Dynaphase: Online Calculation of Thermodynamic Properties during Continuous Casting

Transcription

1 BHM (2014) Vol. 159 (11): DOI /s Springer-Verlag Wien 2014 Dynaphase: Online Calculation of Thermodynamic Properties during Continuous Casting Susanne Hahn and Thomas Schaden Siemens VAI Metals Technologies GmbH, Linz, Austria Received August 20, 2014; accepted August 31, 2014; Published online September 27, 2014 Abstract: The Siemens VAI software model DynaPhase calculates thermodynamic properties depending on the chemical analysis of. It can be used online together with Siemens VAI s secondary cooling model Dynacs 3D, which is a unique feature. Offline it can be used to investigate the thermodynamic properties of s and therefore supports the development of new s. The core of DynaPhase is a substitutional solution model for the Gibbs free energy for calculating multi-component phase diagrams. The parameters of this model are determined by employing the CALPHAD approach. This model is combined with a microsegregation model to account for the interdendritic solidification process. New differential scanning calometry measurements of the Department of Metallurgy at the Mining University of Leoben have been used to extend the DynaPhase database for high Al or Si concentrations. This paper shows how important correct thermodynamic properties calculations with DynaPhase are, for controlling the secondary cooling system in continuous casting. Keywords: Thermodynamics, Continuous casting Simulation, Automation, Dynaphase: Online Berechnung thermodynamischer Materialdaten während des Stranggießens Zusammenfassung: DynaPhase ist ein VAI Software Modell zur Berechnung von thermodynamischen Eigenschaften in Abhängigkeit von der chemischen Analyse der Stahlgüte. Es kann zusammen mit dem VAI Sekundärkühlungsmodell Dynacs 3D online eingesetzt werden, was ein Alleinstellungsmerkmal darstellt. Offline kann es zum S. Hahn ( ) Siemens VAI Metals Technologies GmbH, Turmstr. 44, 4031 Linz, Austria susanne.hahn@siemens.com Untersuchen der thermodynamischen Eigenschaften beliebiger Stahlzusammensetzungen herangezogen werden und unterstützt somit die Entwicklung neuer Stahlgüten. Das Kernstück von DynaPhase ist ein substitutional solution Modell zur Beschreibung der freien Gibbs Energien der verschiedenen Multikomponenten-Phasen. Die Parameter dieses Modells werden mit Hilfe des CALPHAD Ansatzes bestimmt. Dieses Modell ist mit einem Mikroseigerungsmodell gekoppelt, um die interdentritische Erstarrung des Stahls zu beschreiben. Neue differential scanning calometry Messungen des Instituts für Metallurgie der Montanuniversität in Leoben wurden genutzt, um die Datenbank von DynaPhase für Stahlgüten mit hohem Silizium oder Aluminium Gehalt zu erweitern. Im vorliegenden Beitrag soll anhand eines Beispiels gezeigt werden, wie wichtig die korrekte Berechnung der thermodynamischen Eigenschaften mit DynaPhase für die Kontrolle der Sekundärkühlung im Strangguss ist. Schlüsselwörter: Thermodynamik, Simulation, Automation, Stranggießen 1. Introduction In the past, strand treatment was a subject of the rolling process. Historically, continuous casting focused on controlling the strand surface temperature by secondary cooling [1, 2] to prevent surface defects. In a subsequent step, temperature control was extended to account for the second ductility trough caused by phase transitions and precipitation in the solid state. It is very important to consider this effect while unbending the strand as well as in hot direct-charging processes [3, 4]. With the introduction of dynamically adjustable segments, it became possible to control the roll gap during casting [5]. With this innovation, dynamic soft reduction could be introduced on an industrial scale [6, 7]. Today thermo mechanical process- 438

2 ing is a standard feature of continuous casting technology. Employing metallurgical treatments makes it possible to influence the as-cast grain structure, to improve surface quality and product shape, and to reduce segregation and porosity. Metallurgical treatments are also used to make the strand more suitable for hot charging. The modern continuous caster has many features and therefore great potential to actively influence the as-cast strand properties. These can serve to reduce the energetically costly and elaborate strand treatment after the initial solidification in the caster. Therefore they could also help to reduce CO 2 emissions from production. In order to exploit the full potential of a state-of-the-art continuous caster, the underlying physical and chemical processes need to be mapped onto detailed process models. These models must be capable of accurately predicting and controlling the process with respect to heat transfer in the strand, compound formation, and phase transformations during cooling. Dynacs 3D is a secondary cooling model for continuous casting [8 10]. It consists of two modules. One module, the Thermal Tracker 3D, solves the three-dimensional heat transfer equation for the entire strand and predicts the temperature distribution of the strand during casting. The second model is the Setpoint Calculator, which controls the secondary cooling loops. It regulates water flow, air pressure, and the position of the spray nozzles to meet the predefined temperature profile of the strand. Solving the three-dimensional heat-transfer equation is a mathematical problem. Many authors have addressed this problem, but all of their algorithms have one thing in common: They either assume constant density or do not conserve energy and mass [11 13]. Unlike other models, the Dynacs 3D model considers the temperature-dependent density and globally conserves mass and enthalpy. With modern computers, the resulting equation can be handled numerically with great accuracy and efficiency. However, this requires that -specific material properties like liquidus and solid temperature are provided. An additional software package, namely DynaPhase, calculates all the thermo-physical data needed by Dynacs 3D. DynaPhase is available as an online tool that calculates liquidus and solidus temperature and material properties for the actual analysis. This is a unique feature that makes it stand out from the competition. Dynacs 3D then uses this data instead of data generated for groups with a defined concentration range of the chemical analysis. This makes the prediction of quantities as the point of complete solidification on the strand and the temperature distribution of the strand during casting more accurate and therefore allows for precise metallurgical treatments that can lead to an enhanced quality of the products. In this paper we focus on the DynaPhase software package. We start with a brief overview of its models and the thermo-dynamical database it uses. With two examples we then show how important accurate calculation results are for a beneficial utilization of metallurgical treatments. Finally, we discuss how DynaPhase can help to increase the productivity of the caster and the quality of its products. 2. Model and Database DynaPhase is a software package that simulates the phase transitions and microsegregation under cooling conditions in a continuous caster. It also calculates the temperature material data needed by Dynacs 3D. It is available both as offline and online versions. The offline version allows the pre-calculation of material properties for an arbitrary analysis within the scope of the database. The online version takes the chemical analysis of the actual and calculates the material properties for Dynacs 3D just before the start of casting. DynaPhase consists of two main parts. The first part describes the solidification of the liquid in the high temperature range, and the second part deals with the solid-solid phase transitions in the lower temperature range. Part One, the high temperature range, is based on two main models. The first model is a substitutional solution model with Redlich-Kister polynomials for the excess term of the Gibbs free energy and describes the thermodynamic equilibrium [14 16]. This model has many free parameters that must be determined by deploying the CALPHAD approach [17]. To simulate solidification during continuous casting, it is very important to deal with segregation phenomena correctly. Therefore, the second model describes interdendritic solidification depending on external cooling rates. This allows the consideration of a representative volume element located in the mushy zone. At the interface between different phases, a mass balance is requested. The diffusion of the solutes in the different phases obeys Fick s second law. The two models are then combined by assuming thermodynamic equilibrium at the phase interfaces. The resulting system of equations is solved numerically with Newton s method. Part Two, the low temperature range, is described by a kinetic reaction model developed by Johnson-Mehl and by Avrami and a FeC phase diagram that is shifted by the concentration of the alloying elements. The free parameters of the model have been determined by experiments. With this model, the solid-solid phase transformation from austenite to ferrite, pearlite, bainite, and martensite are calculated based on the actual analysis and the cooling curve. As output DynaPhase calculates liquidus and solid temperature, phase fractions depending on temperature and temperature-dependent material properties as density, and thermal conductivity. It is well known that the formation of precipitation may influence quantities like the solidus temperature. Dyna- Phase accounts for non-metallic precipitation through an extension of the model. For example, the enrichment of sulfur in the liquid phase during solidification, which is typically retained by manganese by forming manganese sulfide (MnS), is expressed more correctly by the extended model. So far the model includes precipitation of sulfides as MnS, nitrides as TiN, and carbides as TiC. The benefit of the coupled models in DynaPhase is the ability to characterize the entire solidification process. It describes the transformation from the liquid phase into ferrite or austenite as well as the three-phase region where BHM, 159. Jg. (2014), Heft 11 Springer-Verlag Wien Hahn & Schaden 439

3 liquid is transformed into austenite and the transformation of previously built ferrite into austenite has already begun. This means that all energetically possible phases in the peritectic region are properly accounted for when the solidification interval is determined. 2.1 Database Extension: The CALPHAD Approach A crucial factor in a successful calculation is the quality of the thermodynamic database. The many free parameters of the Gibbs energy model have to be determined by using the CALPHAD approach. In the first step, the database has been built by collecting parameter sets published in the relevant literature over the last forty years. Because we are only interested in continuously cast, we could restrict our search to the iron-rich corner of the phase diagram, with limitations for the concentrations of the other elements. It has been proven in comparisons using experimental measurements and with other commercial thermodynamic software tools as well as in practical applications on continuous casting machines that the resulting database covers carbon s and also stainless s quite well. However, the database is only valid within certain concentration ranges for the alloying elements that are sufficient for most of the common s. Yet, our customers are constantly pushing the limits by designing new s with special material properties. The development of TRIP s with high Al and high Si concentrations are examples of this trend. These new s have been beyond the scope of the DynaPhase database. Inspecting the literature, we could not find experimental data to extend the database in this direction so we started a research project in collaboration with voestalpine stahl, Linz, and the Department of Metallurgy at the Mining University of Leoben. In this project, high-precision DSC (differential scanning calometry) measurements to determine the equilibrium phase transitions have been conducted [18, 19]. So far, the ternary systems FeSiC and FeAlC with Silicon concentration up to 3.3 wt% and Al concentration of up to 3.4 wt% have been systematically investigated. It was possible to experimentally determine pseudo-binary cuts of FeAlC phase diagrams. Comparisons of these cuts to corresponding phase diagrams calculated with FactSage [20] (database SGTE2007) and Thermo-Calc [21] (database TCFE6) have shown that the commercial software packages do not always correctly reproduce the high Al measurements. Both programs reproduce the liquidus line very well, but greater discrepancies between calculation and measurement have been found for the other phase transformation lines. We would like to stress that these differences have only be found for high Al concentrations. For lower Al concentrations, the correspondence between experiment and calculation was good for FactSage and Thermo-Calc. We are aware of the fact that more recent versions of both databases are available that could contain improved parameter sets for the FeAlC system for high Al concentrations. We were using these DSC measurements to tune and extend the DynaPhase database for high Al and high Si content (with the restriction that concentrations of other alloying elements are not extremely high). DynaPhase is now valid for Si and Al concentrations up to 3.5 wt%. More DSC measurements are underway and will be used to further improve and extend the DynaPhase database. 3. Model and Database To show how the changes in the database are reflected in SIMETAL Dynacs 3D, we chose a simple example of a with 0.35 wt% carbon and 2.5 wt% aluminium, which we call Al35. With the old DynaPhase database, s with 2.5 wt% Al are well outside the range of validity. Only s with Al up to 0.5 wt% are allowed when using the old database. Ignoring this fact, we determined the material properties with DynaPhase assuming an average cooling rate of 0.5 C/s using the old database and the new optimized database. In Fig. 1 we plotted the resulting solid fraction against the temperature. The old database calculates the liquidus temperature correctly, but, for the solidus point, we find a discrepancy of almost 20 C between the two simulations. The question arises of what this would mean for continuous casting if SIMETAL Dynacs 3D controlled the spray water of the secondary cooling loops. To investigate this, we ran two SIMETAL Dynacs 3D simulations for a slab caster format mm 2 and a medium cooling practice. In Fig. 2 we show the liquidus and solidus isotherms on the narrow face of the strand at a cut through the center of the slab. The width position 0 m represents the narrow face surface of the strand and the width position m the center of the strand. The red curves represent the results with the material properties calculated using the old database, whereas the results of the simulation with the new database are shown in blue. Because the liquidus temperatures for both sets of material properties are almost identical, we found no difference of the liquidus isotherm on the strand. A shift of approximately 20 C in the solidus temperature leads to a shift in the point of complete solidification of 40 cm on the strand. Such a finding could strongly influence the performance of strand treatment techniques like soft reduction. This is illustrated in Fig. 3. Here two simulations with Dynacs 3D for the Al25 are shown. In the upper panel, the material properties have been calculated with the new database and, in the lower panel, with the old database. In both cases the cross section of the strand at the same position in the caster is shown. The red shaded regions indicate completely solidified, whereas the gray shaded regions represent the mushy zone. With the old database, we still find rather large semi-solid areas which suggest the application of soft reduction, whereas the improved database leads to an almost completely solid cross section. For a beneficial result from soft reduction, it is essential to apply the reduction at the right position for the right solid fraction. If we apply soft reduction too early for a solid fraction that is too low or apply it too 440

4 Fig. 1: Solid fraction for the Al25 calculated with the DynaPhase database before the optimization (blue) and after the optimization (red). The liquidus temperature is the same, but the solidus temperature is 20 C higher for the red curve than for the blue curve Fig. 2: Panel a): Liquidus isotherm and solidus isotherm of the narrow face at the center of the strand for the material parameters calculated with the DynaPhase database before the optimization (blue, called isotherm 1) and after the optimization (red, called isotherm 2). The liquidus isotherms are almost the same (solid lines), whereas large differences can be found in the solidus isotherms (solid lines with points). Panel b): It can be seen that the difference in the solidus point is around 40 cm. For the simulation with the improved database, the solidus point is shifted upwards on the strand late when the strand is already completely solid, this could lead to crack formation or it might have no effect at all. SIMETAL Dynacs 3D does not necessarily need Dyna- Phase. If no DynaPhase is available, SIMETAL Dynacs 3D uses the precalculated material properties of so-called groups. There are several sets of groups, for example, for carbon- s and stainless- s. Each group is valid for a specific concentration range, and the material properties have been calculated for the mean concentrations of the group. All groups of one set together cover the usual scope of s. For an actual, SIMETAL Dynacs 3D will choose the group that is closest to its chemical analysis and will use the corresponding material properties to control the secondary cooling. The grid of groups is rather finely d to keep the discrepancy between used group properties and actual properties small. However, it is impossible to make this grid very finely d for all alloying elements. Otherwise, one would end up with an enormous number of groups. One has to be aware of the fact that, while using SIMETAL Dynacs 3D without DynaPhase usually leads to good results, it only yields an approximation. The need for a precise determination of the final point of solidification is demonstrated on a stainless caster. In the stainless caster, the soft reduction is performed in segments consisting of several rolls. The final point of solidification must correspond with the position of the last roll of a segment in order to prevent centerline segregation, or center cracking, when soft reduction is performed too early or after the strand is already solidified (Fig. 4). The temperature profile is calculated with SIMETAL Dynacs 3D and defines the three different regions of the center of the strand: Liquid, mushy, and completely solid regions are distinguished. The soft reduction is performed in the mushy zone. For relatively small alloying contents, as in carbon s and low casting speeds, the BHM, 159. Jg. (2014), Heft 11 Springer-Verlag Wien Hahn & Schaden 441

5 Fig. 3: Two cross section of the strand at the same position in the caster are shown. Both panels are the results of Dynacs 3D simulations for the Al25. The only differences are the material parameters. In the upper panel, the material parameters have been calculated with the new DynaPhase database and in the lower panel with the old DynaPhase database mushy range is reduced. In stainless s the mushy zone is extended due to the high alloying content. For the application of soft reduction in stainless casting, the mushy zone needs to be determined precisely so that the end of the mushy zone can be controlled to be at the end of a segment. The temperature calculation is an important input for the calculation of the soft-reduction range in DynaGap. The ideal soft reduction line is based on the materials input derived from the DynaPhase and the thermal calculation, which permits the calculation of the range of the mushy zone. The determination of the final point of solidification is crucial for finding the optimal setting for DynaGap (Fig. 5 and 6). The solidus point is linked to the solidus temperature of the different s. DynaPhase is able to calculate the solidus temperature very precisely. On site, it is possible to operate the caster with certain predefined groups, which is sufficiently accurate in many cases. In a specific situation, it was necessary to describe the s more precisely, and it was found that the solidus temperature varies in a range of 40 C for the ferrite group, which is accompanied by a shift of the solidus point of 1.22 m (Table 1). For the austenite group the solidus temperature varies by 44 C, which shifts the solidus point by 1.76 m (Table 2). These findings are used to tune predefined groups. A shift of the solidus point by 1.22 m has an influence on the soft reduction efficiency. An accurate prediction of the solidus point is needed in order to better adjust the DynaGap to control the soft reduction process. Further analysis with SIMETAL Dynacs 3D revealed that, 30 cm before the final point of solidification, a channel filled with mushy with 10 mm in thickness is still present, which needs to be removed by means of soft reduction. The thickness of the channel gives an indication of the reduction amount. 442

6 Fig. 4: The temperature profile of the strand is calculated with SIMETAL Dynacs 3D. The final point of solidification is reached when the center temperature of the slab drops significantly Fig. 5: DynaGap calculates the roll gap based on the natural shrinkage of the strand, which is overlapped by an additional reduction step performed in the mushy zone The calculation with SIMETAL Dynacs 3D showed the ideal soft reduction amount and the accurate position of the solidus point, which are essential for the operation of DynaGap. It has also been shown that the solidus temperature for different s in the same group might differ by a value of 40 C, which is followed by a shift in the solidus point of 1.22 m. A delayed reduction may result in undesired microstructures, with center cracking; a reduction performed too early can be followed by undesired bridge formation. 3.1 DynaPhase Online So far we have discussed how DynaPhase helps control strand treatment technologies like soft reduction and therefore helps improve the quality of the products. But DynaPhase online does more than that. For example, sometimes the chemical analysis of a ladle is somewhat off the usual values. Because DynaPhase online uses the actual chemical analysis of the ladle for its calculation, it informs the operator before starting to cast if the is peritectic. This might be unexpected, and, because peritectic s are more difficult to cast than non-peritectic s, the operator can adjust the casting practice accordingly. If the Siemens VAI software tool Quality Expert is available, Dyna- Phase can inform the Quality Expert tool if the is either peritectic or a low carbon. The Quality Expert tool can then display the correct casting practice for the operator. Fluctuations in the analysis influence the liquidus temperature, which can result in a higher superheat than planned. Again, if the operator knows this before casting, they can try to optimize the casting practice manually, or the casting practice can be adjusted automatically by the Level 2 system of the caster. At present we are working on the development of quality indices. This is a joint project with voestalpine Stahl, Linz, the Department of Metallurgy at the Mining University of Leoben, and the metallurgy research group of at the School of Chemical Technology, Aalto University, Finland [22]. The current chemical analysis indices between 0 and 1 are computed, which indicates the risk of surface cracks and internal crack. The Quality Expert tool will be provided with these indices. The Quality Expert tool in turn uses this information to rate the strand. With this information, the BHM, 159. Jg. (2014), Heft 11 Springer-Verlag Wien Hahn & Schaden 443

7 Fig. 6: The final point of solidification on a specific caster is reached at m (a), for a specific secondary cooling practice and casting speed. About 30 cm before the final point of solidification, a channel containing liquid and mushy with a thickness of 10 mm is still present (b) operator will be in the position to identify slabs with highrisk surface defects that may need to be inspected or may need surface treatment. There are many more options for deploying information from DynaPhase. For instance, DynaPhase calculates density as a function of temperature, which makes it possible to calculate the weight of the ladle and the strand very precisely if no measurements are available. 4. Conclusions We have described the thermodynamic software package DynaPhase in some detail. We have emphasized the importance of a good thermodynamic database for any prediction made by DynaPhase, and so we have used new high-precision DSC measurements to improve our database. So far we have extended the range of validity for Si (up to 3.5 wt%) and Al (up to 3.5 wt%). More experimental investigations are underway to further improve the database. We demonstrated in two examples how the correct calculation of material properties with DynaPhase influences the accuracy of Level 2 cooling control systems like SIMETAL Dynacs 3D. The accurate prediction of solid fractions is indispensable for the effective use of strand treatment technologies such as soft reduction. Accurate calculations of DynaPhase can also help to manage unusual fluctuations of the chemical analysis by adjusting the casting practice. This can prevent quality problems or at least help identify strands that might have quality issues. 444

8 TABLE 1: Different representatives of the typical ferrite group (weight %) Different stainless s Grade group representative Ferrite Default 409L 436L 441 C Si Mn P S Cr Ni Mo Cu N Ti Nb Solidus temp. [ C] Solidus point [m] Shift of the solidus point [m] TABLE 2: Different representatives of the typical austenite group (weight %) Different stainless s Grade group representative Austenite Default SA304 SA309 SA316 C Si Mn P S Cr Ni Mo Cu N Ti Nb Solidus temp. [ C] Solidus point [m] Shift of the solidus point [m] Acknowledgements Financial support by the Austrian Federal Government (in particular by the Bundesministerium für Verkehr, Innovation and Technologie, and the Bundesministerium für Wirtschaft, Familie und Jugend) represented by Österreichische Forschungsförderungsgesellschaft mbh and the Styrian and the Tyrolean Provincial Governments, represented by Steirische Wirtschaftsförderungsgesellschaft mbh and Standortagentur Tirol, within the framework of the COMET Funding Program is gratefully acknowledged. References 1. Dittenberger, K.; Morwald, K.; Hohenbichler, G.; Feischl, U.: DYNACS Cooling Model-Features and Operational Results, Proc. VAI 7th International Continuous Casting Conference, Linz, Austria, 1996, pp Mörwald, K.; Stiftinger, M.; Reichetseder, F.; Resch, H.; Eichinger, A.: Design and Dynamic Control of Secondary Cooling Systems for Slab Casters, AISE, Chimani, C.; Watzinger, J.; Shan, G.; Resch, H.: Metallurgical strand treatment for direct hot charging, CCC, Linz, Austria, 2000, no. 55, pp Resch, H.: Precipitation modeling: A tool for predicting cracks and quality, CCC, Linz, Austria, 2000, no.54, pp Thalhammer, M.; Federspiel, F.; Mörwald, K.; Hödl, H.: Operational and Economic Benefits of VAI SMART/ASTC, Metallurgical, AISE Mini Expo, Ilie, S.; Fuchs, R.; Etzeldorfer, E.; Chimani, C.; Mörwald, K.: Slab quality improvement through soft reduction technology, CCC, Linz, 2008, no.5.5, p Morton, J.; Skrube, S.; Shenn, J.: Application of DynaGap Soft Reduction to High-Quality Blooms, AISTech, Indianapolis, Indiana, 2011, pp Hauser, K.; Dittenberger, K.; Hahn, S.; Chimani, C.; Fürst, C.; Ilie, S.; Lindenberger, S.: Dynamic 3D Heat Transfer Simulation of Continuous Casting, ECCC, Riccione, Italy, Dittenberger, K.; Hahn, S.; Hauser, K.; Chimani, C.; Ilie, S.; Lindenberger, L.: Dynamic 3D heat transfer simulation of continuous casting, International Journal of Cast Metals Research, 22 (2009), no. 1 4, pp Ramstorfer, F.; Dittenberger, K.; Hauser, K.; Hahn, S.: Dynacs 3D The new dimension in secondary cooling for slab casters, ECCC, Düsseldorf, Germany, 2011, session 12/paper Laitinen, E.; Neittaanmäki, P.: On numerical simulation of the continuous casting process. Journal of Engineering Mathematics, 22 (1988), pp Louhenkilpi, S.; Laitinen, E.; Nieminen, R.: Real-time simulation in continuous casting of, Metallurgical Transactions B, Vol. 24B (1993), pp Camisani-Calzolari, F.; Craig, I.; Pistorius, P.: Speed disturbance compensation in the secondary cooling zone in continuous casting, ISIJ International, Vol. 40 (2000), no. 5, pp Miettinen, J.: Mathematical simulation of interdendritic solidification of low-alloyed and stainless s, Metall. Trans. A, Vol. 23A (1992), pp Miettinen, J.: Calculation of solidification-related thermophysical properties for s, Metall. Trans. B, Vol. 28B (1997), pp B 16. Miettinen, J.: Mathematical Simulation of Interdendritic Solidification of Low-alloyed and Stainless Steels, PhD thesis, Laboratory of Metallurgy, PhD thesis, Helsinki University of Technology, Hillert, M.: Hardenability concepts with application to, The Metallurgical Society of AIME, edited by D.V. Doane and J.S. Kirkaldy, Warrendale, PA, 1978, pp Presoly, P.; Pierer, R.; Bernhard, C.: Identification of Defect Prone Peritectic Steel Grades by Analyzing High Temperature Phase Transformations, J. Metall. Trans. A, Vol. 44A (2013), 12, pp BHM, 159. Jg. (2014), Heft 11 Springer-Verlag Wien Hahn & Schaden 445

9 19. Presoly, P.; Pierer, R.; Bernhard, C.: Linking up of HT-LSCM and DSC measurements to characterize phase diagrams of s, IOP Conference Series (MCWASP XIII) Materials Science and Engineering 33 (2012), No FactSage, ( ) 21. Thermo-Calc Software, ( ) 22. Miettinen, J.: Mathematical quality indexes for solidifying s, Internal Report, Casim Consulting Oy, Espoo, (2012) 446