Substitutional Solution Model Research Articles

Experimental investigation and thermodynamic modeling of an innovative molten salt for thermal energy storage (TES)

A novel computational thermodynamic approach based on thermodynamic principles was applied to design and develop innovative molten salt mixtures for thermal energy storage. In this work, the eutectic composition of the NaCl-NaF-Na2CO3 ternary system was predicted based on experimental data via computational thermodynamic approach. Substitutional solution model (SSM) was used to describe the Gibbs energies for all liquid phases. Thus, a set of self-consistent thermodynamic model parameters was obtained for three subsystems and the parameters were used to predict the eutectic composition of the NaF-NaCl-Na2CO3 ternary system. Results manifested that the predicted eutectic point of the ternary system were located at T = 849 K and XNaF = 21.66 mol%, XNaCl = 41.87 mol% and XNa2CO3 = 36.47 mol%. By means of Differential Scanning Calorimetry method, the predicted results were verified experimentally and the agreement between the measured and predicted values was satisfactory. Thermal-physical properties for eutectic salt mixtures, such as enthalpies of fusion, heat capacity, density and thermal stability, were also determined experimentally via thermal analysis methods in this work. Through computational thermodynamics approach, an innovative eutectic salt was designed and developed as thermal energy storage (TES) materials at high temperatures, especially it can be serve as candidate thermal energy storage materials for next generation concentrated solar power (CSP) plants.

A thermodynamic description of the U−Ti−Zr system

The U−Ti−Zr system was assessed by means of the CALPHAD method for the first time. Based on a critical evaluation of experimental phase diagram data available in the literature, a thermodynamic modeling was conducted for the individual phases. The solution phases including the liquid, hcp and bcc were described by a substitutional solution model. The binary compounds, U2Ti and UZr2, with a ternary extension were treated as one single phase using a sublattice model of (U,Zr)2/3(Ti,Zr)1/3. There is no ternary compound in this system. A set of self-consistent thermodynamic parameters for the U−Ti−Zr system was then obtained. Comparisons between the calculated and measured phase diagrams show that the experimental information is satisfactorily accounted for by the present thermodynamic description. The solvus projection and reaction scheme were generated using the present thermodynamic parameters. The presently calculated phase diagrams of U–Zr−Ti alloys can be used for further industrial application.

Thermodynamic assessment of binary erythritol-xylitol phase diagram for phase change materials design

Here, the erythritol-xylitol binary system was thermodynamically optimized based on available experimental phase equilibrium data, to explore compositions suitable as phase change materials (PCMs) for thermal energy storage (TES). A previous experimental study revealed that erythritol-xylitol was a partially isomorphous system with a eutectic. In the thermodynamic evaluation, the CALPHAD method was employed coupling the phase diagram and thermodynamic property information. There, both unary and binary systems’ experimental data were taken into account, and all phases were described using the substitutional solution model. Finally, a self-consistent thermodynamic description for the erythritol-xylitol system was achieved. The calculated eutectic point is at 76.7°C and 26.8mol% erythritol, agreeing well with the experimental data. The calculated phase diagram better-verifies the systems’ solidus and the solvus, disclosing the stable phase relations. Based on the Gibbs energy minimization, phase diagrams can be predicted for the binary and higher order systems, provided the component subsystems are thermodynamically assessed beforehand. In conclusion, to move forward beyond e.g. non-isomorphous simple eutectic systems, methods using Gibbs free energy minimization from a fundamental point-of-view such as CALPHAD are essential.

First principles, thermal stability and thermodynamic assessment of the binary Ni–W system

Abstract The Ni–W binary system was assessed using critically evaluated experimental data with assistance from first principles analysis and the CALPHAD method. The solution phases (liquid, fcc-A1 and bcc-A2) were modeled using the substitutional regular solution model. The recently discovered Ni8W metastable phase was evaluated as Fe16C2-like martensite with three sublattices, and shown to be possibly stable according to first principles calculations. Ni8W was also modeled as an interstitial compound, but the model is not good because the solubility of tungsten in nickel is very low, especially at low temperatures. There is no experimental evidence for such low solubility. The other binary compounds Ni4W and Ni3W were assessed as stoichiometric ones. Compared independent experimental and first principles data agree well with the calculated phase diagram using updated thermodynamic parameters.

Thermodynamic Assessment of the Ti-RE (RE = Ce, Er, Tm, Y) Binary Systems

Based on the available literature experimental phase equilibria, the Ti-RE (RE = Ce, Er, Tm, Y) binary systems have been critically reviewed and modeled by means of the CALPHAD (CALculation of PHAse Diagram) method. No compound exists in these binary systems. The solution phases, i.e., liquid, bcc(βTi, δCe, βY), hcp(αTi, Er, Tm, αY) and fcc(γCe, γY), are described by the substitutional solution model. A set of self-consistent thermodynamic parameters is finally obtained for each of these binary systems. Comparisons between the calculated and measured phase diagrams show that most of the experimental data are satisfactorily accounted for by the present thermodynamic descriptions.

Experimental investigation and thermodynamic modeling of the LiNO3-RbNO3-AgNO3 system and its subsystems

Computational thermodynamics approach based on experimental values is applied to evaluation and optimization of the LiNO3-RbNO3-AgNO3 system and its subsystems in this work. The substitutional solution model (SSM) was used to describe all liquid phase. All the intermediate compounds were treated as stoichiometric of which Gibbs energies comply with the Neumann-Kopp rule. A set of self-consistent database with thermodynamic model parameters obtained for the LiNO3-RbNO3-AgNO3 subsystems and this database were used to predict thermodynamic properties of the LiNO3-RbNO3-AgNO3 ternary system. The calculated results were verified experimentally using differential scanning calorimetry (DSC) and X-ray diffraction (XRD) techniques, and the agreement between the experimental values and predicted values is satisfactory. The phase diagram of the LiNO3-RbNO3-AgNO3 ternary system contain two eutectic types: one eutectic (Liquid ↔ α-AgNO3 + LiRb(NO3)2 + AgRb(NO3)2) at 385.3 ± 1.5 K and another eutectic (Liquid ↔ LiRb(NO3)2 + AgRb(NO3)2 + AgRb2(NO3)3) at 398.8 ± 1.5 K. Through computational thermodynamics approach, a multi-component system was successfully predicted and this approach will be applied to design and develop multi-component molten salt mixtures as thermal energy storage (TES) materials.

Thermodynamic re-assessment of the Fe-Dy and Fe-Tb binary systems

In this work, based on the critical evaluation of previous optimizations and available experimental data in the published literature, the Fe-Dy and Fe-Tb binary systems were re-assessed thermodynamically using the CALPHAD method. The solution phases including liquid, fcc-Fe, bcc-Fe, bcc-Dy, bcc-Tb, hcp-Dy and hcp-Tb, were described by the substitutional solution model and their excess Gibbs energies were expressed with the Redlich-Kister polynomial. Due to their narrow homogeneity ranges, the intermetallic compounds, Fe17Dy2, Fe23Dy6, Fe3Dy, Fe2Dy, Fe17Tb2, Fe23Tb6, Fe3Tb and Fe2Tb, were modeled as stoichiometric compounds. Self-consistent thermodynamic parameters to describe the Gibbs energies of various phases in the Fe-Dy and Fe-Tb binary systems were obtained finally. The calculated results are in good agreement with the reported phase equilibria and thermodynamic properties.

Thermodynamic modeling of the Ca(NO3)2-MNO3 (M: alkali metal) systems

This work presents a thermodynamic evaluation of the Ca(NO3)2-MNO3 (M: Li, Na, K, Rb, Cs) binary systems using the CALPHAD approach. The required Gibbs energy of liquid Ca(NO3)2 is missing in the literature and has been successfully evaluated in the present work with a fusion enthalpy of 23849Jmol−1. The substitutional solution model can thus be employed to describe the Ca(NO3)2-base liquid phase. All the intermediate compounds are treated to be stoichiometric and their Gibbs energies comply with the Neumann-Kopp rule. Empirical functions relating mixing enthalpies to ionic parameters are employed to predict the corresponding values of binary melts which are used as input data to assist in parameters optimization for the liquid phases. The final calculated results show good agreement with most of the experimental and predicted data.

Thermodynamic description of the MCl2-ThCl4 (M: Mg, Ca, Sr, Ba) systems

The phase equilibria for the MCl2-ThCl4(M: Mg, Ca, Sr, Ba) binary systems were critically evaluated and optimized based upon the CALPHAD approach. The substitutional solution model(SSM) was used to describe the liquid phase. All the intermediate compounds were treated as stoichiometric compounds of which Gibbs energies comply with the Neumann-Kopp rule. Thermodynamic model parameters optimization for respective phases was conducted by the least squares minimization procedure with required input data available from experimental measurements. Satisfactory agreements between all calculated results and experimental data were achieved which demonstrates that thermodynamic databases for the MCl2-ThCl4(M: Mg, Ca, Sr, Ba) binary systems were ultimately derived in the present work allowing safe extrapolation into multi-component system for guiding relative industrial applications.

Mixing enthalpies of liquid Bi–Ni and Ag–Bi–Ni alloys

Partial and integral enthalpies of mixing of liquid Bi-Ni alloys were determined at 1273K, while enthalpies of mixing of ternary Ag–Bi–Ni alloys were determined at 1173K over a broad composition range along six sections: x(Ag)/x(Bi)=3/2, 1, 2/3, 3/7, 1/4; x(Bi)/x(Ni)=4. Measurements were carried out using Calvet type microcalorimeters and drop calorimetric technique. It was found that integral enthalpies of mixing of binary Bi-Ni alloys are small exothermic, whereas integral mixing enthalpies of ternary Ag-Bi-Ni alloys change sign from negative to positive with decreasing Bi content. The ternary data were fitted on the basis of an extended Redlich–Kister–Muggianu model for substitutional solutions, and additional ternary interaction parameters were determined. From experimental ternary data the range of liquid at 1173K was deduced.

Experimental Investigation and Thermodynamic Modeling of the Ag-Cu-Ge System

The liquidus surface projection was re-investigated using scanning electron microscopy with energy dispersive spectrometer and differential thermal analysis. The invariant reactions, liq. → fcc(Ag) + diam(Ge) + η at 810 K (537 °C), and liq. + e → η + fcc(Ag) at ~848 K (575 °C) were confirmed, and θ →liq. + η + diam(Ge) at 859 K (586 °C) was inferred in the present work. On the basis of the experimental data in the present work and literature, the Ag-Cu-Ge system was modeled using the CALPHAD (CALculation of PHAse Diagram) method. Solution phases, liquid, hcp, and fcc, were modeled as (Ag, Cu, Ge) using the substitutional solution model in the Ag-Cu-Ge ternary system. The compounds, e, η, and θ, in the Cu-Ge system, were treated as line compounds (Ag, Cu) m Ge n in the Ag-Cu-Ge system. A set of self-consistent thermodynamic parameters was obtained. Using these thermodynamic parameters, the experimental isothermal sections at 763 K, 793 K, 863 K, and 923 K (490 °C, 520 °C, 590 °C, and 650 °C), the vertical section at 38.0 at. pct Cu, the liquidus surface projection, and the invariant reactions in the Ag-Cu-Ge system were well reproduced.

Experimental investigation and thermodynamic description of the Cu-Cr-Zr system

The Cu-Cr-Zr ternary system was investigated via thermodynamic modeling coupled with key experiments. The isothermal section of the Cu-Cr-Zr system at 1123K was determined by means of optical microscopy, X-ray diffraction and electron probe microanalysis, and the phase transformation temperatures were measured by differential scanning calorimetry. The Cu-Cr sub-binary system was re-assessed with a substitutional solution model for the solution phases to ensure its compatibility in multi-component system. A set of self-consistent thermodynamic parameters for the Cu-Cr-Zr systems was obtained using the CALPHAD (CALculation of PHAse Diagram) approach, and the calculated phase diagram is in a satisfactory agreement with the present experimental results and literature information. An increase of the thermodynamic stability for the CuZr and Cr2Zr phases due to the ternary solubility is verified by calculation.

Thermodynamic re-assessment of the Fe-Gd and Fe-Sm binary systems

The Fe-Gd and Fe-Sm binary systems were re-assessed thermodynamically using the CALPHAD method based on the critical evaluation of previous optimizations and available experimental information in the published literature. The solution phases including liquid, fcc-Fe, bcc-Fe, bcc-Gd, hcp-Gd, bcc-Sm, hcp-Sm and rhombohedral-Sm, were described by the substitutional solution model and their excess Gibbs energies were expressed with the Redlich-Kister polynomial. The intermetallic compounds, α-Fe17Gd2, β-Fe17Gd2, Fe23Gd6, Fe3Gd, Fe2Gd, Fe17Sm2, Fe3Sm and Fe2Sm, were modeled as stoichiometric compounds due to their narrow homogeneity ranges. Self-consistent thermodynamic parameters to describe Gibbs energies of various phases in the Fe-Gd and Fe-Sm binary systems were obtained finally. The calculated results in this work are in good agreement with the reported phase equilibria and thermodynamic properties.

Thermodynamic description of the Holmium-Germanium binary system

The Holmium-Germanium system was thermodynamically assessed by the CALPHAD technique based on the available experimental data including the thermodynamic properties and phase equilibria. The solution phases, i.e. liquid, hcp_A3 (Ho), and diamond_A4 (Ge), were described by the substitutional solution model with the Redlich-Kister equation, and all the intermetallic compounds HoGe1.7 (_LT and _HT), HoGe1.8, HoGe2.7, Ho11Ge10, Ho3+Ge4, Ho5Ge4, HoGe, and HoGe1.5 (_LT and _HT) in the Holmium-Germanium system were treated as stoichiometric phases. The compound with a homogeneity range Ho5Ge3, is modeled using two sublattices as (Ho,Ge)0.375(Ho,Ge)0.625. A set of self-consistent thermodynamic parameters for the Holmium-Germanium system was finally obtained. The calculated phase diagram and thermodynamic properties agree reasonably with the literature experimental data.

Thermodynamic assessment of the phase equilibria and prediction of glass-forming ability of the Al–Cu–Zr system

The thermodynamic description of the Al–Cu–Zr system was performed using the CALPHAD method. The solution phases liquid, fcc, bcc and hcp were described using a substitutional solution model. The compounds in the Al–Zr and Cu–Zr systems and the ternary compounds τ3, τ5, τ7 and τ8 were treated as a line compound in the Al–Cu–Zr system. The ternary compounds τ1, τ2, τ4, τ6, τ9 and τ11 were described as a stoichiometric compound. The enthalpies of mixing of the liquid phase at different temperatures and compositions, two invariant reactions, and five isothermal sections at 773, 873, 1073, 1273 and 1373K were taken into account in the present optimization work. A set of self-consistent and reliable thermodynamic parameters of the Al–Cu–Zr system was obtained. By searching the local minimum of the driving force for crystalline phases under the supercooled liquids, the thermodynamic parameters obtained in this assessment were later used for predicting composition dependencies of high glass-forming ability in the Al–Cu–Zr system. The predicted alloy compositions of high glass-forming ability are in satisfactory agreement with the available experimental data.

Thermodynamic reevaluation and experimental validation of the CsNO3-KNO3-NaNO3 system and its subsystems

Phase equilibria and thermodynamic properties of the CsNO3-KNO3-NaNO3 system and its three subsys-tems were optimized thermodynamically and validated experimentally. The liquid and end solid solution phases of the KNO3-NaNO3 and CsNO3-KNO3 systems were modeled using the substitutional solution and compound energy formalism models, respectively. The CsNO3-KNO3-NaNO3 ternary system was described thermodynamically based on the self-consistent thermodynamic parameters of the three binary systems. A set of thermodynamic parameters was obtained to reproduce the available information on the thermodynamic properties and phase equilibria. Melting temperature, enthalpy, and specific heat capacity of a eutectic sample were determined using differential scanning calorimetry(DSC). The results show a good consistency with the calculated results, suggesting the reliability of the current thermodynamic database. This work is useful for the construction of multicomponent nitrates and to provide guidance for the development of new medium for thermal energy storage.

A thermodynamic description of metastable c-TiAlZrN coatings with triple spinodally decomposed domains

A critical thermodynamic assessment of the metastable c-TiAlZrN coatings, which are reported to spinodally decompose into triple domains, i.e., c-TiN, c-AlN, and c-ZrN, was performed via the CALculation of PHAse Diagram (CALPHAD) technique based on the limited experimental data as well as the first-principles computed free energies. The metastable c-TiAlZrN coatings were modeled as a pseudo-ternary phase consisting of c-TiN, c-AlN and c-ZrN species, and described using the substitutional solution model. The thermodynamic descriptions for the three boundary binaries were directly taken from either the CALPHAD assessment or the first-principles results available in the literature except for a re-adjustment of the pseudo-binary c-AlN/c-ZrN system based on the experimental phase equilibria in the pseudo-ternary system. The good agreement between the calculated phase equilibria and the experimental data over the wide temperature range was obtained, validating the reliability of the presently obtained thermodynamic descriptions for the c-TiAlZrN system. Based on the present thermodynamic description, different phase diagrams and thermodynamic properties can be easily predicted. It is anticipated that the present thermodynamic description of the metastable c-TiAlZrN coatings can serve as the important input for the later quantitative description of the microstructure evolution during service life.

Thermodynamic assessment of the Al-Mo-V ternary system

Thermodynamic assessment of the Al-Mo-V ternary system was performed by means of the CALPHAD (CALculation of PHAse Diagram) approach based on the thermodynamic descriptions of three constitutive binary systems (Al-Mo, Al-V and Mo-V) as well as the experimental phase equilibria data available in the literature. The solution phases, i.e. liquid, bcc (Mo, V) and fcc (Al), were described using the substitutional solution models with the Redlich-Kister equation. The binary phases in the Al-Mo and Al-V systems with the solubilities of the third element were modeled using the sublattice models. An optimal set of thermodynamic parameters for the Al-Mo-V system was obtained. Six isothermal sections at 1200, 1000, 750, 715, 675 and 630?C and liquidus projection with isotherm were calculated. The reaction scheme for the entire Al-Mo-V system was also constructed. Comparisons between the calculated and measured phase diagrams indicated that almost all the reliable experimental information was satisfactorily accounted for by the present modeling.

Enthalpies of mixing of liquid Ag–Ga, Au–Ga and Ag–Au–Ga alloys

A literature overview of Ag-Au-Ga system shows that the information about the liquid phase of this system does not exist. Therefore, using MHTC 96 Setaram high temperature drop calorimeter, partial and integral enthalpies of mixing of liquid alloys were determined at first in the binary systems Ag-Ga, Au-Ga and finally in ternary Ag-Au-Ga system. Next, the ternary alloys were investigated along two sections at two temperatures: 1223K and 1323K. Experimental results were used to find ternary interaction parameters by applying the Redlich–Kister–Muggianu model for substitutional solutions, and consequently a full set of parameters describing the concentration dependence of the enthalpy of mixing was derived. The experimental results indicate that the heat of mixing in this system is temperature independent, at least in the measured temperature range.

Experimental investigation and thermodynamic modeling of the Ce-Si system

Phase equilibria and thermodynamic properties of the Ce-Si system were studied experimentally by investigating a Si/(Ce,Si) diffusion couple and thirteen Ce-Si alloys. X-ray diffraction (XRD), electron probe micro-analyzer (EPMA), differential thermal analysis (DTA) and high temperature reaction calorimetry (HTRC) were utilized. A phase with close composition of CeSi1.34 and the decomposition temperature of 1469K is detected. The eutectic reaction liquid↔(Si)+CeSi2 is observed to occurs at 1502.6K. The enthalpy of formation of CeSi1.68 was measured to be −70±6kJmol-atoms−1. A thermodynamic modeling of the Ce-Si system was then performed by considering the reliable literature data and the present experimental results. A substitutional solution model was used for the description of the liquid phase, and all of the compounds are treated as stoichiometric ones. The calculated phase diagram and thermodynamic properties using the obtained thermodynamic parameters are in good agreement with the experimental data.