Calculated Equilibrium Phase Diagram Research Articles

Influence of Co content on microstructure and hardness of AlCoxCrFeNi (0 ≤ x ≤ 1) high-entropy alloys produced by self-propagating high-temperature synthesis

In an effort to reduce energy consumption and expensive Co content, herein we report the effects of Co content on microstructure and microhardness of widely studied AlCoxCrFeNi high-entropy alloys produced by cost-efficient aluminothermic self-propagating high-temperature synthesis (SHS) method. Accordingly, the feasibility of SHS technique in the production of AlCoxCrFeNi master high-entropy alloys was discussed. In order to investigate the effect of further casting, the SHS alloys were also subjected to vacuum arc melting/suction casting process. Prior to SHS; phase diagram, raw material amounts and adiabatic temperatures were calculated via thermochemical modelling. The calculated equilibrium phase diagram suggested a full BCC structure over the whole Co range. However, according to XRD results, as-cast alloys consisted of BCC and FCC phases, having microhardness values ranging in between 385 HV and 504 HV, depending on Co content. The increase in Co content, enlarged the grains, altered the spinodal decomposition morphology and led to the formation of dual-phase (FCC + BCC) alloys, which in return had a significant effect on the microhardness values. Overall hardness values were increased due to finer microstructure obtained by suction casting. Also, Widmanstätten plate-like growth of the FCC phase inside the BCC cores was kinetically suppressed due to higher cooling rate. It was concluded that AlCoxCrFeNi master high-entropy alloys can be successfully produced by SHS method and the attained dual-phase microstructures could be beneficial in tailoring mechanical properties as well as reducing the total cost of the AlCoxCrFeNi HEAs system in addition to the significant energy reduction obtained via SHS route.

Composition optimization for Al-Zn-Mg-Cu alloys based on thermodynamics and first-principles calculations

Composition optimization of Al-Zn-Mg-Cu alloys were systematically investigated by considering the precipitation strengthening and solid solution strengthening, based on thermodynamics and first-principles calculations. The calculated equilibrium phase diagram of Al-Zn-Mg-Cu alloy showed that Al-xZn-yMg-zCu (x = 4.8 ~ 6.3 wt%; y = 1.1 ~ 2.6 wt%; z = 1.6 ~ 3.1 wt%) alloys might contain five precipitates, including η-MgZn2, θ-Al2Cu, S-Al2CuMg, τ-Al2Mg3Zn3 and τ-Al6CuMg4. The first-principles calculated results indicated that θ-Al2Cu and S-Al2CuMg precipitates might be the dominated strengthening precipitates for the alloys. Then, the supercell models of the five solid solutions (Al67Zn2Mg2Cu, Al83Zn2Mg2Cu2, Al68ZnMg2Cu, Al64Zn3Mg4Cu and Al79Zn2Mg2Cu) were established according to the contents of θ-Al2Cu and S-Al2CuMg phases in the designed compositions, and followed the structural, elastic and electronic properties of these solid solutions were calculated. The calculated results showed that Al79Zn2Mg2Cu (Al-5.8 wt.%Zn-1.6 wt.%Mg-2.1 wt.%Cu) might present the optimal mechanical properties.

Promoting austenite formation in laser welding of duplex stainless steel\u2014impact of shielding gas and laser reheating

Avoiding low austenite fractions and nitride formation are major challenges in laser welding of duplex stainless steels (DSS). The present research aims at investigating efficient means of promoting austenite formation during autogenous laser welding of DSS without sacrificing productivity. In this study, effects of shielding gas and laser reheating were investigated in welding of 1.5-mm-thick FDX 27 (UNS S82031) DSS. Four conditions were investigated: Ar-shielded welding, N2-shielded welding, Ar-shielded welding followed by Ar-shielded laser reheating, and N2-shielded welding followed by N2-shielded laser reheating. Optical microscopy, thermodynamic calculations, and Gleeble heat treatment were performed to study the evolution of microstructure and chemical composition. The austenite fraction was 22% for Ar-shielded and 39% for N2-shielded as-welded conditions. Interestingly, laser reheating did not significantly affect the austenite fraction for Ar shielding, while the austenite fraction increased to 57% for N2-shielding. The amount of nitrides was lower in N2-shielded samples compared to in Ar-shielded samples. The same trends were also observed in the heat-affected zone. The nitrogen content of weld metals, evaluated from calculated equilibrium phase diagrams and austenite fractions after Gleeble equilibrating heat treatments at 1100 °C, was 0.16% for N2-shielded and 0.11% for Ar-shielded welds, confirming the importance of nitrogen for promoting the austenite formation during welding and especially reheating. Finally, it is recommended that combining welding with pure nitrogen as shielding gas and a laser reheating pass can significantly improve austenite formation and reduce nitride formation in DSS laser welds.

Designing high entropy alloy-ceramic eutectic composites of MoNbRe0.5TaW(TiC)x with high compressive strength

Combining the advantages of composites and eutectic high entropy alloys, novel MoNbRe0.5TaW(TiC)x high entropy alloy-ceramic eutectic composites with high strength were successfully designed and investigated based on the computer assisted thermodynamic calculation. The MoNbRe0.5TaW(TiC)x composites are composed of body-centered cubic (BCC) solid solution and multi-component (MC) carbide with face-centered cubic (FCC) structure. With increasing TiC addition, microstructure exhibits an evolution from hypo-eutectic to eutectic and then to hyper-eutectic, which is explained by the solidification process analysis in calculated equilibrium phase diagram. The MoNbRe0.5TaW(TiC)x composites possess high strength. The MoNbRe0.5TaW(TiC)1.0 fully eutectic composite has the highest compressive strength of 1943 ± 13 MPa with high yield strength of 1496 ± 17 MPa. The strengthening mechanism is contributed by the synthetic effect of second-phase and boundary strengthening.

Thermodynamics of an austenitic stainless steel (AISI-348) under in situ TEM heavy ion irradiation

The stability of the face-centred cubic austenite (γ-Fe) phase in a commercial stainless steel (AISI-348) was investigated through in situ transmission electron microscopy (TEM) with heavy ion irradiation at 1073 K up to a fluence of 1.3×1017 ions⋅cm−2 (corresponding to a dose of 46 dpa). The γ-Fe phase was observed to decompose at a fluence of around 7.8×1015 ions⋅cm−2 (3 dpa) when a new phase nucleated and grew upon increasing irradiation dose. Scanning transmission electron microscopy (STEM) with energy dispersive X-ray (EDX) spectroscopy and multivariate statistical analysis (MVSA) were used to characterise the irradiated specimens. The combination of such experimental techniques with calculated equilibrium phase diagrams using the CALPHAD method led to the conclusion that the new phase formed upon irradiation is the body-centred cubic Cr-rich α' phase. At the nanoscale, precipitation of M23C6 (τ-carbide) was also observed. The results indicate that ion irradiation can assist the austenitic stainless steel to reach a non-equilibrium state similar to a calculated equilibrium state observed at lower temperatures.

Synthesis and structural control of Fe-based porous layer on Fe substrate for joining with resin parts using combustion reaction

A porous Fe/TiB2 composite layer was synthesized on an Fe substrate by a powder metallurgy process using combustion reactions among Fe, Ti, and B to achieve Fe/resin joints through interpenetrating phase layers. The effects of Fe particle size and the blending ratio of the raw powder mixture on the porous structure, roughness of the top surface of the porous layer, and adhesiveness between the porous layer and Fe substrate were investigated. The peak temperature measured with a thermocouple increased with increasing Fe particle size and blending ratio of Ti and B. An increase in the peak temperature does not affect the porosity of the porous layer. Higher peak temperatures increase the pore size and change the pore morphology from open to semi-closed (although pores are not completely isolated). The change in pore morphology prevents the exposure of pores on the top surface of the porous layer, resulting in decreasing surface roughness. Moreover, an increase in the maximum temperature promotes bonding between the Fe substrate and porous layer. These results are discussed in view of the thermodynamic assessment using the calculated equilibrium phase diagram.

Interpretation of high-temperature tensile properties by thermodynamically calculated equilibrium phase diagrams of heat-resistant austenitic cast steels

High-temperature tensile properties of three heat-resistant austenitic cast steels fabricated by varying W, Mo, and Al contents were interpreted by thermodynamically calculated equilibrium phase diagrams of austenite, ferrite, and carbides as well as microstructural analyses. A two-step calculation method was adopted to cast steel microstructures below the liquid dissolution temperature because the casting route was not an equilibrium state. Thermodynamically calculated fractions of equilibrium phases were well matched with experimentally measured fractions. Ferrites existed at room and high temperatures in both equilibrium phase diagrams and actual microstructures, which has not been reported in previous researches on austenitic cast steels. In the W2Mo1Al1 steel, 38% and 12% of ferrite existed in the equilibrium phase diagram and actual microstructure, respectively, and led to the void initiation and coalescence at ferrites and consequently to the serious deterioration of high-temperature strengths. The present equilibrium phase diagrams, besides detailed microstructural analyses, effectively evaluated the high-temperature performance by estimating high-temperature equilibrium phases, and provided an important idea on whether ferrite were formed or not in the heat-resistant austenitic cast steels.

Processing Low‐Oxide ZrB2 Ceramics with High Strength Using Boron Carbide and Spark Plasma Sintering

A phase diagram‐assisted powder processing approach is shown to produce low‐oxygen (0.06 wt%O) ZrB2 ceramics using minimal B4C additions (0.25 wt%) and spark plasma sintering. Scanning electron microscopy and scanning transmission electron microscopy with elemental spectroscopy are used to identify “trash collector” oxides. These “trash collector” oxides are composed of manufacturer metal powder impurities that form discreet oxide particles due to the absence of standard Zr–B oxides found in high oxygen samples. A preliminary Zr–B–C–O quaternary thermodynamic database developed as a part of this work was used to calculate the ZrO2–B4C pseudobinary phase diagram and ZrB2–ZrO2–B4C pseudoternary phase diagrams. We use the calculated equilibrium phase diagrams to characterize the oxide impurities and show the direct reaction path that allows for the formation of ZrB2 with an oxygen content of 0.06 wt%, fine grains (3.3 μm) and superior mechanical properties (flexural strength of 660 MPa).

Transformation Behavior of Precipitates in a W-alloyed 10 wt pct Cr Steel for Ultra-supercritical Power Plants

Thermodynamic calculation, thermal analysis, and identification and observation of precipitates have been carried out on a W-alloyed 10 wt pct Cr steel by means of ThermoCalc program, differential thermal analysis (DTA), X-ray diffraction (XRD) and transmission electron microscopy (TEM) with an energy dispersive X-ray spectrometer, respectively. Several critical phase transformation points were determined by combining experimental results with calculations. Two individually stable phases of Nb(C, N) and VN, instead of one single phase MX (X: C, N), M(23)C(6) or Laves phases, were predicted in the calculated equilibrium phase diagram. An unstable elongated M(7)C(3) with relatively higher Cr was detected unexpectedly in the normalized and tempered steel. Two kinds of spherical Nb(C, N) with different size were recognized as the primary and the secondary precipitates of Nb(C, N) which contain different V contents. It was observed that one kind of complex precipitate in a special V-wing shape was resulted from two plate-like VN adhering to coarse primary spherical Nb(C, N).

Phase equilibria and ordering in solid Pt–Rh calculated by means of a refined bond-order simulation mixing model

The equilibrium phase diagram of solid Pt–Rh is calculated by means of semi-grand canonical lattice Monte Carlo simulations using thermodynamic integration. Configurational energies are described by a refined BOS model (bond-order simulation mixing), which is fitted to reference data obtained from first-principles calculations. The calculated equilibrium phase diagram shows the ordered face-centered cubic structure 40 and D0 22 structure as stable phases at low temperatures (<250 K) and has no miscibility gap at higher temperatures, which is in contrast to existing assumptions. The calculated short-range order parameters of the solid solution are in full agreement with experimental values and thus confirm that the BOS model provides a sound description of configurational energies.

Influence of chemical disorder on the magnetic behaviour and phase diagram of the FexNi1−x system

In this paper, we calculate the equilibrium phase diagram and the magnetic moment curve for the FexNi1−x system and simulate their Mössbauer spectra assuming a binomial distribution to reproduce the chemical disorder in these alloys. We also assume that the high-spin/low-spin transition for a central iron atom is governed by the number of nearest neighbours and next nearest neighbours of the iron atoms. The calculated equilibrium phase diagram and the magnetic moment curve are very close to that presented in the literature and the simulated Mössbauer spectra are in excellent agreement with that of their corresponding phases measured in our lab.

Thermodynamic assessment of the BaO - TiO 2 quasibinary system

Experimental data from the literature on the BaO-TiO 2 quasibinary system have been evaluated to assess the thermodynamic parameters of all the stable phases by means of the CALPHAD (CALculation of PHAse Diagram) method. The two-sublattice ionic solution model was used to describe the liquid phase, while the compound energy model was applied to describe the high-temperature forms of BaTiO 3. Other compounds were treated as stoichiometric phases. The assessment was conducted using the Thermo-calc software package and a set of parameters was given. Calculated equilibrium phase diagrams and thermochemical properties compared with the experimental data are presented. There is a good agreement between the calculations and the experimental data. Some contradictions are pointed out and discussed.

Thermodynamic studies and the phase diagram of the Li-Mg system

By means of the electromotive force (emf) method of concentration cells of the following scheme: Li (1) / LiCl-LiF (eut) or LiCi-KCl (eut) / Li-Mg (1) or Li (1) / LiCl-LiF (eut) / Li-Mg (s) Li activities for liquid and solid alloys at the (Mg), (Li), and (Mg) + (Li) two-phase region of the Li-Mg system were determined. Liquid alloys were examined at temperatures from 638 to 889 K at various Li concentrations. The (Mg) solid solutions were investigated in two series: at constant temperatures between 773 and 876 K, with varying Li content, and at fixed Li concentrations, equal to 0.125 and 0.160 molar fractions, at different temperatures between 772 and 849 K. At the two-phase region, (Mg) + (Li), emf measurements were performed in the temperature range 773 to 838 K, with fixed Li concentrations equal to 0.20, 0.25, and 0.275 molar fractions. For (Li) solid alloys, experiments were done at temperatures 773 to 849 K for several constant Li concentrations, between 0.30 to 0.45 molar fractions, respectively. Studies on solid alloys enabled us also to determine the boundaries (Li)/[(Mg) + (Li)] and (Mg)/[(Mg) + (Li)] at temperatures 773 to 831 K. The resulting thermodynamic and phase boundary data of this study were used with other selected references for a critical assessment of the Li-Mg system. The Lukas BINGSS optimization program and BINFKT for the calculation of the thermodynamic functions and of the phase diagram were used. The calculated equilibrium phase diagram at temperatures below 750 K indicates a slightly lower solid solubility of Mg in (Li) in comparison with results from thermal analysis and the recently published Saunders evaluation.

Phase diagram of vortices in superfluid 3He-A.

Four alternative but topologically different structures of vorticity exist in rotating ${}^{3}\mathrm{H}\mathrm{e}\ensuremath{-}A$. As a function of magnetic field ( $H$) and rotation velocity $(\ensuremath{\Omega})$, we identify with NMR the type of vortex which is nucleated during cooling from the normal to the superfluid phase. The measurements are compared to the calculated equilibrium phase diagram of vortices in the $H\ensuremath{-}\ensuremath{\Omega}$ plane at temperatures $T\ensuremath{\lesssim}{T}_{c}$. Slow transitions are found to reproduce the calculated equilibrium state.

Pore-fluid chemistry and chemical reactions on the Wasatch normal fault, Utah

Abstract Mineral assemblages and fluid inclusions (F.I.) in hydrothermally altered and tectonically deformed Oligocene quartz monzonite in the footwall of the active Wasatch normal fault, Utah have been used to estimate fluid pressure, temperature, chemical composition, and chemical reactions associated with progressive displacement of the fault. Vein filling and pervasive alteration mineralogy includes (earliest to latest) biotite-K-feldspar, chlorite-epidote-sericite, and laumontite-prehnite-clay. Secondary F.I. in quartz, associated with chlorite-epidote-sericite alteration, consist of CO 2 and salt solution; the homogenization temperature mode is 285°C, X CO 2 is 0.03–0.32, and salinity ranges from 4.5–17.3 wt.% NaCl equivalent; estimated minimum entrapment pressures vary from 600–2950 bars. The homogenization temperature mode of secondary F.I. associated with the laumontite-prehnite assemblage is 100°C, salinity ranges from 2.0–16.0 wt.% NaCl equivalent, and no CO 2 was detected; entrapment pressures are presumed to have been hydrostatic and below 460 bars. Fluid pressure and temperature evolved along a path from lithostatic to hydrostatic with continued displacement of the footwall relative to the hanging wall. Age constraints are provided by a 17.6 ± 0.6 m.y. K-Ar age of hydrothermal seriate from a sample with mean T h of 309°C, and 7.3 to 9.6 m.y. fission track ages of apatite (closure temperature 120 ± 15° C ). Calculated equilibrium phase diagrams illustrate the systematic variation in cation activities, CO 2 fugacity, and alteration minerals as fluid temperature and pressure decrease. The ratios of a Ca 2+ (a H + ) 2 and a Mg 2+ (a H + ) 2 increase and the ratio a K + / a H + decreases by more than two orders of magnitude each as temperature decreases and alteration mineralogy changes from K-feldspar and muscovite to muscovite and clay. The hot aqueous fluids affect the mechanical behavior of the rock during faulting. Crack sealing by alteration product minerals reduces permeability, and the effective stress is decreased by pore fluid pressures substantially greater than hydrostatic in the early alteration.