Measurement and calculation of the phase diagram of the NaClCaCl2SrCl2 system

In this paper the system NaClCaCl₂SrCl₂ and its binary systems were studied. Using a previously calculated phase diagram of the NaClCaCl₂SrCl₂ system as a basis, accurate measurements were carried out by MDTA with high sensitivity. It is a simple eutectic system with a eutectic point at 41.9 mol % NaCl, 40.C mol % CaCl₂, 18.1 mol % SrCl₂, 744 K. In the liquidus surface for saturation with the CaCl₂SrCl₂ solid solution a univariant line starts from a point 24.8 mol % NaCl, 50.1 % CaCl₂, 25.1 mol % SrCl₂ at 823 K. The uncertainty in the liquidus temperatures is estimates to be less than ±5K, for the reason that the errors due to Supercooling and change of sample compositions were reduced by our experimental method.A new calculation of the phase diagram of the NaClCaCl₂SrCl₂ system has been performed with a new asymmetric method. It is based upon a critical assessment of the thermodynamic properties and phase diagrams of the binary systems.The agreement between our present measured and calculated phase diagrams is within ±2.5 mol %. Their good agreement indicates that the phase diagram calculated from the binary data is relatively sensitive to the se1f-consistency between thermodynamic properties and phase diagrams of binary systems.     

CALPHAD: Phase diagram of the system KFK2MoO4SiO2

The phase diagrams of the binary systems KFK₂MoO₄, KFSiO₂, and K₂MoO₄SiO₂, as well as that of the ternary system KFK₂MoO₄SiO₂ in the range up to 50 mole % SiO₂, were measured using the thermal analysis method. The thermodynamically consistent phase diagrams were calculated using the coupled analysis of the thermodynamic and phase diagram data.In the system KFK₂MoO₄ the intermediate compound K₃FMoO₄, melting congruently at 751 °C, is formed. This compound divides this system into two simple eutectic ones. The coordinates of the individual eutectic points are: E₁: 30.5 mole % K₂MoO₄, 720.4 °C, and E₂: 58.8 mole % K₂MoO₄, 744.9 °C. In the binary system KFSiO₂ the liquidus curve of KF shows an inflex point, characteristic for reciprocal systems with chemical reaction taking place between components. Similar course of the liquidus curve of K₂MoO₄ was found in the binary system K₂MoO₄SiO₂, indicating the presence of the chemical reaction between components as well. The strong positive deviation from ideal behavior of the ternary system KFK₂MoO₄SiO₂ was ascribed to the possible formation of heteropolyanions [SiMo₁₂O₄₀]⁴⁻ in the melt.In the investigated concentration range of the ternary system no eutectic point has been found. It lies most probably beyond the investigated part of the system. The standard deviation of approximation of the calculated ternary phase diagram is ± 5.9 °C, which is approximately on the same level of magnitude as the estimated experimental error of ± 4 °C.     

The B-rich side of the B–C phase diagram

The melting behavior of ß-boron at the boron-rich side of the B–C binary phase diagram is a long standing question whether eutectic or peritectic. Floating zone experiments have been employed to determine the melting type on a series of C-containing feed-rods prepared by powder metallurgy and sinter techniques. Melting point data as a function of carbon-content clearly yielded a peritectic reaction isotherm: L+B_4+δC=(ßB). The partition coefficient of carbon is ~2.6. The experimental melting point data were used to improve the existing thermodynamic modeling of the system B–C. Relative to the thermodynamically accepted melting point of pure ßB (T_M=2075 °C), the calculated reaction isotherm is determined at 2100.6 °C, a peritectic point at 0.75 at% C and a maximum solid solubility of 1.43 at% C in (ßB) at reaction temperature. With the new melting data the refractory system Hf–B–C has been recalculated and the liquidus surface is presented. The influence of the melting behavior of (ßB) on the phase reactions in the B-rich corner of M–B–C diagrams will be discussed and demonstrated in case of the Ti–B–C system.     

Thermodynamic reassessment of the Ag–Cu phase diagram at nano-scale

The Ag–Cu phase diagram at nanoscale was reassessed by CALculation of PHAse Diagrams (CALPHAD) method, considering the surface effect on the chemical potential of pure substance and excess Gibbs free energy of mixtures. According to the reported thermodynamic properties of pure Ag and Cu nanoparticles (NPs), and the measured melting eutectic temperatures of Ag₈Cu₂, Ag₇Cu₃, Ag₆Cu₅ to Ag₅Cu₅ NPs, respectively, obtained in the previous works, self-consistent thermodynamic parameters including the size effect were obtained by thermodynamic optimization. Using the obtained thermodynamic parameters, four Ag–Cu nano phase diagrams were constructed, and thermodynamic properties were calculated. It was indicated that the calculated Ag–Cu nano phase diagrams agreed well with experimental data.     

Measurement and calculation of the phase diagram of the Licl-BaCl2-SrCl2 system

The liquidas surface of the ternary LiCl-BaCl₂ SrCl₂ system has been measured by a DTA technique. A complete critical literature assessment and coupled thermodynamic/phase diagram analysis of the 3 binarv sub-systems has been performed. The ternary phase diagram was calculated from the assessed binary thermodynamic properties. Agreement between the calculated and measured ternary liquidus surfaces is good. The estimated accuracy of the calculated diagrams is ±5° for the binaries and ±10° for the ternary.     

Thermodynamic description of the Cu-Ge-Pb system: Experiment and modeling

Decades of scientific work dedicated to the investigation of phase diagrams gave significant benefit to industry and science. After all those years of phase diagram investigation still there is missing information about phase diagram of some ternary systems. One of those systems is Cu-Ge-Pb. It is known importance of Cu-based alloys and Ge-based alloys in electro industry. Since such combination is not tested before this work will provide information about phase diagram of ternary Cu-Ge-Pb system. In this work ternary Cu-Ge-Pb system has been tested experimentally and analytically by using Calphad model. Two isothermal sections at 600 and 400 °C and three vertical sections are experimentally tested and results were compared with calculated corresponding phase diagrams. None of the ternary compound and large solubility of third element in binary compound is not confirmed. Liquidus projection, invariant reaction and scheme of invariant reaction are presented. Scheil and Lever simulation of solid phases for Cu₈₀Ge₁₀Pb₁₀ alloy were calculated.     

Modelling and calculation of the phase diagrams of the LiF–NaF–RbF–LaF3 system

Four ternary phase diagrams of the quaternary system LiF–NaF–RbF–LaF₃ were calculated from the data of LiF–NaF, LiF–RbF, LiF–LaF₃, NaF–RbF, NaF–LaF₃ and RbF–LaF₃ binary phase diagrams using the Kohler symmetric and Kohler–Toop asymmetric approximation. Excess Gibbs parameters of all six mentioned binaries were optimized using the experimental results taken from the literature. For the LiF–RbF system our own data were used. In all cases very good agreement between the experimental data and our optimized values was achieved. Excess Gibbs functions for the liquid phases were obtained using the modified quasi-chemical method based on quadruplet interactions and the excess Gibbs function for the solid solution was calculated by a sublattice model. The quaternary eutectic was determined and a set of pseudo-ternary systems with fixed ratio of LaF₃ was calculated in order to find the optimal composition for a molten salt fuel.     

Thermodynamic analysis of the Zr–Be system using thermochemical properties based on ab initio calculations

A thermodynamic analysis of the Zr–Be system has been carried out by combining ab initio energetic calculations with the CALPHAD approach. The energy of formation of the binary compound phases and some bcc-based ordered phases was calculated using the Full Potential Linearized Augmented Plane Wave method. The CrB-type ZrBe phase, which has been reported as a metastable phase, was found to be stable in the ground state, while the ZrBe phase with a CsCl-type B2 structure was found to be metastable. The Gibbs free energy of formation of the bcc phase was obtained by applying the cluster expansion and the cluster variation methods. To describe the B2 ordering state, the Gibbs energy of the bcc phase was represented using the two-sublattice model with the formula (Zr,Be)_0.5(Zr,Be)_0.5. Although the thermodynamic parameters for the CrB-type ZrBe phase did not satisfy both the experimental data and the ab initio calculations, the calculated phase diagram reproduced the experimental results. In addition, the glass-forming ability of this binary alloy was evaluated by incorporating the thermodynamic quantities from the phase diagram calculation into the Davies–Uhlmann kinetic approach. The evaluated glass-forming compositional range was narrower than the experimental results.     

Experimental investigation of phase transformations in the La-Fe and La-Fe-C systems

Phase equilibria in the La-Fe-C system at crystallization were studied and the binary La-Fe system was reinvestigated using DTA, X-ray diffraction, SEM and electron probe microanalysis. Using the results, the binary La-Fe phase diagram has been redrawn and liquidus and solidus projections for the La-Fe-C system constructed, for the first time, covering the whole concentration range. There is no stable miscibility gap in the liquid phase of La-Fe system, according on our results. The La-Fe system shows a simple eutectic at 88 at.% La. The eutectic temperature was measured to be 788 °C. No intermediate phases were found. In the ternary La-Fe-C system a ternary compound La_3.67FeC₆ (τ) was found in equilibrium with the liquid phase and to coexist with most of the other phases in the system. Additions of carbon to La-Fe alloys caused liquid immiscibility. In this investigation, the liquid separation has been proved with clear microscopic pictures of samples showing this effect. A ternary stable liquid miscibility gap marked L₁ + L₂ develops from a metastable liquid miscibility gap in the La-Fe binary system. None of the binary intermetallic phases show any solubility of the third component.     

Experimental investigation of phase equilibria in the Ce-Fe-Ni system at 950 and 750 °C

The Ce-Fe-Ni system has been experimentally studied by microstructural analysis, electron microprobe analysis and X-ray diffraction over the whole concentration range. Isothermal sections at 950 and 750 °C for this system were constructed for the first time. The phase relations at 750 °C measured in this work are different from those published for 700 °C in particular because of the identification of a new binary phase Ce₅Ni₁₉. A continuous solid solution Ce(Fe,Ni)₂ (MgCu₂-type structure, cF24-Fd-3m), was found at 750 °C, with mutual substitution of Fe and Ni atoms. The liquid phase is present in the system both at 950 and 750 °C. Almost all binary-based phases at these temperatures show wide homogeneity regions and possess a constant Ce content.     

Effects of Al2O3 and “Cr2O3” on phase equilibria of the system “FeO”−MgO−SiO2 at iron saturation

“FeO”, MgO and SiO₂ are the major components of the nickel laterite smelting slags. Significant amounts of Al₂O₃ and “Cr₂O₃” may be present in the slag that come from laterite, coal ash and refractory. Effects of Al₂O₃ and “Cr₂O₃” on liquidus temperatures and solid solutions have been determined in the olivine and spinel primary phase fields in equilibrium with metallic iron. The results are presented in the form of MgO−‘‘FeO’’−SiO₂ pseudo-ternary section at fixed 7 wt% Al₂O₃ and 2 wt% “Cr₂O₃”. A series of pseudo-binary phase diagrams have been constructed to demonstrate the application of phase diagram on smelting reduction of laterite. The liquidus temperatures and the compositions of solid solutions are compared between experimental data and FactSage thermodynamic modelling. The possible reasons for the different results have been discussed which will help FactSage to optimize the relevant databases.     

Experimental investigation and thermodynamic assessment of the Al-Co-Ni system

The Al-Co-Ni system is essential to both Co- and Ni-based superalloys. In this study phase relationships among A1, L1₂ and B2 at 800 °C have been investigated by using equilibrated alloys. Four samples were prepared and annealed at 800 °C for 14 days. SEM-EDXS and XRD were used to analyze the annealed samples. The results indicated that two-phase L1₂+B2 and three-phase A1+L1₂+B2 regions exit.A thermodynamic reassessment of the entire Al-Co-Ni system has been made according to the CALPHAD method. Compared to the previous assessments, more recent experimental results have been considered. In the Al-Co binary system, the phase named Y-Co₄Al₁₃ has been added on the basis of the available literature. The order-disorder model has been adopted to describe the A1/L1₂ and A2/B2 phase relations, respectively. Three ternary compounds in the Al-rich region have been introduced. Three-sublattice model has been selected to describe the τ₁ phase with a considerable solubility extension. Thermodynamic interaction parameters have been optimized, considering the available experimental data. In this work several diagrams were calculated, which can fit experimental results in the whole composition range. A satisfactory agreement was obtained. As a result phase equilibria in the interested ferromagnetic shape memory alloys are calculated.     

Thermodynamics of the Ca(NO3)2 – NaNO3 system

Thermodynamic properties of the quasi binary Ca(NO₃)₂–NaNO₃ system are of interest with respect to thermal energy storage. In the present work the phase diagram as well as thermodynamic properties of the near eutectic mixture 45 mol% Ca(NO₃)₂ – 55 mol% (NaNO₃)₂ were determined experimentally and applied in the assessment of a new Gibbs energy dataset for thermochemical calculations. The enthalpy of fusion of the 45 mol% Ca(NO₃)₂ – 55 mol% (NaNO₃)₂ mixture is determined to be 24.7 ± 0.5 kJ/mol. The melting and crystallization enthalpy have good reproducibility, which makes it possible to use this mixture as a phase change material at temperature 225 °C. The assessed dataset describes liquid phase properties using a subregular solution model in the Redlich-Kister formalism with high accuracy. Therefore it can be used for the prediction of thermodynamic properties of different compositions in the whole Ca(NO₃)₂–NaNO₃ system and be included in databases for calculation of multicomponent systems including other components.     

Thermodynamic optimization and calculation of the ErCl3–MCl (M=Li,Na,K,Rb,Cs ) systems

In this paper, the binary phase diagrams of the ErCl₃–MCl (M = Li, Na, K, Rb, Cs) systems were studied by the CALPHAD (CALculation of PHAse Diagram) approach. The modified quasi-chemical model in the pair-approximation for short-range ordering was used to describe the Gibbs energies of the liquid phase in the systems. From measured phase diagram data and experimental thermochemical properties, a series of thermodynamic functions has been optimized based on computer-assisted analysis. A discussion of thermodynamic functions for strong interaction binary systems was undertaken. The results showed that the calculated phase diagrams and optimized thermodynamic parameters are self-consistent.     

Atom probe analyses and numerical calculation of ternary phase diagram in Ni-Al-V system

The ternary phase diagram in the Ni-Al-V system is studied using three dimensional atom probe (3DAP) analyses and numerical calculations using a mean-field model. Our focus is on the Ni-rich corner of the isothermal section at 800°C of the ternary phase diagram, where disordered f.c.c. matrix coexists with the L1₂ and DO₂₂ ordered phases. Both the experimental measurements and numerical calculations showed that the equilibrium compositions of the coexisting phases are quite different from those predicted by published phase diagrams. It is demonstrated that the aluminium and vanadium compositions in the L1₂ phase are approximately the same, and there is more aluminium in the disordered matrix than that indicated in the existing phase diagram. A possible explanation of this disagreement is discussed.