Assessment of atomic mobilities for fcc Co–Ti–V alloys

Based on the experimental interdiffusion coefficients from our previous work and the critically reviewed experimental diffusivities available in the literature, the atomic mobilities of Co, Ti and V in fcc Co–Ti–V alloys were assessed by means of DICTRA (DIffusion Controlled TRAnsformation) software. Askill's empirical relations were utilized to assess the self-diffusion coefficients of fcc Ti and fcc V. Comprehensive comparisons between the DICTRA-calculated diffusivities and the experimental data indicate that the presently obtained atomic mobilities can reproduce most of the diffusivities in binary and ternary systems. In addition, a further verification on the obtained atomic mobilities was carried out through comparing the DICTRA-simulated concentration profiles/diffusion paths of the diffusion couples with the corresponding experimental ones. This work contributes to the establishment of a kinetic database for multi-component cemented carbide.     

Thermodynamic modeling of the Co–Fe–O system

As a part of the research project aimed at developing a thermodynamic database of the La–Sr–Co–Fe–O system for applications in Solid Oxide Fuel Cells (SOFCs), the Co–Fe–O subsystem was thermodynamically re-modeled in the present work using the CALPHAD methodology. The solid phases were described using the Compound Energy Formalism (CEF) and the ionized liquid was modeled with the ionic two-sublattice model based on CEF. A set of self-consistent thermodynamic parameters was obtained eventually. Calculated phase diagrams and thermodynamic properties are presented and compared with experimental data. The modeling covers a temperature range from 298 K to 3000 K and oxygen partial pressure from 10⁻¹⁶ to 10² bar. A good agreement with the experimental data was shown. Improvements were made as compared to previous modeling results.     

Thermodynamic remodeling of the Co–Ga system

The thermodynamic properties and phase relations of the Co–Ga binary system are remodeled based on the CALPHAD approach. In this work, CoGa(β$\beta$) is considered to be non-stoichiometric and CoGa₃ to be stoichiometric. The β$\beta$ phase is thermodynamically described by a two-sublattice model (Co,Ga)_0.5 (Co,V a)_0.5. The stability of the β$\beta$ phase is restricted in the low-temperature regions by giving necessary driving force constraints. The lattice parameters and enthalpy of formation of the β$\beta$ and CoGa₃ phases have been compared with first-principles calculations based on density functional theory. The calculated Co–Ga phase diagram is compared to previously calculated ones.     

A thermodynamic assessment of the Co–Sn system

A critical evaluation and thermodynamic modeling of the phase diagram and thermodynamic properties have been presented for the Co–Sn system. More attention has been paid to reproduce the thermodynamic properties of the liquid Co–Sn, including the appreciable temperature dependence in the mixing enthalpy and the sign-variable activity with composition observed by experiments. A four-sublattice model has been used to describe the ordering phenomenon between $\beta {\mathrm{Co}}_3{\mathrm{Sn}}_2$ and $\alpha {\mathrm{Co}}_3{\mathrm{Sn}}_2$.     

Experimental study and thermodynamic calculation of the Y–Co–Fe system

In this work, the phase equilibria of the Y–Co–Fe ternary system were studied experimentally by scanning electron microscope (SEM) with energy dispersive spectroscopy (EDS) and X-ray diffraction (XRD). The phase transition temperatures and phase formation of Y–Co–Fe alloys were examined by differential thermal analysis (DTA) and SEM-EDS. No ternary intermetallic compounds were detected. The continuous solid solution phases Y₂(Co, Fe)₁₇, Y(Co, Fe)₃ and Y(Co, Fe)₂ were formed from the respective Y–Co and Y–Fe binary intermetallic compounds. The solubility of Fe in YCo₅ and Y₂Co₇ and the solubility of Co in Y₆Fe₂₃ were determined. Based on the experimental results determined in this work and reported in the literature, the thermodynamic calculation of the Y–Co–Fe ternary system was performed using the CALPHAD method in combination with the previous assessments of three Y–Co, Y–Fe and Co–Fe binary systems. The liquidus projection, isothermal sections and vertical sections of this ternary system were calculated. The good agreement between the calculated results and the experimental results was achieved. A set of self-consistent thermodynamic parameters for describing various phases in the Y–Co–Fe ternary systems was obtained finally, which would provide a good basis for the development of the thermodynamic database of multi-component Y–Co–Fe based alloy systems.     

Experimental investigation and thermodynamic modeling of the Mo–Co–B ternary system

Among the ternary borides, the Mo–Co–B system is of great interest because of its excellent hardness, toughness, and stability performance. Eight samples with 60 at.% Co were designed to investigate the isothermal section of Mo–Co–B system at 1073 K in the Co-rich portion. Scanning electron microscopy, energy-dispersion spectroscopy, electron probe microanalysis, differential scanning calorimetry, and X-ray diffraction were used to investigate the phase equilibria of the samples. The formation enthalpies of the ternary borides were obtained by first-principles calculations to serve as key information for thermodynamic assessment. By coupling the reviewed experimental data from the literature, the presently determined phase equilibria, and the calculated formation enthalpies of the compounds, the thermodynamic parameters for the Mo–Co–B ternary system were optimized and used to calculate the isothermal sections, vertical section, and liquidus projection of the system. Comprehensive comparisons showed that the calculated results are in reasonable agreement with the reported phase diagram and thermodynamic data.     

Critical evaluation and thermodynamic modeling of the Fe–V–O (FeO–Fe2O3–VO–V2O3–VO2–V2O5) system

Critical evaluation and optimization of the Fe–V–O ternary oxide system was carried out based on all the available phase equilibria and thermodynamic property data at 1 atm total pressure. The Fe₃O₄–FeV₂O₄ spinel solid solution was described within the framework of Compound Energy Formalism considering the cation distribution between tetrahedral and octahedral sites. The wüstite phase, corundum phase, and VO₂ solid solution were described using a simple random mixing model. The Modified Quasichemical Model was used to describe liquid oxide solution in consideration of all multivalence states of Fe and V (Fe²⁺, Fe³⁺, V²⁺, V³⁺, V⁴⁺ and V⁵⁺). The variation of phase equilibria depending on the oxygen partial pressures and thermodynamic data in the system were well reproduced in the present study.     

Predictions of the Al-rich region of the Al–Co–Ni–Y system based upon first-principles and experimental data

A thermodynamic database has been produced for the Al–Co–Ni–Y quaternary system, with an emphasis on the Al-rich region of the Al–Ni–Y ternary system. The database was created using the CALPHAD method, combining existing binary systems with relevant experimental and first-principles information for selected Al–Ni–Y and Co-containing compounds. The thermodynamic database was used to produce equilibrium and non-equilibrium Scheil simulations to determine the phases present in Al–Co–Ni–Y alloys. The values for the Scheil simulation show good agreement, when compared with experimentally determined phase fractions of intermetallic particles dispersed in an Al matrix for three Al-rich quaternary alloys.     

Thermodynamic assessment of the Co–Cr–Fe system and atomic mobility study of its fcc phase

In the present work, the Co–Cr–Fe system was thermodynamically assessed by using the CALPHAD approach coupled with first-principles calculations and experimental data from the literature. Subsequently, the fcc Co–Cr–Fe ternary diffusion couples annealed at 1273 and 1473K were scanned by using electron probe microanalysis (EPMA) to obtain the composition profiles, from which the interdiffusion coefficients were extracted by the Whittle-Green method. Based on these interdiffusion coefficients and present thermodynamic parameters, the atomic mobilities of Co, Cr, and Fe in the fcc Co–Cr–Fe alloys were assessed by means of DICTRA software. The calculated interdiffusion coefficients, composition profiles and diffusion paths of the fcc Co–Cr–Fe alloys were consistent with the experimental data, which verifies the accuracy of the assessed atomic mobilities.     

Experimental study and thermodynamic re-assessment of the Co–Sb system

The Co–Sb system is of a special attention due to existence of CoSb₃ skutterudite structure which is the key structure for doped skutterudite based thermoelectric materials. A critical review of this system, performed recently, shows the published thermodynamic assessment may not be fully correct compared to existing studies. Especially, there is a contradiction in the position of the liquidus line on the Sb-rich side of the phase diagram and of the eutectic reaction, liquid ↔ CoSb₃ + (Sb). As these data are crucial for the study of thermal stability of skutterudite based thermoelectric materials, a good knowledge on phase relations in the Sb-rich part of the Co–Sb phase diagram is needed. To obtain reliable data, experimental alloys covering 80 to 100 at.% of Sb were prepared and investigated by differential thermal analysis and phase analysis. The data were compared with existing literature information and thermodynamic re-assessment of this binary system based on the CALPHAD approach was done.     

Experimental investigation and thermodynamic modeling of the Ni–Ti–V system

The liquidus surface projection and isothermal section at 1273 K of the Ni–Ti–V system were established using X-ray diffraction (XRD), scanning electron microscopy (SEM) coupled with energy dispersion spectroscopy (EDS), electron probe micro-analyzer (EPMA) and differential thermal analysis (DTA) techniques. Six primary solidification regions and four invariant reactions were deduced in the liquidus surface projection, and six three-phase regions were derived in the isothermal section at 1273 K. No ternary compound was observed. According to the experimental results in the present work and literatures, the Ni–Ti–V system was modeled by means of the CALPHAD (CALculation of PHAse Diagram) method. Two-sublattice model (Ni,Ti)₁₀(Ni,Ti)₂₀ for binary σ phase was used, and the thermodynamic parameters of the σ and NiV₃ phases in the Ni–V system was reassessed. Solution phases (liquid, fcc, bcc and hcp) were modeled with the substitutional solution model in the Ni–Ti–V system. The compounds, Ni₃Ti, NiTi₂, Ni₃V and σ, were treated as (Ni,Ti,V)_m(Ni,Ti,V)_n, and B2 were treated as (Ni,Ti,V)_0.5(Ni,Ti,V) _0.5Va₃. A set of self-consistent thermodynamic parameters of individual phases was obtained.     

Thermodynamic evaluation and optimization of the As–Co,As–Fe and As–Fe–S systems

A critical evaluation of all available phase diagram and thermodynamic data for the As–Co and As–Fe binary systems as well as the As–Fe–S ternary system has been performed and thermodynamic assessments over the whole composition ranges are presented using the CALPHAD method. To predict thermodynamic properties and phase equilibria for these systems, the Modified Quasichemical Model (MQM) for short range ordering was used for the liquid phases. The Compound Energy Formalism (CEF) was used for the solid solutions. Since Co and Fe are ferromagnetic, magnetic contributions were added to describe the Gibbs energy of cobalt and iron rich solid solutions. Important uncertainties remain for the liquidus of As-rich regions in the binary subsystems.     

High-throughput measurements of interdiffusivities in fcc Co–Ni–Ta alloys at 1373K and 1473K

The composition-dependent interdiffusivities in the fcc Co–Ni–Ta alloys at 1373 K and 1473 K were deduced by using our newly developed numerical inverse scheme that combines two-dimensional (2D) simulations with diffusion triple experiments. This approach largely reduced the experimental efforts by analyzing only one single-phase diffusion triple at each temperature yet covering a much wider composition range than diffusion couples. The reliability of the high-throughput results was firstly verified by reproducing the experimental 2D composition profiles in each triple. In order to further validate the deduced interdiffusivities, several traditional one-dimensional (1D) diffusion couples were also devised, and the widely recognized Sauer-Freise method and Whittle-Green method were then employed to calculate the interdiffusivities for the binaries and at the intersection points within the ternary composition range, respectively. The interdiffusivities extracted from the inverse scheme agree well with those from the traditional approaches, which strongly proves the applicability of the present new scheme. Besides, the constructed main interdiffusivity planes at 1373 K and 1473 K provide an overview of the diffusion behavior in the fcc Co–Ni–Ta system and promote further kinetic studies.     

Thermodynamic modeling of the V–Si system supported by key experiments

The V–Si system is reassessed based on a critical literature review involving recently reported data and the present experimental data. These new data include the thermodynamic stability of V ₆Si₅ and the enthalpies of formation for the compounds calculated by first-principles method. Two alloys were prepared in the region of (Si)+V Si₂ and annealed at 1273 K for 14 days. After X-ray diffraction (XRD) and chemical analysis of these alloys were performed, the eutectic reaction (L⇔(Si)+V Si₂) temperature was determined by differential thermal analysis (DTA). Self-consistent thermodynamic parameters for the V–Si system were obtained by optimization of the selected experimental values. The calculated phase diagram and thermodynamic properties agree well with the experimental ones. Noticeable improvements have been made, compared with the previous assessments.