Thermodynamics and phase diagrams in the binary systems Na2O-SiO2, Na2O-GeO2, Na2O-B2O3, Li2O-B2O3, CaO-B2O3, SrO-B2O3, and BaO-B2O3

We applied our model to the enthalpy of mixing data of the binary systems Na₂O-SiO₂, Na₂O-GeO₂, Na₂O-B₂O₃, Li₂O-B₂O₃, CaO-B₂O₃, SrO-B₂O₃, and BaO-B₂O₃. The most stable composition in the liquid, that is where the enthalpy of mixing is most negative, is with a metal-oxygen ratio of 4 to 3, for monovalent metals (Na and Li) and 3 to 4 for divalent metals (Ba and Ca) in liquid silicates or borates. The same applies to the CaO-SiO₂, CaO-Al₂O₃, PbO-B₂O₃, PbO-SiO₂, ZnO-B₂O₃, and ZnO-SiO₂ systems. The oxygen to metal ratio, its constant value in various types of systems, reflects and describes the structure of the liquid. Using the analyzed enthalpies of mixing data and the available phase diagrams, we calculated the enthalpies of formation of the various binary compounds. The results are in excellent agreement with data in the literature that were obtained from direct solid-solid calorimetry.     

Thermochemical investigation of binary liquid mixtures in glass-forming oxide systems

Methods and equipment successfully employed in high- temperature calorimetry to measure partial and integral enthalpies of mixing in liquid oxide systems are reviewed with special attention given to the drop-mixing method. This technique has been used to measure enthalpies of mixing in binary liq-uid mixtures composed of network forming oxides (e.g. SiO₂) and network modifying oxides (e.g. Na₂O). Results for the systems Na₂O-SiO₂ and Na₂O- B₂O₃ are presented graphically. Entropies of mixing were estimated by combining enthalpies with available data on Gibbs energies of mixing. Prominent thermochemical features of glass-forming oxide melts are pointed out. The observed thermodynamic behavior is discussed in relation to its structural basis.     

Thermochemical investigation of binary liquid mixtures in glass-forming oxide systems

Methods and equipment successfully employed in high- temperature calorimetry to measure partial and integral enthalpies of mixing in liquid oxide systems are reviewed with special attention given to the drop-mixing method. This technique has been used to measure enthalpies of mixing in binary liq-uid mixtures composed of network forming oxides (e.g. SiO₂) and network modifying oxides (e.g. Na₂O). Results for the systems Na₂O-SiO₂ and Na₂O- B₂O₃ are presented graphically. Entropies of mixing were estimated by combining enthalpies with available data on Gibbs energies of mixing. Prominent thermochemical features of glass-forming oxide melts are pointed out. The observed thermodynamic behavior is discussed in relation to its structural basis.     

The quaternary system B2O3-PbO-SiO2-ZnO: Thermodynamics and phase diagram

We evaluated the six binary phase diagrams, B₂O₃-PbO, B₂O₃-SiO₂, B₂O₃-ZnO, PbO-SiO2, PbO-ZnO, and SiO₂-ZnO, to obtain a consistent picture for the quaternary system B₂O₃-PbO-SiO₂-ZnO. We used all the available thermodynamic data: enthalpies of mixing, activity data, complete phase diagrams, and miscibility gaps. The agreement between the various sets of data is good. We also calculated the enthalpy of formation of the ternary compound 5PbO-B₂O₃-SiO₂. Δ_fH/R of 1/8 [5PbO-B₂O₃-SiO₂] =-(2.104 ± 0.057) kK.     

Thermodynamic optimization of the Na2O-B2O3 pseudo-binary system

The Na₂O-B₂O₃ system is thermodynamically optimized by means of the CALPHAD method. A two-sublattice ionic solution model, (Na⁺¹)_P(O⁻²,BO₃ ⁻³,B₄O₇ ⁻²,B₃O_4.5)_Q, has been used to describe the liquid phase. All the solid phases were treated as stoichiometric compounds. A set of thermodynamic parameters, which can reproduce most experimental data of both phase diagram and thermodynamic properties, was obtained. Comparisons between the calculated results and experimental data are presented.     

Thermodynamic optimization of the Na<Subscript>2</Subscript>O-B<Subscript>2</Subscript>O<Subscript>3</Subscript> pseudo-binary system

The Na₂O-B₂O₃ system is thermodynamically optimized by means of the CALPHAD method. A two-sublattice ionic solution model, (Na⁺¹)_P(O⁻²,BO₃ ⁻³,B₄O₇ ⁻²,B₃O_4.5)_Q, has been used to describe the liquid phase. All the solid phases were treated as stoichiometric compounds. A set of thermodynamic parameters, which can reproduce most experimental data of both phase diagram and thermodynamic properties, was obtained. Comparisons between the calculated results and experimental data are presented.     

The quaternary system B2O3-PbO-SiO2-ZnO: Thermodynamics and phase diagram

We evaluated the six binary phase diagrams, B₂O₃-PbO, B₂O₃-SiO₂, B₂O₃-ZnO, PbO-SiO2, PbO-ZnO, and SiO₂-ZnO, to obtain a consistent picture for the quaternary system B₂O₃-PbO-SiO₂-ZnO. We used all the available thermodynamic data: enthalpies of mixing, activity data, complete phase diagrams, and miscibility gaps. The agreement between the various sets of data is good. We also calculated the enthalpy of formation of the ternary compound 5PbO-B₂O₃-SiO₂. Δ_fH/R of 1/8 [5PbO-B₂O₃-SiO₂] =-(2.104 ± 0.057) kK.     

Critical evaluation and optimization of the thermodynamic properties and phase diagrams of the CrO-Cr2O3, CrO-Cr2O3-Al2O3, and CrO-Cr2O3-CaO systems

Available thermodynamic and phase diagram data have been critically assessed for all phases in the CrO-Cr₂O₃, CrO-Cr₂O₂-Al₂O₃, and CrO-Cr₂O₂-CaO systems from 298 K to above the liquidus temperatures and for oxygen partial pressures ranging from equilibrium with metallic Cr to equilibrium with air in the case of the first two systems and toP _{O 2} = 10^?3 atm for the CrO-Cr₂O₃-CaO system. All reliable data have been simultaneously optimized to obtain one set of model equations for the Gibbs energy of the liquid slag and all solid phases as functions of composition and temperature. The modified quasichemical model was used for the slag. The models permit phase equilibria to be calculated for regions of composition, temperature, and oxygen potential where data are not available.     

Selective leaching of arsenic from copper converter flue dust by Na2S and its stabilization with Fe2(SO4)3

The alkaline leaching of arsenic (As₂O₃) by Na₂S, together with its precipitation by Fe₂(SO₄)₃ was studied. Response surface methodology based on central composite design was employed to quantify and qualify the effect of pertinent factors and to develop statistical models for optimization purposes. Based on the obtained results, 89% of arsenic is removed from the dust under following optimum predicted conditions: Na₂S concentration of 100 g/L and solid to liquid ratio of 0.163 g/mL at 80 °C. It is found that solid to liquid ratio and Na₂S concentration are the significant factors influencing the leaching process. In the precipitation process, more than 99.93% of arsenic from the leaching solution is removed in the form of amorphous ferric arsenate, at pH 4.8 when Fe³⁺ to arsenic and H₂O₂ to arsenic molar ratios are set at 5:1 and 4:1, respectively. Also, Fe³⁺ to arsenic ratio and pH are the most significant factors, and the interaction between these terms is significant.     

Critical evaluation and optimization of the thermodynamic properties and phase diagrams of the CrO-Cr2O3-SiO2 and CrO-Cr2O3-SiO2-Al2O3 systems

Available thermodynamic and phase diagram data have been critically assessed for all phases in the CrO-Cr₂O₃-SiO₂ and CrO-Cr₂O₃-SiO₂-Al₂O₃ systems from 298 K to above the liquidus temperatures and for oxygen partial pressures ranging from equilibrium with metallic Cr to equilibrium with air. All reliable data have been simultaneously optimized to obtain one set of model equations for the Gibbs energy of the liquid slag and all solid phases as functions of composition and temperature. The modified quasi-chemical model was used for the slag. The models permit phase equilibria to be calculated for regions of composition, temperature, and oxygen potential where data are not available.     

Thermodynamic Description of $${\hbox{SrO-Al}_{2}\hbox{O}_{3}}$$ System and Comparison with Similar Systems

The Al₂O₃-SrO binary system has been studied using the CALPHAD technique in this paper. The modeling of Al₂O₃ in the liquid phase is modified from the traditional formula with the liquid phase represented by the ionic two-sublattice model as (Al³⁺, Sr²⁺) _P (, O²⁻) _Q . Based on the measured phase equilibrium data and experimental thermodynamic properties, a set of thermodynamic functions has been optimized using an interactive computer-assisted analysis. The calculated results are compared with experimental data. A comparison between this system and similar systems is also given.     

Enthalpies of formation of binary Laves phases

Enthalpies of formation of binary Laves phases have been critically surveyed and reviewed in this paper. The enthalpy-of-formation data indicate that both geometric and electronic factors are important in stabilizing Laves phases. Analysis of enthalpy data reveals that there are metallic, covalent, and ionic bonds, or a mixed metallic-covalent-ionic bond, in Laves phases. The enthalpies of formation for binary transition-metal lanthanide Laves phases including ReCo₂, ReNi₂, ReFe₂, ReRu₂, ReRh₂, ReOs₂, ReIr₂, and RePt₂ (Re—lanthanide element), as calculated by the semiempirical Miedema model, are found to be in good agreement with the available experimental data. This indicates that Miedema's theory is capable of predicting the enthalpy of formation of transition-metal lanthanide Laves-phase systems.     

Wetting characteristics of CaO−SiO2−Al2O3 ternary slag on refractory oxides, Al2O3, SiO2 and TiO2

The wettabilities of the metallurgical slag, CaO−55.2 wt.%SiO₂−15 wt.%Al₂O₃ on refractory oxides, Al₂O₃, SiO₂ and TiO₂ were investigated at temperatures of 1350, 1400 and 1470°C. Contact angle measurements were performed using a combination of the sessile drop method and the X-ray fluoroscopic technique. The contact angle was obtained from the numerical solution of the Young-Laplace equation. The steady contact angles obtained were 31°, 24°, and 15° for SiO₂, Al₂O₃ and TiO₂ at 1470°C, respectively. The spreading rate of the liquid slag was characterized by the formation of cognate interface between the liquid slag and solid oxide, and further enhanced by the formation of a diffuse layer around the slag drop at higher temperatures.     

Ordering tendencies in Pd-Pt,Rh-Pt,and Ag-Au alloys

First-principles quantum-mechanical calculations indicate that the mixing enthalpies for Pd-Pt and Rh-Pt solid solutions are negative, in agreement with experiment. Calculations of the diffuse-scattering intensity due to short-range order also exhibits ordering tendencies. Further, the directly calculated enthalpies of formation of ordered intermetallic compounds are negative. These ordering tendencies are in direct conflict with a 1959 prediction of Raub that Pd-Pt and Rh-Pt will phase-separate below ~760 °C (hence their mixing energy will be positive), a position that has been adopted by all binary alloy phase diagram compilations. The present authors predict that Pd_1-xPt_x will order in the L1₂, L1₀, and L1₂ structures ([001] superstructures) at compositionsx = 1/4, 1/2, and 3/4, respectively, while the ordered structures of Rh_1-xPt_x are predicted to be superlattices stacked along the [012] directions. While the calculated ordering temperatures for these intermetallic compounds are too low to enable direct growth into the ordered phase, diffuse-scattering experiments at higher temperatures should reveal ordering rather than phase-separation characteristics (i.e., off-F peaks). The situation is very similar to the case of Ag-Au, where an ordering tendency is manifested both by a diffuse scattering intensity and by a negative enthalpy of mixing. An experimental reexamination of PdPt and Rh-Pt is needed.     

Ordering tendencies in Pd-Pt, Rh-Pt, and Ag-Au alloys

First-principles quantum-mechanical calculations indicate that the mixing enthalpies for Pd-Pt and Rh-Pt solid solutions are negative, in agreement with experiment. Calculations of the diffuse-scattering intensity due to short-range order also exhibits ordering tendencies. Further, the directly calculated enthalpies of formation of ordered intermetallic compounds are negative. These ordering tendencies are in direct conflict with a 1959 prediction of Raub that Pd-Pt and Rh-Pt will phase-separate below ~760 °C (hence their mixing energy will be positive), a position that has been adopted by all binary alloy phase diagram compilations. The present authors predict that Pd_1-xPt_x will order in the L1₂, L1₀, and L1₂ structures ([001] superstructures) at compositionsx = 1/4, 1/2, and 3/4, respectively, while the ordered structures of Rh_1-xPt_x are predicted to be superlattices stacked along the [012] directions. While the calculated ordering temperatures for these intermetallic compounds are too low to enable direct growth into the ordered phase, diffuse-scattering experiments at higher temperatures should reveal ordering rather than phase-separation characteristics (i.e., off-F peaks). The situation is very similar to the case of Ag-Au, where an ordering tendency is manifested both by a diffuse scattering intensity and by a negative enthalpy of mixing. An experimental reexamination of PdPt and Rh-Pt is needed.     

Process optimization and modeling of recycling Mo (VI) from spent Mo-Fe2O3/Al2O3 catalyst by roasting with sodium carbonate using response surface methodology (RSM)

The oil-containing spent Mo-Fe₂O₃/Al₂O₃ catalyst can be deemed as an environmental threat and an attractive source of minerals that can reduce the consumption of natural resources. Herein, recovery of Mo from spent Mo-Fe₂O₃/Al₂O₃ catalyst was conducted by the Na₂CO₃ roast-leach process, response surface methodology (RSM) coupled with central composite design (CCD) was employed to optimize the roasting process and a polynomial equation was derived to predict the response. The three roasting independent variables the roasting temperature, the Na₂CO₃/sample weight ratio, and the roasting duration were investigated in the Na₂CO₃ roasting process while water-leaching parameters were identical. The predictions of model showed that the roasting temperature had a major effect on the response with respect to other parameters. According to analysis of variance (ANOVA), the proprosed model equation had shown satisfactory agreement with the experimental data with a correlation coefficient (R²) of 0.9811. The optimum conditions for Mo recovery were predicted to be as the roasting temperature of 771.2 °C, the Na₂CO₃/sample weight ratio of 2.09 and the roasting duration of 93.56 min. Under the optimum conditions, maximal value of Mo recovery rate was reached as 92.58%.     

Critical evaluation and optimization of the thermodynamic properties and phase diagrams of the CrO-Cr2O3, CrO-Cr2O3-Al2O3, and CrO-Cr2O3-CaO systems

Available thermodynamic and phase diagram data have been critically assessed for all phases in the CrO-Cr₂O₃, CrO-Cr₂O₂-Al₂O₃, and CrO-Cr₂O₂-CaO systems from 298 K to above the liquidus temperatures and for oxygen partial pressures ranging from equilibrium with metallic Cr to equilibrium with air in the case of the first two systems and toP _{O 2} = 10⁻³ atm for the CrO-Cr₂O₃-CaO system. All reliable data have been simultaneously optimized to obtain one set of model equations for the Gibbs energy of the liquid slag and all solid phases as functions of composition and temperature. The modified quasichemical model was used for the slag. The models permit phase equilibria to be calculated for regions of composition, temperature, and oxygen potential where data are not available.     

Ab-Initio Calculations and Thermodynamic Description of the Yb-Cd and Yb-Sn Systems

The phase diagrams of Yb-Cd and Yb-Sn systems were calculated by coupling the CALPHAD method and ab initio calculations. The enthalpies of formation of nine binary compounds (YbCd, αYbCd₂, Yb₂Sn, αYb₅Sn₃, βYb₅Sn₃, Yb₅Sn₄, YbSn, Yb₃Sn₅ and YbSn₃) were determined via ab initio density functional theory using the VASP code. Based on the available experimental data and the computed enthalpies of formation of the compounds, a thermodynamic assessment was carried out. The liquid phases and the γYb(bcc) and βYb(fcc) solid solutions were described by the Redlich–Kister polynomial model, while all the intermetallic compounds were treated as stoichiometric phases. A set of optimized model parameters were obtained for Yb-Cd and Yb-Sn systems. The calculated phase diagrams of these binary systems and their thermodynamic properties are presented and compared with the experimental data.     

Thermodynamic reassessment of the BaO-B2O3 system

The BaO-B₂O₃ pseudobinary system is assessed. A two-sublattice ionic solution model, (Ba²⁺) _P (O²⁻, BO₃³⁻, B₄O₇²⁻, B₃O_4.5) _Q , is adopted to describe the liquid phase. All the solid phases are treated as stoichiometric compounds. A set of parameters consistent with most of the available experimental data on both phase diagram and thermodynamic properties is obtained by using CALPHAD technique. A comparison between the calculated results and experimental data as well as a previous assessment is presented.     

Phase Relations in the Systems SrO-Y2O3-CuO-O2 and CaO-Y2O3-CuO-O2 at 1173 K

Phase relations in the systems SrO-Y₂O₃-CuO-O₂ and CaO-Y₂O₃-CuO-O₂ at 1173 K were estab-lished by equilibrating different compositions in flowing oxygen gas at a pressure of 1.01 × 10⁵ Pa. The quenched samples were examined by optical microscopy, X-ray diffraction (XRD), energy dis-persive analysis of X-rays (EDAX), and electron spin resonance (ESR). In the system SrO-Y₂O₃-CuO-O₂, except for the limited substitution of Y₃+ for Sr₂+ ions in the ternary oxide Sr₁₄ Cu₂₄O₄₁, no new quaternary phase was found to be stable. The compositions corresponding to the solid solution Sr_14-xY_xCu₂₄O₄₁ and the compound SrCuO₂+δ lie above the plane containing SrO, Y₂O₃, and CuO, displaced towards the oxygen apex. However, in the system CaO-Y₂O₃-CuO-O₂ at 1173 K, all the condensed phases lie on the plane containing CaO, Y₂O₃, and CuO, and a new quaternary oxide YCa₂Cu₃O_6.5 is present. The quaternary phase has a composition that lies at the center of the non-stoichiometric field of the analogous phase YBa₂Cu₃O_7-δ in the BaO-Y₂O₃-CuO-O₂ system. The com-pound YCa₂Cu₃O_6.5 has the tetragonal structure and does not become superconducting at low temperature. Surprisingly, phase relations in the three systems CaO-Y₂O₃-CuO-O₂, SrO-Y₂O₃-CuO-O₂, and BaO-Y₂O₃-CuO-O₂ are found to be quite different.