Bo Sundman

The Thermo-Calc databank system☆

Abstract A description is given of Thermo-Calc, a databank for thermochemistry and metallurgy developed at the division of Physical Metallurgy of the Royal Institute of Technology (KTH) in Stockholm. Using the facilities of Thermo-Calc one can tabulate thermodynamic data, calculate the heat change of chemical reactions and their driving force, evaluate equilibria for chemical systems and phase transformations and calculate various types of multicomponent phase diagrams by an automatic mapping procedure. The databank is quite general and can be applied to all systems where data assessed by a model implemented in the databank are available. The assessment procedure necessary to develop and extend the the databank is discussed. A brief description of the modules of Thermo-Calc is given and two examples are included which demonstrate how flexibly the calculations can be made. These examples will also show that the system is quite easy to use and that there are extensive on-line help facilities.

THERMO-CALC & DICTRA, computational tools for materials science

Software for calculation of phase diagrams and thermodynamic properties have been developed since the 1970s. 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.

A regular solution model for phases with several components and sublattices, suitable for computer applications

Abstract A thermodynamic model, based on the regular solution approximation is presented and a formalism, suitable for phases with an arbitrary number of sublattices, is developed. A new concept, the component array, is introduced in order to simplify the analytical expressions for the integral Gibbs energy. The definition of the component array allows a straightforward procedure for the derivation of expressions describing the Gibbs energy for any kind of phase. Expressions for the partial Gibbs energy are derived. The implementation of the model on a computer is discussed.

Thermodynamic assessment of the AlNi system

The sub-lattice model is used to describe the thermodynamic behaviour of the ordered phases existing in the AlNi system. The model parameters are derived from an optimisation procedure using all available experimental data. The order-disorder transformation f.c.c.-Al:Ll2 phase is modelled using either two or four sub-lattices which are mathematically equivalent.

A two-sublattice model for molten solutions with different tendency for ionization

Different models accounting for the introduction of an excess of cations or anions in an ionic melt are considered. A new model which describes the variation in the thermodynamic properties in a melt as it gradually changes its composition from purely metallic state to complete ionization is developed. The model is based upon Temkin’s expression for the configurational entropy of mixing. Neutral species and hypothetical vacancies with an induced charge are introduced on the anion sublattice. The induced charge is equal to the average valency of the species occupying the cation sublattice. When the tendency of ionization is weak, the model approaches the substitutional model. For binary systems the new model is formally identical to the associate solution model if the associates are defined in such a way that they contain one atom of the electronegative element. For higher-order systems the new model works with a lower number of composition variables and parameters than the associate solution model.

A treatment of the solute drag on moving grain boundaries and phase interfaces in binary alloys

Abstract A previous treatment of the solute drag effect on the movement of grain boundaries and phase interfaces, which was based upon the evaluation of the free-energy dissipation, is developed further. The new treatment becomes identical to the treatments by Cahn and Lucke and Stuwe for grain boundaries in dilute solutions but is not limited to low solute contents, to ideal solutions or to single-phase systems. Some numerical calculations for grain boundaries are presented and the dissipation of free energy in different zones of the interface is discussed. The maximum solute drag, calculated with a variable diffusivity. is always lower than the value found by using any average value of the diffusivity. The simple expression for the estimation of the solute drag, previously given, is approximately correct at constant diffusivity. only. A number of calcultions for diffusionless phase transformations are presented and allow some conclusions regarding the spontaneous start of such a transformation.

Thermodynamic properties of the CrFe system

Abstract A revised thermodynamic assessment of the CrFe system is presented. Some of the major improvements are: Altered composition dependence of the Curie temperature, improved description of the bcc/sigma phase equilibrium and thermodynamic properties of bcc and a lower minimum of the gamma loop. A set of parameters describing the Gibbs energy in each phase is given.

An Assessment of the Fe-C-Si System

Precise knowledge of the Fe-C-Si system has been the subject of numerous previous studies because of the importance of this system for steelmaking processes and cast iron foundry. How-ever, the most recent articles on this subject still reveal uncertainties or insufficient information. The purpose of this work was to assess this system and to give it a precise description, but one which was simple enough for practical applications. An evaluation of the parameters describing the thermodynamic properties of the phases involved in the binary Fe-Si system has been achieved, mainly based on values of the silicon activity in the body-centered cubic (bcc) phase and on knowledge of the phase diagram. The A2-B2 ordering reaction of the bcc phase has been included. It has been shown that this reaction is of paramount importance for the description of the thermodynamic properties of this phase and its field of stability. This preliminary work and previous similar studies of the Fe-C and Si-C systems were used as a base for the evaluation of the ternary stable and metastable Fe-C-Si systems. Optimization of the parameters describing the properties of the phases involved in both of these systems was achieved using experimental thermodynamic data and the critical assessment of the phase diagrams.

A compound-energy model of ordering in a phase with sites of different coordination numbers

Abstract When applied to a phase where all the sites do not have the same coordination number, the bond-energy model gives a term in u AA − u BB , which cannot be assigned a numerical value because the energy of different elements cannot be compared. As an alternative a compound-energy model is now developed from the well-known model for reciprocal systems. It gives a similar result but the u AA − u BB term does not appear. In addition, the new model takes into account two kinds of factors resulting in ordering, those which make different elements prefer different kinds of lattice sites and those which give a preference for unlike neighbors. The ordering in the sigma phase is considered in some detail.

Thermodynamic modeling of ordered phases in the NiAl system

The thermodynamic properties of the ordering in the L12, D513 and B2 phases existing in the AlNi system were described using the sub-lattice model. For the B2 phase, aluminium and nickel are considered to occupy one of the sub-lattices whereas vacancies and nickel occupy the second. For the L12, D513 phases, aluminium and nickel mix on both sub-lattices. When, the phases are disordered the site fractions of the two elements are equal on both sub-lattices. The interaction parameters are evaluated using an assessment procedure taking into account available experimental information on thermochemical properties and phase diagram data. The calculated phase diagram is compared to previously calculated ones using different models.