Calorimetric measurement of the standard enthalpy of formation of ZnSb at 298 K

After a critical review of the literature data on the standard enthalpy of formation of ZnSb, discrepancies between various experimental studies are highlighted. Moreover, experimental values disagree with values calculated by ab initio methods. As many of the experimental methods used suffer from some serious drawbacks, a new determination of the standard enthalpy of formation of ZnSb by an alternative calorimetric method, drop solution calorimetry in liquid tin, has been performed. Two different synthesis methods have been used to obtain a pure ZnSb phase and drop solution experiments were performed at 665 and at 974 K. The standard enthalpy of formation values derived from these experiments are − 6.1±2.5 kJ mol of atoms⁻¹ for the ZnSb sample prepared by ball milling and − 7.9±0.4 kJ mol of atoms⁻¹ for the ZnSb sample prepared by melting. These results are discussed and compared to literature data.     

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

Using MHTC 96 Setaram high temperature drop calorimeter, partial and integral enthalpies of mixing of liquid alloys were determined in the Ag–Ga, Cu–Ga and in the ternary Ag–Cu–Ga system. The ternary alloys were investigated along two cross-sections at two different temperatures: 1128 K and 1273 K, respectively. Experimental data were used to find ternary interaction parameters by applying the Redlich–Kister–Muggianu model for substitutional solutions, and a full set of parameters describing the concentration dependence of the enthalpy of mixing was derived. The experimental data indicate that the heat of mixing in this system is slightly temperature dependent, at least in the measured temperature range.     

Thermodynamics of liquid In-Ga-Zn alloys determined by vapor pressure method

Application of the Knudsen method for liquid In-Ga-Zn alloys in the range from 618 to 818 K provided experimental data which made it possible to characterize the thermodynamic properties of the liquid and gaseous phases of the In-Ga-Zn system. The examined alloys were selected along four cross sections for the mole fraction ratios x_In/x_Ga equal to 4/1, 3/2, 2/3, 1/4. For each of the cross sections, the value of the mole fraction of zinc in the tested alloys was approx.: 0.2, 0.4, 0.6 and 0.8. Based on the obtained experimental data, the values of the activity of zinc were calculated and then used in the optimization procedure, leading to the determination of parameters of the equations characterizing the Gibbs free energy of liquid In-Ga-Zn alloys as a function of temperature and composition. The Gibbs free energy of the ternary In-Ga-Zn liquid alloys was described with the application of the extrapolation method based on the binary systems as given by the Jacob-Fitzner-Muggianu approach.     

Thermodynamic and surface properties of liquid Ge–Si alloys

In the present work, the surface tension of liquid Si and Ge has been measured by the pendant/sessile drop combined method over the temperature range of 1723–1908 K and 1233–1313 K, respectively. The new surface tension data, the molar volumes and the melting temperatures of silicon and germanium as well as the excess Gibbs energy data of the Ge–Si liquid phase are the inputs for Calphad type modelling to study the mixing behaviour in alloy melts. The energetics of mixing in liquid Ge–Si system has been analysed through the study of the concentration dependence of various thermodynamic (activity, enthalpy of mixing, Gibbs energy of mixing), surface (surface tension and surface composition) and transport (diffusivity) properties as well as the microscopic functions (concentration fluctuations in the long-wavelength limit and chemical short-range order parameter) in the framework of statistical mechanical theory in conjunction with the Quasi-Lattice Theory (QLT).     

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 1123 K 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.     

Enthalpies of formation of Cd–Pr intermetallic compounds and thermodynamic assessment of the Cd–Pr system

In the present study standard enthalpies of formation were measured by reaction and solution calorimetry at stoichiometric compositions of Cd₂Pr, Cd₃Pr, Cd₅₈Pr₁₃ and Cd₆Pr. The corresponding values were determined to be −46.0, −38.8, −35.2 and −24.7 kJ/mol(at), respectively. These data together with thermodynamic data and phase diagram information from literature served as input data for a CALPHAD-type optimization of the Cd–Pr phase diagram. The complete composition range could be described precisely with the present models, both with respect to phase equilibria as well as to thermodynamic input data. The thermodynamic parameters of all intermetallic compounds were modelled following Neumann–Kopp rule. Temperature dependent contributions to the individual Gibbs energies were used for all compounds. Extended solid solubilities are well described for the low- and high-temperature modifications of Pr and also for the intermetallic compound CdPr. A quite good agreement with all viable data available from literature was found and is presented.     

Modeling of thermodynamic properties of ABr-PrBr3 (A=Li-Cs ) systems

The thermodynamic properties of ABr-PrBr₃(A=Li-Cs) systems were assessed by the CALPHAD method. The liquid phase in the systems was described by the non-stoichiometric associate model. The entropies of mixing in the liquid were evaluated from experimental liquidus and enthalpy of mixing data. For the pseudobinary compounds A₃PrBr₆,APr₂Br₇, and A₂PrBr₅ (A=K,Rb) and Cs₃PrBr₆ and CsPr₂Br₇, the dependences of Gibbs energies of formation on temperature were calculated. The anomalies of sequences of thermodynamic properties in RbBr-PrBr₃ were observed and discussed. The nature of the liquid phase and precision of calculations of the Rb₂PrBr₅(s) compound were discussed.     

Experimental and thermodynamic study of the high temperature microstructure of tantalum containing nickel-based alloys

Experiments and thermodynamic calculations were performed on three nickel-based alloys containing chromium, carbon and tantalum. Solidus and liquidus temperatures, and natures and surface fractions of the carbides after exposure for 100 h at 1000, 1100 and 1200 ^∘C were determined for each alloy. These results are compared with calculated results, using a thermodynamic database. Good agreement was generally found for the solidus temperatures but less good agreement for the liquidus ones. For alloys containing chromium carbides alone, carbide fractions and matrix compositions correspond to calculation results. But the presence of tantalum carbides in the third alloy was not predicted by calculations.     

Experimental reinvestigation and thermodynamic description of Bi-Te binary system

The Bi-Te phase diagram was determined by equilibrium alloy method, combined with electron probe microanalysis (EPMA), X-ray diffraction (XRD) and thermal analysis (DSC). The experimental result shows that there is a β-phase with a large composition range at low temperature, while Bi₂Te and Bi₄Te₃ are relatively stable in the solid-liquid region. A consistent phase diagram that covers the experimental findings has been achieved. Based on the new experimental phase diagram, coupling with the reported thermodynamic data, the thermodynamic optimization of the Bi-Te binary system was carried out with the help of CALPHAD approach. A group of reasonable thermodynamic parameters was obtained.     

First-principles-based statistical thermodynamic study of atomic interactions and phase stability in Ni-rich Ni-W alloys

Atomic interactions and phase stability in Ni-rich Ni-W alloys have been investigated by using first-principles methods and statistical thermodynamic simulations. First-principles methods have been employed to explore lattice expansion, enthalpies of formation, atomic interactions, and ordering energies of ordered as well as random structures in Ni-rich Ni-W alloys with consideration of the corresponding temperature-dependent magnetic states. It is found that atomic interactions in Ni-rich Ni-W alloys depend on alloy composition, atomic volume, and magnetic state. Nevertheless, the magnetic state of Ni greatly affects the formation enthalpies, which leads to a diverse phase separation behavior at finite temperature in Ni-rich Ni-W alloys. By using atomic interactions that reproduce the ordering energies obtained in the direct total energy calculations, our statistical thermodynamic simulations of chemical short-range order results show that fcc-based ordered D1${}_{\mathrm{a}}$, D0₂₂, and Pt${}_2$Mo phases can be observed in Ni-20 at.% W, Ni-25 at.% W, and Ni-33 at.% W alloys, respectively. Moreover, the short-range order diffuse intensity and atomic stacking for aforementioned ordered phases have been analyzed, the order–disorder transition behaviors have been also investigated in detail for the Ni-rich Ni-W alloys up to 35 at.% W with comparison of current experimental results. Both magnetic state and alloy composition have the potential to induce the formation of distinct ordered phases, offering promising avenues for designing Ni-based alloys. The methodologies we used in this study can be applied to investigate the atomic interactions as well as phase stability in other alloy systems.     

Limitations of a regular associated solution approximation in describing the thermodynamic behaviour of complex liquid alloys

The validity of the regular associated solution (RAS) model for describing the thermodynamic properties of complex liquid alloys has been analysed by applying it to the Cu-In system. The presence of Cu₃In as the associated species in equilibrium with the free atoms in the liquid state was assumed. Liquid copper-indium alloys exhibit a very complex thermodynamic behaviour where the deviations from ideality of activities and integral enthalpy of mixing vary from positive to strongly negative and the properties are strongly temperature dependent. It is seen that a regular solution type interaction among species is insufficient to model the thermodynamic properties of liquid Cu-In alloys and the temperature dependence of interaction energies among the species has to be taken into account. A modified associated solution model incorporating volume effects and temperature dependence of interaction energies could successfully describe the thermodynamic properties of liquid Cu-In alloys.     

Prediction of liquid–liquid phase diagrams of aqueous salt+PEG systems using a thermodynamic model

In this study a thermodynamic model for the phase behavior of aqueous salt+polymer solutions is developed. The model is based on the solution theory of Hill, which included scaling laws for the polymer molecular mass dependence and Pitzer–Debye–Hückel theory. This model was tested for systems composed of two different molecular mass of polyethylene glycols (PEG) and five different inorganic salts. All the model parameters were determined from independent measurements. The agreement between the experimental and predicted phase diagrams by this model is good.     

Comparison between calculated and measured thermodynamic data of liquid (Ag, Au, Cu)-Sn-Zn alloys

The activity of zinc was measured in a series of liquid alloys in the three ternary systems, Ag-Sn-Zn [94Kar], Au-Sn-Zn [96Kar] and Cu-Sn-Zn [97Pen], with an emf (electromotive for e) method. From these measurements and the slope of the emf vs. temperature (dE/dT) all thermodynamic properties were derived. The experimental values were compared with calculated results. For these calculations four different models were applied and the thermodynamic data of the binary systems, obtained from the literature, were used.     

Molecular dynamics simulations and thermodynamic modeling of NaCl–KCl–ZnCl2 ternary system

The NaCl–KCl–ZnCl₂ ternary system is examined and modeled using the CALPHAD methodology in conjunction with molecular dynamics (MD) simulations. In particular, MD simulations are used for calculating liquid enthalpies of mixing as a function of composition for the ternary and its binary sub-systems. In addition, key structural features are obtained from MD that is then used for informing the employed two-sublattice ionic liquid model (Na⁺¹, K⁺¹: Cl⁻¹, ZnCl₂), which describes the ternary liquid phase. The structure of the simulated liquid systems show that Zn⁺² cations primarily exhibit 4-fold coordination in addition to a smaller percentage of 5-fold followed by 3-fold coordination; in contrast, the coordination of both Na+ and K+ cations are distributed between 2- and 4-fold states. The optimized self-consistent thermodynamic model parameters show good agreement with MD data obtained in this work and available experimental literature data.