A thermodynamic analysis of the Fe–Nb–B ternary system has been carried out by estimating the unknown thermodynamic properties of various borides and solid solutions with using a first-principles method. The calculations showed that, at least in the ground state, the solid solution, in which the B atoms substitute for the Fe atoms, was more probable than that where the B atoms dissolved in the octahedral interstitial sites. Furthermore, the calculated values for the binary borides in the Fe–B and Nb–B systems were in reasonable agreement with those found by experiment. The thermodynamic properties such as formation enthalpies for the FeNbB and Nb3B2 phases were also determined for ternary borides. The thermodynamic functions determined using these theoretical values, as well as the available experimental information on the phase boundaries, successfully revealed the phase equilibria in the Fe–Nb–B ternary system over the entire composition and temperature ranges.

Thermodynamic Analysis of the Fe–Nb–B Ternary 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 AlmZrn except Al2Zr in the Al–Zr system were treated as line compounds (Al,Fe)mZrn 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 λ 1 with C14 structure and λ 2 with C15 structure in the Al–Fe–Zr system were treated as λ 1 - (Al,Fe,Zr)2(Fe,Zr) with Al2Zr in the Al–Zr system and λ 2 - (Al,Fe,Zr)2(Fe,Zr) with Fe2Zr in the Fe–Zr system, respectively. And the ternary compounds τ 1 , τ 2 and τ 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.

Thermodynamic description of the Al–Fe–Zr system

This paper presents a Calphad-type thermodynamic database for the Fe–Nb–Ni system. The stable phases in this ternary system are liquid, fcc_A1, bcc_A2, C14 Laves, D0a, D85 and L12_fcc but we took also into account the C15 Laves and the metastable D022 phase because of their engineering interest. Available optimizations of the unary and binary systems were selected from the literature with the constraint that the Gibbs energy descriptions must be compatible. The only amendment needed to the selected assessments concerned the parameters for the D85 in the Fe–Nb system. In addition, ab-initio calculations have been performed using the VASP in order to help with estimating enthalpies of formation of some binary end members of the intermetallic compounds. The optimization of the Fe–Nb–Ni ternary system was performed using mostly experimental data available in the literature.

Calphad-type assessment of the Fe–Nb–Ni ternary system

Phase equilibria in the Fe corner of the Fe–Al–Nb system between 800 and 1150 °C

The novel double-layered metal-ceramic hollow spheres made of 316L stainless steel powder and Al2O3 hollow spheres were sintered by powder metallurgy method at 1100 °C, 1150 °C and 1200 °C for 3h under vacuum condition in this study. The characteristics of double-layered metal-ceramic hollow spheres were investigated by X-ray diffractometer (XRD), optical microscope (OM) and a field emission scanning electron microscopy (FE-SEM) equipped with an energy dispersive spectroscopy (EDS). And the mechanical properties of hollow spheres were carried out via uniaxial compressive tests. The experimental results showed that metal-ceramic hollow spheres with smooth surface macrograph were prepared under 1200 °C sintering temperature and the interface between metal and ceramic layers was well combined without obvious gap. The porosity of metal layer decreased with increasing sintering temperature. Secondary phases, such as σ phase, carbide and NbS, formed in 316L stainless steel metal layer during supersolidus liquid phase sintering process at 1200 °C sintering temperature. Compressive engineering stress-stain curve of hollow spheres with optimal preparation process showed platform area and the compressive strength of this hollow sphere was 9.84 MPa. The deformation mechanism of metal-ceramic hollow spheres sintered at 1100 °C and 1150 °C was brittle shear fracture, while that of hollow spheres sintered at 1200 °C was plastic deformation. Correspondingly, the failure modes of hollow spheres changed from shear fracture to plastic deformation and densification of hollow shell structures as sintering temperature rose. The fracture characteristics of hollow spheres were also discussed.

Preparation, microstructure and mechanical property of double-layered metal-ceramic hollow spheres

The Gibbs energy of formation of the solution and compounds phases in the Fe-Nb system were derived from an optimization procedure using all the available experimental thermodynamic and phase diagram data. The thermodynamic description of the stoichiometric and non-stoichiometric compounds was made using two, three or four sublattice models, while a Redlich-Kister polynomial was used for the solution phases.

Thermodynamic assessment of the Fe-Nb system

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Thermodynamic assessment of the Fe-Nb system