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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    KTH, Superseded Departments, Materials Science and Engineering.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. Abe, T.
    et al.
    Sundman, Bo
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Onodera, H.
    Thermodynamic assessment of the Cu-Pt system2006In: Journal of Phase Equilibria and Diffusion, ISSN 1547-7037, Vol. 27, no 1, p. 5-13Article in journal (Refereed)
    Abstract [en]

    A CALPHAD assessment of the Cu-Pt system has been carried out. Two and four sublattice models were applied to describe the Gibbs free energies of ordered phases where the contribution of SRO is taken explicitly into account through the reciprocal parameters. The disordered fcc A1 and liquid phases were treated as substitutional solutions. A consistent set of parameters for the phases in the Cu-Pt system as obtained, and those parameters can satisfactorily reproduce the experimental phase equilibria and thermodynamic properties, such as enthalpies, activity of Cu, and long-range order parameters.

  • 3. Ahlen, N.
    et al.
    Johnsson, M.
    Larsson, A. K.
    Sundman, Bo
    KTH, Superseded Departments, Materials Science and Engineering.
    On the carbothermal vapour-liquid-solid (VLS) mechanism for TaC, TiC, and TaxTi1-xC whisker growth2000In: Journal of the European Ceramic Society, ISSN 0955-2219, E-ISSN 1873-619X, Vol. 20, no 14-15, p. 2607-2618Article in journal (Refereed)
    Abstract [en]

    The growth of TaC, TiC and TaxTi1-xC whiskers has been studied in some detail. The whiskers were synthesised via a vapour-liquid-solid (VLS) growth mechanism in the temperature range 1220-1400 degreesC. The starting materials were Ta2O5, TiO2, C, NaCl, and a catalyst metal (Ni, Co, Fe, and Cu were tested). The main reaction during synthesis was a carbothermal reduction of Ta2O5 and TiO2, and NaCl was added to form the oxochlorides and chlorides of Ta and Ti that account for the transport to the catalyst metal. The syntheses were made in a protecting Ar atmosphere. From experiments interrupted after different times at the synthesis temperature it is clear that sodium tantalates form as intermediate products, whereas sodium titanates cannot be identified. Only metals that are able to dissolve the elements building up the whiskers work as catalysts. Whisker growth starts either from a catalyst droplet in contact with carbon or from an oxide particle in contact with both catalyst metal and carbon. For TaC and TaxTi1-xC the only growth direction observed is [100], while TiC may grow either along [100] or along [111].

  • 4. 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.

  • 5. 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)
  • 6.
    Baykov, Vitaly
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Jerlerud Perez, Rosa
    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.
    Sundman, Bo
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Johansson, Börje
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Applied Material Physics.
    Structural stability of intermetallic phases in the Zr-Sn system2006In: Scripta Materialia, ISSN 1359-6462, E-ISSN 1872-8456, Vol. 55, no 5, p. 485-488Article in journal (Refereed)
    Abstract [en]

    A thermodynamic description of the intermetallic compounds in the Zr-Sn binary system has been obtained using total energy calculations by means of the Vienna ab initio simulation package. Our calculations show that hexagonal compounds Zr5Sn4 and Zr5Sn3 are the most stable phases in the Zr-Sn binary system. Their high stability is found to be due to hybridization of the Sn 5p with Zr 4d electronic states. Based on the calculated energies, the conclusion is made that Zr substitution on the Sri sites takes place in the Zr4Sn phase, which accounts for the unusual stoichiometry of this Cr3Si structure type compound.

  • 7.
    Bratberg, Johan
    et al.
    Swed. Institute for Metals Research.
    Sundman, Bo
    KTH, Superseded Departments, Materials Science and Engineering.
    A thermodynamic assessment of the Co-V system2003In: Journal of phase equilibria (Print), ISSN 1054-9714, E-ISSN 1544-1032, Vol. 24, no 6, p. 495-503Article in journal (Refereed)
    Abstract [en]

    A thermodynamic evaluation of the binary Co-V system has been done using experimental thermochemical and phase diagram data. A consistent thermodynamic description, using a Redlich-Kister model for solution phases and sublattice models for the intermetallics, was obtained, and it agreed well with the critically evaluated experimental data. The model for the solid phases accounts for the magnetic contribution to the Gibbs energy. The addition of a composition dependent magnetic term also led to the prediction of an fcc-Co miscibility gap. The model parameters have been determined using a computerized optimization technique. Several diagrams and tables concerning phase equilibria are presented.

  • 8. Chen, Q
    et al.
    Engstrom, A
    Höglund, Lars
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Strandlund, Henrik
    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.
    Thermo-Calc program interfaces and their applications - Direct insertion of thermodynamic and kinetic data into modeling of materials processing, structure, and property2005In: PRICM 5: THE FIFTH PACIFIC RIM INTERNATIONAL CONFERENCE ON ADVANCED MATERIALS AND PROCESSING, PTS 1-5 / [ed] Zhong, ZY; Saka, H; Kim, TH; Holm, EA; Han, YF; Xie, XS, ZURICH-UETIKON: TRANS TECH PUBLICATIONS LTD , 2005, Vol. 475-479, p. 3145-3148Conference paper (Refereed)
    Abstract [en]

    Thermodynamic and kinetic data are generally essential for quantitative modeling of materials processing, structure, and property. Thermo-Calc program interfaces, including TQ, TC-API, and TC MATLAB Toolbox, provides a hierarchy of APIs for application programmers to access thermodynamic and kinetic data via the kernel of Thermo-Calc and DICTRA, the most widely used software and database system for multi-component phase equilibrium and phase transformation calculations. With these program interfaces, variation of thermodynamic and kinetic properties can be directly obtained in real time as the local temperature, pressure, or composition changes. The structure and usage of the Thermo-Calc program interfaces will be introduced in this article. Successful application examples will be illustrated.

  • 9. Chen, Q.
    et al.
    Engström, A.
    Lu, X. -G
    Sundman, Bo
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Thermodynamic calculation and kinetic simulation related to solidification process2006In: Modeling of Casting, Welding and Advanced Solidification Processes - XI, 2006, p. 529-536Conference paper (Refereed)
    Abstract [en]

    This paper presents a brief review and some new results of the thermodynamic calculation and kinetic simulation related to the micro-modelling of solidification processes by using ThermoCalc and DICTRA. Emphasis is given on a partial-equilibrium approach developed as a modification of the Scheil-Gulliver non-equilibrium approximation to treat effectively the back diffusion of fast diffusing elements in solid phases. We start with a DICTRA simulation and successfully explain why the P peak drifts away from those of Mn and Si in the experimentally observed composition profiles of a carbon steel. Then, for this steel and other 16 carbon and low alloy steels, we perform both non-equilibrium and partial-equilibrium solidification calculations and demonstrate the significant improvement of the partial-equilibrium approach by comparing the freezing range results with those from either DICTRA simulations or experimental observations.

  • 10. Chen, Q.
    et al.
    Sundman, Bo
    KTH, Superseded Departments, Materials Science and Engineering.
    Calculation of Debye temperature for crystalline structures - A case study on Ti, Zr, and Hf2001In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 49, no 6, p. 947-961Article in journal (Refereed)
    Abstract [en]

    The methods to calculate the Debye temperature from elastic moduli have been reviewed. The approximation approach due to Moruzzi e al was critically examined by considering experimental elastic constant data for all the cubic elements. It was found that many cubic elements are exceptions with regard to the assumed constant scaling factor for the expression of the average sound velocity in terms of the bulk modulus, and consequently the Debye temperature of a cubic element must be calculated from the knowledge of all the elastic constants of the system. On the other hand, a fairly constant scaling factor has been found to exist fur the hexagonal elements. Through the study of experimental data, some empirical relationships have been observed between the high temperature entropy-Debye temperature theta (D)(0) and the low temperature limit of the Debye temperature theta (D)(-3). For those structures that are dynamically unstable at low temperatures, we proposed a way to obtain their theta (D)(0) from the calculated isotropic bulk moduli. The methods have been applied to calculate the Debye temperatures of hcp, bcc, and fee Ti, Zr, and Hf from their elastic moduli derived from ah initio calculations. The calculated results agree very well with the experimental data.

  • 11. Chen, Q.
    et al.
    Sundman, Bo
    KTH, Superseded Departments, Materials Science and Engineering.
    Computation of partial equilibrium solidification with complete interstitial and negligible substitutional solute back diffusion2002In: Materials transactions, ISSN 1345-9678, E-ISSN 1347-5320, Vol. 43, no 3, p. 551-559Article in journal (Refereed)
    Abstract [en]

    A simple numerical scheme is presented to simulate partial equilibrium solidification with complete interstitial and negligible substitutional solute back diffusion in multi-component and multi-phase systems. Based on this scheme, a computing tool capable of using Thermo-Calc databases directly has been developed for the estimation of solidification behavior of steels and other interstitial-containing alloys. Agreements between calculated and experimental as well as DICTRA results have been obtained on the microsegregation, fraction of eutectic, and freezing range of several steels, This suggests that the partial equilibrium assumption and proposed numerical scheme are reasonable and satisfactory, and confirms that the carbon back diffusion plays a very important role in the solidification of steels.

  • 12. 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.

  • 13. Dupin, N.
    et al.
    Fries, S. G.
    Joubert, J. M.
    Sundman, Bo
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Sluiter, M. H. F.
    Kawazoe, Y.
    Pasturel, A.
    Using first-principles results to calculate finite-temperature thermodynamic properties of the Nb-Ni mu phase in the Bragg-Williams approximation2006In: Philosophical Magazine, ISSN 1478-6435, E-ISSN 1478-6443, Vol. 86, no 12, p. 1631-1641Article in journal (Refereed)
    Abstract [en]

    Results of first-principles (FP) total energy calculations for 32 different configurations of the mu phase in the binary system Nb-Ni are used in the compound energy formalism (CEF) to model finite-temperature thermodynamic properties. A comparison with Cluster Expansion Hamiltonian-Cluster Variation Method (CEH-CVM) calculations indicates that the CEF describes temperature-dependent site occupancies as well as the CEH-CVM within the temperature range of interest for applications. This suggests that the Bragg-Williams-Gorsky approximation (BWGA) used in the CEF is sufficient to describe site occupancies and thermodynamics of the mu phase. A phase diagram is calculated using the mu phase description derived in the present work together with a previous Calphad description for the other phases of this system. The FP-CEF approach significantly improves the description of the thermodynamic properties as a function of composition compared to the Calphad procedure generally used up to now.

  • 14. Dupin, N.
    et al.
    Sundman, Bo
    KTH, Superseded Departments, Materials Science and Engineering.
    A thermodynamic database for Ni-base superalloys2001In: Scandinavian journal of metallurgy, ISSN 0371-0459, E-ISSN 1600-0692, Vol. 30, no 3, p. 184-192Article in journal (Refereed)
    Abstract [en]

    A thermodynamic database has been developed for Ni-base superalloys. Following the CALPHAD procedure, it is based on the assessment of thermodynamic behaviour of the relevant constituting sub-systems of the complex system of interest. The current database contains 7 elements: Al, Co, Cr, Ni, Ti, W, Re. The thermodynamics of the gamma and gamma' phases are modelled with a single Gibbs energy function taking into account the crystallographic relation between these two phases. The formalism of the thermodynamic models used is briefly introduced. A few phase diagrams calculated with the current database in assessed binary and ternary systems are presented. Some experiments available in higher order systems are compared with the results of calculations with the current database. The ability of extrapolation of the database is verified for solid state equilibria as well as for solidification behaviour (liquidus temperature and partition ratios). The introduction of Mo and Ta to the current database is in progress. Other elements (Nb, Fe, Zr, Hf, C, B, . . .) are planed to be introduced.

  • 15.
    Dupin, Nathalie
    et al.
    Calcul Thermodynam, F-63670 Orcet, France..
    Kattner, Ursula R.
    NIST, Gaithersburg, MD 20899 USA..
    Sundman, Bo
    KTH.
    Palumbo, Mauro
    COMPUMAT, I-10095 Grugliasco, TO, Italy..
    Fries, Suzana G.
    Ruhr Univ Bochum, D-44801 Bochum, Germany..
    Implementation of an Effective Bond Energy Formalism in the Multicomponent Calphad Approach2018In: Journal of research of the National Institute of Standards and Technology, ISSN 1044-677X, E-ISSN 2165-7254, Vol. 123, article id 020Article in journal (Refereed)
    Abstract [en]

    Most models currently used for complex phases in the calculation of phase diagrams (Calphad) method are based on the compound energy formalism. The way this formalism is presently used, however, is prone to poor extrapolation behavior in higher-order systems, especially when treating phases with complex crystal structures. In this paper, a partition of the Gibbs energy into effective bond energies, without changing its configurational entropy expression, is proposed, thereby remarkably improving the extrapolation behavior. The proposed model allows the use of as many sublattices as there are occupied Wyckoff sites and has great potential for reducing the number of necessary parameters, thus allowing shorter computational time. Examples for face centered cubic (fcc) ordering and the sigma phase are given.

  • 16. Fernandes, P. B.
    et al.
    Coelho, G. C.
    Ferreira, F.
    Nunes, C. A.
    Sundman, Bo
    KTH, Superseded Departments, Materials Science and Engineering.
    Thermodynamic modeling of the Nb-Si system2002In: Intermetallics (Barking), ISSN 0966-9795, E-ISSN 1879-0216, Vol. 10, no 10, p. 993-999Article in journal (Refereed)
    Abstract [en]

    Optimized coefficients of the Gibbs free energy expression for each stable phase of the binary Nb-Si have been obtained, using the Thermo-Calc program for this purpose. The Nb3Si, alphaNb(5)Si(3), NbSi2 and Diamond (Si) have been modeled as stoichiometric phases and the liquid L, BCC (Nb) and the betaNb(5)Si(3) phases as solutions, with the excess term described using the Redlich-Kister formalism. The Si solubility in the betaNb(5)Si(3) phase has been modeled according to two possibilities: (i) Si substituting for Nb and (ii) vacancies in the Nb positions. The calculated diagrams compare well with the experimental information taken from the literature.

  • 17. 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.

  • 18. Fries, S. G.
    et al.
    Sundman, Bo
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Development of multicomponent thermodynamic databases for use in process modelling and simulations2005In: Journal of Physics and Chemistry of Solids, ISSN 0022-3697, E-ISSN 1879-2553, Vol. 66, no 04-feb, p. 226-230Article in journal (Refereed)
    Abstract [en]

    Thermodynamic databases describe the Gibbs energy of each phase in a given system, as a function of temperature, pressure and its constitution taking into account various properties like crystal structure, solubility of different element on different types of sites, magnetism, etc. The energetics from first principles calculations, crystallographic information and atomistic modelling results can be incorporated into the parametric Gibbs energies models in order to construct thermodynamic databases, being, however, experimental data obtained, e.g. from calorimetry, emf, thermal analyse, metallography, etc. which provides enthalpies, chemical potentials, phase boundary, etc. the basic type of information used. These thermodynamic databases can be an intermediate level between atomistic and macroscopic modelling, bridging scales and theoretical and empirical modelling. Thermodynamic databases provide consistent and accurate information for understanding the macroscopic behaviour of processes and transformations in real materials. This is essential to make realistic modelling and simulations for improving the production as well as teaching of phenomena which are too complex to be modelled directly from a pure theoretical approach. The majority of the phases present in materials for technical applications are solution phases, being its modelling the most complex part of the development of databases. In this paper, we show some features of the making of these databases, as well as the feedback obtained from their different applications and how that results in improvements.

  • 19. Fries, S. G.
    et al.
    Sundman, Bo
    KTH, Superseded Departments, Materials Science and Engineering.
    Using Re-W sigma-phase first-principles results in the Bragg-Williams approximation to calculate finite-temperature thermodynamic properties2002In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 66, no 1Article in journal (Refereed)
    Abstract [en]

    First-principles (FP) calculations of total energies for 32 different configurations of Re-W sigma phase were used to fit a compound energy formalism (CEF) Hamiltonian that was used in phenomenological Calphad method calculations to model finite-temperatures thermodynamic properties. A comparison with Connolly-Williams method-cluster variation method (CWM-CVM) calculations indicates that the first-principles CEF (FP-CEF) describes temperature-dependent site occupancies as well as the CWM-CVM approximation within the temperature range of interest for applications. This result seems to indicate that the Bragg-Williams approximation (BWA) is sufficient to describe the Re-W sigma phase. A complete Re-W phase diagram is calculated using the FP-CEF Hamiltonian for the sigma phase. Differences between the phase diagrams, and single phase properties calculated both with, and without, the first-principles results are striking. It is expected that using the FP-CEF sigma-phase description that takes into account the first-principles energetics will yield more reliable extrapolations into higher-order system.

  • 20. Frisk, K.
    et al.
    Dumitrescu, L.
    Ekroth, M.
    Jansson, B.
    Kruse, O.
    Sundman, Bo
    KTH, Superseded Departments, Materials Science and Engineering.
    Development of a database for cemented carbides: Thermodynamic modeling and experiments2001In: Journal of phase equilibria (Print), ISSN 1054-9714, E-ISSN 1544-1032, Vol. 22, no 6, p. 645-655Article in journal (Refereed)
    Abstract [en]

    A new database, for thermodynamic information for cemented carbides has been developed. A full description of the alloy system C-Co-N-Nb-Ta-Ti-W is presented. The work has involved both thermodynamic evaluations of lower order systems and experimental investigations. Full new assessments of the quaternary Ti-W-C-N, Ta-W-C-N, and Nb-W-C-N systems have been performed, including tests of the influence of model parameters on miscibility gaps in higher order systems. A new improved description of the Co-W-C system based on new experiments is used in the present work. The main results of the experimental work are measurements of the composition of the cubic carbide in selected equilibria; measurements of the temperatures of the liq + fcc + WC + gr. and liq + fcc + WC + M6C equilibria in the Co-W-C and Co-W-X-C (X = Ti, Ta, Nb) systems; and measurements of the solubility of Ti, Ta, and Nb in liquid in multicomponent alloys. The results of the assessments have been implemented into a new database. The database has successfully been used in a parallel project to simulate the formation of gamma -phase free zones in cemented carbides. A few other applications of industrial relevance are presented.

  • 21. Gueneau, C.
    et al.
    Baichi, M.
    Labroche, D.
    Chatillon, C.
    Sundman, Bo
    KTH, Superseded Departments, Materials Science and Engineering.
    Thermodynamic assessment of the uranium-oxygen system2002In: Journal of Nuclear Materials, ISSN 0022-3115, E-ISSN 1873-4820, Vol. 304, no 03-feb, p. 161-175Article in journal (Refereed)
    Abstract [en]

    A thermodynamic assessment of the uranium-oxygen system is presented. A consistent set of experimental data is selected among the numerous data in the literature on the phase diagram and oxygen chemical potential. The thermodynamic properties of the phases are described using the compound energy model with ionic constituents for the solids and an ionic two-sublattice model for the liquid. For the uranium dioxide, the structure is described using three sublattices, one for the cations U3+, U4+ and U6+, one for the normal site of oxygen ions, and one for the interstitial oxygen ions. Vacancies are included in both oxygen sublattices. In this first approach, the homogeneity ranges of the U4O9-y, and U3O8-y compounds are not represented. A set of consistent model parameters that describes both the phase diagram and the oxygen chemical potential data in the whole composition range is thus obtained. The description of this basic binary system will be used to calculate higher order systems such as O-U-Zr and Fe-O-U which are important for simulating severe nuclear accidents.

  • 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.
    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.

  • 25.
    Jerlerud Pérez, Rosa
    et al.
    KTH, Superseded Departments, Materials Science and Engineering.
    Sundman, Bo
    KTH, Superseded Departments, Materials Science and Engineering.
    Thermodynamic assessment of the Mo–Zr binary phase diagram2003In: Calphad, ISSN 0364-5916, Vol. 27, no 3, p. 253-262Article in journal (Refereed)
    Abstract [en]

    The Mo-Zr binary system has been optimized using the available experimental data on the phase diagram and two estimated enthalpy values, one for the formation of the Laves phase and one for the mixing of the liquid phase. During the optimizing procedure all the experimental data were optimized simultaneously. The excess Gibbs energy of the stable phases, liquid, body centred cubic (bcc), hexagonal closed packed (hcp) and Laves(-)c15, has been obtained. The solution phases: liquid, bcc and hcp, have been treated as substitutional solutions and the intermetallic phase Laves(-)c15 has been modelled using the sublattice model. A set of model parameters is given.

  • 26.
    Jerlerud Pérez, Rosa
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Tofflon-Masclet, C.
    Sundman, Bo
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Jourbert, J.-M.
    The Sn-Zr binary system: experiments and thermodynamic assessmentArticle in journal (Other academic)
  • 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. 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)
  • 29.
    Kjellqvist, Lina
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Selleby, Malin
    Sundman, Bo
    Thermodynamic assessments of the Al2O3-TiO2, CaO-TiO2, FeO-TiO2, Fe2O3-TiO2, MgO-TiO2 and MnO-TiO2 systemsManuscript (Other academic)
  • 30.
    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.

  • 31.
    Kjellqvist, Lina
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Sundman, Bo
    Simulation of decarburization of a high alloyed liquid steel using a reactor model within Thermo-CalcManuscript (Other academic)
  • 32.
    Korzhavyi, Pavel A.
    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.
    Selleby, Malin
    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.
    Atomic, electronic, and magnetic structure of iron-based sigma-phases2005In: Integrative and Interdisciplinary Aspects of Intermetallics / [ed] MIlls, MJ; Inui, H; Clemens, H; Fu, CL, WARRENDALE: MATERIALS RESEARCH SOCIETY , 2005, Vol. 842, p. 517-522Conference paper (Refereed)
    Abstract [en]

    A combination of ab initio total energy calculations with Calphad approach is applied to model the site occupancy and thermodynamic properties of the Fe-Cr, Co-Cr, Fe-V, and Fe-Mo binary sigma-phases as a function of composition and temperature. For each binary sigma-phase the parameters of the model are the ab initio calculated total energies of so-called end-member compounds, which represent all the 2(5)=32 variants of complete occupancy of each of the five crystallographically inequivalent sites by one or the other alloy component, The paramagnetic state of the sigma-phases has been taken into account within the disordered local moment approach. The Fe and Co atoms are found to retain high spin moments when they occupy high-coordination-number sites in the structure. Using our model we were able to reproduce the experimentally observed site occupancy in the FeCr sigma-phase. The calculated site occupancies in the Co-Cr, Fe-V, and Fe-Mo sigma-phases are also presented and discussed.

  • 33. 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.

  • 34. Lee, Byeong-Joo
    et al.
    Sundman, Bo
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Kim, Sung Il
    Chin, Kwang-Geun
    Thermodynamic calculations on the stability of Cu2S in low carbon steels2007In: ISIJ International, ISSN 0915-1559, E-ISSN 1347-5460, Vol. 47, no 1, p. 163-171Article in journal (Refereed)
    Abstract [en]

    Thermodynamic stability of Cu2S sulfide in low carbon steels has been investigated using a CALPHAD type thermodynamic calculation method. Thermodynamic properties of the Cu-S binary and Fe-Cu-S ternary systems were critically assessed. By combining the newly assessed thermodynamic parameters to an existing thermodynamic database for steels, a thermodynamic description for low carbon steels involving sulfur and Cu could be obtained and be used to calculate phase equilibria and thermodynamic stability of precipitating phases such as AlN, MnS, and Cu2S. It was predicted that the Cu2S sulfide often observed in low carbon steels is actually a thermodynamically unstable phase and can precipitate when thermodynamic equilibrium state is not reached during steel making processes. Probable reasons and conditions for the formation of this unstable phase are discussed.

  • 35.
    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.

  • 36.
    Lu, Xiao-Gang
    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.
    Calculations of thermophysical properties of cubic carbides and nitrides using Debye-Grüneisen model2007In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 55, no 4, p. 1215-1226Article in journal (Refereed)
    Abstract [en]

    The thermal expansivities and heat capacities of NIX (M = Ti, Zr, Hf, V, Nb, Ta; X = C, N) carbides and nitrides with NaCl structure were calculated using the Debye-Gruneisen model combined with ab initio calculations. Two different approximations for the Gruneisen parameter gamma were used in the Debye-Gruneisen model, i.e. the expressions proposed by Slater and by Dugdale and MacDonald. The thermal electronic contribution was evaluated from ab initio calculations of the electronic density of states. The calculated results were compared with CALPHAD assessments and experimental data. It was found that the calculations using the Dugdale-MacDonald gamma can account for most of the experimental data. By fitting experimental heat capacity and thermal expansivity data below the Debye temperatures, an estimation of Poisson's ratio was obtained and Young's and shear moduli were evaluated. In order to reach a reasonable agreement with experimental data, it was necessary to use the logarithmic averaged mass of the constituent atoms. The agreements between the calculated and the experimental values for the bulk and Young's moduli are generally better than the agreement for shear modulus.

  • 37.
    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.

  • 38.
    Lu, Xiao-Gang
    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.
    Theoretical modeling of molar volume and thermal expansion2005In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 53, no 8, p. 2259-2272Article in journal (Refereed)
    Abstract [en]

    The molar volumes and thermal expansions of transition cubic metals were studied by means of the Calphad approach and the Debye-Gruneisen model. Experimental data were collected and assessed using Calphad procedures, and consistent results were obtained which give the best description of all experimental data. In order to put the prediction of the thermodynamic properties of metastable phases on a sound physical basis, the Debye-Gruneisen model was chosen to account for the vibrational contribution and calculate the coefficients of linear thermal expansion (CLEs) of stable cubic metals. Two approximations for Gruneisen parameter gamma, i.e. Slater ' s and Dugdale and MacDonald ' s expressions were adopted. A modified calculation scheme, first proposed by Wang et al., was derived in a straightforward way and used to evaluate the Debye temperature from ab initio electronic total-energy calculations at T = 0 K. The thermal electronic contribution to CLE was also evaluated from the electronic density of states. The calculated total CLEs were compared with those from the Calphad assessments. A satisfactory agreement is reached.

  • 39.
    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.

  • 40.
    Mao, Huahai
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Fabrichnaya, Olga
    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 assessment of the MgO-AL(2)O(3)-SiO2 system2005In: Journal of Materials Research, ISSN 0884-2914, E-ISSN 2044-5326, Vol. 20, no 4, p. 975-986Article in journal (Refereed)
    Abstract [en]

    Thermodynamic properties of the phases in the MgO-Al2O3-SiO2 system were assessed, resulting in a set of self-consistent thermodynamic data. The two ternary Compounds, cordierite and sapphirine, were optimized from subsolidus reactions. The liquid phase was described by the ionic two-sublattice model with a new species AlO2-1 yielding the formula (Al+3,Mg+2)(p)(AlO2-1 O-2,SiO4-4,SiO2o)(Q). Projection of the liquidus surface was calculated. Various isothermal and isoplethal sections were compared with the experimental data.

  • 41.
    Mao, Huahai
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Hillert, Mats
    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.
    Sundman, Bo
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Thermodynamic assessment of the CaO-Al2O3-SiO2 system2006In: Journal of The American Ceramic Society, ISSN 0002-7820, E-ISSN 1551-2916, Vol. 89, no 1, p. 298-308Article in journal (Refereed)
    Abstract [en]

    The CaO-Al2O3-SiO2 system has been assessed with the CALP-HAD technique, based on recent assessments of its binary systems. A new species AlO2-1 was introduced for modeling liquid Al2O3. The ternary liquid phase was described using the ionic two-sublattice model as (Al+3, Ca+2)(p) (AlO2-1, O-2, SiO4-4 SiO20)(Q). The available experimental data were critically examined and a self-consistent set of thermodynamic descriptions was obtained. Various phase diagrams and property diagrams, including isothermal sections, isoactivity lines, and a projection of the liquidus surface, are presented. Information on viscosity seems to support the use of the AlO2-1 species.

  • 42.
    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.

  • 43.
    Mao, Huahai
    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.
    Phase equilibria and thermodynamics in the Al(2)O(3)-SiO(2) system: Modeling of mullite and liquid2005In: Journal of The American Ceramic Society, ISSN 0002-7820, E-ISSN 1551-2916, Vol. 88, no 9, p. 2544-2551Article in journal (Refereed)
    Abstract [en]

    The AI(2)O(3)-SiO2 system has been reassessed using a solution model for mullite extending from sillimanite to a hypothetical state of alumina. The property of sillimanite, to be used to describe one of the end-members, was extracted from an analysis of the T-P phase diagram for AI(2)SiO(5) polymorphs. It was possible to represent the information on the range of stability of mullite, including some showing that mullite extends to higher SiO2 contents than represented by the composition of 3:2 mullite. An attempt was made to model the liquid with the ionic two-sublattice model using a new species AIO(2)(-1). The pressure dependence of AI(2)SiO(5) polymorphs was optimized by a new model recently implemented in Thermo-Cale.

  • 44.
    Mao, Huahai
    et al.
    KTH, Superseded Departments, Materials Science and Engineering.
    Sundman, Bo
    KTH, Superseded Departments, Materials Science and Engineering.
    Wang, Z. W.
    Saxena, S. K.
    Volumetric properties and phase relations of silica - thermodynamic assessment2001In: Journal of Alloys and Compounds, ISSN 0925-8388, E-ISSN 1873-4669, Vol. 327, no 1-2, p. 253-262Article in journal (Refereed)
    Abstract [en]

    Taking into account various available experimental data, an improved internally consistent data set for the SiO2 system is obtained by thermodynamic assessment. The volumetric properties for SiO2 polymorphs are reassessed using the CALPHAD method. A two-coefficient expression is used to describe the thermal expansion and bulk modulus. For liquid phase, one equation is achieved in the temperature range of 298-4000 K either for thermal expansion or for bulk modulus. Phase diagrams have been calculated up to 40 GPa. It has been concluded that, in the pressure range lower than 20 GPa, there is no significant difference between the phase diagrams calculated by the Birch-Murnaghan equation of state (EOS) and by Murnaghan EOS.

  • 45. Markström, Andreas
    et al.
    Sundman, Bo
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Frisk, Karin
    A revised thermodynamic description of the Co-W-C system2005In: Journal of Phase Equilibria and Diffusion, ISSN 1547-7037, Vol. 26, no 2, p. 152-160Article in journal (Refereed)
    Abstract [en]

     A thermodynamic reassessment of the Co-W-C system is presented. New information on the liquid (L)+face-centered cubic (fcc)+graphite+WC and L+fcc+WC+M6C equilibria has recently been published. Because these equilibria are very important for extrapolation to higher-order systems, the ternary system has been revised. A revision of the Co-W system also has been performed.

  • 46. Odqvist, J.
    et al.
    Sundman, Bo
    KTH, Superseded Departments, Materials Science and Engineering.
    Ågren, John
    KTH, Superseded Departments, Metallurgy.
    A general method for calculating deviation from local equilibrium at phase interfaces2003In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 51, no 4, p. 1035-1043Article in journal (Refereed)
    Abstract [en]

    A general method to calculate the deviation from local equilibrium at phase interfaces in multicomponent systems is suggested. The deviation is caused by solute drag and finite interfacial mobility. In the limit of low transformation rates the new method degenerates to the well-known local equilibrium condition. The phase interface is divided into three zones, each with a finite thickness. In each zone a variation in thermodynamic properties and diffusional mobilities is assumed.

  • 47. Ohnuma, I.
    et al.
    Enoki, H.
    Ikeda, O.
    Kainuma, R.
    Ohtani, H.
    Sundman, Bo
    KTH, Superseded Departments, Materials Science and Engineering.
    Ishida, K.
    Phase equilibria in the Fe-Co binary system2002In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 50, no 2, p. 379-393Article in journal (Refereed)
    Abstract [en]

    alpha (A2)/gamma (A1) phase equilibria of the Fe-Co system between 400 and 800degreesC were determined by means of lattice parameter measurement using thin film specimens. Bulk specimens were also analyzed to compare the extent of attainment to the equilibrium. The thin film technique was found to be greatly advantageous for obtaining the phase equilibria at lower temperatures where solid-state reactions are too slow to reach the equilibrium state in the conventional methods using bulk specimens. It was confirmed that the alpha + gamma two-phase region extends below the temperature at which the alpha (A2)/alpha' (B2) transus meets the alpha/alpha + gamma boundary. Thermodynamic analysis was also conducted by taking the magnetic and chemical ordering contributions of the B2 structure into account, findings of which confirmed the extension of the alpha + gamma two-phase region below the alpha/alpha' ordering temperature.

  • 48. Ohtani, H.
    et al.
    Matsumoto, S.
    Sundman, Bo
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Sakuma, T.
    Hasebe, M.
    Equilibrium between fluorite and pyrochlore structures in the ZrO2-Nd2O3 system2005In: Materials transactions, ISSN 1345-9678, E-ISSN 1347-5320, Vol. 46, no 6, p. 1167-1174Article in journal (Refereed)
    Abstract [en]

    The phase diagram of the ZrO2-Nd2O3 system has been characterized showing isolated two-phase regions for a cubic fluorite-type ZrO2 solid solution and Nd2Zr2O7 with a pyrochlore-type structure. A thermodynamic analysis was carried out to elucidate the origin of this interesting phase equilibrium. A compound energy model with the formula (Zr4+,Nd3+)(0.5)(Nd3+,Zr4+)(0.5)(O2-,va)(2) was applied to describe the Gibbs energy for these phases in consideration of the ordering of the cation sites in the structure. The ordering arrangement on the anion sites was not taken into account. The Gibbs energy for the liquid was described using an ionic solution model, while the binary compounds, such as tetragonal and monoclinic ZrO2, and cubic and hexagonal Nd2O3, were treated as stoichiometric solid phases. The thermodynamic assessment was based on the experimental phase boundaries as well as the evaluated formation energy for the stoichiometric Nd,2Zr2O7 phase. The phase diagram calculations showed that the peculiar feature of this phase diagram was reproduced well in our work. The results strongly suggest that the two-phase boundaries between the cubic fluorite-type ZrO2 solid solution and the pyrochlore-type structure occur due to the ordering of the Zr4+ and Nd3+ cations.

  • 49. Pecanha, Rockfeller Maciel
    et al.
    Ferreira, Flavio
    Coelho, Gilberto Carvalho
    Nunes, Carlos Angelo
    Sundman, Bo
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Computational Thermodynamics.
    Thermodynamic modeling of the Nb-B system2007In: Intermetallics (Barking), ISSN 0966-9795, E-ISSN 1879-0216, Vol. 15, no 8, p. 999-1005Article in journal (Refereed)
    Abstract [en]

    In the present work, the Nb-B binary system was thermodynamically optimized. The stable phases in this system are BCC (niobium), Nb3B2, NbB, Nb3B4, Nb5B6, NbB2, B (boron) and liquid L. The borides Nb3B2, NbB, Nb3B4 and Nb5B6 and the B (boron) were modeled as stoichiometric phases and the liquid L, BCC (niobium) and NbB2 as solutions, using the sublattices model, with their excess terms described by the Redlich-Kister polynomials. The Gibbs energy coefficients were optimized based on the experimental values of enthalpy of formation, low temperature specific heat, liquidus temperatures and temperatures of invariant transformations. The calculated Nb-B diagram reproduces well the experimental values from the literature.

  • 50. Prins, S. N.
    et al.
    Cornish, L. A.
    Stumpf, W. E.
    Sundman, Bo
    KTH, Superseded Departments, Materials Science and Engineering.
    Thermodynamic assessment of the Al-Ru system2003In: Calphad, ISSN 0364-5916, E-ISSN 1873-2984, Vol. 27, no 1, p. 79-90Article in journal (Refereed)
    Abstract [en]

    The CALPHAD technique was used to calculate the Al-Ru binary phase diagram. The RuAl (B2) phase was described with the sublattice model (SL), also designated Compound Energy Formalism (CEF), as well as the Modified Sublattice Formalism (MSL), which describes the order disorder transformation with one Gibbs energy function. The RuAl6 phase was described as a stoichiometric phase and the remaining intermetallic phases (Ru4Al13, RuAl2 and Ru2Al3) were modelled with the sublattice model. The solubility of Ru in (Al) was considered negligible. Good agreement was obtained between the calculated and the experimental phase diagrams.

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