Thermodynamic modelling of the Cr–Fe–Ni–O system

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

Thermodynamic modelling of the plutonium–oxygen system

The published data for the thermodynamic functions and phase equilibria of the plutonium–oxygen system have been examined. Some inconsistencies have been found for oxygen chemical potential and vaporization data of [Pu2O3 + PuO2−x] and PuO2−x domains. As the original chemical potential data were not performed at the same temperature and O/Pu ratio, a chart with fixed temperature and composition ranges was built in order to compare all the experimental data. The discrepancies remain difficult to explain. Thermodynamic models of all the phases have been derived by the least-squares minimization procedure using the Thermo-Calc software. The compound energy formalism with the sublattice models (Pu3+, Pu4+)1(O2−, Va)2 and (Pu3+, Pu4+)2(O2−)3(O2−, Va)1 have been chosen to account for the crystal structure, defect chemistry and thermodynamic properties of respectively PuO2−x and PuO1.61 phases. The liquid phase was described using the ionic two-sublattice model (Pu3+)P(O2−, VaQ−, PuO2, O)Q. The reliability of the refined parameters is demonstrated by calculation of the phase diagram, the thermodynamic properties of the phases and the equilibrium partial pressures in the Pu2O3–PuO2 region. Considering the large uncertainties on the experimental information, an overall good agreement was obtained. To improve the thermodynamic description of the system, some missing experimental data are listed

Thermodynamic modeling of the NbeB system

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

Calculations of thermophysical properties of cubic carbides and nitrides using the Debye–Grüneisen model

The thermal expansivities and heat capacities of MX (M = Ti, Zr, Hf, V, Nb, Ta; X = C, N) carbides and nitrides with NaCl structure were calculated using the Debye–Gru¨neisen model combined with ab initio calculations. Two different approximations for the Grüneisen parameter c were used in the Debye–Gru¨neisen 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 c 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

Computational Thermodynamics and Kinetics in Materials Modelling and Simulations

Over the past two decades, Computational Thermodynamics and Kinetics have been tremendously contributed to materials modeling and simulations and the demands on quantitative conceptual design and processing of various advanced materials arisen from various industries and academic institutions involved in materials manufacturing, engineering and applications are still rapidly increasing

Assessment of the al corner of the ternary Al-Fe-Si system

The present work provides a review of the information available on the Al-rich corner of the Al-Fe-Si system as well as a CALPHAD type assessment making use of the COST 507 database as a starting point. The description of the intermetallic compounds has been modified to account for substitution of Al and Si in the ternary Al-Fe-Si system and to take new experimental information into account

The Zr–Sn binary system: New experimental results and thermodynamic assessment

The Zr–Sn binary system has been reinvestigated by several experimental techniques: X-ray diffraction, electron probe micro-analysis, mass density and calorimetry measurements. The existence of a miscibility gap inside the homogeneity domain of the phase (Zr5Sn3–Zr5Sn4) has been confirmed. It has been also shown that Zr substitution on the Sn sublattice is responsible for the non-stoichiometry of the A15 phase (Zr4Sn). The temperature of the peritectoid reaction Zr+A15 $ Zr has been determined to be at 1216 K that is 40 below the temperature reported in the literature. All these new experimental data have been taken into account for a new thermodynamic assessment of this system

Implementation of the UNIQUAC model in the OpenCalphad software

The UNIQUAC model is often used, for example in engineering, to obtain activity coefficients in multicomponent systems, while the CALPHAD method is known for its capability in phase stability assessment and equilibrium calculations. In this work, we combine them by representing the UNIQUAC model according to the CALPHAD method and implementing it in the OpenCalphad software. We explain the harmonization of nomenclature, the handling of the model parameters and the equations and partial derivatives needed for the implementation. The successful implementation is demonstrated with binary and multicomponent phase equilibrium calculations and comparisons with literature data. Additionally we show that the implementation of the UNIQUAC model in the OpenCalphad software allows for the calculation of various thermodynamic properties of the systems considered. The combination provides a convenient way to assess interaction parameters and calculate thermodynamic properties of phase equilibria

Structural stability of intermetallic phases in the Zr–Sn system

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 Sn sites takes place in the Zr Sn phase, which accounts for the unusual stoichiometry of this Cr3Si structure type compound