A thermodynamic modeling of the Pd-Ti system

The thermodynamic properties of the Pd-Ti system were optimized using the CALPHAD (CALculation of PHAse Diagram) technique. The solution phases, liquid, bcc, fcc and hcp, were described by the substitutional-solution model. Both compounds Pd₂Ti and PdTi₂ with tetragonal MoSi₂-type structure were treated as one phase with the formula (Pd,Ti)₂(Pd,Ti) by a two-sublattice model. The intermetallic compounds Pd₃Ti, Pd₃Ti₂, and PdTi₃ were treated as stoichiometric compounds. The intermetallic compound αPdTi, which had a homogeneity range, was treated as the formula (Pd,Ti)(Pd,Ti) by a two-sublattice model. A two-sublattice model (Pd,Ti)_0.5(Pd,Ti)_0.5 was applied to describe the compound βPdTi in order to cope with the order-disorder transition between βPdTi with CsCl-type structure (B2) and body-centered cubic solution (A2) in the Pd-Ti system. A set of self-consistent thermodynamic parameters was obtained.     

Re-assessment of the Mg–Zn–Ce system focusing on the phase equilibria in Mg-rich corner

The Mg–Zn–Ce alloys exhibit good creep resistance and strength at elevated temperature due to the formation of intermetallic compounds. However, the ternary compounds and phase equilibria in the Mg-rich corner are still controversial which restrains the development of Mg–Zn–Ce alloys. The present work experimentally investigated the phase equilibria in Mg-rich corner of the Mg–Zn–Ce system at 350 and 465 °C and thermodynamically assessed the Mg–Zn–Ce system. The existence of ternary compounds τ₁ and τ₃ were confirmed by a combination of X-ray diffraction (XRD) and scanning electron microscopy (SEM). The crystal structure of τ₁ was resolved as space group of Cmc21 with a = 0.9852(2)–1.0137(2) nm, b = 1.1361(3)–1.1635(3) nm and c = 0.9651(2)–0.9989(2) nm by Rietveld refinement of the XRD pattern. Three invariant reactions, L→τ₃+CeMg₃+CeMg₁₂, L+CeMg₁₂→α-Mg+τ₁ and L+τ₁→τ₂+α-Mg, were revealed by differential scanning calorimeter (DSC) measurement and microstructure characterization. Then, a set of self-consistent thermodynamic parameters was thereafter constructed by assessing the phase equilibria, solid solubilities of CeMg₁₂, τ₁, CeMg₃ and τ₃, as well as the formation enthalpies of binary and ternary compounds calculated by density functional theory. The comparison of calculated phase diagram with experimental results and the literature were discussed. The calculated isothermal section of Mg–Zn–Ce system at 465 °C agreed with our experimental data. The two three-phase equilibria, τ₁+α-Mg+CeMg₁₂ and CeMg₃+τ₃+CeMg₁₂, were confirmed in the Mg-rich corner. This thermodynamic database can be used for the further alloys design of Mg–Zn–Ce system.     

Isothermal section of Mg-Zn-Zr ternary system at 345 ° C

Isothermal section of Mg-Zn-Zr ternary system at 345 ^°C has been determined by X-ray diffraction, differential scanning calorimetry and scanning electron microscopy assisted with energy dispersive X-ray spectroscopy using a series of Mg-Zn-Zr alloys. The results show that there exist three intermetallic compounds ZnZr, Zn₂Zr₃, (Mg,Zn)₂Zr, and a liquid phase in equilibrium with the α-Mg phase. The presence of two other three-phase regions in equilibrium, Liquid+MgZn+(Mg,Zn)₂Zr and MgZn+Mg₂Zn₃+(Mg,Zr)Zn₂, has also been confirmed. The addition of Zn can significantly increase the solubility of Zr and vice-versa in the α-Mg matrix.     

Thermodynamic description of the Al–Fe–Zr system

The Fe–Zr and Al–Fe–Zr systems were critically assessed by means of the CALPHAD technique. The solution phases, liquid, face-centered cubic, body-centered cubic and hexagonal close-packed, were described by the substitutional solution model. The compounds with homogeneity ranges, hex.- Fe₂Zr, Fe₂Zr, FeZr₂ and FeZr₃ in the Fe–Zr system, were described by the two-sublattice model in formulas such as hex.- Fe₂(Fe,Zr), (Fe,Zr)₂(Fe,Zr), (Fe,Zr)Zr₂ and (Fe,Zr)(Fe,Zr)₃ respectively. The compounds Al_mZr_n except Al₂Zr in the Al–Zr system were treated as line compounds (Al,Fe)_mZr_n in the Al–Fe–Zr system. The compounds FeZr₂ and FeZr₃ in the Fe–Zr system were treated as (Al,Fe,Zr)Zr₂ and (Al,Fe,Zr)(Fe,Zr)₃ in the Al–Fe–Zr system, respectively. All compounds in the Al–Fe system and hex.- Fe₂Zr in the Fe–Zr system have no solubilities of the third components Zr or Al, respectively, in the Al–Fe–Zr system. The ternary compounds _λ1${\lambda }_1$ with C14 structure and _λ2${\lambda }_2$ with C15 structure in the Al–Fe–Zr system were treated as _λ1${\lambda }_1$- (Al,Fe,Zr)₂(Fe,Zr) with Al₂Zr in the Al–Zr system and _λ2${\lambda }_2$- (Al,Fe,Zr)₂(Fe,Zr) with Fe₂Zr in the Fe–Zr system, respectively. And the ternary compounds _τ1${\tau }_1$, _τ2${\tau }_2$ and _τ3${\tau }_3$ in the Al–Fe–Zr system were treated as (Al,Fe)₁₂Zr, Fe(Al,Zr)₂Zr₆ and Fe₇Al₆₇Zr₂₆, respectively. A set of self-consistent thermodynamic parameters of the Al–Fe–Zr system was obtained.     

Interdiffusion behaviors and mechanical properties of Zn–Cr system

Diffusion couple technique has been utilized to study the interdiffusional behaviors of Zn–Cr system. Two intermetallic compounds (Zn₁₃Cr, Zn₁₇Cr) have been found in the diffusion zone between 598 K and 653 K. For the existence of Zn₁₃Cr phase, the incremental diffusion couple has been used to confirm, and the results show that the Zn₁₃Cr phase can be determined in the present work. However, the thickness of Zn₁₃Cr is very thinner than that of Zn₁₇Cr, which indicate the growth of Zn₁₃Cr is very slow. The thickness of Zn₁₇Cr satisfied the parabolic growth law. EPMA was used to obtain the composition profiles and the interdiffusion coefficients of Zn₁₃Cr, Zn₁₇Cr and Zn (hcp) have been extracted by forward simulation analysis embedded in ‘Pydiffusion’ code. The mechanical properties of Zn₁₇Cr were also determined by nanoindentation technique, and the hardness and Young's modulus of Zn₁₇Cr is 3.01 GPa and 165.78 GPa, respectively.     

Alloying behavior of zinc with rare earth metals: The Dy–Gd–Zn system

The isothermal section at 400 °C of the Dy–Gd–Zn system was studied, and the vertical sections at the Dy/Gd ratio=1 was investigated. The experimental techniques used were Differential Thermal Analysis (DTA), X-ray powder diffraction (XRPD) and scanning electron microscopy (SEM) coupled with electron probe microanalysis (EPMA-EDX).No ternary compounds were found in the system. As regard to the intermetallic phases, the (Dy,Gd)Zn, (Dy,Gd)Zn₂, (Dy,Gd)Zn₃, (Dy,Gd)₃Zn₁₁, (Dy,Gd)₁₃Zn₅₈, (Dy,Gd)₂Zn₁₇ and (Dy,Gd)Zn₁₂ solid solutions form in the full field of composition, while the Gd₃Zn₂₂ compound did not show dysprosium dissolution.     

Experimental phase diagram study of the TiAl-rich part of the Ti–Al–Ni ternary system

Phase equilibria of the TiAl-rich part of the Ti–Al–Ni ternary system have been studied experimentally by scanning electron microscopy and electron probe micro-analysis of heat-treated alloys. Partial isothermal sections involving the liquid, β-Ti, α-Ti, α₂-Ti₃Al, γ-TiAl and τ₃-Al₃NiTi₂ phases were constructed between 1623 and 1273 K. Eight three-phase regions of the L + β + α, L + α + γ, L + β + γ, β + α + γ, L + β + τ₃, β + γ + τ₃, β + α₂ + τ₃ and α₂ + γ + τ₃ were derived. Extrapolations of these tie-triangles indicate the occurrence of three transition-type reactions; L + α = β + γ at around 1593 K, L + γ = β + τ₃ at around 1553 K, and β + γ = α + τ₃ at around 1393 K. The Ni solid solubility in the α and α₂ phase is extremely low, less than 1 at.% in all studied temperature ranges.     

Phase equilibria and thermodynamic investigation of the In–Li system

Phase equilibria and thermodynamic properties of the In–Li system were analyzed by combining the first-principles approach and Computer Coupling of Phase Diagrams and Thermochemistry (CALPHAD) methodology. The enthalpies of formation for all the stable compounds were calculated by first-principles calculations based on the density functional theory (DFT). Phase diagram of the In–Li system was calculated for the first time, and a set of self-consistent thermodynamic parameters was finally obtained by CALPHAD approach coupling experimental measurements and first-principles calculations. An associate model of (In, In₂Li₃, Li) was used to describe the liquid phase, and InLi and InLi₂ were treated by sub-lattice models. Other intermediate phases were considered to be stoichiometric compounds. The calculated phase diagram, voltage curve and thermodynamic properties can reproduce the available experimental data reasonably.     

The V-Zn binary system: New experimental results and thermodynamic assessment

Experimental investigation followed by thermodynamic assessment of the V-Zn system was carried out in the present study. A series of V-Zn alloys annealed at various temperatures were examined using scanning electron microscopy coupled with energy dispersive spectroscopy/wavelength dispersive X-ray spectrometer, X-ray diffraction and differential thermal analysis. It was confirmed that V Zn₁₆, with a V content of about 5.8 at.%, was indeed an equilibrium phase. DTA results indicated that the peritectic temperature for V Zn₁₆ was about 427 ^°C. Two new metastable compounds, V Zn₉ and V ₃Zn₂, with V contents of 8.5-11.3 at.% and 60 at.%, respectively, were discovered. DTA results together with SEM-EDS examinations revealed that V Zn₉ was formed at around 450 ^°C in Zn75V25 alloy with a cooling rate greater than 12 ^°C/min. The V Zn₉ phase, however, decomposed into V Zn₃ and liquid Zn when the alloy was held above 442 ^°C. The peritectic temperatures for two equilibrium phases, V ₄Zn₅ and V Zn₃, were 651 ^°C and 621 ^°C, respectively. These measurements were slightly lower than the values determined in prior studies. The onset temperature for forming V Zn₃ decreased significantly with increasing cooling rate while its exothermic peak widened during fast cooling. These phenomena indicated that both the nucleation and growth processes for V Zn₃ were kinetically challenged.In addition, the solubility of Zn in α-V was measured. It was 2.1 at.%, 2.5 at.%, 2.6 at.%, 2.9 at.% and 3.3 at.% at 450 ^°C, 600 ^°C, 670 ^°C, 800 ^°C and 1000 ^°C, respectively. Based on the results obtained in the present study and previous investigations, the V-Zn system was reassessed thermodynamically. The assessment was in good agreement with experimental results.     

Experimental study and thermodynamic assessment of the Zn-Fe-Ni system

The Zn-rich corner of the Zn-Fe-Ni system was experimentally determined. It was found that the T phase, which was believed previously to be an extension of the binary Γ₁ phase in the Zn-Fe system, is a true ternary compound. The composition range of this phase has been determined in this study. Based on the results of the assessments of the Zn-Fe and Zn-Ni systems carried out by the authors and using information on the Fe-Ni system available in the open literature, a preliminary assessment of the Zn-Fe-Ni system was carried out. A two-sublattice model (Fe,Ni,Zn)Zn₅ was used to describe the ternary T phase. The calculated phase boundaries in the Zn-rich corner are in good agreement with experimental results. However, reproduction of the complex homogeneity range of the ternary T phase has proven challenging.     

Thermodynamic assessment of the ordered B2 phase in the Ti-V-Cr-Al quaternary system

Thermodynamic assessment of the ordered B2 phase in the quaternary Ti-V-Cr-Al system is carried out. A set of self-consistent thermodynamic parameters is presented. A two-sublattice model (Al,Cr,Ti,V )_0.5: (Al,Cr,Ti,V )_0.5 is used. The predicted phase equilibria and order/disorder transformation temperature are in good agreement with experimental information, both in the Ti-V-Cr-Al quaternary and in the important binary and ternary subsystems. The thermodynamic dataset can be used to predict compositions which are prone to the order/disorder reaction.     

Thermodynamic modeling of the Si-Y system aided by first-principles and phonon calculations

Thermodynamic modeling of the Si-Y binary system has been performed by the CALPHAD (CALculation of PHAse Diagram) method based on phase diagram and thermochemical data in the literature combined with Gibbs energies of end-members of compounds predicted by first-principles phonon calculations. In particular, non-stoichiometric compounds Si₂Y and Si₃Y₅ are modelled to accommodate their homogeneity ranges in terms of two-sublattice models (Si,Y)₂(Si,Y) and (Si)₃(Si,Y)₅, respectively. Formation of SiY is treated as a peritectic reaction according to experimental results, instead of an eutectic one as described in the previous models. The calculated phase equilibriums and thermodynamic properties are in a satisfactory agreement with available experimental data.     

Thermodynamic description of the Cr–Ge system

The Cr–Ge binary system was thermodynamically optimized using the CALPHAD method. The liquid phase was described by means of an associate solution model. The BCC terminal solid solution was described by the substitutional solution model. The two-sublattice model was used to describe the non-stoichiometric compounds Cr₃Ge, αCr₅Ge₃ and βCr₅Ge₃. The Cr₁₁Ge₈, CrGe and Cr₁₁Ge₁₉ phases were modeled as stoichiometric compounds. A set of thermodynamic parameters for the Cr–Ge system was obtained via thermodynamic optimization using assessed experimental data. The calculated phase diagram and thermodynamic properties agree well with most of the experimental data.     

Thermodynamic optimization of the binary CaO–ZnO and ternary CaO–ZnO–SiO2 systems

Liquidus phase equilibrium data of the present authors for the CaO–ZnO–SiO₂ system (as a part of research program on the characterization of the multicomponent PbO–ZnO–FeO–Fe₂O₃-“Cu₂O”-CaO-SiO₂ system), combined with phase equilibrium and thermodynamic data from the literature, have been used to obtain a self-consistent set of parameters of the thermodynamic models for all phases. The modified quasichemical model is used for the liquid slag phase; lime (Ca,Zn)O, zincite (Zn,Ca)O, α- and α′-dicalcium silicate (Ca,Zn)₂SiO₄ and tricalcium silicate (Ca,Zn)₃SiO₅ are described within Bragg-Williams formalism; tridymite, cristobalite SiO₂, wollastonite, pseudowollastonite CaSiO₃, rankinite Ca₃Si₂O₇, willemite Zn₂SiO₄, melilite (hardystonite) Ca₂ZnSi₂O₇ and Ca–Zn feldspar CaZnSi₃O₈ are treated as stoichiometric compounds. From these model parameters, the optimized ternary phase diagram is back calculated.