Previous Thermodynamic Descriptions Research Articles

Phase equilibrium investigations and thermodynamic modelling of the ZrO2-HfO2-Ta2O5 system

The phase equilibria in the ZrO2-HfO2-Ta2O5 system were studied at 1673 K and 1873 K by equilibration technique and in the temperature range up to 2473 K by differential thermal analysis (DTA). The phase and chemical composition of the samples were characterized by X-ray diffraction (XRD) and scanning electron microscopy (SEM) with energy dispersive X-ray analysis (EDX). Melting relations were studied by DTA followed by microstructural investigation by SEM/EDX. The composition dependence of the eutectic and peritectic temperatures was shown. The heat capacity of the (Zr,Hf)6Ta2O17 compound with different compositions was measured by differential scanning calorimetry (DSC) in three temperature ranges from 100 K to 230 K, from 220 K to 570 K, and from 330 K to 1295 K. Based on the obtained results and our previous thermodynamic descriptions, a database for the ternary ZrO2-HfO2-Ta2O5 system using the CALPHAD approach was created.

Thermodynamic re-modelling of the Cu–Nb–Sn system: Integrating the nausite phase

Currently available Cu–Nb–Sn phase diagrams lack the recently discovered nausite phase (Cu,Nb)Sn2, which is an important intermediate in the course of thermal processing of superconducting Nb3Sn wires. Processing decisively determines the resulting microstructure of Nb3Sn and, thus, its superconducting properties. Lack of suitable and complete phase diagrams, however, obstructs rational design of such thermal processing procedures. To close this gap and to obtain valid knowledge of homogeneity and stability range of nausite, various Cu–Nb–Sn samples, which are heat-treated between 300 °C and 500 °C, are investigated. By means of energy-dispersive X-ray spectroscopy (EDX), a temperature-dependent homogeneity range of nausite is observed, which covers average mole fractions of Cu between 0.09 and 0.15. This is correlated with a change in the mean atomic volume and can be seen in the lattice parameters determined by X-ray diffraction (XRD). Additionally performed first-principles calculations on different CuSn2 and NbSn2 model structures confirm this trend. Furthermore, the peritectic decomposition of nausite to NbSn2 and liquid at 586 °C is determined by means of in situ XRD and differential scanning calorimetry (DSC). By using the CALPHAD (CALculation of PHase Diagrams) approach, all these findings are used to extend a previous thermodynamic description of the Cu–Nb–Sn system by including the nausite as an additional phase. With this noteworthy integration, the updated modelling of the Cu–Nb–Sn system can be used for optimizing the multistage heat-treatment steps during processing superconducting Nb3Sn wires.

Thermodynamic description of the Ti-Mo-Nb-Ta-Zr system and its implications for phase stability of Ti bio-implant materials

Titanium alloys are great candidates for applications such as biomedical implants that require biocompatibility, a low Young's modulus and a high strength. However, the properties of Ti alloys are highly dependent on phase stability. In the present work, a database for the Ti-Mo-Nb-Ta-Zr system has been evaluated using the CALPHAD (CALculation of PHAse Diagram) approach. The database was completed by evaluating the accuracy of previously modeled systems from literature and modeling systems that, to the best of the authors’ knowledge, had no modeling available in literature. All of the binary systems that make up the Ti-Mo-Nb-Ta-Zr system had previously modeled thermodynamic descriptions available in the literature and in most cases had multiple different descriptions available, which meant determining which previous thermodynamic description most accurately modeled the binary system with a direct focus on the bcc phase. In order to determine the accuracy of the multiple available thermodynamic descriptions from literature a combination of experimental data (also obtained from the literature) and computed thermochemical properties of the bcc phase from DFT (Density Functional Theory)-based first-principles calculations (present work) were used. Once the thermodynamic descriptions for the binary systems were chosen, focus shifted to the Ti-containing ternary systems. The Ti-Mo-Zr, Ti-Nb-Zr and Ti-Ta-Zr systems had previous thermodynamic description available in literature, which were incorporated without changes into the working database. The Ti-Mo-Ta, Ti-Nb-Ta and Ti-Mo-Nb systems had, to the authors’ knowledge, no descriptions available in the literature. Interaction parameters were determined for the Ti-Mo-Ta and Ti-Nb-Ta systems, and no interaction parameters were introduced for the Ti-Mo-Nb system. The database introduced by this work satisfactorily predicts the thermodynamics of the Ti-Mo-Nb-Ta-Zr system.

Thermodynamic Modeling of B-Ta and B-C-Ta Systems

A thermodynamic assessment of the B-Ta system is performed using the CALPHAD method incorporating the latest experimental data and results from first-principles calculations of the formation enthalpies of TaB2, Ta3B4, TaB, Ta3B2, and Ta2B. The sublattice model of (Ta, B)0.333(Ta, B)0.667 is used to describe the homogeneity range of TaB2, while the other four intermetallic compounds are treated as stoichiometric compounds. As a results, noticeable improvement were made over previous thermodynamic description of the B-Ta system. The thermodynamic parameters obtained in this study can effectively reproduce the most recently published experimental data. The thermodynamic assessment of the ternary phase diagram of B-C-Ta system could be carried out by combining the thermodynamic parameters of the C-Ta and B-C systems from the literature with the re-assessed B-Ta system. Reliable experimental data are satisfactorily accounted for the present thermodynamic description.

Calorimetric measurements and assessment of the binary Cu–Si and ternary Al–Cu–Si phase diagrams

Using dynamic scanning calorimetry the temperature, composition and reaction enthalpy of a number of invariant reactions in the Cu–Si and Al–Cu–Si systems were determined. The temperatures and compositions are in good agreement with previous experimental data. Reaction enthalpies have not been previously measured. The Cu–Si system was thermodynamically modelled in detail using all available data. Experimental data are well reproduced, including the presently measured reaction enthalpies. Compared to the best previous thermodynamic description some improvements could be achieved. The Al–Cu–Si system was tentatively modelled using a new model for the γ-Al4Cu9 phases and without using large ternary interactions with large temperature dependencies. The Cu-rich part is very complex and the complete system could be reasonably described. Though it was not possible to present a detailed assessment in this work there are important improvements compared to previous thermodynamic descriptions.

Thermodynamic Assessment of the Bi–Ni and Bi–Ni–X (X = Ag, Cu) Systems

The Bi–Ni system was reassessed by means of the calculation of phase diagrams (CALPHAD) method by considering the latest published experimental data. To maintain the compatibility in higher-order systems, the excess Gibbs energy of the solution phases was modeled with the Redlich–Kister polynomials, and a three-sublattice model, (Bi)0.3334(Ni,Va)0.3333(Va,Ni)0.3333, was used to describe the intermetallic compound BiNi with NiAs-type crystal structure. Compared with the previous thermodynamic description for the Bi–Ni system, noticeable improvements are achieved in the present work. The current thermodynamic parameters can well reproduce the newly published experimental data on thermodynamic properties. Based on the newly obtained parameters for the Bi–Ni system, as well as the thermodynamic descriptions for the Bi-Ag, Ni-Ag, Bi-Cu, and Ni-Cu systems in literature, a thermodynamic database of the Bi–Ni–Ag and Bi–Ni–Cu ternary systems was established by considering the available experimental data. The calculated phase equilibria in these ternary systems are in satisfactory agreement with experimental observations.

Thermodynamic assessment of the Cu–Fe–Ni system

• The thermodynamic description of the Cu–Fe–Ni system has been updated. • The new experimental data have been used to refine thermodynamic model of the system. • The four-sublattice model has been adopted to predict the equilibria involving the ordered L1 2 phase. • A significant improvement in comparison with the previous assessments has been achieved. • The liquidus and solidus projections have been presented. The thermodynamic description of the Cu–Fe–Ni system has been updated considering the newly available experimental data, as well as compatibility of the present modeling with those used for the Cu and Fe systems. All of the experimental data available in the literature have been critically reviewed, and the inconsistent information has been excluded. The thermodynamic parameters have been evaluated in order to properly describe the thermodynamic properties of the liquid phase and miscibility gap in the solid state. A significant improvement in comparison with the previous thermodynamic descriptions has been achieved. Additionally, for the ordered L1 2 phase the four-sublattice model has been adopted to predict the ternary phase equilibria involving this phase. A set of thermodynamic parameters for the phases is given.

Re-analysis of the critical nucleation work in the case of diffusive interface

Regarding the inherent limitations of previous thermodynamic description on nucleation, the nucleation work has been re-analyzed for undercooled melts by introducing temperature- and position-dependent thermodynamic quantities in the diffusive interface. At the small undercoolings, the obtained critical nucleation work matches that derived from the classical nucleation theory. With the increasing undercooling, the nucleation work approaches and finally becomes smaller than that from the published theories based on the diffusive interface. Substituting the critical nucleation work predicted by the present approach into the steady-state homogeneous nucleation rate, the nucleation rates for pure Hg and Ga have been calculated. It is shown that the results from the present approach fit the experimental values much better than those from the classical nucleation theory. Particularly, for some metals or alloys, the temperature at which the nucleation work vanishes can be predicted using the present approach.

Enthalpy change of the hcp/ fcc martensitic transformation in the Fe–Mn and Fe–Mn–Si systems

An evaluation of enthalpy change of the hcp/ fcc transformation in Fe–Mn and Fe–Mn–Si alloys, in the composition ranges from 0 to 12 at.% and from 17 to 32 at.% of Si and Mn, respectively, is performed. The calculation is based on a phenomenological description of the energy of Gibbs of the fcc- and hcp-phases and on the Redlich–Kister model. This result is compared with a systematic determination of the enthalpy change of transformation obtained by combining Differential Scanning Calorimetry experiments and the hcp-phase relative fractions extracted from Mössbauer spectroscopy, dilatometry and neutron diffraction measurements. The present calculation reproduces well the experimental data, reinforcing the validity of the previous thermodynamic description of the Gibbs energy of hcp- and fcc-phases.

On the melting of Cr 5Si 3 and update of the thermodynamic description of Cr–Si

The melting behavior of Cr 5Si 3 was redetermined from micrographs of as-cast alloys. It is found that this phase melts incongruently into L+Cr 3Si rather than congruently, as generally accepted. The previous thermodynamic description of the Cr–Si binary system is adjusted to account for this new finding.

Thermodynamic investigation of the Ag–Bi–Sn ternary system

The activities of Sn of liquid Ag–Bi–Sn alloys for three cross-sections with the constant molar ratios of Ag:Bi = 2:1, 1:1, and 1:2 are measured at 627 and 727 ∘C by an electromotive force (emf) method with a liquid electrolyte. The previous thermodynamic descriptions of the Ag–Bi–Sn ternary system are modified by considering the literature data and our own experimental results. The thermodynamic interaction parameters of the Bi–Sn binary and the Ag–Bi–Sn ternary liquid phase are optimized using the emf and calorimetric data from the present work. Based on the self-consistent optimized thermodynamic parameters the phase diagram and thermodynamic properties of the Ag–Bi–Sn ternary system are calculated and compared with the experimental data. The agreement between the calculated results and the experimental data has been significantly improved.

Thermodynamic modeling of the Cu–Mn system supported by key experiments

The Cu–Mn system was investigated via a combination approach of experiment and thermodynamic modeling. Based on the critically assessed Cu–Mn phase diagram, eight crucial alloys were selected and the phase relations resulting from the alloys were obtained using X-ray diffraction, scanning electron microscopy with energy-dispersive X-ray spectrometry, differential thermal analysis and differential scanning calorimetry. In particular, the temperature associated with the peritectoid reaction CUB_A13 + FCC_A1 = CBCC_A12 was measured to be 725 °C accurately. A thermodynamic modeling of the Cu–Mn system was then performed by considering the reviewed literature data and incorporating the present experimental results. The computed phase diagram and thermodynamic properties using the optimization thermodynamic parameters are in good agreement with the experimental ones. Noticeable improvements to previous thermodynamic descriptions of this binary system are made.

Phase diagram and thermodynamics of the La2O3–Ga2O3 system revisited

Previous thermodynamic description of the La 2 O 3 –Ga 2 O 3 system has been updated based on new experimental data on the liquidus and the enthalpies of formation of LaGaO 3 and La 4 Ga 2 O 9 measured by high-temperature oxide melt drop solution calorimetry as well as calculated from first-principles. The existing contradictions were successfully resolved. Both the phase diagram and thermodynamic data were reproduced with high accuracy by thermodynamic calculations using the CALPHAD method.

Thermodynamic analysis of the stable and metastable Co–Cu and Co–Cu–Fe phase diagrams

The binary Co–Cu and the ternary Co–Cu–Fe systems have been optimized using the CALPHAD approach. Experimental data that have appeared recently in the literature have been used to improve the description of the metastable miscibility gap on both binary and ternary liquid phases. In the Co–Cu–Fe system, ternary parameters have been obtained to properly describe the miscibility gap. A significant improvement with respect to previous thermodynamic descriptions has been achieved. A set of model parameters for the liquid, f.c.c., and b.c.c. phases is given.

Modification of the thermodynamic model for the Mg–Zr system

A previous thermodynamic model for the Mg–Zr system has been modified by using new information derived from first-principles calculations in combination with existing experimental data on phase boundaries, invariant reactions as well as limited thermochemical measurements in the liquid phase. Special quasirandom structures for the hcp and bcc structures are used to simulate random solid solutions at 25, 50 and 75 at.%. The total energies of these structures are calculated through first-principles methods and the enthalpies of mixing are used in combination with the available experimental information as input data in the thermodynamic modelling . In addition to experiments and first-principles calculations, stability conditions are also used to prevent unrealistic metastable and higher-order extrapolations. In general, the calculated phase diagram is found to agree well with experiments. The present model is also compared to previous thermodynamic descriptions and it is shown that some of the inconsistencies of the previous model can be resolved by the combined first-principles/CALPHAD approach.

A thermodynamic analysis of the NiAl system

Abstract Phase equilibrium and thermodynamic data of the binary NiAl system are analyzed using thermodynamic models. The liquid and fcc (γ) phases are treated as disordered solutions, the intermetallic compounds with appreciable ranges of homogeneity, i.e. γ′-(Ni3Al), B2-(NiAl) and Al3Ni2, are described by compound energy models, and the other intermetallic phases are taken to be line compounds. The phase equilibrium and thermodynamic properties calculated from the model parameters are in accord with most of the experimental data reported in the literature. For γ′-(Ni3Al) and B2-(NiAl), the model-calculated defect concentrations as functions of temperature and composition are in agreement with experimental data. In comparison to previous thermodynamic descriptions reported in the literature, the present one has fewer model parameters with more reasonable values. Despite this, the agreement between model-calculated thermodynamic values and phase boundaries and experimental data is as good as or better than that obtained in earlier studies.

Phase Relations in the Aluminum Carbide–Aluminum Nitride–Aluminum Oxide System

The phase diagram of the pseudobinary Al4C3‐AlN system was predicted using thermodynamic models. It was combined with previous thermodynamic descriptions of the pseudobinary Al4C3‐Al2O3 and AlN‐Al2O3systems, and then thermodynamic properties of the pseudoternary Al4C3‐AlN‐Al2O3system were assessed by modeling the Gibbs energy of the various phases. An ionic‐liquid model was applied to the liquid phase and a compound‐energy model was applied to the solid‐solution phase (2H) that formed between Al2OC and AlN. A series of isothermal sections of the system were calculated in the temperature range of 1000°‐2100°C, and reasonable phase relations were established. The calculated isothermal section at 1600°C showed satisfactory agreement with experimental results. The calculated liquidus projection in the Al2O3‐rich corner can explain the experimental observation of the microstructure after solidification very well. However, the present description cannot account for the phase segregation inside the solution phase but could be modified in the future, when more experimental information would be available.