The liquidus surface projection of the Co–Mo–Ru system was constructed by analyzing the solidification paths of the as-cast alloys, and five primary solidification regions bcc(Mo), fcc(Co), hcp, μ and σ were experimentally identified. The isothermal sections at 1473 and 1373 K were obtained through analyzing microstructures and phase compositions of the annealed alloys. Six and seven two-phase regions were detected in the isothermal sections at 1473 and 1373 K, respectively. Furthermore, the free energies of σ with varying compositions were calculated via ab initio calculations, which included contributions from vibrational energy, electronic energy and configurational entropy. The addition of the third element in the Co–Mo or Mo–Ru systems could reduce the free energy of σ, thereby enhancing its stability. The electronic mechanisms underlying the stabilization of σ were elucidated through the analyses of the differential charge density and density of states. Based on the experimental data in this work, the thermodynamic parameters of the Co–Mo–Ru system were optimized, and the experimental data were reproduced well.

The high-temperature phase equilibria of the Al-Mo-Zr system are essential for optimizing process and designing composition of refractory high-entropy alloys (RHEAs). This work investigated the isothermal sections at 1373 and 1473 K and the liquidus projection of the Al-Mo-Zr system. The ternary compounds Al6MoZr and AlMo4Zr9 were identified, in which AlMo4Zr9 was first reported in this work. Compositional analysis revealed that the maximum solubility of Mo in the Al2Zr phase was 26.6 at% at 1373 K, which increased to 30.5 at% at 1473 K. 21 primary phase regions were determined in the liquidus projection. The thermodynamic modeling of the Al-Mo-Zr system was conducted on the basis of the present experimental data, and a set of reasonable and selfconsistent thermodynamic parameters was obtained. The results provided a theoretical foundation for developing RHEAs and contributed to the expansion of the materials database.

Four novel Co-based superalloys were designed based on the thermodynamic database. A preliminary evaluation was conducted on the compression mechanical properties, density, and transition temperature of alloys. After aging at 1000 degrees C for 720 h, the alloys exhibited a stable gamma/gamma(y) two-phase microstructure, and no harmful secondary phase, such as the topologically close-packed phase (TCP), was observed in the alloys. The novel Co-based superalloy Co30.0Ni9.0Al3.0W1.0Ta4.0Ti9.0Cr (at.%) possesses a higher gamma(y) solvus temperature (1117 f 2 degrees C) and a lower density (8.55 f 0.03 g/cm3). Furthermore, the yield strength exhibits a positive temperature dependence from room temperature to 600 degrees C in the compression process. The yield strength of the alloy is 797 f 3 MPa at 600 degrees C, which is appreciably higher than that of the commercial Mar-M-509 superalloy.

A series of annealed and as-cast Al-Hf-Zr alloys were investigated using scanning electron microscope (SEM) and X-ray diffraction (XRD) characterization methods. The liquidus projection of the Al-Hf-Zr system was established. Nine primary solidification regions, fcc(Al), Al3(Hf, Zr), Al2(Hf, Zr), Al3(Hf, Zr)2, Al(Hf, Zr), Al2(Hf, Zr)3, Al4Zr5, Al3Zr5, and bcc(Hf, Zr), and three invariant reactions were confirmed. The isothermal sections at 1273 and 1473 K were constructed based on the phase constituents of equilibrated alloys, and both of them included six three-phase regions, eighteen two-phase regions, and thirteen one-phase regions. The Al3Hf and Al3Zr, Al2Hf and Al2Zr, Al3Hf2 and Al3Zr2, AlHf and AlZr, and Al2Hf3 and Al2Zr3 at 1273 and 1473 K formed continuous solid solutions from Al-Hf side to Al-Zr side and named as Al3(Hf, Zr), Al2(Hf, Zr), Al3(Hf, Zr)2, Al(Hf, Zr), and Al2(Hf, Zr)3, respectively. The thermodynamic evaluation of the Al-Hf-Zr system was carried out by CALPHAD method, and a set of self-consistent thermodynamic parameters was obtained. Thermodynamic analyses of the Al-Hf-Zr system were undertaken to provide theoretical framework for the development of Zr-based alloys as candidate cladding materials for accident-tolerant fuel (ATF).

The accurate description of phase stability and melting behavior is essential for the development of Co-based superalloys. A multiscale thermodynamic framework integrating molecular dynamics simulations (MD), first-principles calculations, and CALPHAD modeling was established for the Co–Ru binary system in this work. The temperature-dependent free energies of solid and liquid phases were evaluated through rigorous thermodynamic integration approaches. The results demonstrated that both computational frameworks accurately reproduced experimental benchmarks of the hcp(Co)→fcc(Co) and fcc(Co)→liquid transitions. The transition temperatures predicted by MD were 712 K and 1752 K, while they were 730 K and 1807 K from first-principles calculations. Furthermore, the solidus temperature of the Co0.5Ru0.5 alloy was determined through ab initio. The calculated phase transition temperatures showed good agreement with experimental measurements, providing reliable thermodynamic constraints for reassessment of the Co–Ru phase diagram. By incorporating atomic-scale free-energy data, the high-temperature liquidus description is improved and a self-consistent thermodynamic database is developed, offering a robust foundation for thermodynamic design of Co-based superalloys.

The Al-doped Nd-Fe-B-based magnets exhibits superior magnetic performance and cost-effectiveness. However, the lack of thermodynamic description of the crucial Nd-Fe-Al ternary system hinders further improvement in coercivity. In this study, the reasonable thermodynamic database of the Nd-Fe-Al system, with which the calculated phase diagrams agree fairly well with those of the current literature and experimental data, has been developed. Besides, the formation mechanisms of various Al-containing intergranular phases in the Al-doped NdFe-B-based magnets, such as the 6:13:1-type crystalline phase, Nd-rich and Fe-rich amorphous phases, have been analyzed. The 6:13:1-type phase is most likely formed from the Nd-rich liquids through the deep ternary eutectic reaction, L(Liquid) -> Nd6Fe13-xAl1+x + NdAl3 + Nd, at 860 K. The Nd-rich amorphous phase directly forms from the under-cooled liquid with a high glass-forming ability. The Fe-rich amorphous phase forms from the undercooled liquid during the gradual phase evolution toward the final 6:13:1-type crystalline phase.

The Nd-Fe-Al hard magnetic alloys commonly exhibit excellent glass-forming ability, requiring systematic investigation of solidification behavior to reveal the possibly formed competing crystalline phase, experimental glass-forming region, and the nanocrystallite precipitation for explaining the coercivity and designing magnetic alloys. In this work, based on the solidification microstructures of alloys with various compositions and three theoretically evaluated boundary binary phase diagrams, the liquidus surface projection of the Nd-Fe-Al system was constructed. And both the glass-forming region and the precipitation of nanocrystallites embedded in amorphous matrix were confirmed. It was found that the complex of nanocrystallites + amorphous matrix (NCAM) only can be formed during solidification process involving the Nd-rich corner ternary deep eutectic reaction and/or multiple quasi-peritectic reactions. The glass-forming region is surrounded by the primary solidification regions of dhcp-Nd, Nd3Al, Nd2Al, Nd6Fe13-xAl1+x, and Nd2Fe17-xAlx. Furthermore, two possible formation sequences of nanocrystallites embedded in the amorphous matrix are suggested. One is the primary crystallization together with the eutectic crystallization (dhcp-Nd/Nd6Fe13-xAl1+x -> dhcp-Nd + Nd6Fe13-xAl1+x), and another is only the eutectic crystallization including the pseudo-eutectic crystallization (dhcp-Nd + Nd6Fe13xAl1+x). The obtained results are conducive for controlling the grain boundary phase in the widely used Al doped Nd-Fe-B based permanent magnetic materials and for developing Nd-Fe-Al based bulk-metallic glasses and nanocrystallite materials.

The partial phase relationships in the Nb-Ru binary system were investigated using diffusion couple and equilibrium alloy methods. Two-phase equilibria between Ru2Nb and Ru3Nb were observed at 1373 and 1473 K. Additionally, the phase stability of Ru2Nb and Ru3Nb was investigated via ab initio calculations. The Ru2Nb with C37 structure and Ru3Nb with Ni3Sn prototype were found to be dynamically and thermodynamically stable at 1473 K, which were consistent with the experimental results. The second-order phase transition between bcc(Nb) and B2(RuNb) was determined by analyzing the Gibbs energy. The calculation results indicated that the vibrational and electronic contributions to the Gibbs energy were crucial for predicting the phase transition. Furthermore, Nb atoms gained electrons and Ru atoms lost electrons in the ordered structure B2(RuNb), which strengthened the metal bonds and made the ordered structure more stable than disordered structure bcc(Nb). Finally, the Nb-Ru phase diagram at high temperatures was reconstructed based on experimental and calculated results.

In the Fe-Nb-Zr system, six primary solidification regions were identified in the liquidus surface projection by analyzing microstructures and phase constituents of 26 as-cast alloys. The equilibrium areas of 4 three phases and 7 two phases were determined by measuring the phase constituents of 24 equilibrated alloys at 1273 K. The solubility of Nb in Fe23Zr6 and lambda(2) at 1273 K was similar to 0.7 and 9.0 at. %, respectively, and that of Zr in mu and lambda(1) at 1273 K was similar to 8.1 and 38.4 at. %, respectively. The compound tau with NiTi2 structure was confirmed to be stable at 1273 K, and the homogeneity range of Nb was similar to 10.1-16.8 at. %. Combining the experimental results in literature and those of the current study, the Fe-Nb-Zr system was assessed by CALPHAD method. A set of self-consistent reliable thermodynamic parameters was derived.

The phase relationships of the Sc-Sb binary system were experimentally investigated using the heat-treated alloys as well as the as-cast alloys by scanning electron microscopy with energy dispersive spectrometer (SEM-EDS), powder X-ray diffraction (XRD) and differential scanning calorimetry (DSC). Four stable intermetallic phases, Sc2Sb, Sc4Sb2.52, Sc5Sb3 and ScSb, are confirmed to exist in the Sc-Sb binary system. The phases Sc5Sb3, Sc4Sb2.52 and ScSb solidify congruently while the phases Sc2Sb is formed through the peritectic transformation. There are six invariant reactions in the Sc-Sb system. The liquid compositions of the four eutectic isothermal reactions are approximately 16.3 at.% Sb at 1188 degrees C for L -> alpha-Sc + Sc2Sb, 38.3 at.% Sb at 1548 degrees C for L -> Sc5Sb3 + Sc4Sb2.52, 48.4 at.% Sb at 1442 degrees C for L -> Sc4Sb2.52 + ScSb and 88.0 at.% Sb at 575 degrees C for L -> ScSb + Rhom-Sb, and a peritectic isothermal reaction is about 23.2 at.% Sb at 1349 degrees C for L + Sc5Sb3 -> Sc2Sb. The liquid composition of the metatectic isothermal reaction beta-Sc -> alpha-Sc + L is 14.39 at.% Sb at 1263 degrees C. The solubilities of Sb in alpha-Sc are 3.8, 4.8 and 5.5 at.% Sb at 1000, 1100 and 1200 degrees C, respectively. According to the experimental heat capacity of the Sc4Sb2.52 compound, the Gibbs energy of this compound was firstly determined from 0 to 2000 K. Based on the presently obtained experimental data and the data from literatures, the Sc-Sb system was thermodynamically described and critically assessed by means of the CALPHAD approach. A self-consistent set of thermodynamic parameters was obtained. The calculated results show good agreement with the experimental data.

To establish a foundation for further understanding the crystallization kinetics of the cache-type phase change material, the bulk phase change material is the research basis for the study of the behaviour of nano/microlayers. In this work, the amorphous structure and the glassy nature of Sb6Si14Te80 were confirmed by x-ray diffraction, transmission electron microscopy and differential scanning calorimetry. The experimental results revealed that the glass transition is followed by three exothermic crystallization peaks. The final eutectic crystallization is in the form of Te + Sb2Si2Te6 + alpha-SiTe2. A relatively low Gibbs free energy difference Delta G between the supercooled liquid and the crystalline state indicates that the alloy has a good glass forming ability. In nonisothermal conditions, the activation energy for the glass transition (Eg) is comparable with or even higher than the microlite crystallization (Ex and Ep), implying that the amorphous has good stability in thermodynamics. The strong liquid behavior is exhibited according to the estimated fragility index and the value is about 35. The local activation energies were also determined by using the Kissinger-Akahira-Sunose and the Flynn-Wall-Ozawa methods, from which the local Avrami exponent n(x) was calculated, suggesting that the crystallization process is mainly diffusion-controlled three-dimensional growth. Isothermal crystallization results indicate the variation of the Avrami exponent n(x) from 1.09 to 1.31, in accordance with the diffusion-controlled process with a near-zero nucleation rate. It suggests that non-isothermal processes promote nucleation more effectively than isothermal processes, resulting in a greater kinetic factor.

The development of a thermodynamic database is essential for designing alloy materials capable of cyclic transitions between high-resistance amorphous and low-resistance polycrystalline states, and for determining controllable composition ranges and temperature intervals. According to the solidification microstructure of ascast alloys and the phase constituents of annealed samples, the liquidus surface projection and the phase equilibrium relationships at 500 degrees C for the Sb-Si-Te system have been constructed. For the isothermal section at 500 degrees C over the entire composition range, there are 10 two-phase regions, and 7 three-phase regions. The maximum solubilities of Si in the intermetallic phases delta with P3m1 and gamma with R3m space groups are about 3.1 and 4.1 at%, respectively. In the liquidus surface projection, there are 10 primary solidification regions and 9 invariant reactions. The Sb-Te binary system is reoptimized based on the available literature to ensure compatibility with the thermodynamic database of multi-component systems. On the basis of experimental data, the thermodynamic parameters of all the phases in the Sb-Si-Te system are optimized by CALculation of PHAse Diagram (CALPHAD) method. The liquid phase is described as the solution phase with the associated model (Sb, Sb2Te3, Si, Si2Te3, Te). The phases delta and gamma are modeled as (Sb, Si)0.4(Sb, Te, Si)0.6. Sb2Si2Te6 is described as (Sb)0.2(Si)0.2(Te)0.6 by a three-sublattice model. A set of self-consistent thermodynamic parameters of the Sb-Si-Te system are obtained, which facilitate the design of phase-change materials.

The liquidus surface projection of the Ni-Ta-Ti system was constructed in this work. Thirty-seven as-cast alloys were characterized using scanning electron microscope equipped with energy dispersive spectrometer (SEM/ EDS) and X-ray diffraction (XRD) methods to analyze the primary phases and solidification paths of alloys. Ten primary solidification regions of bcc(Ta,Ti), fcc(Ni), NiTi, NiTi2, NiTa2, Ni2Ta, Ni3Ta, Ni3Ti, mu and tau were determined. The crystal structure of the intermetallic phase tau was identified as the Ni3Sn type with space group P63/mmc. Moreover, the thermodynamic parameters of the Ni-Ta-Ti system were optimized via the CALculation of PHAse Diagram (CALPHAD) method based on the available experimental data. In this work, NiTi2, Ni3Ti, NiTa2, Ni2Ta, Ni3Ta and tau were modelled by two-sublattice model (Ni,Ta,Ti)m(Ni,Ta,Ti)n. A four-sublattice model (Ni,Ta,Ti)1(Ta,Ti)4(Ni,Ta,Ti)2(Ni,Ta,Ti)6 was adopted to describe mu. The calculated liquidus surface projection and isothermal sections with the obtained thermodynamic parameters were consistent with the experimental data.

Microstructures and phase constituents of alloys in the Al–Hf–Ta system were investigated. The liquidus projection of this system was constructed, and 12 primary solidification regions, fcc(Al), βAl3Hf, Al2Hf, Al3Ta, Al69Ta39, Al3Hf2, AlHf, Al3Hf4, τ, Al2Hf3, σ, and bcc(Hf, Ta) were identified. Fifteen and 14 three-phase equilibria were constructed at 1000 °C and 1200 °C, respectively. The maximum solubility of Ta in βAl3Hf, Al2Hf, AlHf, and τ was measured to be ∼ 5.5, ∼ 10.3, ∼ 16.9, and ∼ 20.2 at. pct at 1000 °C and ∼ 6.2, ∼ 10.8, ∼ 18.9, and ∼ 21.9 at. pct at 1200 °C, respectively. And the solubility of Hf in Al3Ta, Al69Ta39, φ, and σ was determined to be ∼ 7.3, ∼ 10.6, ∼ 6.0, and ∼ 39.3 at. pct at 1000 °C and ∼ 7.5, ∼ 10.8, ∼ 6.4, and ∼ 40.5 at. pct at 1200 °C, respectively. Finally, the thermodynamic parameters of each phase in the Al–Hf–Ta system were optimized using the CALPHAD method to obtain a set of self-consistent thermodynamic parameters.

According to the experimental information of 40 as-cast alloy samples, the liquidus surface projection of the Co–Fe–Nb system for the whole composition range was built. Six primary solidification regions bcc(Nb), fcc(Co,Fe), μ, λ3, λ2, and λ1 were experimentally identified, and the possible ranges of primary solidification regions of λ1 and λ2 were distinguished using electron backscatter diffraction (EBSD) and energy dispersive spectrometry (EDS) in the scanning electron microscopy (SEM). The isothermal sections at 1200 °C, 1100 °C, and 1000 °C were re-constructed by microstructure and phase constituents of equilibria alloys. A new two-phase equilibrium fcc(Co,Fe) + λ3 was experimentally determined at 1200 °C, 1100 °C, and 1000 °C, and Fe had a considerable solubility in λ3 at above temperatures. Based on the experimental data, the thermodynamic optimization of this system was made using the CALculation of PHAse Diagrams (CALPHAD) method, and a set of self-consistent and reasonable thermodynamic parameters was obtained.

In the Nd-Fe-Al ternary system, thermodynamic stabilities of three compounds, NdFe3Al2, Nd5Fe17 and μ, were determined by the equilibrated alloys, indicating that both NdFe3Al2 and μ ternary compounds are metastable phases, while Nd5Fe17 compound is a stable phase. Meantime, the microstructures of five representative as-cast alloy buttons are illustrated, which are consisted of crystalline phases and the complex of nanocrystallites + amorphous matrix (NCAM). The crystalline phases including Nd, Nd3Al, Nd2Fe17-xAlx and Nd6Fe13-xAl1+x as well as the nanocrystallites such as dhcp-Nd, fcc-Nd and Nd6Fe13-xAl1+x embedded in the amorphous matrix were observed. Particularly, it is concluded that the fcc-Nd nanocrystallites may be transformed from the fcc dense packing clusters of the amorphous matrix and/or dhcp-Nd nanocrystallites. The hard magnetic properties of these as-cast alloys can be attributed to NCAM and present a non-strict proportionate effect. The alloy composed of Nd + NCAM, with curie temperature (Tc) 515 K, displays the highest intrinsic coercivity Hci 305 kA/m and remanent magnetization Br 10.8 emu/g. Its good glass-forming ability is presented by the high ratio (Tx/Tm) 0.88 and the small interval (Tm-Tx) 105 K of the crystallization temperature (Tx) with the melting temperature (Tm). Since the present investigation focuses on phase stabilities, microstructural characterizations, magnetic properties and glass-forming ability of the Nd-Fe-Al alloys, the obtained results can provide a better understanding for advancing the design of the Nd-Fe-Al based hard magnets and amorphous materials.

The gamma + gamma ' microstructure in novel Co-based superalloys is often obtained by means of alloying method. Therefore, this study focuses on exploring the evolution of the gamma + gamma ' microstructure through the addition of Zr using CALculation of PHAse Diagram (CALPHAD) method. The heat capacity of tau was experimentally determined by the sapphire method, and the enthalpy of formation of tau at 0 K was calculated using Density Functional Theory (DFT). The thermodynamic parameters were derived based on experimental results from phase equilibrium data and first-principles calculations using CALPHAD method. According to the thermodynamic analyses, the alloy Co80.0V18.5Zr1.5 (at. %) was homogenized at 1473 K for 10 h and aged at 1173 K for different time, the ordered L12-gamma ' precipitates coarsened and dissolved after 2 h, and transformed into needle-like D019-Co3V after 67 h of aging, which indicated that the gamma ' phase was not in a thermodynamically stable state in the Co-V-Zr system. If the stable gamma ' phase is obtained, additional alloying elements is necessary to be added.

To determine the homogeneity range of the bcc phase in the Fe-Mo-V system, the isothermal section of the Fe-Mo-V system at 1373 K was constructed by analyzing phase constituents of annealing samples using X-ray diffraction (XRD) and scanning electron microscopy (SEM) techniques. Two groups of diffusion couples A and B with the terminal alloys located in the V-rich bcc phase region were prepared and annealed at 1473 K for 96 h and 1373 K for 288 h, respectively. Based on the obtained concentration profiles, the ternary diffusion behaviors of the V-rich bcc phase in the Fe-Mo-V alloys were investigated by the electron probe microanalysis (EPMA) technique combined with the Whittle and Green method. Depending on DICTRA software, the atomic mobility parameters for the bcc phase of the Fe-Mo-V system were optimized. The experimental concentration profiles and diffusion paths in the Fe-Mo-V alloys can be well reproduced using the atomic mobility and thermodynamic parameters.

Ternary alloys samples with 22, 25 and 23 different compositions were prepared for determining isothermal sections at 1123, 1223 and 1373 K, respectively. The microstructures, phase constituents and phase compositions of the annealed Cu-Nb-Ni alloys were analyzed by scanning electron microscopy (SEM) with energy dispersive spectroscopy (EDS) and x-ray diffraction (XRD) methods. Two three-phase regions, fcc + NbNi_3+Nb_7Ni_6 , fcc + bcc(Nb) + Nb7Ni6, and three two-phase regions, fcc + NbNi_3,Nb_7Ni_6+NbNi_3 , fcc + Nb7Ni6, are determined for isothermal sections at 1123 and 1223 K. Two three-phase regions, liquid + NbNi_3+Nb_7Ni_6 , liquid + bcc(Nb) + Nb7Ni6, and three two-phase regions, fcc + NbNi_3,Nb_7Ni_6+NbNi_3 , liquid + Nb7Ni6, are determined for isothermal sections at 1373 K. The solubilities of Cu in NbNi3 and Nb7Ni6 were determined to be 9.6 at.