For solidification purposes in multicomponent systems, the crystallisation sequences which occur upon cooling are important for the properties of the material. The nature and the compositions of the various phases which precipitate can affect casting properties, microstructures, hence mechanical properties. It is difficult to determine these sequences by microanalysis because quantities such as partition coefficients are difficult to measure. In addition, the thermal effect associated with the process is a parameter which is difficult to evaluate experimentally.

The problem presented here was caused by an attempt to modify an alloy produced by a continuous casting process. This process worked well for a stainless steel with 20 wt% Cr and the manufacturer now wanted to use the same process for a steel with 25 wt% Cr. However, he then obtained problems with clogging by solid oxide formation which prevented the flow of liquid steel. The oxide formed at the outlet was found to consist mainly of Cr2O3. The manufacturer thus faced an expensive and time consuming experimental scheme in order to find out how to prevent the formation of this Cr2O3. As an alternative route he tried to use the Thermo-Calc thermodynamic databank in order to simulate the process on the computer in order to find out a remedy. Such a simulation can usually be made in less than a day if the necessary thermodynamic data are available.

The discussion on thermodynamic modelling of solution that started at the Ringberg meeting 1996 is continued with some revisions and some details. In particular the methods to implement chemical ordering for a multicomponent system, also on interstital sublattices and the contributions due to strain energies are discussed.

The aim of this work has been to develop a model for short range order within the compound energy formalism. The short range order contribution to the Gibbs energy is described as a number of internal variables, here called epsilon-variables. This work is restricted to ordered and disordered phases with fcc structures.

The effect of interaction between the magnetic and chemical ordering reactions on the phase equilibria between the bcc phases, A2, B2 and DO3 has been studied by using the four-sublattice Compound Energy Model (CEM) taking account of the magnetic contribution to the Gibbs energy. An interaction between the magnetic and chemical ordering arises when the Curie temperature is formulated as a function of the site fraction of elements on each sublattice. A positive interaction arises from the higher deviation of the Curie temperature of the ordered state from that of the disordered one and leads to a two-phase separation between the ferro- and paramagnetic B2 phases. A lower deviation causes a negative interaction which introduces a convexity in the Gibbs energy curve around the composition of the intersection point between the Curie temperature and the order-disorder transition temperature. As a result, two-phase separations between either para- or ferro-magnetic A2 phase and paramagnetic B2 phase are introduced.

The Co-Ge binary system was reassessed by CALPHAD method in view of new phase diagram data and drawbacks of the previous modeling. A three-sublattice model (Co,Va)(1)(Co)(1)(Ge)(1 )was used to describe the B8(2)-type beta Co5Ge3-phase based on its crystal structure. In order to describe the transformation between ordered L1(2)-type phase (Co3Ge) and the disordered fcc_Al phase (alpha Co), one single Gibbs energy function was used for both ordered and disordered phases. In almost all the previous thermodynamic calculations, the ordered phase with a negligible homogeneity range, such as Co3Ge, is treated as a stoichiometric compound. Such a treatment is not physically sound. For (alpha Co) and (alpha Co), the magnetic contribution to Gibbs energy is taken into account. Both substitutional solution model and associated model were applied to describe the liquid phase, and thus two sets of self-consistent thermodynamic parameters for this system were obtained. It was found that the associated model can account for the experimental data more satisfactorily than the substitutional solution model, especially for the partial enthalpy of mixing data for the liquid phase. Five representative as-cast Co-Ge alloys were prepared to compare the solidified microstructure with that predicted according to thermodynamic calculations. According to the calculated Scheil solidification curves of two key alloys, the solidified microstructure for the alloys was analyzed. Also, the calculated amounts of the solidified phases in five as-cast alloys are compared with the experimental data resulting from automatic image analysis of the BSE images, showing a good agreement between the calculation and experiment, in particular for the case in which the associated model is used to describe the properties of the liquid phase. It is demonstrated that the combined use of the thermodynamic calculation and decisive experiment is an efficient strategy to obtain the desired microstructure.

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.

This paper examines the development of a consistent thermodynamic model for the uranium (U) - molybdenum (Mo) - oxygen (0) system for incorporation into the Thermodynamics of Advanced Fuels - International Database (TAF-ID). Phase diagram data and thermodynamic properties from the literature are reviewed. Density functional theory ab initio calculations at 0 K are combined with a quasi -harmonic statistical thermodynamic model to calculate thermodynamic functions (e.g., integral Delta H-298.15K(0), S-298.15K(0), and C-p(0) (T))of the relevant ternary compounds when little or no thermodynamic literature data are available. A CALPHAD method is employed to derive a model describing the Gibbs energy functions for all the relevant ternary compounds, the liquid phase, and the gas phase of the U-Mo-O system. A consistent thermodynamic model is obtained for the Mo-U-0 system with a special emphasis placed on the oxygen rich portion of the ternary (ie., MoO2-UO2-O). Finally, supporting binary and pseudo binary diagrams (e.g., Mo-O, UO2-MoO3 and UO3-MoO3) are computed and compared to literature data.

Knudsen effusion mass spectrometry measurements on neptunium dioxide are reported in this work, which have allowed to improve the understanding of its vapourization behaviour and solved discrepancies noticed in the literature: the enthalpy of formation of NpO2(g) has been re-assessed and the composition of neptunia at congruent vapourization has been determined at 2262 K. In addition, a thermodynamic model for the neptunium-oxygen system has been developed using the CALPHAD method. The non stoichiometric NpO2-x phase is described herein using the compound energy formalism with ionic constituents (Np3+, Np4+)(1) (O2-, Va)(2), while the liquid phase is represented with the ionic two-sublattice model (Np4+)(P) (O2-, Va(Q-), O)(Q). The reliability and consistency of all optimized Gibbs energies have been verified by calculating the phase equilibria, thermodynamic data, oxygen chemical potential and equilibrium partial pressures. Finally, a number of ill-defined data in the Np-O system have been identified after critical review of the literature and comparison with the present experimental results and CALPHAD model.

We review and discuss methods for including the role of point defects in calculations of the free energy, composition and phase stability of elements and compounds. Our principle aim is to explain and to reconcile, with examples, the perspectives on this problem that are often strikingly different between exponents of CALPHAD, and others working in the overlapping fields of physics, chemistry and materials science. Current methodologies described here include the compound energy formalism of CALPHAD, besides the rather different but related canonical and grand-canonical formalisms. We show how the calculation of appropriate defect formation energies should be formulated, how they are included in the different formalisms and in turn how these yield equilibrium defect concentrations and their contribution to free energies and chemical potentials. Furthermore, we briefly review the current state-of-the-art and challenges in determining point defect properties from first-principles calculations as well as from experimental measurements.