John Ågren

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.

DICTRA, a tool for simulation of diffusional transformations in alloys

In the present paper, a general survey of the diffusion-controlled transformations (DICTRA) software is given. DICTRA is an engineering tool for diffusion simulations in multicomponent alloys. The simulations are based on multicomponent diffusion and thermodynamic data, both obtained by analyzing and assessing experimental information. This allows for many different cases to be studied as soon as the underlying data are available. DICTRA is not a complete simulation tool because only geometries that can be transformed into one space variable can be treated, but many well posed problems of practical interest may be solved. The program contains several different models, which are discussed in the present paper. Each model has its own applications and several examples from recent simulations are given in order to demonstrate the usage of the particular models.

Models for numerical treatment of multicomponent diffusion in simple phases

A general formalism for multicomponent diffusion in simple phases is presented in some detail. The formalism is mainly based on previous work by various authors. The purpose of the present work is to develop the formalism to such an extent that it is suitable for implementation on a computer. Expressions for the multicomponent diffusion‐coefficient matrix is given. The concentration dependence of the kinetic coefficients is discussed in terms of simple models.

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.

COMPUTER-SIMULATION OF DIFFUSION IN MULTIPHASE SYSTEMS

A general model to treat multicomponent diffusion in multiphase dispersions is presented. The model is based on multicomponent diffusion data and basic thermodynamic data and contains no adjustable parameters. No restriction is placed on the number of components or phases that take part in the calculations, as long as the necessary thermodynamic and kinetic data are available. The new model is implemented into the DICTRA software, which makes use of THERMO-CALC to handle the thermodynamics. The model is applied to carburization of Ni alloys and heat treatment of welded joints between dissimilar materials. In both cases, the diffusion is accompanied by carbide formation or dissolution. A good agreement between experiments and calculations is found, despite the fact that no adjustable parameters are needed.

A thermodynamic analysis of the Fe−C and Fe−N phase diagrams

The experimental information on the Fe−C and Fe−N phase diagrams are evaluated in order to be able to recalculate the phase diagrams in close agreement with the experimental information available. Analytical expressions for the Gibbs energy of pure iron in the bcc and liquid states relative to the fcc state have been obtained by means of power series expansions. A set of parameters describing the Gibbs energy of the individual phases is presented.

Phase-field simulations of non-isothermal binary alloy solidification

A phase-field method for two-dimensional simulations of binary alloy solidification is studied. Phase-field equations that involve both temperature and solute redistribution are formulated. The equations are solved using the finite element method with triangular elements on unstructured meshes, which are adapted to the solution. Dendritic growth into a supersaturated melt is simulated for two temperature regimes: (a) the temperature is prescribed on the boundary of the computational domain; and (b) the heat is extracted through the domain boundary at a constant rate. In the former regime the solute redistribution is compared with the one given by an isothermal model. In the latter case the influence of the size of the computational domain and of the heat extraction rate on dendritic structure is investigated. It is shown that at high cooling rates the supersaturation is replaced by thermal undercooling as the driving force for growth.

Numerical treatment of diffusional reactions in multicomponent alloys

Abstract This report describes a numerical method to treat diffusional reactions in alloys where a thermodynamic description, complete enough to represent phase equilibria, as well as diffusion coefficients is available. The method combines a rigorous treatment of the thermodynamic equilibrium locally at a moving phase interface with an ambitious treatment of the diffusion inside the one-phase regions. The method contains no formal restrictions on the number of components. Different kinds of phases, substitutional and interstitial solutions and phases, with stoichiometrie constraints, e.g. carbides and nitrides, can be handled. The implementation on computer is discussed in several appendices.

The phase-field approach and solute drag modeling of the transition to massive γ → α transformation in binary Fe-C alloys

The transition between diffusion controlled and massive transformation gamma --> alpha in Fe-C alloys is investigated by means of phase-field simulations and thermodynamic functions assessed by the ...

σ-PHASE PRECIPITATION IN STABILIZED AUSTENITIC STAINLESS STEELS

Experimental observations of sigma-phase precipitation in two stabilized austenitic stainless steers, AISI 321 and AISI 347, aged up to 80,000 h at temperatures between 500 and 800 degrees C, are c ...