Phase equilibria and thermodynamic investigation of the In–Li system

Phase equilibria and thermodynamic properties of the In–Li system were analyzed by combining the first-principles approach and Computer Coupling of Phase Diagrams and Thermochemistry (CALPHAD) methodology. The enthalpies of formation for all the stable compounds were calculated by first-principles calculations based on the density functional theory (DFT). Phase diagram of the In–Li system was calculated for the first time, and a set of self-consistent thermodynamic parameters was finally obtained by CALPHAD approach coupling experimental measurements and first-principles calculations. An associate model of (In, In₂Li₃, Li) was used to describe the liquid phase, and InLi and InLi₂ were treated by sub-lattice models. Other intermediate phases were considered to be stoichiometric compounds. The calculated phase diagram, voltage curve and thermodynamic properties can reproduce the available experimental data reasonably.     

Thermodynamic modeling of the Sn–V binary system

The Sn–V binary system was thermodynamically modeled using the CALPHAD approach combined with first-principles calculations. The predicted Gibbs free energy of the end-members in sublattice models of “ V ₃Sn” phase by the first-principles calculations was used to describe the lattice stabilities. A set of thermodynamic parameters for the Sn–V system was obtained using the PanOptimizer program in Pandat software. The calculated phase diagram and thermodynamic properties agree well with the reported experimental data.     

Thermodynamic assessment of the V–Zn system supported by key experiments and first-principles calculations

The V–Zn system was investigated by a combination of CALPHAD modeling with key experiments and first-principles calculations. Based on a critical literature review, one diffusion couple and nine alloys were designed to reinvestigate the stabilities of the phases reported in the literature. The samples were annealed and cooled under different conditions, followed by examination with X-ray diffraction and scanning electron microscopy with energy-dispersive X-ray spectrometry. Four phases ((V), (Zn), V Zn₃ and V ₄Zn₅) were confirmed to exist in the phase diagram, while V Zn₁₆ and V ₃Zn were not observed. By means of first-principles calculations, the enthalpies of formation for V Zn₃ and V ₄Zn₅ were computed to be −4.55 kJ mol-atoms⁻¹ and −4.58 kJ mol-atoms⁻¹, respectively. A set of self-consistent thermodynamic parameters for this system was obtained by considering the reliable experimental phase diagram data and the enthalpies of formation acquired from first-principles calculations. The calculated V–Zn phase diagram agrees well with the experimental data.     

A summary of the CALPHAD XXXVIII conference

CALPHAD XXXVIII was held in Prague on 17–22 May 2009, organized jointly by Masaryk University and the Institute of Physics of Materials ASCR. There were 149 active participants who presented 63 oral contributions and 87 posters. A “Young Scientists Session” was organized on the evening of 18 May with L. Kaufman and Y.M. Muggianu as invited speakers. The presentations and posters covered a broad spectrum of topics: besides CALPHAD-type thermodynamic modeling and related experimental work, a significant number of contributions on first-principles calculations were presented. The use of the information that can be obtained by first-principles calculations using different techniques, together with traditional thermodynamic and phase diagram data was highlighted in the first sessions. Important advances in the calculation of magnetic properties were also presented. Phonon spectra, all-electron and other vibration/relaxation calculation techniques that include dynamic features and temperature effects were themes of presentations, together with ab initio modeling of diffusion processes. Hydrogen-containing systems were discussed and databases for specific problems were presented. During the presentations, several examples of CALPHAD predictions compared with experimental results confirmed the power of the CALPHAD method for industrial applications. A cultural program (including a concert in Aula Carolina, sponsored by the Charles University, and an excursion to the medieval Karlštejn castle) completed the program of the conference.     

An overview on phase equilibria and thermodynamic modeling in multicomponent Al alloys: Focusing on the Al-Cu-Fe-Mg-Mn-Ni-Si-Zn system

Knowledge of thermodynamics and phase diagram is a prerequisite for understanding many scientific and technological disciplines. To establish a reliable thermodynamic database, an integrated approach of key experiments and thermodynamic modeling, supplemented with first-principles calculations, can be utilized. In this paper, first investigations of phase diagram and thermodynamics of technologically important Al alloys (focusing on the Al-Cu-Fe-Mg-Mn-Ni-Si-Zn system, which covers the major elements in most commercial Al alloys) is reviewed with an emphasis on the need of the integrated approach. Second, the major experimental methods (X-ray diffraction, metallography, electron probe microanalysis, differential thermal analysis, diffusion couple method, and calorimetry), which are widely employed to provide phase diagram and thermodynamic data, are briefly described. Third, the basics of the first-principles calculations and CALPHAD are presented focusing on the integration of these two computational approaches. Case study for the representative Al-Fe-Ni ternary system is then demonstrated, followed by a thermodynamic modeling of the quinary Al-Fe-Mg-Mn-Si system and a brief summary to our recent activities on investigations of phase equilibria in multicomponent Al alloys.     

Thermodynamic modeling of the Si-Y system aided by first-principles and phonon calculations

Thermodynamic modeling of the Si-Y binary system has been performed by the CALPHAD (CALculation of PHAse Diagram) method based on phase diagram and thermochemical data in the literature combined with Gibbs energies of end-members of compounds predicted by first-principles phonon calculations. In particular, non-stoichiometric compounds Si₂Y and Si₃Y₅ are modelled to accommodate their homogeneity ranges in terms of two-sublattice models (Si,Y)₂(Si,Y) and (Si)₃(Si,Y)₅, respectively. Formation of SiY is treated as a peritectic reaction according to experimental results, instead of an eutectic one as described in the previous models. The calculated phase equilibriums and thermodynamic properties are in a satisfactory agreement with available experimental data.     

Thermodynamic assessment of Fe–Ti–S ternary phase diagram

A thermodynamic analysis of the Fe-Ti-S ternary system was performed by incorporating first-principles calculations into the calculation of phase diagrams (CALPHAD) method. To evaluate the Gibbs energy, the Debye-Grüneisen model was applied for some sulfides of the Ti-S binary system. In addition, the cluster expansion and cluster variation methods were used for the solid solution phases in the Ti-S binary and (Fe,Ti)S phases. The calculated Ti-S binary phase diagram showed good agreement with the experimental results. The very low solubility of the Ti solid solution in the Ti-S system, as reported by Murray, agreed well with our calculated results. A binodal phase decomposition of the liquid phase was expected in the S-rich region. The Gibbs energy curve of (Fe,Ti)S between FeS and TiS was found to be convex downward. This is characteristic of an isomorphic solid solution, attributed to the attractive interaction between Fe and Ti in (Fe,Ti)S. The vertical phase diagram between FeS and TiS, obtained using the thermodynamic database, was in good agreement with the experimental results of Mitsui et al. The solubility products of (Fe,Ti)S have been experimentally estimated previously. The calculated solubility product agreed with the experimental value of TiS.     

Experimental study and thermodynamic modelling of the B-Fe-Mn ternary system

This work is focused on an experimental study of phase equilibria in the B-Fe-Mn ternary system combined with a CALPHAD theoretical analysis with the aim of creating a reliable theoretical thermodynamic dataset for calculation of the phase diagram of the ternary system. Boron is modelled as an interstitial element in all solid solutions of Fe and Mn. In the experimental study, B-Mn-Fe alloys were prepared and heat-treated at 873 K for 90 days/2160 h and at 1223 K for 60 days/1440 h. Following heat treatment, the phase equilibria and composition of the coexisting phases were determined using scanning electron microscopy and X-ray diffraction analysis. The experimental results obtained, together with experimental results collected from the literature, were used in the optimization of the thermodynamic parameters by using the CALPHAD method. The result of this work is an optimized thermodynamic dataset for the B-Fe-Mn ternary system allowing the phase diagram and thermodynamic properties to be calculated.     

Thermodynamic modeling of the ternary Ce–Fe–Sb system: Assessment of the Ce–Sb and Ce–Fe systems

The two Ce–Sb and Ce–Fe binary systems have been evaluated using the calculation of phase diagram method (CALPHAD). All of the binary compounds are treated as stoichiometric compounds. Solution phases are described with an ordinary substitutional solution model. The model parameters were derived from an optimization procedure using all available experimental data. The reproduction of the thermochemical and phase diagram information is reported in a series of figures and tables.     

Phase equilibria of the Zn-Ti system: Experiments,first-principles calculations and Calphad assessment

The phase equilibria and thermodynamic properties of the Zn-Ti system have been investigated by experiments, first-principles calculations and Calphad assessment. Differential scanning calorimetry measurement and microstructure characterization confirmed the Zn richest eutectic reaction to occur at 691.3 ± 0.4 K with about 0.27 at% Ti in the liquid. Density functional theory (DFT) calculations have been performed to calculate the finite-temperature heat capacity (C_p) of the intermetallics, providing also the absolute entropies. A full thermodynamic assessment of the Zn-Ti system has been performed by using the experimental and DFT results obtained in this work together with the collection of all available data from previous publications. In the present work, the Calphad results show good agreement not only in thermodynamic properties with DFT data, but also phase equilibria data with experimental results, especially in the Zn-rich side, which significantly improved from previous Calphad assessment. Phase diagrams including the gas phase have also been calculated and discussed.