Björn Jönsson

Computer simulation of multicomponent diffusional transformations in steel

ABSTRACT The thermodynamic and kinetic basis for simulation of multicomponent diffusional transformations is reviewed. The concepts underlying a new program package called DICTRA are described. The new software utilizes a new numerical procedure for solving a system of coupled diffusion equations and is interfaced with the THERMO-CALC system for calculation of local equilibrium at a moving phase interface.

An experimental and theoretical study of cementite dissolution in an Fe-Cr-C alloy

The dissolution of cementite at 910 °C in an Fe-2.06Cr-3.91C (at. pct) alloy is investigated experimentally. The Cr concentration profiles in austenite and cementite are measured by means of the scanning transmission electron microscopy/energy dispersive spectrometry (STEM/EDS) technique at different dissolution times. The measurements show the Cr enrichment in the cementite during the dissolution process. The measurements suggest that the main part of the reaction for this alloy is controlled by Cr diffusion in the cementite or in the austenite matrix. This observation is in agreement with predictions of the local equilibrium hypothesis. The carbide fraction and average particle diameter are evaluated as functions of dissolution time. The Cr enrichment of the cementite results in a supersaturation and a possible decomposition of the cementite. Microstructural evidence for such a decomposition is found by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). A new program package called DICTRA,[11] which is suitable for the simulation of diffusional reactions in multicomponent alloys, has been applied to the present case. The simulation is compared with the experimental data, and a good agreement between the two is found.

Thermodynamic and kinetic aspects of crystallization of supercooled AgCu liquids

Abstract When performing thermodynamic calculations at temperatures outside the temperature range where the liquid is the stable phase and where its properties can be measured, it is important to extrapolate the properties in a reasonable way. Many different methods have been proposed over the years. The methods are based on various approximations on how the difference in heat capacity between the liquid and the solid ΔCPL−S varies with temperature T. The simplest approach is ΔCPL−S = 0 or perhaps a constant value. Both of these approximations have recently been used by Murray and by Hayes et al. in their evaluations of the thermodynamic properties of the AgCu system. As these approximations are known to be less satisfactory for large supercoolings we have re-evaluated the thermodynamic properties of the AgCu system by applying a new model, recently presented by Agren. It is a phenomenological model suitable for the thermodynamic description of a highly undercooled liquid. The new model, previously applied only to pure elements, was extended here to alloy melts. After having established a sound thermodynamic basis of the AgCu system the kinetics of solidification were considered. We calculated the growth rate of a dendritic tip, taking into account the effect of interface kinetics, the Gibbs-Thomson effect and the so-called solute-drag effect. This allowed us to model the transition from diffusion-controlled growth, occurring at low supersaturations, to diffusionless growth, occurring at high supersaturations. It was found that when the ratio between the solute mobility at the interface and the solute diffusivity in the liquid was small the transition occurred close to the so-called T0 line. However, if the ratio was large the transition to diffusionless growth occurred close to the solidus.

The thermo Calc project

Abstract The Thermo Calc project was launched more than a decade ago and is concerned with the development of software and data bases for thermodynamic calculations in non-organic systems. Calculations may be performed for a wide range of materials, for example, metals, ceramics and molten salts as well as aqueous solutions and gas mixtures. The practical use of experimental data produced by thermal analysis or calorimetry is discussed.

On the massive transformation

Abstract The massive transformation γ → α in binary FeC alloys is explored by means of a model taking into account the thermodynamic properties of the α and γ phases. In addition the model takes into account the finite mobility of the phase interface and the solute drag, i.e. the dissipation of the driving force caused by a finite solute gradient over the interphase. It is found that inside a region bounded by the α / α + γ phase boundary of the FeC phase diagram and a critical line below the T 0 line there are two solutions to the growth equations. One solution corresponds to a high growth rate controlled mainly by the finite mobility of the phase interface and corresponding to a weak solute drag. The other solution represents a lower growth rate controlled mainly by a strong solute drag. As the carbon content of the austenite is increased at a constant temperature the two solutions move closer to each other and at a critical composition before the T 0 line is reached they coincide and beyond that no massive transformation is possible. The position of the critical composition depends on L/M, the ratio of the solute diffusivity, inside the interphase, and the phase interface mobility. Inside the α one-phase region there is only one solution corresponding to a high growth rate and a weak solute drag.

A theoretical evaluation of chemical ordering and glass transition in liquid Mg-Sn alloys

The thermochemical properties and experimental phase diagram of the Mg-Sn system are assessed by means of a computer operated method in order to obtain thermodynamic functions for the individual phases. The extrapolation of the properties of the liquid to low temperatures is discussed and a method based on an isentropic temperature (where the liquid and the crystalline phases have the same entropy) at a third of the melting point of the crystalline phase is applied. A new model, which accounts for the tendency for chemical order in the liquid, is applied and excellent agreement with the various kinds of experimental information is obtained. The new thermodynamic description is compared with previous ones based on the associate solution model, and it is concluded that the present analysis is superior because more information has been taken into account. T0, isentropic, and nucleation temperatures are calculated in order to investigate the glass forming ability. For alloys the isentropic temperature may be defined with or without the positional entropy due to chemical disorder. The results are different. An alternative assessment based on a different way of extrapolating the properties of the liquid to low temperatures is found to yield an almost identical result for stable phases and phase equilibria but a very different result for the glass transition. It is thus concluded that it is not possible to extract information for the glass transition from the high-temperature data.

Modelling of crystal growth during rapid solidification

Models for computer simulation of solidification of alloys in two different geometries have been developed. These models allow us to study the roles of crystal nucleation and heat transfer and the effects of different modes of growth on the evolution of the microstructure during solidification. In particular, by applying the powerful and versatile tool comprised of the solute-drag model and the thermodynamic modeling of the alloy system, we are able to predict the formation of a microstructure consisting of alternating layers parallel to the growth front. This type of banded microstructure, experimentally observed in Al-Cu, Al-Fe, and Ag-Cu alloys, has not been satisfactorily explained before.

Modeling of crystal growth during rapid solidification

Models for computer simulation of solidification of alloys in two different geometries have been developed. These models allow us to study the roles of crystal nucleation and heat transfer and the effects of different modes of growth on the evolution of the microstructure during solidification. In particular, by applying the powerful and versatile tool comprised of the solute-drag model and the thermodynamic modeling of the alloy system, we are able to predict the formation of a microstructure consisting of alternating layers parallel to the growth front. This type of banded microstructure, experimentally observed in Al-Cu, Al-Fe, and Ag-Cu alloys, has not been satisfactorily explained before.

Thermochemical Applications of Thermo-Calc

Thermo-Calc is a databank for thermochemistry and metallurgy, It consists of sophisticated and generalized software for calculation of equilibria and phase diagrams together with several databases for inorganic chemistry and metallurgy. Initially, its main application was for alloy design and the development of steels. Recently, a number of new databases have extended the applicability of ThermoCalc considerably. A substance database from SGTE (Scientific Group Thermodata Europe) and a slag database assessed by IRSID have been incorporated into Thermo-Calc. Combined with a dilute solution database assessed by Sigworth and Elliott, the IRSID database forms a very useful tool for understanding the metal/slag equilibrium in practical applications. A new geological database for solid oxides and silicates assessed by Saxena and coworkers also includes high pressure properties. Finally, at KTH, new assessments of oxide systems have been started using a more generalized model for the liquid phase. Thermo-Calc is available on line from Europe or can be obtained on a license basis.