47]), Al-V (Gong et al. [81] and Ti-V (Saunders [79]), produces isothermal
sections that deviate drastically from experimental data. Some of the sections
together with experimental data from Ahmed and Flower [116] and Maeda [117]
are shown in Fig. 2.12.
1.0
1.0
0.9
1.0
0.9
0.8
0.9
0.8
0.7
0.8
0.7
0.6
0.7
0.6
0.5
0.6
0.5
0.4
0.5
0.4
0.3
0.4
0.3
0.2
0.3
0.2
0.1
0.2
0.1
0
0.1
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0
0
Mole fraction Ti
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0
Mole fraction Ti
◦
Mole fraction Ti
◦
(a) 600 C
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
(c) 800 ◦ C
(b) 700 C
1.0
1.0
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mole fraction Ti
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mole fraction Ti
◦
(e) 1200 ◦ C
(d) 900 C
Figure 2.12: Extrapolated isothermal sections using descriptions by [47] (Al-Ti),
[81] (Al-V) and [51] (Ti-V). Experimental phase boundary information is from
Maeda [117] and Ahmed and Flower [116].
28
The isothermal sections deviate quite drastically from experimental data at
low temperatures. The main reason for the deviation is a miscibility gap in
the BCC phase that originates from the Al-V system. Since no other sufficient
description of the Al-V system existed it was reassessed in this work.
Combining the new description of the Al-V system with the binary descriptions by Witusiewicz et al. [98] (Al-Ti) and Saunders [51] (Ti-V) the extrapolations are greatly improved and agree well with the experimental data from
Ahmed and Flower [116] and Maeda [117] without the addition of ternary parameters as can be seen in Fig. 2.13.
1.0
1.0
ϴϳϯ< 0.9
0.8
ϭϬϳϯ< 0.9
0.8
ďĐĐ
0.7
0.8
0.7
0.6
0.7
ďĐĐ
0.6
0.5
0.4
0.5
0.4
0.4
0.3
ůdŝ
0.3
ůdŝ
0.2
ůdŝϯ
0.1
ŚĐƉ
0.1
ŚĐƉ
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mole fraction Ti
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mole fraction Ti
ŚĐƉ
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mole fraction Ti
1.0
0.8
0.8
0.7
ďĐĐ
0.6
0.5
0.5
0.4
ďĐĐ
ůϴsϱ
0.4
0.3
0.2
0
ϭϰϳϯ< 0.9
0.9
0.7
0.6
ůdŝϯ
0
0
1.0
ϭϭϳϯ<
ůdŝ
0.2
ůdŝϯ
0.1
0
ďĐĐ
0.6
0.5
0.3
0.2
1.0
ϵϳϯ< 0.9
0.3
ůdŝ
0.1
0.2
ůdŝϯ
ŚĐƉ
ůdŝ
ŚĐƉ
0.1
0
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mole fraction Ti
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mole fraction Ti
Figure 2.13: Extrapolations into ternary Al-Ti-V using assessment of Al-V derived in this work. The experimental points are from Ahmed and Flower [116]
(#) and Maeda [117] (#).
C-Fe-Mn
The C-Fe-Mn system has been evaluated twice in the literature. The first assessment was made by Huang [118], who based her assessment on the binary
descriptions by Gustafson [48] (C-Fe), Huang [95] (C-Mn) and Huang [97] (FeMn). Within the PrecHiMn project Djurovic et al. [50] reassessed the C-Fe-Mn
system based on the binary systems listed in table 2.1. This assessment used
experimental data published after the assessment by Huang and using ab initio
calculations to determine the enthalpies of formation for the carbides at 0 K.
The description by Djurovic et al [50] has been used in this work.
29
Chapter 3
Applications of the
database
The basis of all TWIP and L-IP steels is the quaternary Al-C-Fe-Mn system.
In this work, the thermodynamic properties of this system have been studied.
All the phases in this system are shown in table 2.2.
The addition of Al to these steels can sometimes be problematic. With
the wrong composition a hard and very brittle phase called κ can form. It is
very important to have accurate thermodynamic descriptions of this system in
order to properly predict what compositions are safe to use without forming
this κ-phase.
The κ-phase is a carbide that appears in ternary or higher order systems
containing Al. It is a perovskite phase with Strukturbericht designation E21
and the formula M3 AlC, where M in this case would be Fe or Mn. The atomic
structure of the κ phase is seen in Fig. 3.1 and can be regarded as an ordered form of FCC with ordering on both the substitutional and the interstitial
sublattices where the carbon atoms order on the octahedral sites.
Currently there are no models that can describe simultaneous ordering on
both the substitutional and the interstitial lattices so the model proposed by
Connetable et al. [44] has been adopted in this work.
(M1 , M2 )0.25 (M1 , M2 ...)0.25 (M1 , M2 ...)0.25 (M1 , M2 ...)0.25 (C, V a)0.25
(3.1)
In a previous description of the Al-C-Fe-Mn system by Chin et al. [110] the
κ-phase was described using a much less advanced model
(F e, M n)3 (Al)1 (C, V a)1
(3.2)
Although this is an important system, the phase equilibria have not been studied
many times. The most extensive experimental study of this system was by Ishida
et al. [120]. They investigated the Fe-rich part of this system at 20 and 30 mass% Mn at 900, 1000, 1100 and 1200 ◦ C. In Figs. 3.2 – 3.9 comparisons are made
30
Al
F
e,
Mn
C
Figure 3.1: cubic unit cell of the κ-phase figure produced using the VESTA
program [119].
between the thermodynamic description of the Al-C-Fe-Mn system produced
in this work and the experimental data from Ishida et al. [120] and the same
comparison using the description from Chin et al. [110, 107].
5.0
5.0
4.5
fcc+κ
bcc+κ
fcc+M3C
fcc
ʃ
4.0
3.5
3.5
3.0
3.0
Wt.-% C
Wt.-% C
4.0
2.5
2.0
fcc + M3C
fcc+κ
bcc+κ
fcc+M3C
fcc
4.5
2.5
1.5
fcc + κ
fcc + M3C
2.0
fcc + κ
1.5
bcc + κ
1.0
1.0
0.5
fcc
bcc + κ
fcc
0.5
fcc+bcc
0
fcc + bcc
0
0
2
4
6
8
10
12
14
16
18
20
0
Wt.-% Al
2
4
6
8
10
12
14
16
18
20
Wt.-% Al
(a) this work
(b) Chin et al. [110]
Figure 3.2: Isoplethal sections at 20 mass-% Mn, 900 ◦ C. Comparison between
the description by Chin et al. [110] and current work. Experimental data is
from Ishida et al. [120], filled symbols are from this work.
The overall fit to the experimental data is good and exhibits a clear improvement compared to the previous description. The extension of the FCC phase
region is somewhat underestimated, see e.g. Fig. 3.5. In e.g. Fig. 3.3 the M5 C2 carbide forms a three-phase region together with FCC and κ. By suspending
this phase the fit to the experimental data is improved further. It might be because the kinetics of the carbide are slow similarly to that of graphite or because
the stability of the carbide is overestimated in the current description. Similar
31
5.0
5.0
4.5
fcc+κ
bcc+κ
fcc+M3C
4.0
3.5
3.5
3.0
3.0
2.5
Wt.-% C
Wt.-% C
4.0
fcc + κ
fcc + M3C
2.0
fcc + κ
2.5
2.0
1.5
bcc + κ
1.5
bcc + κ
1.0
fcc+κ
bcc+κ
fcc+M3C
4.5
fcc + graphite
κ
fcc
1.0
fcc
0.5
0.5
fcc + bcc
0
fcc + bcc
0
0
2
4
6
8
10
12
14
16
18
20
0
2
4
Wt.-% Al
6
8
10
12
14
16
18
20
Wt.-% Al
(a) this work
(b) Chin et al. [110]
Figure 3.3: Isoplethal sections at 20 mass-% Mn, 1000 ◦ C. Comparison between
the description by Chin et al. [110] and current work. Experimental data is
from Ishida et al. [120].
5.0
5.0
4.5
4.0
3.5
3.0
2.5
Wt.-% C
Wt.-% C
3.5
fcc + graphite
κ
fcc + graphite
4.0
fcc+κ
bcc+κ
fcc+M3C
4.5
fcc+κ
bcc+κ
fcc+M3C
fcc + κ
2.0
fcc + κ
3.0
2.5
2.0
1.5
bcc + κ
1.5
fcc
fcc
1.0
1.0
bcc + κ
fcc+bcc
0.5
fcc + bcc
0.5
0
0
0
2
4
6
8
10
12
14
16
18
20
0
Wt.-% Al
2
4
6
8
10
12
14
16
18
20
Wt.-% Al
(a) this work
(b) Chin et al. [110]
Figure 3.4: Isoplethal sections at 20 mass-% Mn, 1100 ◦ C. Comparison between
the description by Chin et al. [110] and current work. Experimental data is
from Ishida et al. [120].
phase regions form in the description by Chin et al. [110] although they do not
appear in the published isothermal sections, indicating that they hindered the
carbide from appearing in their calculations.
The database for the Al-C-Fe-Mn system will be available for download
together with paper IV.
32
5.0
5.0
4.5
fcc+κ
bcc+κ
fcc+M3C
κ
4.0
3.0
4.0
3.5
Wt.-% C
Wt.-% C
3.5
fcc + liquid
2.5
fcc + κ
2.0
fcc+κ
bcc+κ
fcc + graphite
4.5
fcc + κ
3.0
fcc + liquid
2.5
2.0
1.5
fcc
1.5
bcc + κ
fcc
1.0
1.0
bcc + κ
fcc + bcc
0.5
fcc + bcc
0.5
0
0
0
2
4
6
8
10
12
14
16
18
20
0
2
4
Wt.-% Al
6
8
10
12
14
16
18
20
Wt.-% Al
(a) this work
(b) Chin et al. [110]
Figure 3.5: Isoplethal sections at 20 mass-% Mn, 1200 ◦ C. Comparison between
the description by Chin et al. [110] and current work. Experimental data is
from Ishida et al. [120].
5.0
5.0
κ
fcc+κ
bcc+κ
fcc+M3C
fcc+bcc
4.5
4.0
3.5
3.5
3.0
3.0
2.5
Wt.-% C
Wt.-% C
4.0
fcc + κ
fcc + M3C
2.0
fcc+κ
bcc+κ
fcc+M3C
4.5
2.5
1.5
fcc + κ
fcc + M3C
2.0
1.5
bcc + κ
bcc + κ
1.0
1.0
fcc
fcc
0.5
0.5
fcc + bcc
0
fcc + bcc
0
0
2
4
6
8
10
12
14
16
18
20
0
2
4
Wt.-% Al
6
8
10
12
14
16
18
20
Wt.-% Al
(a) this work
(b) Chin et al. [110]
Figure 3.6: Isoplethal sections at 30 mass-% Mn, 900 ◦ C. Comparison between
the description by Chin et al. [110] and current work. Experimental data is
from Ishida et al. [120], filled symbols are from this work.
3.1
Experimental investigation
As mentioned in the beginning of this chapter the phase equilibria in the quaternary Al-C-Fe-Mn system have previously been studied by Ishida et al. [120]. In
the present work new samples were prepared by our project parters to confirm
the results by Ishida et al. [120] and investigate the phase relations at higher
Mn-contents. The sample compositions are shown in table 3.1. The samples
33
5.0
5.0
fcc+κ
bcc+κ
fcc+M3C
fcc+bcc
κ
4.5
4.0
4.0
3.5
3.5
fcc + κ
fcc + κ
3.0
2.5
Wt.-% C
Wt.-% C
fcc+κ
bcc+κ
fcc+M3C
fcc+bcc
4.5
fcc + M3C
2.0
3.0
2.5
fcc + M3C
2.0
1.5
1.5
bcc + κ
1.0
fcc
bcc + κ
1.0
fcc
0.5
0.5
fcc + bcc
0
fcc + bcc
0
0
2
4
6
8
10
12
14
16
18
20
0
2
4
Wt.-% Al
6
8
10
12
14
16
18
20
Wt.-% Al
(a) this work
(b) Chin et al. [110]
Figure 3.7: Isoplethal sections at 30 mass-% Mn, 1000 ◦ C. Comparison between
the description by Chin et al. [110] and current work. Experimental data is
from Ishida et al. [120].
5.0
5.0
fcc+κ
bcc+κ
fcc+M3C
fcc+bcc
4.0
4.5
4.0
fcc + κ
3.5
fcc+κ
fcc+M3C
fcc+bcc
fcc + graphite
κ
4.5
3.5
fcc + κ
Wt.-% C
Wt.-% C
fcc + M3C
3.0
2.5
2.0
3.0
2.5
2.0
1.5
1.5
bcc + κ
1.0
fcc
bcc + κ
1.0
fcc
0.5
fcc + bcc
0.5
fcc + bcc
0
0
0
2
4
6
8
10
12
14
16
18
20
0
Wt.-% Al
2
4
6
8
10
12
14
16
18
20
Wt.-% Al
(a) this work
(b) Chin et al. [110]
Figure 3.8: Isoplethal sections at 30 mass-% Mn, 1100 ◦ C. Comparison between
the description by Chin et al. [110] and current work. Experimental data is
from Ishida et al. [120].
were heat treated at 900 and 1050 ◦ C and then quenched in brine. Details on
the experimental investigation can be found in paper IV.
After heat treatment the samples were all examined using Scanning Electron
Microscopy (SEM) and in some samples, where it was necessary to clarify which
phases were present, they were also examined using XRD. The phases present
in the different samples at different temperatures are shown in table 3.2.
In Figs. 3.10 and 3.11 the experimental phase equilibria are compared to the
34
5.0
5.0
4.5
4.0
fcc + κ
4.0
fcc + κ
3.5
3.0
Wt.-% C
Wt.-% C
3.5
fcc+κ
4.5
fcc+κ
bcc+κ
fcc+M3C
fcc+bcc
κ
fcc + liquid
2.5
2.0
3.0
fcc + liquid
2.5
2.0
1.5
1.0
bcc + κ
1.5
bcc + κ
fcc
1.0
fcc
0.5
fcc + bcc
0.5
fcc + bcc
0
0
0
2
4
6
8
10
12
14
16
18
20
0
2
4
Wt.-% Al
6
8
10
12
14
16
18
20
Wt.-% Al
(a) this work
(b) Chin et al. [110]
Figure 3.9: Isoplethal sections at 30 mass-% Mn, 1200 ◦ C. Comparison between
the description by Chin et al. [110] and current work. Experimental data is
from Ishida et al. [120].
Table 3.1: Composition of quaternary samples studied in this work, the amounts
are given in mass-%.
Sample name
TKSE1
T1
T6
T7
T8
Al
1.5
10
10
10
5
C
0.3
2
1
3
3.5
Fe
78.2
58
49
47
51.5
Mn
20
30
40
40
40
Table 3.2: Comparison between calculations and experiments.
Sample
TKSE1
T1
T6
T7
T8
Temperature [◦ C]
900
1050
900
1050
900
1050
1050
1050
Phases (experimental)
FCC
FCC
FCC+κ
FCC+κ
FCC
FCC
FCC+κ
FCC+κ+carbide
Phases (calculated)
FCC
FCC
FCC+κ
FCC+κ
FCC+BCC
FCC+BCC
FCC+κ
FCC+κ+M5 C2
thermodynamic description developed in this work as well as the description by
Chin et al. [110].
The current thermodynamic description provides an improvement also at
higher Mn-contents.
35
5.0
5.0
T1
T6
4.5
T1
T6
T7
4.5
κ
4.0
4.0
fcc + κ + M5C2
3.5
3.0
Wt.-% C
Wt.-% C
3.5
fcc + κ
2.5
2.0
3.0
fcc + κ
2.5
2.0
bcc + fcc + κ
1.5
fcc
fcc
1.5
1.0
bcc + fcc + κ
1.0
bcc + fcc
0.5 bcc + κ
bcc + fcc
0.5
0
0
0
5
10
15
20
25
30
35
40
45
50
0
5
10
Wt.-% Mn
(a) 900 ◦ C this work
20
25
30
35
40
45
50
(b) 1050 ◦ C this work
5.0
5.0
4.5
4.5
T1
T6
4.0
T1
T6
T7
4.0
3.5
3.5
3.0
2.5
Wt.-% C
Wt.-% C
15
Wt.-% Mn
fcc + κ
3.0
2.0
2.0
1.5
1.5
1.0
1.0
0.5
fcc + κ
2.5
fcc + bcc
0.5
fcc
0
0
0
5
10
15
20
25
30
35
40
45
50
0
Wt.-% Mn
5
10
15
20
25
30
35
40
45
50
Wt.-% Mn
(c) 900 ◦ C Chin et al. [110]
(d) 1050 ◦ C Chin et al. [110]
Figure 3.10: Isoplethal sections at 10 mass-% Al including experimental data
from this work. Comparison between description produced in current work and
description by Chin et al [110]
36
5.0
5.0
4.5
4.5
T6
4.0
3.5
3.0
2.5
Wt.-% C
Wt.-% C
3.5
T8
T6
T7
fcc + κ + M5C2
4.0
fcc + κ + M5C2
fcc + cementite
2.0
3.0
fcc + cementite
fcc + κ
2.5
2.0
1.5
1.5
fcc + bcc
1.0
fcc
1.0
fcc
0.5
0.5
fcc + bcc
fcc + bcc + β-Mn
0
0
0
5
10
15
0
5
Wt.-% Al
(a) 900 ◦ C this work
5.0
T8
T6
T7
4.0
4.0
3.5
3.0
3.0
Wt.-% C
3.5
fcc + M3C
fcc + κ
2.0
fcc + κ
fcc + M3C
κ
2.5
2.0
bcc + κ
1.5
T8
T6
T7
4.5
bcc +
4.5
2.5
15
(b) 1050 ◦ C this work
5.0
Wt.-% C
10
Wt.-% Al
1.5
fcc
1.0
fcc
1.0
fcc + bcc
0.5
0.5
0
fcc + bcc
0
0
5
10
15
0
Wt.-% Al
5
10
15
Wt.-% Al
(c) 900 ◦ C Chin et al. [110]
(d) 1050 ◦ C Chin et al. [110]
Figure 3.11: Isoplethal sections at 40 mass-% Mn including experimental data
from this work. Comparison between description produced in current work and
description by Chin et al [110]
37
Chapter 4
Conclusions and Future
work
4.1
Conclusions
In this work, the thermodynamic properties of systems related to TWIP steels
have been studied, specifically thermodynamic descriptions for the Al-C-Fe-Mn
and Al-Ti-V systems have been developed. All the available subsystems have
been critically evaluated and new thermodynamic descriptions have been developed when necessary. The FCC, BCC and κ phases are described using
models with 4 sublattices for the substitutional elements in order to be able to
describe order-disorder transformations. The modeling of complicated ordered
compounds such as the D03 compound is not merely of academic interest. Brittle compounds such as these can form from the BCC phase during production in
industry which means that knowledge of the thermodynamics of ordered compounds is crucial for successful production of viable products. When modeling
the ordering in BCC alloys it was found that assessing the formation energy of
ordered compounds in binary systems, even the ones where the ordered compounds are metastable can greatly improve the extrapolations.
In the cases where no experimental information is available the use of DFT
can greatly improve the thermodynamic descriptions. In this work, enthalpies
of formation calculated using DFT have been used, not only when there is a lack
of experimental data but also to confirm the available experimental data. When
using data calculated using DFT or other ab initio methods it is important to
realize that the reference states might be different.
Within this work some experimental investigations have been undertaken.
Samples within the Al-C-Fe-Mn system have been heat treated to reach equilibrium, quenched and investigated mainly using microscopy. It has been found
that it is problematic using elements with very different melting temperatures
and the high vapor pressure of manganese may cause problems. It is crucial
to let the samples properly reach equilibrium before characterizing their prop-
38
erties, otherwise the results can be misleading. Within the PrecHiMn project,
a thermodynamic database including Al, C, Fe, Mn, Ti, V, Nb, N has been
created.
4.2
Future work
In order to fully understand the thermodynamics of TWIP steels the twin formation needs to be studied further. Specifically, more attention needs to be
given to the meta-stable HCP phases. Modeling the volume dependence would
also be of great interest.
The Al-Ti-V system is quite well described without ternary parameters. The
information on the BCC solvus can be fitted using ternary parameters. The
solubility of vanadium in the AlTi (L10 ) and AlTi3 (D019 ) is underestimated,
especially in the AlTi phase. According to the experimental data, the AlTi phase
should extend quite far toward the Al-V system. Using the current description,
the AlTi phase is described as a separate phase instead of as an ordered form of
FCC. Describing the AlTi phase separately causes a miscibility gap near the Ti
side that prevents further solubility of vanadium. Fig. 4.1 shows the metastable
AlTi phase diagram.
6000
5000
Temperature [K]
ĚŝƐŽƌĚĞƌĞĚ ůdŝ
4000
3000
2000
ŽƌĚĞƌĞĚ ůdŝ
1000
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mole fraction Ti
Figure 4.1: Metastable AlTi (L10 ) phase diagram for the Al-Ti system.
The Al-Ti system needs to be reassessed treating the AlTi phase as an
ordered form of FCC in order to properly describe the ternary Al-Ti-V system.
39
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