Thermodynamic investigation of systems related to TWIP steels
Transcription
Thermodynamic investigation of systems related to TWIP steels
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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 Bibliography [1] B. Hallstedt, A.V. Khvan, B.B. Lindahl, and M. Selleby. Thermodynamic database for high-manganese steels. In Calphad XLIV, Loano, Italy, 2015. [2] O. Bouaziz, S. Allain, C.P. Scott, P. Cugy, and D. Barbier. High manganese austenitic twinning induced plasticity steels: A review of the microstructure properties relationships. Current Opinion in Solid State and Materials Science, 15(4):141–68, 2011. [3] K. Sato, M. Ichinose, Y. Hirotsu, and Y. Inoue. Effects of Deformation Induced Phase Transformation and Twinning on the Mechanical Properties of Austenitic Fe–Mn–Al Alloys. ISIJ Int., 29:868–77, 1989. [4] R. Hadfield. Hadfield’s Manganese Steel. Science (New York, N.Y.), 12(306):284–6, 1888. [5] J.H. Hall. Studies of Hadfield’s Manganese Steel with the High-power Microscope. AIME transactions, 84:382, 1929. [6] V.N. Krivobok. trans. ASST, page 893, 1929. [7] W. Tofaute and K. Linden. Transformations in solid state of manganese steels containing to 1.2% C and 17% Mn. Arch Eisenhuttenwes, 10:515–9, 1936. [8] P. Ch´evenard. M´etaux, 10:203, 1935. [9] A.R. Troiano and F.T. McGuire. A Study of the Iron-rich Iron-manganese Alloys. Transactions, American Society for Metals, 31:340–64, 1943. [10] W. Schmidt. Arch Eisenhuttenwes, 3:293, 1929. [11] H.M. Otte. The formation of stacking faults in austenite and its relation to martensite. Acta Metallurgica, 5(November):614–27, 1957. [12] V.V. Sagaradze, I.I. Kositsyna, M.L. Mukhin, Y.V. Belozerov, and Y.R. Zaynutdinov. High-strength precipitation-hardening austenitic FeMnVMoC steels with shape memory effect. Materials Science and Engineering: A, 481-482:747–51, 2008. 40 [13] L. Bracke, L. Kestens, and J. Penning. Direct observation of the twinning mechanism in an austenitic FeMnC steel. Scripta Materialia, 61(2):220–2, 2009. [14] H. Idrissi, L. Ryelandt, M. Veron, D. Schryvers, and P.J. Jacques. Is there a relationship between the stacking fault character and the activated mode of plasticity of FeMn-based austenitic steels? Scripta Materialia, 60(11):941–4, 2009. [15] T.S. Byun. On the stress dependence of partial dislocation separation and deformation microstructure in austenitic stainless steels. Acta Materialia, 51(11):3063–71, 2003. [16] A. Saeed-Akbari, J. Imlau, U. Prahl, and W. Bleck. Derivation and Variation in Composition-Dependent Stacking Fault Energy Maps Based on Subregular Solution Model in High-Manganese Steels. Metallurgical and Materials Transactions A, 40(13):3076–90, 2009. [17] L. Remy. Kinetics of fcc deformation twinning and its relationship to stress-strain behaviour. Acta Metallurgica, 1978. [18] Y.-K. Lee and C.-S. Choi. Driving force for γ → martensitic transformation and stacking fault energy of γ in Fe-Mn binary system. Metallurgical and Materials Transactions A, 31(February):355–60, 2000. [19] D. Canadinc, C. Efstathiou, and H. Sehitoglu. On the negative strain rate sensitivity of Hadfield steel. Scripta Materialia, 59(10):1103–6, 2008. [20] P.H. Adler, G.B. Olson, and W.S. Owen. Strain Hardening of Hadfield Manganese Steel. Metallurgical and Materials Transactions A, 17(October):1725–35, 1986. [21] P. Hedstr¨ om. Deformation and martensitic phase transformation in stainless steels. PhD thesis, Lule˚ aUniversity of Technology, 2007. [22] O. Bouaziz, C.P. Scott, and G. Petitgand. Nanostructured steel with high work-hardening by the exploitation of the thermal stability of mechanically induced twins. Scripta Materialia, 60(8):714–6, 2009. [23] Y.N. Dastur and W.C. Leslie. Mechanism of work hardening in Hadfield manganese steel. Metallurgical Transactions A, 12(5):749–59, 1981. [24] J.-K. Kim, L. Chen, H.-S. Kim, S.-K. Kim, Y. Estrin, and B.C. Cooman. On the Tensile Behavior of High-Manganese Twinning-Induced Plasticity Steel. Metallurgical and Materials Transactions A, 40(13):3147–58, 2009. [25] X. Liang, J.R. McDermid, O. Bouaziz, X. Wang, J.D. Embury, and H.S. Zurob. Microstructural evolution and strain hardening of Fe24Mn and Fe30Mn alloys during tensile deformation. Acta Materialia, 57(13):3978– 88, 2009. 41 [26] H. Idrissi, K. Renard, L. Ryelandt, D. Schryvers, and P.J. Jacques. On the mechanism of twin formation in FeMnC TWIP steels. Acta Materialia, 58(7):2464–76, 2010. [27] J.A. Venables. On dislocation pole models for twinning. Philosophical Magazine, 30(5):1165–9, 1974. [28] JP Hirth. Deformation Twinning. page 112, New York, 1963. Gordon & Breach. [29] J.B. Cohen and J. Weertman. A dislocation model for twinning in fcc metals. Acta Metallurgica, 11:996–8, 1963. [30] T. Mori and H. Fujita. Dislocation reactions during deformation twinning in Cu-11 at.% Al single crystals. Acta Metallurgica, 28(6):771–6, 1980. [31] S. Mahajan and G.Y. Chin. Twin-slip, twin-twin and slip-twin interactions in Co-8 wt.% Fe alloy single crystals. Acta Metallurgica, 21(2):173–9, 1973. [32] S. Miura, J. Takamura, and N. Narita. Orientation Dependence of the Flow Stress for Twinning in Silver Crystals. Transactions of the Japan Institute of Metals, 9:555, 1968. [33] G. Dini, A. Najafizadeh, R. Ueji, and S.M. Monir-Vaghefi. Improved tensile properties of partially recrystallized submicron grained TWIP steel. Materials Letters, 64(1):15–8, 2010. [34] A.T. Dinsdale. SGTE data for pure elements. Calphad, 15(4):317–425, 1991. [35] M. Hillert and L.-I. Staffansson. The Regular Solution Model for Stoichiometric Phases and Ionic Melts. Acta Chemica Scandinavica, 24:3618–26, 1970. [36] H. Harvig. The iron-carbon system in the temperature range 500-1150 ◦ c. Jernkontorets Annaler, 155:157–61, 1971. [37] B. Sundman and J. ˚ Agren. A regular solution model for phases with several components and sublattices, suitable for computer applications. Journal of Physics and Chemistry of Solids, 42(4):297–301, 1981. [38] M. Hillert. The compound energy formalism. Journal of Alloys and Compounds, 320(2):161–76, 2001. [39] K. Frisk and M. Selleby. The compound energy formalism: applications. Journal of Alloys and Compounds, 320(2):177–88, 2001. [40] M. Hillert and M. Jarl. A model for alloying in ferromagnetic metals. Calphad, 2(3):227–38, 1978. 42 [41] O. Redlich and A.T. Kister. Algebraic representation of thermodynamic properties and the classification of solutions. Industrial & Engineering Chemistry, 371:1–4, 1948. [42] W.L. Bragg and E.J. Williams. The Effect of Thermal Agitation on Atomic Arrangement in Alloys. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 145(855):699–730, 1934. [43] W. Gorsky. R¨ ontgenographische Untersuchung von Umwandlungen in der Legierung Cu Au. Zeitschrift f¨ ur Physik, 50(1-2):64–81, 1928. [44] D. Connetable, J. Lacaze, P. Maugis, and B. Sundman. A Calphad assessment of Al-C-Fe system with the κ carbide modelled as an ordered form of the fcc phase. Calphad, 32(2):361–70, 2008. [45] B. Sundman, I. Ohnuma, N. Dupin, U.R. Kattner, and S.G. Fries. An assessment of the entire AlFe system including D03 ordering. Acta Materialia, 57(10):2896–908, 2009. [46] Y. Du, J. Wang, and J. Zhao. Reassessment of the Al-Mn system and a thermodynamic description of the Al-Mg-Mn system. International journal of materials research, 98:855–71, 2007. [47] V.T. Witusiewicz, A.A. Bondar, U. Hecht, S. Rex, and T.Y. Velikanova. The AlBNbTi system III. Thermodynamic re-evaluation of the constituent binary system AlTi. Journal of Alloys and Compounds, 465(1-2):64–77, 2008. [48] P. Gustafson. A Thermodynamic Evaluation of the FeC System. Scand. J. Metall., 14(5):259–67, 1985. [49] D. Djurovic, B. Hallstedt, J. von Appen, and R. Dronskowski. Thermodynamic assessment of the Mn-C system. Calphad, 34(3):279–85, 2010. [50] D. Djurovic, B. Hallstedt, J. von Appen, and R. Dronskowski. Thermodynamic assessment of the FeMnC system. Calphad, 35(4):479–91, 2011. [51] N. Saunders. System Ti-V. In I Ansara, A Dinsdale, and M Rand, editors, COST 507: Thermochemical Database for Light Metal Alloys, vol. 2, pages 297–8. Brussels, 1998. [52] J. Gr¨ obner, H.-L. Lukas, and F. Aldinger. Thermodynamic calculations in the Y-Al-C system. Journal of Alloys and Compounds, 220(1-2):8–14, 1995. [53] N. Saunders and V.G. Rivlin. Al-Fe. Zeitschrift f¨ ur Metallkunde, 78:795, 1987. [54] U.R. Kattner and B.P. Burton. Al-Fe (Aluminum-Iron). In H. Okamoto, editor, Phase Diagrams of Binary Alloys, pages 12 – 28. ASM International, 1993. 43 [55] M. Seiersten. The Al-Fe system. Technical report, Oslo, Norway, 1993. [56] I. Ansara, A.T. Dinsdale, and M.H. Rand. COST 507, Thermochemical Database for Light Metal Alloys, vol. 2. Technical report, Office for Official Publications of the European Communities, Luxembourg, 1998. [57] Y. Du, J.C. Schuster, Z.-K. Liu, R. Hu, P. Nash, W. Sun, W. Zhang, J. Wang, L. Zhang, C. Tang, Z. Zhu, S. Liu, Y. Ouyang, W. Zhang, and N. Krendelsberger. A thermodynamic description of the AlFeSi system over the whole composition and temperature ranges via a hybrid approach of CALPHAD and key experiments. Intermetallics, 16(4):554–70, 2008. [58] M.H.G. Jacobs and R. Schmid-Fetzer. Phase behavior and thermodynamic properties in the system FeAl. Calphad, 33(1):170–8, 2009. [59] L. Kaufman. Coupled phase diagrams and thermochemical data for transition metal binary systems-III. Calphad, 2(2):117–46, 1978. [60] ˚ A. Jansson. A thermodynamic evaluation of the Al-Mn system. Metallurgical Transactions A, 23(11):2953–62, 1992. [61] X.J. Liu, I. Ohnuma, R. Kainuma, and K. Ishida. Thermodynamic assessment of the Aluminum-Manganese (Al-Mn) binary phase diagram. Journal of Phase Equilibria, 20(1):45–56, 1999. [62] X.J. Liu. PhD thesis, Tohoku University, Japan, 1998. [63] M. Ohno and R. Schmid-Fetzer. Thermodynamic assessment of Mg-Al-Mn phase equilibria, focusing on Mg-rich alloys. Zeitschrift f¨ ur Metallkunde, 96(8):857–69, 2005. [64] D. Djurovic. Parameters for ordering in bcc in the al-mn system. Work performed within the PrecHiMn project, 2012. [65] L. Kaufman and H. Nesor. Coupled phase diagrams and thermochemical data for transition metal binary systems V. Calphad, 2(4):325–48, 1978. [66] J.L. Murray. Calculation of the titanium-aluminum phase diagram. Metallurgical Transactions A, 19(2):243–7, 1988. [67] J.P. Gros, B. Sundman, and I. Ansara. Thermodyhamic modeling of the Ti-rich phases in the TiAl system. Scripta Metallurgica, 22(10):1587–91, 1988. [68] U.R. Kattner, J.-C. Lin, and Y.A. Chang. Thermodynamic Assessment and Calculation of the Ti-Al System. Metallurgical Transactions A, 23(8):2081–90, 1992. [69] C. McCullough, J.J. Valencia, C.G. Levi, and R. Mehrabian. Phase equilibria and solidification in Ti-Al alloys. Acta Metallurgica, 37(5):1321–36, 1989. 44 [70] F. Zhang, S.L. Chen, Y.A. Chang, and U.R. Kattner. A thermodynamic description of the Ti-Al system. Intermetallics, 5(6):471–82, 1997. [71] I. Ohnuma, Y. Fujita, H. Mitsui, K. Ishikawa, R. Kainuma, and K. Ishida. Phase equilibria in the TiAl binary system. Acta Materialia, 48(12):3113– 23, 2000. [72] H. Wang, R.C. Reed, J.-C. Gebelin, and N. Warnken. On the modelling of the point defects in the ordered B2 phase of the TiAl system: Combining CALPHAD with first-principles calculations. Calphad, 39(null):21–6, 2012. [73] H. Okamoto. Al-V (aluminum-vanadium). Journal of Phase Equilibria, 22(1):86, 2001. [74] H. Okamoto. Al-V (Aluminum-Vanadium). Journal of Phase Equilibria and Diffusion, 33:491, 2012. [75] J.L. Murray. Al-V (aluminum-vanadium). Bulletin of Alloy Phase Diagrams, 10(4):351–7, 1989. [76] D.M. Bailey, O.N. Carlson, and J.F. Smith. The aluminium-rich end of the aluminiumvanadium system. Trans. ASM, 51:1097–102, 1959. [77] L.A. Willey. Technical report, Alcoa Research Labs, 1953. [78] V.N. Eremenko, Ya.V. Natanzon, and V.P. Titov. Kinetics of Dissolution of Vanadium in Liquid Aluminum. Russian Metallurgy, 5:34–7, 1981. [79] N. Saunders. System AlV. In I Ansara, A Dinsdale, and M Rand, editors, COST 507: Thermochemical Database for Light Metal Alloys, vol. 2, pages 95–8. European Communities, Brussels, 1998. [80] K.W. Richter and H. Ipser. The Al-V Phase Diagram Between 0 and 50 Atomic Percent Vanadium. Zeitschrift f¨ ur Metallkunde, 91(5):383–8, 2000. [81] W. Gong, Y. Du, B. Huang, R. Schmid-Fetzer, C. Zhang, and H. Xu. Thermodynamic reassessment of the AlV system. International journal of materials research, 95(11):978–86, 2004. [82] O. Kubaschewski and G. Heymer. Heats of formation of transition-metal aluminides. Transactions of the Faraday Society, 56:473–8, 1960. [83] S.V. Meschel and O.J. Kleppa. The standard enthalpies of formation of some 3d transition metal aluminides by high-temperature direct synthesis calorimetry. In J. S. Faulkner and R. G. Jordan, editors, Metallic Alloys: Experimental and Theoretical Perspectives, 1, pages 103–12. Kluwer Academic Publishers, 1994. 45 [84] A. Neckel and H. Nowotny. In Int. Leichtmetalltagung, page 72, Leoben, 1968. [85] V.V. Samokhval, P.A. Poleshchuk, and A.A. Vecher. Thermodynamic Properties of Aluminum-Titanium and Aluminum-Vanadium Alloys. Russian Journal of Physical Chemistry, 45(8):1174–6, 1971. [86] A. Roth. An Investigation of the Aluminum-Vanadium System. Zeitschrift f¨ ur Metallkunde, 32:356–9, 1940. [87] O.N. Carlson, D.J. Kenney, and H.A. Wilhelm. The Aluminum-Vanadium Alloy system. Trans. ASM, 47:520–37, 1955. [88] M.G. Benz and J.F. Elliott. The Austenite Solidus and Revised IronCarbon Diagram. Transactions of Metall. Soc. AIME, 221(April):323–31, 1961. [89] J. Chipman. Thermodynamics and phase diagram of the fe-c system. Met. Trans., 3:55–64, 1972. [90] J. ˚ Agren. A thermodynamic analysis of the Fe-C and Fe-N phase diagrams. Metallurgical Transactions A, 10(12):1847–52, 1979. [91] P. Franke. Estimated parameter within sgte, 2007. [92] B. Hallstedt, D. Djurovic, J. von Appen, R. Dronskowski, A. Dick, F. K¨ ormann, T. Hickel, and J. Neugebauer. Thermodynamic properties of cementite (Fe3 C). Calphad, 34(1):129–33, 2010. [93] R. Naraghi, M. Selleby, and J. ˚ Agren. Thermodynamics of stable and metastable structures in Fe-C system. Calphad: Computer Coupling of Phase Diagrams and Thermochemistry, 46:148–58, 2014. [94] B.-J. Lee and D.-N. Lee. A thermodynamic study on the MnC and FeMn systems. Calphad, 13(4):345–54, 1989. [95] W. Huang. Thermodynamic Assessment of the Mn–C System. Scand. J. Metall., 1990. [96] W. Huang. An assessment of the Fe-Mn system. Calphad, 11(2):183–6, 1987. [97] W. Huang. An assessment of the Fe-Mn system. Calphad, 13(3):243–52, 1989. [98] V.T. Witusiewicz, F. Sommer, and E.J. Mittemeijer. Reevaluation of the Fe-Mn Phase Diagram. Journal of Phase Equilibria & Diffusion, 25(4):346–54, 2004. [99] J. Nakano and P.J. Jacques. Effects of the thermodynamic parameters of the hcp phase on the stacking fault energy calculations in the FeMn and FeMnC systems. Calphad, 34(2):167–75, 2010. 46 [100] S.M. Cotes, A. Fern´ andez Guillermet, and M. Sade. Fcc/Hcp martensitic transformation in the Fe-Mn system: Part II. Driving force and thermodynamics of the nucleation process. Metallurgical and Materials Transactions A, 35(1):83–91, 2004. [101] H. Okamoto. Ti-V (titanium-vanadium). Journal of Phase Equilibria, 14(2):266–7, 1993. [102] J.L. Murray. The TiV (Titanium-Vanadium) system. Bulletin of Alloy Phase Diagrams, 2(1):48–55, 1981. [103] M. Palm and G. Inden. Experimental determination of phase equilibria in the Fe-Al-C system. Intermetallics, 3(6):443–54, 1995. [104] L.L. Oden, R.P. Beyer, and P.O. Box. Heat capacity of 2Al4C3·SiC from 447 to 1447 K and enthalpy of peritectic decomposition of Al4C3, 2Al4C3·SiC, and Al4C3·SiC. Thermochimica acta, 115:11–9, 1987. [105] H. Ohtani, M. Yamano, and M. Hasebe. Thermodynamic Analysis of the Fe-Al-C Ternary System by Incorporating ab initio Energetic Calculations into the CALPHAD Approach. ISIJ International, 44(10):1738–47, 2004. [106] A.T. Phan, M.-K. Paek, and Y.-B. Kang. Phase equilibria and thermodynamics of the FeAlC system: Critical evaluation, experiment and thermodynamic optimization. Acta Materialia, 79:1–15, 2014. [107] A.V. Dobromyslov, A.E. Ermakov, N.T. Taluts, and M.A. Uimin. Electron microscopy investigation of phase transformations in Mn-Al-C alloy. physica status solidi (a), 88(2):443–54, 1985. [108] C. M¨ uller and H.H. Stadelmaier. Constitution of Mn-Al-(Cu, Fe, Ni or C) alloys near the magnetic tau phase. Zeitschrift f¨ ur Metallkunde, 88(8):620– 4, 1997. [109] C. M¨ uller, H.H. Stadelmaier, B. Reinsch, and G. Petzow. Metallurgy of the magnetic t-phase in Mn-Al and Mn-Al-C. Zeitschrift fur Metallkunde, 87(7):594–7, 1996. [110] K.-G. Chin, H.-J. Lee, J.-H. Kwak, J.-Y. Kang, and B.-J. Lee. Thermodynamic calculation on the stability of (Fe,Mn)3AlC carbide in high aluminum steels. Journal of Alloys and Compounds, 505(1):217–23, 2010. ˚. Jansson. Thermodynamic assessment of the Al-Fe-Mn system. Tech[111] A nical report, KTH Royal Institute of Technology, 1987. [112] X.J. Liu and S.M. Hao. A Thermodynamic Calculation Of The Fe-Mn-Al Ternary System. calphad, 17(1):79–91, 1993. [113] T. Nishizawa, S.M. Hao, M. Hasebe, and K. Ishida. Thermodynamic Analysis of Miscibility Gap due to Ordering in Ternary Systems. Acta Metall., 31(9):1403–16, 1983. 47 [114] I. Ohnuma, N. Kamiya, R. Kainuma, and K. Ishida. Untitled manuscript. reference in Umino2006, private comunications. [115] R. Umino, X.J. Liu, Y. Sutou, C.P. Wang, I. Ohnuma, R. Kainuma, and K. Ishida. Experimental determination and thermodynamic calculation of phase equilibria in the FeMnAl system. Journal of Phase Equilibria and Diffusion, 27:54–62, 2006. [116] T. Ahmed and H.M. Flower. Partial isothermal sections of TiAlV ternary diagram. Materials Science and Technology, 10(4):272–88, 1994. [117] T. Maeda. PhD thesis, University of London (Imperial college), 1988. [118] W. Huang. A thermodynamic assessment of the Fe-Mn-C system. Metallurgical and Materials Transactions A, 21(August):2115–23, 1990. [119] K. Momma and F. Izumi. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr., 44:1272–6, 2011. [120] K. Ishida, H. Ohtani, N. Satoh, R. Kainuma, and T. Nishizawa. Phase Equilibria in FeMnAlC Alloys. ISIJ International, 30(8):680–6, 1990. 48