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  • 1. Abe, T.
    et al.
    Sundman, Bo
    KTH, Superseded Departments, Materials Science and Engineering.
    A description of the effect of short range ordering in the compound energy formalism2003In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 27, no 4, p. 403-408Article in journal (Refereed)
    Abstract [en]

    The current state of the compound energy formalism (CEF) to model ordering and the technique to handle short range ordering (SRO) were discussed. Although there are some methods which allow better treatment for SRO, such as the cluster variation method (CVM) or the Monte Carlo method (MC), these methods are difficult to handle in multi-component systems because of their complexity. In the compound energy formalism, SRO is not explicitly described. However it is possible to take the contribution of SRO to the Gibbs free energy into account through the reciprocal parameter, which has the same concentration dependency as DeltaG(m)(SRO). Introducing the reciprocal parameter of the form, L-i,L-j:i,L-j for the two sublattice model and L-i,L-j:i,L-j:*:* for the four sublattice model, one can satisfactorily describe the contribution of SRO to the Gibbs free energy in the CEF.

  • 2.
    Andersson, David A.
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Korzhavyi, Pavel A.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Johansson, Börje
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Applied Material Physics.
    First-principles based calculation of binary and multicomponent phase diagrams for titanium carbonitride2008In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 32, no 3, p. 543-565Article in journal (Refereed)
    Abstract [en]

    In this paper we have used a combined first principles and Calphad approach to calculate phase diagrams in the titanium-carbon-nitrogen system, with particular focus on the vacancy-induced ordering of the substoichiometric carbonitride phase, TiCxNy (x + y <= 1). Results from earlier Monte Carlo simulations of the low-temperature binary phase diagrams are used in order to formulate sublattice models for TiCxNy within the compound energy formalism (CEF) that are capable of describing both the low temperature ordered and the high-temperature disordered state. We parameterize these models using first-principles calculations and then we demonstrate how they can be merged with thermodynamic descriptions of the remaining Ti-C-N phases that are derived within the Calphad method by fitting model parameters to experimental data. We also discuss structural and electronic properties of the ordered end-member compounds, as well as short range order effects in the TiCxNy phase.

  • 3. Andersson, J. O.
    et al.
    Helander, T.
    Hoglund, L. H.
    Shi, P. F.
    Sundman, Bo
    THERMO-CALC & DICTRA, computational tools for materials science2002In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 26, no 2, p. 273-312Article in journal (Refereed)
    Abstract [en]

    Software for calculation of phase diagrams and thermodynamic properties have been developed since the 1970's. Software and computers have now developed to a level where such calculations can be used as tools for material and process development. In the present paper some of the latest software developments at Thermo-Calc Software are presented together with application examples. It is shown how advanced thermodynamic calculations have become more accessible since: - A more user-friendly windows version of Thermo-Calc, TCW, has been developed. - There is an increasing amount of thermodynamic databases for different materials available. - Thermo-Calc can be accessed from user-written software through several different programming interfaces are available which enables access to the thermodynamic software from a user-written software. Accurate data for thermodynamic properties and phase equilibria can then easily be incorporated into software written in e.g. C++, Matlab and FORTRAN. Thermo-Calc Software also produces DICTRA, a software for simulation of diffusion controlled phase transformations. Using DICTRA it is possible to simulate processes such as homogenization, carburising, microsegregation and coarsening in multicomponent alloys. The different models in the DICTRA software are briefly presented in the present paper together with some application examples.

  • 4. Ansara, I.
    et al.
    Sundman, Bo
    KTH, Superseded Departments, Materials Science and Engineering.
    Calculation of the magnetic contribution for intermetallic compounds2000In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 24, no 2, p. 181-182Article in journal (Refereed)
  • 5. Bjorkvall, J.
    et al.
    Du, S. C.
    Seetharaman, Seshadri
    KTH, Superseded Departments, Materials Science and Engineering.
    Thermodynamic description of Al2O3-CaO-MnO and Al2O3-FeO-MnO melts - a model approach2000In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 24, no 3, p. 353-376Article in journal (Refereed)
    Abstract [en]

    Assessments for the binary systems. Al2O3-CaO, Al2O3-FeO and Al2O3-MnO were carried out using a slag model developed at the present department. Calculations of the oxide activities in the homogenous liquid phase have been performed for the Al2O3-CaO-MnO and Al2O3-FeO-MnO systems, The activities in the ternary systems were calculated using the parameters obtained from the binary subsystems. Comparison between experimental data and the model calculations demonstrates the ability of the model to describe the thermodynamics of ternary systems using only information ti-om the binary systems. In the case of the Al2O3-CaO-MnO system, the comparison between model calculations and the results of the only available experimental measurements is less satisfactory. This could partly be attributed to the non availability of experimental data for the subsystem CaO-MnO. Future experimentation in the Al2O3-CaO-MnO system is strongly recommended.

  • 6.
    Bratberg, Johan
    et al.
    Swedish Inst. for Metals Research.
    Frisk, Karin
    Swedish Inst. for Metals Research.
    A thermodynamic analysis of the Mo-V and Mo-V-C systems2002In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 26, no 3, p. 459-503Article in journal (Refereed)
    Abstract [en]

    A new thermodynamic evaluation of the binary Mo-V system and the ternary Mo-V-C system using thermodynamic models for the Gibbs energy of individual phases is presented. The CALPHAD method has been used, with predictions of unknown thermodynamic quantities, to optimize a set of thermodynamic parameters taking related experimental information into consideration. The predictions are based on regularities in bonding properties and vibrational entropy of 3d-transition metal carbides. The results are summarized in tables of thermodynamic parameters, calculated binary phase diagrams and isothermal sections of the ternary phase diagram compared with experimental information. Finally the influence of ternary interaction parameters, especially in the fcc phase, on calculations of equilibria in multicomponent systems is discussed.

  • 7.
    Brusewitz Lindahl, Bonnie
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Liu, Xuan L.
    Liu, Zi-Kui
    Selleby, Malin
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    A thermodynamic re-assessment of Al-V toward an assessment of the ternary Al-Ti-V system2015In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 51, p. 75-88Article in journal (Refereed)
    Abstract [en]

    Titanium alloys are highly sought after due to their excellent mechanical properties. One of the most commonly used Ti alloys is Ti-6Al-4V, which contains 6% Al and 4% V by weight. Despite the popularity of this alloy, no thermodynamic description of the ternary Al-Ti-V system has been published in the open literature. In this work an assessment procedure of the ternary Al-Ti-V system was initiated based on the binary descriptions by Witusiewitcz et al. (J. Alloys Compds. 465 (2008) 64-77 [1]) for (Al-Ti), Gong et al. (Int. J. Mater. Res. 95 (2004) 978-986 [2]) for (Al-V) and Saunders (COST 507, 2 (1998) 297-298 [3]) for (Ti-V). When combining the three binary systems and looking at the extrapolated ternary isothermal sections, it was found that there was a very large miscibility gap in the bcc phase. The origin of this miscibility gap was mainly the Al-V system and therefore it was decided to reassess this system. The Al-V system was reassessed according to available experimental data along with the enthalpies of formation of all compounds as well as the enthalpies of mixing for all terminal phases obtained by first-principles calculations based on the density functional theory. For the Al8V5 phase there are two different sets of data for the enthalpies of formation. These two sets are investigated in this work and it is found that the set not used by Gong et al. in their assessment of the Al-V binary system gives better extrapolations. The final description produced improved extrapolated ternary isothermal sections.

  • 8.
    Brusewitz Lindahl, Bonnie
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Selleby, Malin
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    The Al-Fe-Mn system revisited-An updated thermodynamic description using the most recent binaries2013In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 43, p. 86-93Article in journal (Refereed)
    Abstract [en]

    The so-called TWinning Induced Plasticity (TWIP) steels have gained a lot of attention in the last couple of years due to their excellent mechanical properties; they show very high strength and are at the same time very ductile. The TWIP steels are austenitic and form mechanical twins under deformation. All TWIP steels have very high manganese content and a certain sub-group of these steels, lightweight steels with induced plasticity (so-called L-IP), also have high aluminum content. These steels are the lightweight versions of the TWIP steels and are therefore of high interest to the automotive industry. However, the grades existing today have too low yield strength. The yield strength can be improved by alloying and/or by precipitation hardening. Both these techniques require detailed insight on the thermodynamic properties of the alloy system in question. In this work, a thermodynamic reassessment of the entire Al-Fe-Mn system has been performed as a first step to describe the Fe-Al-C-Mn system, the core system for L-IP steels. All available experimental information has been taken into consideration and a set of data has been selected to be used in the optimization. The new thermodynamic description is based on the most recent thermodynamic descriptions of the constituent binaries and reproduces the experimental information in a satisfactory manner. This description, as opposed to previous descriptions has been optimized to fit experimental results in both the aluminum-rich part and the iron-manganese rich part of the system.

  • 9. Costa e Silva, Andre
    et al.
    Ågren, John
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Clavaguera-Mora, Maria Teresa
    Djurovic, D.
    Gomez-Acebo, Tomas
    Lee, Byeong-Joo
    Liu, Zi-Kui
    Miodownik, Peter
    Seifert, Hans Juergen
    Applications of computational thermodynamics - the extension from phase equilibrium to phase transformations and other properties2007In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 31, no 1, p. 53-74Article in journal (Refereed)
    Abstract [en]

    Complex equilibria and phase transformations involving diffusion can now be calculated quickly and efficiently. Detailed examples are given for cases which involve varying degrees of non-equilibrium and therefore time-dependence. Despite very good agreement between such calculations and experimental results, many potential end-users are still not convinced that such techniques could be usefully applied to their own specific problems. Friendly graphic interface versions of calculating software are now generally available, so the authors conclude that the most likely source of the reluctance to use such tools lies in the formulation of relevant questions and the interpretation of the results. Although the potential impact of such tools was foreseen many years ago [M. Hillert, Calculation of phase equilibria, in: Conference on Phase Transformations, 1968], few changes in the relevant teaching curricula have taken into account the availability and power of such techniques. This paper has therefore been designed not only as a collection of interesting problems, but also highlights the critical steps needed to achieve a solution. Each example includes a presentation of the "real" problem, any simplifications that are needed for its solution, the adopted thermodynamic formulation, and a critical evaluation of the results. The availability of such examples should facilitate changes in subject matter that will both make it easier for the next generation of students to use these tools, and at the same time reduce the time and effort currently needed to solve such problems by less efficient methods. The first set of detailed examples includes the deoxidation of steel by aluminum; heat balance calculations associated with ladle additions to steel; the determination of conditions that avoid undesirable inclusions; the role of methane in sintering atmospheres; interface control during the physical vapour deposition of cemented carbide; oxidation of gamma-TiAl materials; and simulation of the thermolysis of metallorganic precursors for Si-C-N ceramics and interface reaction of yttrium silicates with SiC-coated C/C-SiC composites for heat shield applications. A second set of examples, more dependent on competitive nucleation and growth, includes segregation and carburization in multicomponent steels and features a series of sophisticated simulatons using DICTRA software. Interfacial and strain energies become increasingly important in defining phase nucleation and morphology in such problems, but relatively little information is available compared to free energy and diffusion databases. The final section therefore demonstrates how computational thermodynamics, semi-empirical atomistic approaches and first-principles calculations are being used to aid filling this gap in our knowledge. (c) 2006 Elsevier Ltd. All rights reserved.

  • 10.
    Dilner, David
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Thermodynamic description of the Fe-Mn-Ca-Mg-S system2016In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 53, p. 55-61Article in journal (Refereed)
    Abstract [en]

    A thermodynamic description of the Fe-Mn-Ca-Mg-S system is presented. The compound energy formalism is used to describe all solution phases. This work includes assessments of all quaternary systems as well as the ternary systems Ca-Mg-S, Ca-Mn-S and Mg-Mn-S and the binary Ca-Mn system. The remaining ternary sulphur systems and lower-order systems were taken from previous assessments. The description of the solid phases reproduces the available experimental information well. However, due to lack of experimental data, approximations are used for the liquid in the Ca-Mg-S and Mg-Mn-S systems. The thermodynamic description presented in this work can be used to perform calculations related to sulphides in steels.

  • 11.
    Dilner, David
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Mao, Huahai
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Selleby, Malin
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Thermodynamic assessment of the Mn-S and Fe-Mn-S systems2015In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 48, p. 95-105Article in journal (Refereed)
    Abstract [en]

    The Fe-Mn-S system is of great importance for the steelmaking process. As part of the work for the development of a large self-consistent thermodynamic database for such applications, the aim of the present assessment was to obtain a thermodynamic description of the Fe-Mn-S system using the ionic two-sublattice model for the liquid. Previous compatible descriptions of all unaries as well as two of the constituent binaries, Fe-Mn and Fe-S, were accepted. The third binary, Mn-S, was assessed in this work. Ternary parameters were optimised for the liquid, the alabandite, the pyrrhotite and the pyrite phases. Calculations using the present description agree well with experimental data.

  • 12.
    Dilner, David
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Selleby, Malin
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Thermodynamic description of the Fe-Ca-O-S system2017In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 57, p. 118-125Article in journal (Refereed)
    Abstract [en]

    In an effort to describe sulphur in steels, particularly in steelmaking, a thermodynamic description of the Fe-Ca-O-S and its subsystems is presented. The ionic two-sublattice liquid model has been used to describe all liquids. For the Fe-O-S part of the system the calculations reproduce available experimental data well. Experimental data is scarce in the Ca-O-S system and in the quaternary and we to trust that the system is well reproduced by extrapolation by previously assessed sub-systems.

  • 13. Dupin, N.
    et al.
    Ansara, I.
    Sundman, Bo
    KTH, Superseded Departments, Materials Science and Engineering.
    Thermodynamic re-assessment of the ternary system Al-Cr-Ni2001In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 25, no 2, p. 279-298Article in journal (Refereed)
    Abstract [en]

    A re-assessment of the ternary system AI-Cr-Ni following Dupin's thesis work using a single Gibbs energy function for the gamma and gamma' phases is presented taking into account new experimental liquidus temperatures. The disordered bcc A2 and ordered B2 phases are also modelled with a single equation. The existence of vacancies as defects in this structure is described. The other phases are modelled as substitutional solutions, or as stoichiometric or non-stroichiometric binary compounds. The present assessment is limited to the sub system AlNi-Cr-Ni where no ternary phase exists. The parameters describing the Gibbs energy of all the assessed phases are given. Extensive comparisons between calculation and experimental data are presented.

  • 14. Fredriksson, P.
    et al.
    Sundman, Bo
    KTH, Superseded Departments, Materials Science and Engineering.
    A thermodynamic assessment of the Fe-Pt system2001In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 25, no 4, p. 535-548Article in journal (Refereed)
    Abstract [en]

    The present work will present a complete assessment of the Fe-Pt system by means of the CALPHAD method. The liquid and the bee phase have been modelled as substitutional solutions where the interaction parameter is composition dependent in the form of a Redlich-Kister series. The ordered phases and the disordered fee phases were modelled in CEF formalism with a single Gibbs energy function. The obtained phase equilibria and activities of iron and platinum agree reasonably well with the literature data. Validation of the liquidus maxima around 50 at% Pt, found in the optimisation work, was performed by a quenching experiment followed by SEM analysis.

  • 15.
    Frisk, Karin
    et al.
    Computational Thermodynamics, Corrosion and Metals Research Institute.
    Bratberg, Johan
    Computational Thermodynamics, Corrosion and Metals Research Institute.
    Markström, Andreas
    Computational Thermodynamics, Corrosion and Metals Research Institute.
    Thermodynamic modelling of the M6C carbide in cemented carbides and high-speed steel2005In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 29, no 2, p. 91-96Article in journal (Refereed)
    Abstract [en]

    Newly published experimental information on phase equilibria in cemented carbides and high-speed steel has shown that the solubility of Co, Nb, Si, Ta and V in the M6C carbide is higher than predicted by thermodynamic calculations. To account for this new information the model for M6C was extended. A thermodynamic description of the M6C carbide in cemented carbides and high-speed steels is presented. Several experimental studies have shown that there is a solubility of Si in M6C in high-speed steels, and the new model describes this solubility. A significant solubility of Co and Nb has also been observed, and was accounted for. The solubility of Nb, Ta and V in M6C in cemented carbide systems is described. The models are discussed, and the calculated equilibria are compared with the new experimental information.

  • 16.
    Gran, Jimmy
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Micro-Modelling.
    Song, Minho
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Micro-Modelling.
    Sichen, Du
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Micro-Modelling.
    Activity of magnesium in liquid Ag-Mg alloys2012In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 36, p. 89-93Article in journal (Refereed)
    Abstract [en]

    Activity measurements of magnesium in liquid Ag-Mg solutions were carried out at 1573, 1673. 1773 and 1823 K using two different techniques. While most measurements were carried out using the vapor pressure method at 1573 and 1673 K, a number of measurements were made at 1773 and 1873 K using the gas equilibration technique. The latter method was used mostly for obtaining Ag-Mg solution at very low Mg contents. It was found that magnesium had a negative deviation from ideality in Ag-Mg solutions. The excess Gibbs energy of Ag-Mg solutions seemed to have a quite weak temperature dependency in the temperature region studied. The excess Gibbs energy of Ag-Mg solution can be described as;

  • 17.
    Gran, Jimmy
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Micro-Modelling.
    Wang, Yanli
    Sichen, Du
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Micro-Modelling.
    Experimental determination of the liquidus in the high basicity region in the Al2O3(30 mass%)-CaO-MgO-SiO2 system2011In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 35, no 2, p. 249-254Article in journal (Refereed)
    Abstract [en]

    The liquidus in the high basicity region in the Al2O3(30 mass%)-CaO-MgO-SiO2 system were determined experimentally at 1773 and 1873 K using the quench technique followed by EPMA analysis. Based on the experimental data, a phase diagram of the Al2O3(30 mass%)-CaO-MgO-SiO2(< 20 mass%) section was constructed for 1773 and 1873 K. The solubilities of 2CaO center dot SiO2 and 3CaO center dot SiO2 at 1773 K were found to be considerably higher in comparison with the existing phase diagram. Even the solubility of MgO at 1873 K was found to be somewhat higher. In addition, the activities of MgO, CaO and Al2O3 at 1773 K were estimated using the phase diagram information.

  • 18. Granas, O.
    et al.
    Korzhavyi, Pavel A.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Applied Material Physics.
    Kissavos, A. E.
    Abrikosov, I. A.
    Theoretical study of the Mo-Ru sigma phase2008In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 32, no 1, p. 171-176Article in journal (Refereed)
    Abstract [en]

    The thermodynamic properties of the Mo-Ru binary sigma-phase are investigated using a combination of ab initio calculations and CALPHAD modeling. Total energy calculations have been performed for the complete set of 32 end-member compounds of a 5-sublattice compound energy model. The internal crystallographic parameters for each end-member compound have been determined by minimising the total energy. A simpler, 3-sublattice model of the Mo-Ru a-phase is formulated on the basis of calculated total energies. The site occupancy is acquired by minimising the free energy given by the compound energy model. A strong preference of Mo and Ru towards high-coordination sites and icosahedral sites in the Mo-Ru a-phase is found and analysed in terms of the electronic structure.

  • 19.
    Gunasekara, Saman Nimali
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Energy Technology.
    Mao, Huahai
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Bigdeli, Sedigheh
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Chiu, Justin
    KTH, School of Industrial Engineering and Management (ITM), Energy Technology.
    Martin, Viktoria
    KTH, School of Industrial Engineering and Management (ITM), Energy Technology.
    Thermodynamic assessment of binary erythritol-xylitol phase diagram for phase change materials design2018In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 60, p. 29-36Article in journal (Refereed)
    Abstract [en]

    Here, the erythritol-xylitol binary system was thermodynamically optimized based on available experimental phase equilibrium data, to explore compositions suitable as phase change materials (PCMs) for thermal energy storage (TES). A previous experimental study revealed that erythritol-xylitol was a partially isomorphous system with a eutectic. In the thermodynamic evaluation, the CALPHAD method was employed coupling the phase diagram and thermodynamic property information. There, both unary and binary systems’ experimental data were taken into account, and all phases were described using the substitutional solution model. Finally, a self-consistent thermodynamic description for the erythritol-xylitol system was achieved. The calculated eutectic point is at 76.7 °C and 26.8 mol% erythritol, agreeing well with the experimental data. The calculated phase diagram better-verifies the systems’ solidus and the solvus, disclosing the stable phase relations. Based on the Gibbs energy minimization, phase diagrams can be predicted for the binary and higher order systems, provided the component subsystems are thermodynamically assessed beforehand. In conclusion, to move forward beyond e.g. non-isomorphous simple eutectic systems, methods using Gibbs free energy minimization from a fundamental point-of-view such as CALPHAD are essential.

  • 20. Hallstedt, B.
    et al.
    Khvan, A. V.
    Lindahl, Bonnie B.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Selleby, Malin
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Liu, S.
    PrecHiMn-4—A thermodynamic database for high-Mn steels2017In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 56, p. 49-57Article in journal (Refereed)
    Abstract [en]

    This paper concerns a Calphad database that was developed to describe precipitation of cubic carbides and nitrides (V, Nb and Ti) in high manganese steels and to describe phase equilibria in high manganese steels with high aluminium content. The database has also been shown to be useful for calculations on medium manganese steels and low-density steels with varying aluminium additions. Thus the database covers a significant fraction of the steels that are termed advanced high strength steels (AHSS) of the second and third generation. A number of systems were assessed (or reassessed) for the database, namely Fe–Mn–Al, Fe–Mn–C, Fe–Nb, Mn–Nb, Fe–Mn–Nb, Fe–Nb–V, Fe–Nb–C, Mn–Nb–C, Fe–Mn–Nb–C, Nb–N, Fe–Mn–Nb–N. The remaining systems were taken from published assessments. The database covers the elements Fe, Mn, Al, Si, V, Nb, Ti, C and N.

  • 21. Hallstedt, Bengt
    et al.
    Dupin, Nathalie
    Hillert, Mats
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Höglund, Lars
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Lukas, Hans Leo
    Schuster, Julius C.
    Solak, Nuri
    Thermodynamic models for crystalline phases. Composition dependent models for volume, bulk modulus and thermal expansion2007In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 31, no 1, p. 28-37Article in journal (Refereed)
    Abstract [en]

    The thermodynamic modelling of solid (crystalline) phases forms a central topic within the Calphad approach and a variety of aspects have been discussed at previous Ringberg workshops. At the present Ringberg workshop, modelling of volume and its temperature, pressure and composition dependence formed a major part of the discussions. In addition, modelling of the heat capacity above the (equilibrium) melting temperature, sublattice modelling of complex phases, modelling of ordering and interstitial solutions in the bcc lattice and the effect of magnetism were addressed.

  • 22. Hillert, M.
    et al.
    Sundman, Bo
    KTH, Superseded Departments, Materials Science and Engineering.
    Predicting miscibility gaps in reciprocal liquids2001In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 25, no 4, p. 599-605Article in journal (Refereed)
    Abstract [en]

    There is a strong correlation between the appearance of liquid miscibility gaps in reciprocal phases and the standard Gibbs energy of the reciprocal reaction, DeltadegreesG. The associate solution model does not predict such a correlation but the two-sublattice model does. Physically, the critical temperature of a reciprocal miscibility gap is related to DeltadegreesG and is also affected by the presence of short range order. The latter effect can be estimated from DeltadegreesG using the conformal solution theory which was developed for reciprocal systems with univalent ions. In that approximation the short range order effect is described with a reciprocal parameter. The estimate of that parameter for systems with different valencies is now discussed. The calculated phase diagram may be reasonable for low values of the reciprocal parameter, relative to DeltadegreesG, but is not satisfactory for large values because two asymmetric miscibility gaps will appear when the critical temperature has been suppressed to 3/4 of the value predicted without a reciprocal term. An alternative form of the reciprocal term is now proposed, which does not produce the splitting into two miscibility gaps.

  • 23.
    Hillert, Mats
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Kjellqvist, Lina
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Mao, Huahai
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Selleby, Malin
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Sundman, Bo
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Parameters in the compound energy formalism for ionic systems2009In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 33, no 1, p. 227-232Article in journal (Refereed)
    Abstract [en]

    The compound energy formalism, CEF, involves many model parameters. They are evaluated to give the best fit to the experimental information. The optimisation is simpler if less parameters need to be adjusted.The maximum number of independent parameters that can be evaluated depends on the information available. The best choice of parameters is first discussed for simple ionic substances with an internal variable, then for solutions of two or four such substances.

    To reduce the number of parameters, independent parameters are conveniently defined as combinations of primary model parameters. That may be possible when there is an internal variable,which can take only one value, the value that minimizes the Gibbs energy. Such combinations may be regarded as the true optimisation parameters and they may be used actively during an optimisation. The present discussion deals with substances with an internal variable and mixtures, which may have more than one internal variable.

    The conclusions apply equally well to non-ionic systems if the information is limited to stoichiometric compositions. The optimisation parameters should then be defined for stoichiometric overall compositions.

  • 24.
    Hillert, Mats
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Selleby, Malin
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Methods for storage of Gibbs energy data of substances2016In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 53, p. 146-150Article in journal (Refereed)
    Abstract [en]

    There are two popular methods for storing Gibbs energy data for pure substances. They are inspired by Planck and by Lewis and Randall and may appear as very different but it will be demonstrated that they only differ by the choice of references. The derivation of functions to be stored will then be described and a crude but very simple method for extending them to 0. K by interpolation instead of extrapolation will be presented.

  • 25.
    Hou, Ziyong
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. Northeastern University, China.
    Hedström, Peter
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Chen, Q.
    Xu, Y.
    Wu, D.
    Odqvist, Joakim
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Quantitative modeling and experimental verification of carbide precipitation in a martensitic Fe-0.16 wt%C-4.0 wt%Cr alloy2016In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 53, p. 39-48Article in journal (Refereed)
    Abstract [en]

    Precipitation of carbides during tempering of a martensitic Fe-0.16 wt% C-4.0 wt% Cr alloy has been investigated by experimental analysis and quantitative modeling. It is found that both M7C3 and M23C6 form, at low- and high-angle grain boundaries in the martensite, as well as, at dislocations inside individual laths of martensite, during tempering at 700 °C. The applied Kampmann-Wagner numerical (KWN) modeling, utilizing CALPHAD thermodynamic and kinetic databases together with an assumption of local equilibrium and a constant tie-line, captures the main features of the precipitation, with a transient formation of metastable M23C6, and with M7C3 as the stable carbide. The predicted volume fraction and size are in reasonable agreement with extraction experiments for M7C3. However, for the metastable minority carbide M23C6, the modeling underestimates the size and overestimates the volume fraction within the transient time. With sound thermodynamic databases and physical parameter input, the adopted simplified modeling scheme is a valuable tool for materials design and optimization. Furthermore, by treating conditions at the phase interface more rigorously it is possible to account for different mechanisms of precipitation, such as e.g., non-partitioning local equilibrium, which could be important in systems where interstitial elements diffuse much faster than the substitutional ones.

  • 26.
    Jerlerud Perez, Rosa
    et al.
    KTH, Superseded Departments, Materials Science and Engineering.
    Sundman, Bo
    KTH, Superseded Departments, Materials Science and Engineering.
    Thermodynamic assessment of the CR-SN binary system2001In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 25, no 1, p. 59-66Article in journal (Refereed)
    Abstract [en]

    A thermodynamic description of the Cr-Sn binary system has been obtained using the CALPHAD technique. The excess Gibbs energy of the stable solution phases (liquid and bcc) has been assessed using phase diagram and thermodynamic data.

  • 27. Joubert, J. M.
    et al.
    Sundman, Bo
    KTH, Superseded Departments, Materials Science and Engineering.
    Dupin, N.
    Assessment of the niobium-nickel system2004In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 28, no 3, p. 299-306Article in journal (Refereed)
    Abstract [en]

    A reassessment of the Nb-Ni system is proposed taking into account new experimental data. According to recent crystallographic work, the g phase has been modelled using three independent sublattices of variable occupation. This has been made possible by including experimental site fractions in the different sublattices as data for parameter optimization. A consistent set of parameters is proposed. Good agreement is obtained between calculated and experimental values for all kinds of data (thermodynamic, crystallographic and phase diagram data).

  • 28.
    Kaplan, Bartek
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics. Sandvik Coromant R&D, Stockholm, Sweden.
    Blomqvist, Andreas
    Selleby, Malin
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Norgren, Susanne
    Thermodynamic analysis of the W-Co-Cr system supported by ab initio calculations and verified with quaternary data2015In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 50, p. 59-67Article in journal (Refereed)
    Abstract [en]

    The present work aims at assessing the W-Co-Cr system with focus on including the ternary R-phase in the thermodynamic description. Enthalpies of formation at 0 K of all considered R-phase end-members are calculated using density functional theory and used in the assessment due to the scarceness of the experimental information. The resulting assessment is verified by comparing with recent experimental data in the W-Co-Cr-C quaternary system.

  • 29.
    Kaplan, Bartek
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering. Sandvik Coromant R and D, Sweden.
    Korbmacher, D.
    Blomqvist, A.
    Grabowski, B.
    Finite temperature ab initio calculated thermodynamic properties of orthorhombic Cr3C22016In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 53, p. 72-77Article in journal (Refereed)
    Abstract [en]

    Due to severe discrepancies between reported Gibbs energies of formation we calculate the thermodynamic properties of orthorhombic Cr3C2 ab initio in an attempt to resolve the experimental scatter. All relevant excitation mechanisms are considered, including the T=0 K formation energy, electronic entropy and quasi-harmonic and anharmonic vibrations. We find that derivative quantities of the free energy, such as isobaric heat capacity and relative thermal expansion are well described by this approach, serving as a benchmark for the calculations. Comparison shows that the final ab initio Gibbs energy has a less steep temperature dependence than what has previously been obtained by assessment.

  • 30.
    Kaplan, Bartek
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics. Sandvik Coromant RandD, Sweden .
    Markström, Andreas
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics. Thermo-Calc Software AB, Sweden .
    Blomqvist, Andreas
    Sandvik Coromant R&D, Stockholm.
    Norgren, Susanne
    Sandvik Mining R&D, Stockholm.
    Selleby, Malin
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Thermodynamic analysis of the Co-Cr-C system2014In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 46, p. 226-236Article in journal (Refereed)
    Abstract [en]

    A reassessment of the thermodynamic description of the Co–Cr–C system was performed to take into account recent experimental information on the solubility of Co in Cr-based carbides. Density Functional Theory (DFT) calculations coupled with phonon calculations were performed to calculate the heat capacity and Gibbs energies of formation of stable and metastable carbides in the Co–Cr–C system as a function of temperature, within the limits of the Harmonic or the Quasi Harmonic Approximation. Resulting Gibbs energies were compared with earlier experimental studies and assessments, where calculated values for Cr23C6, Cr7C3 and Cr3C2 from the present work were seen to fall within the experimental scatter. The calculated heat capacity and Gibbs energy of formation as a function of temperature for the metastable Co3C2 compound together with recent experimental information was used in the evaluation of the thermodynamic parameters. As a result, the new and improved thermodynamic description accounts for the solubility of Co in M3C2 in contrast to previous descriptions, where this was neglected due to a complete lack of experimental information. Furthermore, a better representation of previously reported liquidus temperatures was achieved, without increasing the number of parameters in the liquid phase. Other relevant features of the phase diagram and thermochemical properties were also well represented.

  • 31. Kattner, U. R.
    et al.
    Eriksson, G.
    Hahn, I.
    Schmid-Fetzer, R.
    Sundman, Bo
    KTH, Superseded Departments, Materials Science and Engineering.
    Swamy, V.
    Kussmaul, A.
    Spencer, P. J.
    Anderson, T. J.
    Chart, T. G.
    Silva, A. C. E.
    Jansson, B.
    Lee, B. J.
    Schalin, M.
    Applications of Computational Thermodynamics: Groups 4 and 5: Use of thermodynamic software in process modelling and new applications of thermodynamic calculations2000In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 24, no 1, p. 55-94Article in journal (Refereed)
  • 32.
    Kjellqvist, Lina
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Selleby, Malin
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Adding C to the thermodynamic description of the Cr-Fe-Ni-O system2009In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 33, no 2, p. 393-397Article in journal (Refereed)
    Abstract [en]

    The Cr–Fe–Ni–O system has been studied in an earlier work with the intention to thermodynamically describe the influence of oxygen in highly alloyed steels. The aim of this study was to also include carbon in this description, with an emphasis on the modelling of the liquid phase. The liquid phase is assessed using the ionic two-sublattice model and good agreement between calculated and experimental data is achieved in the C–Fe–O system. In the C–Ni–O system the calculated solubility of oxygen in the liquid phase is about two orders of magnitude lower than the experimental data. Due to the very low oxygen solubility in liquid C–Ni, no ternary parameter could have any effect on the calculated solubility. By comparing with other oxide bearing ternary systems, it is suggested that the thermodynamic calculations probably give more reliable results than the experimental measurements when the oxygen solubility is very low. For the C–Cr–O system, no experimental information is available. The interaction parameters in the liquid phase were therefore set to zero.

  • 33.
    Kjellqvist, Lina
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Selleby, Malin
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Sundman, Bo
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Thermodynamic modelling of the Cr-Fe-Ni-O system2008In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 32, no 3, p. 577-592Article in journal (Refereed)
    Abstract [en]

    There is a need to describe the influence of oxygen on high alloyed steels, both regarding oxidation processes–as in the formation of oxide layers–and regarding steel/slag processes in a metallurgical context. As a first step and in order to be able to perform calculations and simulations on these different processes, the thermodynamic properties need to be described, as done for the Cr–Fe–Ni–O system. Previous attempts to describe this system has resulted in an inconsistent description, more specifically concerning the spinel phase. The aim of the present study is to obtain a consistent thermodynamic database for the Cr–Fe–Ni–O system with an emphasis on the modelling of the spinel phase. The solid phases are described using the compound energy formalism and the metallic and ionized liquid is modelled using the ionic two-sublattice model. A complete list of all binary and higher order parameters is included.

  • 34. Kong, Yi
    et al.
    Xiong, Wei
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Guo, Haibo
    Sun, Weihua
    Du, Yong
    Zhou, Yichun
    Elastic and thermodynamic properties of the Ni-B system studied by first-principles calculations and experimental measurements2010In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 34, no 2, p. 245-251Article in journal (Refereed)
    Abstract [en]

    The elastic and thermodynamic properties of NiB, Ni2B, Ni3B, orthorhombic Ni4B3(O-Ni4B3), monoclinic Ni4B3(M-Ni4B3), and Ni23B6, are calculated via first-principles method for the Ni-B system. The ground state energies, the full sets of elastic constants and the associated macroscopic elastic parameters of these Ni-B alloys are computed for the first time. Taking contributions from lattice vibrations and thermally excited electrons into account, thermodynamic properties at finite temperatures are then predicted. In addition, we measure the molar heat capacity at constant pressure for NiB and compare the results with the theoretical predictions. Various calculations demonstrate that the first-principles calculation can be used to clarify the diverse experimental data, and provide reliable thermodynamic data. (C) 2010 Elsevier Ltd. All rights reserved.

  • 35. Kusoffsky, A.
    et al.
    Dupin, N.
    Sundman, Bo
    KTH, Superseded Departments, Materials Science and Engineering.
    On the compound energy formalism applied to fcc ordering2001In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 25, no 4, p. 549-565Article in journal (Refereed)
    Abstract [en]

    The influence on the phase diagram and thermodynamic properties of some parameters in the Compound Energy Formalism (CEF) is studied for different simple binary and ternary cases showing fcc ordering. It is shown that the flexibility of this formalism should enable to model most real cases. Recommendations for the ternary parameters that should be set from the binary systems are made.

  • 36.
    Larsson, Henrik
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. Thermocalc Software, SE-11364 Stockholm, Sweden.
    Höglund, Lars
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. Thermocalc Software, SE-11364 Stockholm, Sweden.
    A scheme for more efficient usage of CALPHAD data in simulations2015In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 50, p. 1-5Article in journal (Refereed)
    Abstract [en]

    A method is suggested that allows thermodynamic data to be dynamically stored and retrieved. The purpose of the method is to reduce computer simulation time when Calphad type databases are being used. Some test simulations are presented and these indicate that simulations can be made to run 5-40 times faster without any significant loss of accuracy.

  • 37.
    Larsson, Henrik
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Höglund, Lars
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Multiphase diffusion simulations in 1D using the DICTRA homogenization model2009In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 33, no 3, p. 495-501Article in journal (Refereed)
    Abstract [en]

    A model for multiphase simulations in 1D previously reported in [H. Larsson, A. Engstrom, Acta Mater. 54 (2006) 2431] has been further developed and incorporated in the DICTRA software. The model is based on the assumption of local equilibrium and locally averaged kinetic properties, which computationally transforms the problem into a single-phase diffusion process. The applicability of the model is discussed and example simulations are presented.

  • 38.
    Larsson, Henrik
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy. Thermo-Calc Software, Stockholm, Sweden.
    Jansson, Magnus
    Rate of change at equilibrium2015In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 51, p. 220-223Article in journal (Refereed)
    Abstract [en]

    A general procedure to evaluate derivatives of thermodynamic quantities with respect to equilibrium conditions (external variables, parameters) at equilibrium is outlined. An example calculation is given.

  • 39.
    Li, Zhou
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Mao, Huahai
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Korzhavy, Pavel
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Selleby, Malin
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Thermodynamic re-assessment of the Co-Cr system supported by first-principles calculations2016In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 52, p. 1-7Article in journal (Refereed)
    Abstract [en]

    The phase equilibria and thermochemical properties of the Co-Cr system was re-assessed using the Calphad method with the aid of ab initio calculations. Four solution phases, liquid, bcc, fcc and hcp phases are modeled using the substitutional solution model. The sigma phase, as an intermetallic compound with certain homogeneous composition range, is modeled by a full five sublattices partitioned CEF model. The formation enthalpies of all end-members are obtained from ab initio calculations. The calculated results fit the experimental data reasonably well which indicates that this ab initio aided model is a proper description for the sigma phase.

  • 40.
    Li, Zhou
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Mao, Huahai
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Selleby, Malin
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    A new thermodynamic description of stable Cr-carbides for the third generation of thermodynamic database2017In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 59, p. 107-111Article in journal (Refereed)
    Abstract [en]

    An updated thermodynamic description of the stable Cr-carbides was obtained by applying the same models as used for the elements within the 3rd generation of thermodynamic databases. The Einstein model was used and a scaling factor was introduced to take into account the coupling effect between the stoichiometry (C to Cr ratio) and the structure of the compound. Using this model we could accurately describe the thermodynamic properties of these stoichiometric compounds using available experimental heat capacity data. The new description is now more physically sound and results in a better agreement with the experimental heat capacity data.

  • 41.
    Lindahl, Bonnie B.
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Burton, Benjamin P.
    Selleby, Malin
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Ordering in ternary BCC alloys applied to the Al-Fe-Mn system2015In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 51, p. 211-219Article in journal (Refereed)
    Abstract [en]

    TWIP (TWinning Induced Plasticity) steels are attracting a lot of attention due to their combination of strength and ductility. In a previous work [1] (B. Lindahl, M. Selleby, Calphad 43 (2013) 86-93) a thermodynamic assessment of the Al-Fe-Mn system, which forms the basis of TWIP steels, was presented. The previous assessment treated the A2/B2 order-disorder transformation in the bcc phase using a two-sublattice model. In the present work a four-sublattice model has been used in order to also be able to describe the transition into the ordered DO3 compound that occurs at lower temperatures. pair interaction energies for the Fe-Mn system are evaluated which prove crucial to the extrapolations into the Al-Fe-Mn system. Along with this various aspects of modeling chemical ordering using the Calphad approach are discussed. Equations for determining the ternary compound energies from binary pair interactions energies are presented and equations for determining the parameter values from the ordered parameters are derived.

  • 42.
    Lindvall, Mikael
    et al.
    Swerea MEFOS.
    Gran, Jimmy
    Swerea MEFOS.
    Sichen, Du
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Determination of the vanadium solubility in the Al2O3-CaO(25mass%)-SiO2 system2014In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 47, p. 50-55Article in journal (Refereed)
    Abstract [en]

    Vanadium (V) solubility in the Al2O3-CaO(25mass%)-SiO2 system was determined experimentally at 1873K and at a fixed oxygen potential of 9.37•10-11 bar. EPMA microanalyses were employed to identify the phases and their compositions in the quenched samples. It showed that the solubility of V-oxide increased slightly with decreasing Al2O3-content in the interval from 3mass% to 53mass%. The maximum V-solubility was up to 7mass% (as V). A solid solution rich in V-oxide was detected. The Al2O3 solubility in this solid solution was found to increase with increasing Al2O3-content in the liquid.

  • 43.
    Lu, XiaoGang
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Selleby, Malin
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Sundman, Bo
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Assessments of molar volume and thermal expansion for selected bcc, fcc and hcp metallic elements2005In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 29, no 1, p. 68-89Article in journal (Refereed)
    Abstract [en]

     The molar volume and thermal expansion of selected metallic elements with the bcc, fcc and hcp structures were studied by means of the Calphad approach. Experimental data were critically assessed, and model parameters were obtained yielding reasonable descriptions of all experimental data on molar volume and thermal expansion. The descriptions are valid between room temperature and the melting points at atmospheric pressure.

  • 44.
    Lu, Xiaogang
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Selleby, Malin
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Sundman, Bo
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Implementation of a new model for pressure dependence of condensed phases in Thermo-Calc2005In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 29, no 1, p. 49-55Article in journal (Refereed)
    Abstract [en]

    The high pressure modelling of condensed phases has mainly been a topic for geophysics, but there is an interest in modelling moderate pressure dependence also for materials science and engineering. The Murnaghan equation of state has been implemented in the Thermo-Calc software to represent the pressure-dependent part of the Gibbs energy. Recently it has been shown by Jacobs and Oonk that an equation of state derived from an empirical relationship between volume and isothermal bulk modulus can be applied to represent experimental data in volume-pressure-temperature space with equal or better accuracy then the Murnaghan equation of state. In this paper we extend this equation of state and show that a simpler expression for the Gibbs energy can be derived than that given by Jacobs and Oonk. The resulting expression for the Gibbs energy has been implemented in the Thermo-Calc software.

  • 45.
    Lu, Xiao-Gang
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Sundman, Bo
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Ågren, John
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Physical Metallurgy.
    Thermodynamic assessments of the Ni-Pt and Al-Ni-Pt systems2009In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 33, no 3, p. 450-456Article in journal (Refereed)
    Abstract [en]

    The Ni-Pt system is assessed using the CALPHAD method. The four fcc-based phases, i.e. disordered solid solution phase, Ni3Pt-L1(2), NiPt-L1(0) and NiPt3-L1(2), are described by a four-sublattice model. The calculated thermodynamic properties and order/disorder phase transformations are in good agreement with the experimental data. In order to facilitate the assessment, first-principles pseudopotential calculations are also performed to calculate the enthalpy of formation at 0 K, and comparison with the assessed values is discussed. By combining the assessments of Al-Ni and Al-Pt, the Al-Ni-Pt ternary system is assessed within a narrow temperature range, focusing on the fcc-based phases and their phase equilibria with B2 phase.

  • 46.
    Mao, Huahai
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Selleby, Malin
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Thermodynamic reassessment of the Si3N4-AlN-Al2O3-SiO2 system - Modeling of the SWON and liquid phases2007In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 31, no 2, p. 269-280Article in journal (Refereed)
    Abstract [en]

    The technically important quasi-ternary section Si3N4-AlN-Al2O3-SiO2 of the Si-Al-O-N system has been then-nodynamically reassessed. Improved descriptions for the Gibbs energies of the beta and O'-sialon phases are applied. Different modelings according to the different behaviors of the reciprocal system within the beta-sialon phase are discussed. The liquid phase is modeled with a new formula based on the ionic twosublattice model. The thermodynamic properties of the sialon phases are discussed and various phase diagrams are presented. The self-consistent thermodynamic dataset is useful for the computer simulation of sialon synthesis. Some examples of such applications are illustrated.

  • 47.
    Mao, Huahai
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Selleby, Malin
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Fabrichnaya, Olga
    Thermodynamic assessment of the Y2O3-Al2O3-SiO2 system and its subsystems2008In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 32, no 2, p. 399-412Article in journal (Refereed)
    Abstract [en]

    Phase equilibria and thermodynamic properties at I bar in the Y2O3-Al2O3-SiO2 ternary system and its constituent binaries Y2O3-Al2O3 and Y2O3-SiO2 have been reevaluated using the CALPHAD approach. The liquid phase is described by the ionic two-sublattice model with the formula (Al+3, Y+3)(p)(AlO2-1, O-2, SiO4-4, SiO4-4, SiO20)(Q). The SiO2 solubility in the YAM phase was described using a Compound energy model. Two clatasets of self-consistent model parameters are presented. However, the rather meagre and scattered experimental data imply that the present assessments should be regarded as provisional. Some critical experiments are suggested for this system.

  • 48.
    Mao, Huahai
    et al.
    KTH, Superseded Departments, Materials Science and Engineering.
    Selleby, Malin
    KTH, Superseded Departments, Materials Science and Engineering.
    Sundman, Bo
    KTH, Superseded Departments, Materials Science and Engineering.
    A re-evaluation of the liquid phases in the CaO-Al2O3 and MgO-Al2O3 systems2004In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 28, no 3, p. 307-312Article in journal (Refereed)
    Abstract [en]

    The thermodynamic properties of the liquid phases in the CaO-Al2O3 and MgO-Al2O3 systems are reassessed in order to provide an adequate basis for fitting information on the ternary CaO-Al2O3-SiO2 and MgO-AI(2)O(3)-SiO2 systems, especially the miscibility gap. The modelling of Al2O3 in the liquid phase is modified from the traditional formulae with the liquid phase now described by the ionic two-sublattice model as (Al+3, Ca+2)p(AlO2-1, O-2)(Q) and (Al+3, Mg+2)(P)(AlO2-1, O-2)(Q), respectively.

  • 49.
    Markström, Andreas
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Andersson, David
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Frisk, Karin
    Combined ab-initio and experimental assessment of A1-xBxC mixed carbides2008In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 32, no 4, p. 615-623Article in journal (Refereed)
    Abstract [en]

    The excess energies for A1 - x Bx C mixed carbides (where A and B are metals) have been calculated using ab-initio calculations, for 14 systems. A thorough comparison has been made with experimentally assessed excess energies. The comparison shows that conventional ab-initio calculations applied to rather simple structural models can be used to predict the sign, magnitude and symmetry of the excess energy for A1 - x Bx C mixed carbides. The calculated excess energies have also successfully been used to describe several AC-BC systems where the experimental information does not give a unique determination of the excess energy in traditional CALPHAD modelling. The systems that have been studied are CrC-TiC, HfC-NbC, HfC-TaC, HfC-TiC, HfC-VC, NbC-TaC, NbC-VC, NbC-ZrC, TaC-VC, TaC-ZrC, TiC-VC, TiC-ZrC and VC-ZrC.

  • 50.
    Markström, Andreas
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Frisk, Karin
    Experimental and thermodynamic evaluation of the miscibility gaps in MC carbides for the C-Co-Ti-V-W-Zr system2009In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 33, no 3, p. 530-538Article in journal (Refereed)
    Abstract [en]

    Experimental work on the C-Co-Ti-V-W-Zr system in order to determine the extension of the miscibility gaps in TiC-ZrC and VC-ZrC is presented. Thermodynamic calculations were used to design samples that will form a miscibility gap in equilibrium with liquid, WC and graphite. Samples were produced from powder and sintered for 1 week in controlled atmosphere at 1300, 1410 and 1500 {ring operator}C. From the microstructure it could be concluded that the samples form a miscibility gap in equilibrium with liquid, WC and graphite at all temperatures. The composition of the MCx carbides was measured using an analytic SEM. The new experimental information was used to assess the thermodynamic description for the TiC-ZrC system. This work provides valuable information on the miscibility gap in the C-Co-Ti-V-W-Zr system not published previously.

12 1 - 50 of 73
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