Calculated Phase Diagram Research Articles

Phase formation and elemental transport in the vacuum diffusion bonding between CoCrFe0.2NiMn and CoCrFe16NiMn multicomponent alloys

To efficiently explore the influence of Fe content on the phase stability of the multicomponent CoCrFexNiMn (hereafter abbreviated as Fex) alloys. A diffusion layer with continuous, concentration gradient of Fe element is created based on diffusion couple technique. The microstructure and element distribution of the diffusion bonded layer between Fe0.2 and Fe16 alloys are analyzed. A new layer of FCC and HCP solid solution phases generates in the diffusion zone, which is consistent with the prediction of parametric approach and phase diagram calculation. As diffusion proceeds, the FCC phase is transformed from the BCC phase with the decreasing of Fe content and the HCP phase might be the transitional phase during this transition. The newly formed FCC and HCP phases are shown specific orientation relationships with the BCC phase. Elemental analysis indicated that the diffusion rate of the alloy components in the FCC phase is Cr > Mn > Co > Ni. The large concentration gradient in the diffuse interface and grain boundaries diffusion of BCC phase promoted the Fe diffusion, causing the BCC phase to transform into FCC phase.

A novel method to accelerate the three-phase flash calculation of the hydrocarbon-CO2 system

To achieve high computational efficiency and simulation accuracy in the equation-of-state-based compositional simulation, the fast multiphase flash calculation approach is required for the hydrocarbon-CO2 system, allowing for the simultaneous existence of vapour, CO2-lean, and CO2-rich phases. However, the conventional step-by-step method for multiphase flash calculation is associated with a high cost in identifying the three-phase equilibrium, thereby significantly impeding the computation efficiency of compositional simulation when the three-phase equilibrium appears in most grids.To address this challenge, a novel approach to multiphase flash calculation is proposed. In this study, all trial phases exhibiting negative tangent plane distance are employed to identify the three-phase equilibrium, eliminating the need for additional phase stability analysis and two-phase split calculations. Furthermore, this new method incurs minimal computational cost and requires only minor modifications to the existing stepwise procedure. Phase diagram calculations conducted on four cases demonstrate that the newly proposed method dramatically accelerates the identification of the three-phase equilibrium.

Revisiting thermodynamics in (LiF, NaF, KF, CrF2)–CrF3 by first-principles calculations and CALPHAD modeling

The thermodynamic description of the (LiF, NaF, KF, CrF2)–CrF3 systems has been revisited, aiming for a better understanding of the effects of Cr on the FLiNaK molten salt. First-principles calculations based on density functional theory (DFT) were performed to determine the electronic and structural properties of each compound, including the formation enthalpy, volume, and bulk modulus. DFT-based phonon calculations were carried out to determine the thermodynamic properties of compounds, for example, enthalpy, entropy, and heat capacity as functions of temperature. Phonon-based thermodynamic properties show a good agreement with experimental data of binary compounds LiF, NaF, KF, CrF3, and CrF2, establishing a solid foundation to determine thermodynamic properties of ternary compounds as well as to verify results estimated by the Neumann-Kopp rule. Additionally, DFT-based ab initio molecular dynamics (AIMD) simulations were employed to predict the mixing enthalpies of liquid salts. Using DFT-based results and experimental data in the literature, the (LiF, NaF, KF, CrF2)–CrF3 system has been remodeled in terms of the CALculation of PHAse Diagrams (CALPHAD) approach using the modified quasichemical model with quadruplet approximation (MQMQA) for liquid. Calculated phase stability in the present work shows an excellent agreement with experiments, indicating the effectiveness of combining DFT-based total energy, phonon, and AIMD calculations, and CALPHAD modeling to provide the thermodynamic description in complex molten salt systems.

Field-assisted sintering of high-entropy alloy-reinforced aluminium matrix composites: phase identification and microstructural properties

This study investigates the design, phase identification, and microstructural properties of high-entropy alloy (HEA)-reinforced aluminium (Al) matrix composites. Thermophysical expressions for HEAs were employed during the design phase of the HEA; both theoretical frameworks and experimental analyses were used to anticipate stable phases while a field-assisted sintering technique was employed to consolidate the samples. Calculation of phase diagram (CALPHAD) predictions for the phases present in the HEA align with valence electron concentration (VEC) calculations as both predicted the presence of BCC and FCC phases. The microhardness results reveal a substantial increase in the hardness value of the composites as compared to the pure Al, such that as low as 5 wt% HEA addition resulted in over a 100% improvement, while the densification of the composites was found to decrease with an increase in the wt% of HEA. SEM micrographs and XRD analyses show fair dispersion, bonding, and phase integration in the HEA-reinforced composites.

Thermodynamic Assessment of the P2O5-Na2O and P2O5-MgO Systems.

Knowledge about the thermodynamic equilibria of the P2O5-Na2O and P2O5-MgO systems is very important for controlling the phosphorus content of steel materials in the process of steelmaking dephosphorization. The phase equilibrium and thermodynamic data of the P2O5-Na2O and P2O5-MgO systems were critically evaluated and re-assessed by the CALPHAD (CAlculation of PHAse Diagram) approach. The liquid phase was described by the ionic two-sublattice model for the first time with the formulas (Na+1)P(O-2, PO3-1, PO4-3, PO5/2)Q and (Mg+2)P(O-2, PO3-1, PO4-3, PO5/2)Q, respectively, and the selection of the species constituting the liquid phase was based on the structure of the phosphate melts. A new and improved self-consistent set of thermodynamic parameters for the P2O5-Na2O and P2O5-MgO systems was finally obtained, and the calculated phase diagram and thermodynamic properties exhibited excellent agreement with the experimental data. The difference in the phase composition of invariant reactions from the experimentally determined values reported in the literature is less than 0.9 mol.%. The present thermodynamic modeling contributes to constructing a multicomponent oxide thermodynamic database in the process of steelmaking dephosphorization.

High activity retention Al–Bi–Zn-base composite powder with mild hydrogen generation

Al–10Bi–7Zn and Al–10Bi–7Zn–1.5X (X: Cu, Fe, Ni, in wt.%) composite powders were designed and prepared through phase diagram calculation and gas atomization method. The effects of Cu, Fe, and Ni on the hydrolysis of Al–Bi–Zn-base composite powders for hydrogen production were investigated respectively. The composition and morphology of powders were characterized by X-ray diffraction (XRD) and scanning electron microscopy (SEM) with energy disperse spectroscopy (EDS) analyses. Hydrolysis performance test results indicate that the additions of Cu, Fe, or Ni can modify the hydrogen production rate and enhance oxidation resistance in Al–10Bi–7Zn ternary alloy composite powder. In the quaternary composite powder system, Al–10Bi–7Zn–1.5Ni (wt.%) exhibits the best performance with the hydrogen generation yield of 75.3% (954.1 mL/g) within 500 min when reacting with distilled water at 60 °C and maintains a hydrogen yield of 57.9% (733.7 mL/g) within 1500 min after being stored (30 °C, relative humidity of 60%) for 7 d. In addition, the mechanism investigation suggested that the additions of Cu, Fe, or Ni in Al–Bi–Zn-base composite powders can stabilize the Al matrix to retain the high activity of powders resulting from inhibiting the cracking of composite powders in the air.

Floquet engineering of axion and high-Chern number phases in a topological insulator under illumination

Quantum anomalous Hall, high-Chern number, and axion phases in topological insulators are characterized by its Chern invariant C (respectively, C=1, integer C>1, and C=0 with half-quantized Hall conductance of opposite signs on top and bottom surfaces). They are of recent interest because of novel fundamental physics and prospective applications, but identifying and controlling these phases has been challenging in practice. Here we show that these states can be created and switched between in thin films of Bi_22Se_33 by Floquet engineering, using irradiation by circularly polarized light. We present the calculated phase diagrams of encountered topological phases in Bi_22Se_33, as a function of wavelength and amplitude of light, as well as sample thickness, after properly taking into account the penetration depth of light and the variation of the gap in the surface states. These findings open pathways towards energy-efficient optoelectronics, advanced sensing, quantum information processing and metrology.

Determination of hardness and Young's modulus in fcc Cu–Ni–Sn–Al alloys via high-throughput experiments, CALPHAD approach and machine learning

Hardness and Young's modulus are critical indicators in the design of innovative Cu–Ni–Sn–Al alloys with desired elastic and strength properties. In this study, the composition-dependent hardness and Young's modulus in the fcc Cu–Ni–Sn–Al alloys were determined using high-throughput experiments, the CALPHAD (CALculation of PHAse Diagrams) approach, and machine learning (ML) model. By combining the diffusion-couples tool, nanoindentation, and electron probe microanalysis (EPMA) techniques, the 341 sets of composition-related hardness and Young's modulus in the fcc Cu–Ni–Sn–Al system, as well as its sub-binary and sub-ternary systems, were effectively determined. These measured data were subsequently utilized to establish the relationship of Young's modulus and hardness with respect to composition in the fcc Cu–Ni–Sn–Al system through the combined application of CALPHAD and back propagation (BP) artificial neural network machine learning models. A comparison between the two approaches revealed that the ML method achieves higher accuracy in ternary and quaternary alloys compared to the CALPHAD method. The impact of alloying elements on the values of hardness and Young's modulus was analyzed, demonstrating that the Ni content has the largest effect on hardness, while the Young's modulus increases with addition of Ni but decreases with the addition of Al and Sn. Finally, the effects of solute elements on the nanomechanical properties of aged Cu1-x(Ni3Sn)x and Cu–9Ni–6Sn-xAl alloys were examined.

Multi-scale simulation of microstructural evolution for molten U–Zr–O ternary system

The morphological evolution of the molten corium is critical to the success of the “in-vessel retention” (IVR) strategy, which is of great significance for the safety of the nuclear industry under severe accidents. However, the direct observation of microstructural evolution by experiments is impossible in extreme conditions. Herein, a multi-scale simulation approach was employed to investigate the microstructural evolution and related mechanisms for the molten U–Zr–O ternary system. First, based on the reported calculated phase diagram, a simplified free energy formula describing a phase diagram of U–Zr–O was determined, where only liquid phases are focused. Then, the atomic diffusion coefficients were calculated by ab-initio molecular dynamics simulations. Based on such information, a homemade phase-field model was developed, which was coupled with Cahn–Hillard and Navier–Stokes equations. Accordingly, the microstructural evolution of molten U–Zr–O materials was systematically investigated. The results reveal that the evolution of the molten core was driven by both the decreasing free energy and gravity potential, accessing the final morphology of the system as a two-layer structure, including a metallic layer and an oxidized layer. Moreover, diverse intermediate morphologies could be observed from different initial component distributions, although their average compositions were identical. Finally, some intermediate simulated microstructural patterns agreed well with experimental observation, demonstrating the unstable structures captured by experiments and the validity of the simulations. The present study provides an effective approach to investigate the microstructural evolution of molten core and a guideline for optimizing the IVR strategy based on different morphologies in the corium.

μ2mech: A software package combining microstructure modeling and mechanical property prediction

We have developed a graphical user interface (GUI) based package μ2mech to perform phase-field simulation for predicting microstructure evolution. The package can take inputs from ab initio calculations and CALPHAD (Calculation of Phase Diagrams) tools for quantitative microstructure prediction. The package also provides a seamless connection to transfer output from the mesoscale phase field method to the microscale finite element analysis for mechanical property prediction. Such a multiscale simulation package can facilitate microstructure-property correlation, one of the cornerstones in accelerated materials development within the integrated computational materials engineering (ICME) framework.

Calculation of Littlewood predominance diagrams for metal electrodeposition from molten chlorides using CALPHAD software and databases

Littlewood predominance diagrams are maps of phase stability with a potential in the ordinate and a pO2− on the abscissa. pO2− is the negative logarithm of the activity of O2− ions.In the current work, a new method for calculation of Littlewood predominance diagrams is presented. The method is particularly suitable for software and databases constructed according to the CALPHAD (CALculation of Phase Diagrams) methodology. This enhances the consistency of the calculations and enables inclusion of elaborate descriptions of non-stoichiometric phases. The calculation is based on Gibbs energy minimization so that identification of relevant reaction equations is not needed as input.A thermodynamic database with all the relevant phases, including metals, chlorides, oxides and oxychlorides is a perquisite for the calculation. The calculation results depend on the thermodynamic modeling and data. However, the algorithm does not depend on the details of the thermodynamic models used. That is, the same calculation method is applied irrespective of the thermodynamic model chosen. Sample calculations are given for the simple Mg-Cl-O system and for the more-complex Ca-Ti-Cl-O system. We use thermodynamic datasets published in the literature, as well as a small CALPHAD database for the Ca-Ti-Cl-O system constructed in the course of the present work.

Controlling the Fe-intermetallic phases and mechanical properties of secondary Al-9Si-1Fe alloy with Cr and Mn additions

In secondary Al-Si based alloys, microalloying with Mn and Cr can modify harmful platelet-type AlxFeySiz intermetallic phases to less detrimental α-Alx(Fe, Mn, Cr)ySiz phase (script or polygonal morphologies). However, the α-Alx(Fe, Mn, Cr)ySiz phase morphology, phase composition and the addition of Fe-correcting elements can be influenced by solidification conditions. Therefore, this research is aimed to highlight the morphological evolution and mechanisms of α-Alx(Fe, Mn, Cr)ySiz phase in a Cr added Al-9 %Si-1 %Fe-0.2 %Cr (all weight percentage thereafter, unless otherwise stated) alloy with varying Mn concentrations (0.25 %, 0.5 %, and 0.8 %). Microstructure evolution of Fe intermetallic phases is investigated under different casting conditions using a wedge-shaped die, Cu-chill block and melt quenching experiments. Thermodynamic simulations have been performed using CALculation of PHAse Diagrams (CALPHAD) method and compared with the experimental results for phase composition and formation temperatures of α-Alx(Fe, Mn, Cr)ySiz phase. The results indicated that for 0.25Mn-0.2Cr addition to Al-9Si-1Fe alloy, compact morphology containing polygonal phases are formed in Cu-chill casting, while the wedge castings predominantly show a mixed structure with platelets and script type morphologies. Tensile tests revealed a higher elongation value of 6.6 % for mixed structure with platelet and script phases, which is decreased to 4.2 % for polygonal phases in Al-9Si-1Fe-0.2Cr-0.25Mn alloy. This study highlights the importance of solidification conditions on morphologies of Fe-intermetallic phases and the mechanical properties by comparing selected literature relevant to high pressure die-casting process.

Numerical analysis of Al2O3 and TiO2 growth and oxygen dissolution in a metal substrate during the isothermal oxidation of an α-Ti alloy at 973 K

Oxide growth of Al2O3 and TiO2 as well as O dissolution during the oxidation of an α-Ti alloy at 973 K were simulated using the finite volume method coupled with the calculation of phase diagrams (CALPHAD) method. The results indicated that the addition of 11.02 at.% Al to a Ti–O system resulted in the formation of an 18-nm-thick Al2O3 layer, which decelerated TiO2 growth and O dissolution in the substrate. An increase in the O concentration at the oxide–metal interface was also inhibited by Al2O3 formation. A thin Al-depletion zone was formed at the oxide–metal interface. Furthermore, Al2O3 formation was restricted by the low concentration and diffusivity of Al in the substrate.

Calculation and Experimental Verification of Zn–Al–Mg Phase Diagram

The liquid phase projection diagram, three-dimensional phase diagram, and vertical section diagram of the Zn–x%Al–x%Mg alloy system was calculated using the phase diagram calculation software Pandat. Simultaneously making full use of the self-developed hot-dip galvanizing process simulation machine by China Steel Research produced a 75%Zn–19%Al–6%Mg coating. A method combining phase diagram calculations and experimental verification was used to investigate the equilibrium phases and solidification process of the alloy. The microstructure of the 75%Zn–19%Al–6%Mg coating was studied using scanning electron microscopy and energy dispersive spectrometry. The results indicate that the coating structure consists of primary Al dendrite phase, MgZn2 inter-metallic compound and Zn-rich phase. There is no ternary eutectic structure in the coating structure. Al dendrites grow on the surface of the coating, while there are no Al dendrites on the cross-section. The experimental results strongly concur with the calculated results from the Pandat phase diagram. The solidification sequence of the 75%Zn–19%Al–6%Mg coating is L→L + Al→L + Al + MgZn2→Al + MgZn2 + Zn. The phase diagram guides industrial production significantly, avoiding the waste of transitional materials and zinc caused by small scale trial and error experiments, thus reducing unnecessary production costs. The factory can select a reasonable coating composition designing scheme in the phase diagram, based on the performance requirements of customers for the coating.

Search for eutectic high entropy alloys by integrating high-throughput CALPHAD, machine learning and experiments

We present a comprehensive study on the identification of eutectic high entropy alloys (EHEAs) through integration of CALculation of PHAse Diagrams (CALPHAD), machine learning (ML), and experimental data. By performing high-throughput CALPHAD calculations to obtain the temperature differences between liquidus and solidus phases (ΔT) and employing gradient descent optimization to identify local minima in ΔT surface, we obtained a reliable dataset for EHEAs across 5–6 component alloy families, which effectively addresses current limitations in both the quality and availability of EHEA data. In conjunction with literature-based experimental data, this dataset serves as the foundation for ML models trained with an XGBoost classifier. The physical descriptors with the most significant effects on the classification of eutectics and non-eutectics are identified. Our study reveals that configurational entropy alone yields a remarkable 98% classification accuracy, elucidating its dual role in phase stabilization and melting point depression. For the first time, an explicit phase selection rule to identify eutectics has been derived from an artificial neural network model, which facilitates efficiently screening EHEAs without resorting to CALPHAD nor ML models. This study presents a robust, data-driven strategy applicable not only to EHEAs but also to a broader range of alloy systems.

Ab initio calculations of the chemisorption of atomic H and O on Pt and Ir metal and on bimetallic Pt x Ir y surfaces

Abstract Understanding the chemisorption of atoms on precious metal surfaces is of substantial interest for the rational design of heterogeneous and electrochemical catalysts. In this study, we report density functional theory (DFT) investigations of the chemisorption of atomic H and O on bimetallic Pt x Ir y (111) surfaces for bifunctional anode catalyst materials in polymer electrolyte membrane (PEM) fuel cells. We found that for both adsorbates, the adsorption on the Pt(111) surface is in general less exothermic than on the Ir(111) surface. Our study has revealed that chemisorption on the bimetallic surfaces becomes more stable with increasing number of Ir surface atoms at the adsorption site. While for hydrogen atoms the ONTOP sites yield the most negative adsorption energies, the chemisorption of oxygen atoms appears to be most stable on the FCC sites for both the mono- and bimetallic surfaces. Using the ab initio thermodynamics approach, we calculated phase diagrams for the chemisorption of H and O atoms on these metal surfaces in order to transfer our findings to finite temperature and pressure conditions. Our theoretical results may provide an improved understanding of the hydrogen oxidation reaction (HOR) and oxygen evolution reaction (OER) on intermetallic Pt x Ir y (111) surfaces and may be helpful for the rational design of new bifunctional PEM fuel cell anode catalyst materials.

Phase equilibria and solidification behavior of Mg–Al–Gd casting alloys

The Mg–Al–Gd ternary system was re-assessed by the CALPHAD (CALculation of PHAse Diagrams) method and a set of self-consistent thermodynamic parameters of the system were obtained. The long-period stacking ordered (LPSO) phases, 14H and 18R, were described by thermodynamic model of Mgx(TM,Mg)6(RE,Mg)8 (TM=Transition Metal, RE=Rare Earth). Representative isothermal sections, vertical sections, liquidus projections and the related invariant reactions were calculated and compared with the experimental data, showing the reliability of the obtained thermodynamic parameters. Reaction scheme for the whole ternary system was also presented. The Scheil solidification paths and the phase fractions of several Mg–Al–Gd alloys were calculated and analyzed. The phase formation during solidification and the phase content of γ and LPSO phases are clearly described with the increase of Gd content, which is crucial to the microhardness, ultimate tensile strength and yield strength of Mg–Al–Gd casting alloys.

Design and validation of refractory alloys using machine learning, CALPHAD, and experiments

Refractory multicomponent alloys (RMCAs) have garnered attention as potential materials for high-temperature structural applications, due to their excellent mechanical properties. However, conventional alloy design has limitations in terms of constrained compositional space and a lack of computational databases with adequate coverage. To address this, we present a design framework that leverages machine learning (ML), the CALculation of PHAse Diagram (CALPHAD) method, and experimental validation to efficiently develop refractory alloys. The present study focuses on the Mo-Nb-W ternary system. Six ternary alloys were inversely designed by means of the conditional generative adversarial network (cGAN) and fabricated via arc melting. The ternary alloys exhibit a single BCC phase which is consistent with CALPHAD calculations as well as Scheil simulations. The present interactive design loop between the ML surrogate model and experiments is demonstrated through the accurate hardness prediction, resulting in cGAN models capable of rapid exploration of the higher-order design space. The hardness of the Mo-Nb-W alloys is in the range of 5–6 GPa due to their solid solution strengthening.

Study on the Cleanliness of SWRS82B Hard Wire Steel Refined by Fluorine‐Free Slag with Medium and High Basicity

In order to apply and develop fluorine‐free slag in steelmaking, it is of great significance to study the effect of composition for fluorine‐free refining slag on the cleanliness of molten steel which affects its performance directly. The effect of composition of fluorine‐free refining slag with medium and high basicity on the contents of impurity elements for sulfur and oxygen, and characteristics of inclusions in SWRS82B hard wire steel, are investigated systematically. Sulfide capacity of refining slag is estimated based on the Royal Swedish Institute of Technology model. Dissolved oxygen content in molten steel equilibrated by refining slag is calculated based on Factsage software and classical thermodynamics. The calculated results are in good agreement with experimental results. The plasticity of inclusions at high temperature and low temperature is analyzed by phase diagram and Young's modulus calculation. The best cleanliness and inclusions of SWRS82B steel are obtained with slag composition of 53%CaO–19%SiO2–19%Al2O3–7%MgO, which has good melting characteristics. The impurity elements sulfur and oxygen in steel can be controlled for 26 and 19 ppm, respectively, and the average size of inclusions is 2.84 μm.

Boron and lithium aqueous thermochemistry to model crud deposition in pressurized water reactors

A comprehensive database of boron and lithium aqueous thermochemistry has been developed for use at elevated temperatures. The Helgeson-Kirkham-Flowers (HKF) formalism provides a framework to describe thermodynamic properties over a broad range of temperatures and pressures. Accuracy at high temperatures is vital to modeling nickel oxide and ferrite fuel deposits that occur in pressurized water nuclear reactors (PWRs). CALPHAD (CALculation of PHAse Diagrams) calculations are performed at PWR crud conditions to predict the stability regions of the solid lithium metaborate (LiBO2) and lithium tetraborate (Li2B4O7) precipitates. In addition, similar calculations are performed using sodium and potassium instead of lithium in order to assess the thermodynamics associated with preventing the formation of such precipitates. This database contributes to understanding of crud formation and composition and will aid in the prediction of phenomena such as Crud-Induced Power Shifts (CIPS).