Thermodynamic Optimization of the Ternary Ga-Sn-Te System Using Modified Quasichemical Model

Thermoelectric (TE) materials are of great interest to many researchers because they directly convert electric and thermal energy in a solid state. Various materials such as chalcogenides, clathrates, skutterudites, eutectic alloys, and intermetallic alloys have been explored for TE applications. The Ga-Sn-Te system exhibits promising potential as an alternative to the lead telluride (PbTe) based alloys, which are harmful to environments because of Pb toxicity. Therefore, in this study, thermodynamic optimization and critical evaluation of binary Ga-Sn, binary Sn-Te, and ternary Ga-Sn-Te systems have been carried out over the whole composition range from room temperature to above liquidus temperature using the CALPHAD method. It is observed that Sn-Te and Ga-Te liquids show the strong negative deviation from the ideal solution behavior. In contrast, the Ga-Sn liquid solution has a positive mixing enthalpy. These different thermodynamic properties of liquid solution were explicitly described using Modified Quasichemical Model (MQM) in the pair approximation. The asymmetry of ternary liquid solution in the Ga-Sn-Te system was considered by adopting the toop-like interpolation method based on the intrinsic property of each binary. The solid phase of SnTe was optimized using Compound Energy Formalism (CEF) to explain the high temperature homogeneity range, whereas solid solution, Body-Centered Tetragonal (BCT) was optimized using a regular solution model. Thermodynamic properties and phase diagram in the Ga-Sn-Te and its sub-systems were reproduced successfully by the optimized model parameters. Using the developed database, we also suggested several ternary eutectic compositions for designing TE alloy with improved properties.

Experimental Determination of the MnO Activity Coefficient in High-Manganese Slags Using the Chemical Equilibrium Method

The thermodynamics of manganese oxide in high-MnO-containing slags was investigated using the chemical equilibrium method in the temperature range of 1623 to 1723 K. MnO-SiO2-Al2O3 slags were brought into equilibrium with molten silver (Ag) under controlled CO/CO2 gas atmosphere. The equilibrium Mn concentration in the silver was measured by ICP-AES (inductively coupled plasma atomic emission spectroscopy) analysis after the experiment. Slag samples were analyzed by EPMA (electron probe microanalyzer) analysis. The obtained activity aMnO and activity coefficient γMnO were derived as a function of the slag composition and temperature. The activity coefficient of MnO within the investigated slag system increased with an increasing MnO/SiO2 ratio. The derived temperature dependence of the activity coefficient and partition ratio of Mn between the metal and the slag was strongly influenced by the slag composition. The thermodynamic assessment of the activity and activity coefficient of MnO was carried out by applying the regular solution model (RSM) on the basis of interaction energies of the cations and with FactSageTM 7.3. The theoretical calculations were compared with the experimentally derived values.

FORMAÇÃO DE AZEÓTROPOS DO PONTO DE VISTA DA TERMODINÂMICA DE SOLVATAÇÃO

FORMATION OF AZEOTROPES FROM THE STANDPOINT OF SOLVATION THERMODYNAMICS. The formation of azeotropes is related to the deviation of the ideality of liquid mixtures. This deviation is expressed by the activity coefficient of each component. However, the physical origin of this behavior is not well quantified in terms of molecular interactions. In this work, a regular solution model was used, relating the β parameter to the solvation free energy of pure liquids in themselves and in the other component. A mathematical expression was derived that indicates when an azeotrope is formed. This equation shows that the greater the difference in vapour pressure between components, the greater the solvation difference of each liquid in itself and in the other component is needed to form the azeotrope. A set of 10 mixtures were randomly chosen and investigated as a test, and the equation worked in all cases.

Effect of redox on Fe–Mg–Mn exchange between olivine and melt and an oxybarometer for basalts

The Fe–Mg exchange coefficient between olivine (ol) and melt (m), defined as $${\text{Kd}}_{{{\text{Fe}}^{T} {-} {\text{Mg}}}}$$ Kd Fe T - Mg = (Feol/Fem)·(Mgm/Mgol), with all FeT expressed as Fe2+, is one of the most widely used parameters in petrology. We explore the effect of redox conditions on $${\text{Kd}}_{{{\text{Fe}}^{T} {-} {\text{Mg}}}}$$ Kd Fe T - Mg using experimental, olivine-saturated basaltic glasses with variable H2O (≤ 7 wt%) over a wide range of fO2 (iron-wüstite buffer to air), pressure (≤ 1.7 GPa), temperature (1025–1425 °C) and melt composition. The ratio of Fe3+ to total Fe (Fe3+/∑Fe), as determined by Fe K-edge µXANES and/or Synchrotron Mössbauer Source (SMS) spectroscopy, lies in the range 0–0.84. Measured Fe3+/∑Fe is consistent (± 0.05) with published algorithms and appears insensitive to dissolved H2O. Combining our new data with published experimental data having measured glass Fe3+/∑Fe, we show that for Fo65–98 olivine in equilibrium with basaltic and basaltic andesite melts, $${\text{Kd}}_{{{\text{Fe}}^{T} {-} {\text{Mg}}}}$$ Kd Fe T - Mg decreases linearly with Fe3+/∑Fe with a slope and intercept of 0.3135 ± 0.0011. After accounting for non-ideal mixing of forsterite and fayalite in olivine, using a symmetrical regular solution model, the slope and intercept become 0.3642 ± 0.0011. This is the value at Fo50 olivine; at higher and lower Fo the value will be reduced by an amount related to olivine non-ideality. Our approach provides a straightforward means to determine Fe3+/∑Fe in olivine-bearing experimental melts, from which fO2 can be calculated. In contrast to $${\text{Kd}}_{{{\text{Fe}}^{T} {-} {\text{Mg}}}}$$ Kd Fe T - Mg , the Mn–Mg exchange coefficient, $${\text{Kd}}_{{{\text{Mn}} {-} {\text{Mg}}}}$$ Kd Mn - Mg , is relatively constant over a wide range of P–T–fO2 conditions. We present an expression for $${\text{Kd}}_{{{\text{Mn}} {-} {\text{Mg}}}}$$ Kd Mn - Mg that incorporates the effects of temperature and olivine composition using the lattice strain model. By applying our experimentally-calibrated expressions for $${\text{Kd}}_{{{\text{Fe}}^{T} {-} {\text{Mg}}}}$$ Kd Fe T - Mg and $${\text{Kd}}_{{{\text{Mn}} {-} {\text{Mg}}}}$$ Kd Mn - Mg to olivine-hosted melt inclusions analysed by electron microprobe it is possible to correct simultaneously for post-entrapment crystallisation (or dissolution) and calculate melt Fe3+/∑Fe to a precision of ≤ 0.04.

Thermodynamic modeling of the In-Sc and In-Y systems supported by first-principles calculations

Based on an assessment of the phase equilibria and thermodynamic data in the literature, the thermodynamic modeling of the In?Sc and In?Y systems was carried out by means of the calculation of phase diagram (CALPHAD) method supported by first-principles calculations. The solution phases, i.e., liquid, (In), (?Sc), (?Sc), (?Y) and (?Y), were modeled with the substitutional regular solution model. Ten intermetallic compounds, including InSc3, InSc2, In4Sc5, InSc, In2Sc, In3Sc, InY2, InY, In5Y3, and In3Y were described as stoichiometric phases, while In3Y5 was modeled with a sublattice model with respect to its homogeneity range. The enthalpies of formation of the intermetallic compounds at 0 K were computed using firstprinciple calculations and were used as input for the thermodynamic optimization. A set of self-consistent thermodynamic parameters for both the In?Sc and In?Y systems were obtained and the calculated phase diagrams are in good agreement with the experimental data.

MODELING OF THERMOCHEMICAL PROPERTIES AND GLASSFORMING TENDENCY OF THE MELTS OF TERNARY Mn–Al–Gd SYSTEM

In the present work, the enthalpies of mixing of liquid alloys of the ternary Mn-Al-Gd system have been calculated using the regular solution model by the Redlich-Kister-Muggianu formula. Also a comparison was made of calculated values of enthalpies of mixing in this system with the experimentally determined thermochemical properties of liquid alloys of the Mn-In-Gd ternary system obtained previously. In general, we estimate that the values of the enthalpies of mixing in the Mn-Al-Gd ternary system should be more exothermic than in the Mn–In-Gd one. This fact can be explained taking into consideration the main features of the component interaction in the boundary binary systems, namely, such important characteristics as electronegativity of the components, their electron work functions and a large difference in size of atoms. It can be concluded that it is the binary Mn–Al system that makes a significant contribution to the formation energy of ternary alloys. An imaginary line drawn through the points of maximum curvature of the isoenthalpic lines is considerably shifted towards the binary Mn–Al boundary, thus expanding significantly the region of rather exothermic enthalpies of mixing in the corresponding ternary system. For the two indicated ternary systems the size mismatch entropy has been calculated within the framework of hard spheres model and the Sσ/kB parameter has been determined. On the basis of the comprehensive analysis carried out, the criteria for the probability of occurrence of regions of easy amorphization in these ternary systems are proposed. The determination of the topology of the mixing enthalpy surface and the Sσ/kB parameter for the melts of studied ternary systems together with the data on binary and ternary compounds existing in these systems allowed to reasonably assume the concentration regions where the investigated ternary alloys have tendency for easy amorphization while rapid cooling of the melt. The simultaneous realization of the following three conditions was taken as a criterion for the possible existence of a region of easy amorphization: the absolute value of the enthalpies of mixing is at least 6 kJ/mol, the Sσ/kB parameter is not less than 0.3–0.4 and a certain distance from the concentration region corresponding to the exact composition of binary or ternary compounds.

Theoretical investigation of mixing properties of Sb-Sn binary liquid alloy at 905K

The thermodynamic, microscopic, surface and transport properties of Sb-Sn liquid alloy at 905K have been studied using regular solution model. In thermodynamic properties, free energy of mixing(GM) , activity(a), entropy of mixing(SM), heat of mixing (HM) have been studied. To understand structural behavior of the liquid alloys concentration fluctuations in the long wavelength limit i.e. (Scc(0)) and short range order parameter (α1) have been computed. Surface property is studied with the help of Butler’s model while transport property is computed from Moelwyn-Hughes equation. The theoretical and experimental values of thermodynamic and microscopic properties of Sb-Sn liquid alloy at 905K have been compared. In present work the value of interchange energy (w) is found to be negative suggesting that there is a tendency of unlike atoms pairing (i.e. Sb-Sn) as the nearest neighbor indicating the ordering behavior in Sb-Sn liquid alloy. The symmetric behavior of concentration fluctuations of the liquid alloy has been well explained by the model. The temperature dependence of interchange energy (w) has been found during the computation of entropy of mixing (SM) and heat of mixing (HM) of the liquid alloy.BIBECHANA 15 (2018) 1-10