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.
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Critical assessment of the thermodynamic data for pure copper was carried using careful analysis of the existing experimental data. An extended Einstein model was used for the crystalline phase and the two state model was applied for the liquid phase. Special attention is paid in this work to the precise description of the following thermodynamic functions: So298, Ho298–Ho0, the melting temperature, and the entropy and enthalpy of fusion. In order to fullfill the need for a precise evaluation of So298 we needed to use an additional technique, which allows the experimental heat capacity and enthalpy data for the solid phase to be approximated accurately from 0K up to the melting point. Relative stabilities of the BCC_A2 and HCP_A3 phases were derived.
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The columnar-to-equiaxed transition (CET) is known to impact crack formation during the additive manufacturing of metallic alloys. While previous experiments have shown that CET is tunable via its alloying elements, a rigorous multicomponent model to demonstrate the impact of multi-alloying components on CET is still lacking. In this study, we developed a multicomponent model by fully coupling the phase diagram of the kinetic interface condition. Building upon the binary model reported by Gaumann et al. our model replaces the restrictive approach of calculating the non-equilibrium partition coefficient and liquidus slopes with kinetic phase diagram calculation. The extended multicomponent model was validated by comparing it with the Al–Cu results reported by Gaumann et al. CET transition curves were computed for two Al–Cu–Mg–Si–Zn alloys manufactured using laser powder bed fusion. The results are in qualitative agreement with our own and previously reported experimental results. These findings suggest that the proposed multicomponent CET model is a valuable tool for designing AM alloys and optimising processing parameters. Graphical abstract The figure above shows the predicted columnar to equiaxed transitions curve of Al-1.6 wt%Cu-2.56 wt%Mg-1.2 wt%Si-5.44 wt%Zn (original AA7075) and Al-1.6 wt%Cu-2.56 wt%Mg-5.0 wt%Si-5.44 wt%Zn (Si rich AA7075) alloys. For a given temperature gradient, the addition of Si greatly reduces the critical interface growth rate for Columnar to Equiaxed Transition (CET) thus promoting CET. The prediction is in good agreement with the two alloys grain morphology shown with EBSD orientation map in the figure below. The EBSD orientation maps of (a) an original 7075 alloy sample and (b) Si-rich AA7075 alloy. The observed plane is parallel to the building direction. It is color-coded by inverse pole figure, and black lines indicate grain boundaries. Download : Download high-res image (313KB) Download : Download full-size image
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A novel method, based on the Debye model of the density of the lattice vibration energy [1], [2], is used to predict the thermal conductivity of insulator materials from room temperature up to the melting point. The model links the density of the lattice vibration energy and the mean free path of the phonons to the high temperature limit of the Debye temperature, θ D ¯ ( ∞ ) , and to the Grüneisen parameter, γ(∞). The phonon contribution to the thermal conductivity can be predicted from the knowledge of θ D ¯ ( ∞ ) and γ(∞). The contribution of the present work is a new CALPHAD (CALculation of PHAse Diagrams) Method, based on physical models, where the heat capacity, the thermal expansion and the adiabatic bulk modulus are optimized simultaneously in order to calculate θ D ¯ ( ∞ ) and γ(∞). In addition, a simple method to predict θ D ¯ ( ∞ ) and γ(∞), and thus the thermal conductivity without any experimental data, is also presented. Results are given for the thermal conductivities of some typical insulator materials such as salts (halides), oxides and semiconductors. It is found that the agreement between the calculations and the available experimental data is excellent.
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Solution-based thermodynamic descriptions of the Ni–Ta and Ni–Mo–Ta systems are developed with supporting first-principles calculations and reported experimental data for parameter evaluation. For the Ni–Ta system, the liquid, bcc and fcc phases are described with a random solution model, D022–Ni3Ta is treated as a stoichiometric compound, and the remaining compounds are modeled as solid solutions on multiple sublattices. The resulting model for the Ni–Ta system is integrated with reported treatments of the Ni–Mo and Mo–Ta systems, and a thermodynamic model for the ternary Ni–Mo–Ta system is developed. The zero-Kelvin enthalpies of formation for the intermetallic compounds in the Ni–Mo–Ta system and the enthalpies of mixing for the bcc and fcc special quasirandom structures (SQS) in the binary Ni–Ta system are computed using the Vienna Ab-initio Simulation Package (VASP). Phase equilibria modeling results for the ternary Ni–Mo–Ta system are summarily presented in the form of isothermal sections and liquidus projections, with appropriate comparisons with available experimental data.
Cited: 41
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In the present work, the liquidus and solidus for a series of NixCo1-2xCrx alloys were measured by means of differential scanning calorimetry, and the first-principles calculations were performed to obtain total energies for all solid solutions and end-members of the intermediate phases in the Ni–Co–Cr ternary system. Various types of data from the present work and the literature were used in the assessments of the Ni–Co–Cr ternary system and sub-binary systems by the CALPHAD method, and were well reproduced by the present thermodynamic database. In addition, diffusion couples of fcc Co–Cr and Ni–Co–Cr alloys were assembled and annealed at different temperatures to extract interdiffusion coefficients. Experimental diffusion data from the present work and the literature, in conjunction with thermodynamic parameters, were adopted to assess the atomic mobilities of the fcc phase in the Ni–Co–Cr system. The calculated and experimental diffusion coefficients reach a satisfactory agreement. The diffusional kinetic database developed was further validated by appropriate predictions of composition profiles and diffusion paths.
Cited: 36
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The present work reports on a thermodynamic modeling of the Mo–Pt system using a combined first-principles/CALPHAD approach. First-Principles (FP) calculations are performed to obtain the enthalpies of formation for the four ordered phases of the system (A15, B19, D019 and MoPt2) at 0 K. The liquid, bcc, fcc and hcp phases have been modeled as substitutional solutions where the excess term is in the form of the Redlich–Kister polynomial. The four ordered phases are modeled using the NACEF approach taking into account the three order-disorder transitions (B19/A3, D019/A3 and MoPt2/A1). FP calculations, experimental phase equilibria and site occupancies data are used to evaluate the model parameters. The thermodynamic description of the Mo–Pt system obtained in this work agree well with all the available data with a limited number of parameters used.
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In this work, the composition dependent tracer and interdiffusion coefficient with phase change in γ/γ′ Ir/Ir3Nb superalloy are studied by means of first-principles calculation together with nudged elastic band, and quasi−harmonic thermodynamics. The formulae scattered in the literature for composition dependence tracer diffusion coefficient are summarized and executed using first principles calculation. Each term in the newly derived formulae, such as energy barrier, jump frequency, defect concentration, correlation, solvent enhancement factor, effective escape frequency, etc. is meticulously calculated. We find the composition dependent tracer diffusion coefficient of Nb in L12 γ′-Ir3Nb phase is contributed mainly from the antisite bridge rather than five-frequency model proposed in FCC γ-Ir dilute solid solution. The faster diffuser is Nb in γ-Ir, while Ir in γ′-Ir3Nb. Based on the tracer diffusion coefficient, the interdiffusion coefficient is obtained using Darken-Manning equation. The composition profile and phase boundary movement of γ/γ′ Ir/Ir3Nb superalloy are evaluated through an analytical solution of Matano-Boltzmann equations. The calculated diffusion coefficients and composition profile are in good agreement with experiments. Our findings not only serve as a successful example for the quantitative calculation of composition dependent tracer diffusion coefficient, but also shed lights on the physics behind the diffusion in intermetallics. Graphical abstract Download : Download high-res image (282KB) Download : Download full-size image
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Phase equilibria knowledge on the Al–V–Zr system has an important role for designing low-density Al-containing refractory multi-principal element alloys. In order to contribute to the literature data related to this system, the liquidus projection of the Al–V–Zr ternary system was experimentally investigated in this work by microstructural characterization of as-cast alloys. Sixty alloys were produced in an arc furnace, the microstructures of the as-cast alloys were characterized using scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS) for the determination of the chemical composition of the phases and microconstituents as well as X-ray diffractometry (XRD). The liquidus projection of the Al–V–Zr system is presented in this work for the first time in the literature. Through microstructural analysis and thermodynamic extrapolation, three Class I, eleven Class II and one Class III ternary invariant reactions are proposed. The results showed that the ternary compound Zr0.9V0.4Al2.7 is formed from the liquid through the following reaction: L + ZrAl2 → Zr0.9V0.4Al2.7. The limits of the 12 primary solidification regions are established and the nature of the monovariant and ternary invariant reactions are determined. The ZrAl2 primary solidification region significantly extends into the liquidus projection, participating in most reactions involving the other phases in equilibrium with the liquid.
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