CALPHAD Calculations Research Articles

Low-density CoAlTi-B2 strengthened Al-Co-Cr-Mo-Ti bcc refractory high-entropy superalloy designed with the assistance of high-throughput CALPHAD method

Superalloys are being widely used across the globe, in the power plants and turbine engines, due to the superior mechanical performance at elevated temperatures and oxidation resistance in crucial environments. To enhance the currently commercial Ni-based superalloys, refractory elements are desired candidates for novel alloy development, due to their ultrahigh melting points. In the past decade, refractory high-entropy superalloys (RSAs), which are the multi-principal refractory element-based alloys with the microstructure of ordered body-centered cubic (bcc) (B2) precipitates coherently embedded in the disordered bcc (A2) matrix, have attracted great attentions. However, most reported RSAs possess the reversed microstructure of the continuous B2 phase with the discrete A2 phase forming via the spinodal decomposition, which have poor thermal stability at elevated temperatures. Herein we designed a coherent precipitate-strengthened Al-Co-Cr-Mo-Ti RSA with the assistance of high-throughput CALPHAD (HT-CALPHAD) calculations. Pandat software with PanHEA 2021 database were used in searching desired compositions. The alloy was fabricated by vacuum arc melting (VAM) and characterized with X-ray fluorescence spectroscopy (XRF), differential thermal analysis (DTA), X-ray diffractometry (XRD), scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The desired microstructure of CoAlTi-B2 homogeneously dispersed in the A2 matrix was obtained, resulting in the high hardness. The coherent bcc/B2 RSA with high hardness-to-density ratio is being developed.

Predicting hydrogen microporosity in long solidification range ternary Al-Cu-Li alloys by coupling CALPHAD and cellular automata model

Aluminum-lithium alloys have wide applications in aerospace industries in the 21st century but their manufacturing is extremely difficult due to the 10 times more equilibrium hydrogen concentration in the liquid than the solubility limit in traditional Al alloys (0.036 mL/100gSTP). The reduction of solubility from liquid to solid by 95% leads to hydrogen porosity being hard to control. In this work, a three-dimensional multicomponent cellular automaton (CA) model is coupled with CALPHAD calculations to simulate the nucleation and growth of hydrogen porosity and its interaction with surrounding dendritic structures during the solidification of Al-Cu-Li alloys. By quantifying the effects of hydrogen concentration, cooling rate, and Li content, it was found the solidification conditions can effectively reduce porosity size. To validate the model, X-ray computed tomography (XCT) has been used to obtain not only the size but also the morphology of porosity as a function of cooling conditions. It was found that porosity grows elongated and tortuous shape at slow cooling rates between columnar dendrites, filling up the empty spaces of secondary arms, while it tends to be dispersed spherical shape when its surrounding grains are refined to equiaxed structures at high cooling rates.

Accelerated alloy discovery using synthetic data generation and data mining

The search for new alloys with improved properties is never ending with infinite combinations and amounts of alloying elements in the alloy. Advancements in machine learning have made navigating this enormous search space feasible. However, training the machine learning models and tuning their hyper-parameters to make accurate predictions can be time-consuming and often require high-performance computing resources. Furthermore, the quality of the predictions depend on the availability of sufficient training data. Here, we present a generic approach to accelerate alloy discovery by coupling high throughput CALPHAD calculations, synthetic data generation, and data mining. As a demonstration of the approach, we design super bainitic steels that form bainite at 200∘C in lower transformation times.

Effects of Mn addittion, cooling rate and holding temperature on the modification and purification of iron-rich compounds in AlSi10MnMg(Fe) alloy

The use of secondary aluminum alloys in industry is still limited by the high Fe contents in recycled alloys. In general, the Fe-rich intermetallic compounds deteriorate the performance of secondary Al–Si alloys, specially the β-Fe phase. To mitigate the detrimental effects of iron, the influence of diferent cooling rates and holding temperatures on the modification and purification of iron-rich compounds in commercial AlSi10MnMg alloy with 1.1 wt % Fe was studied. According to the results obtained by CALPHAD calculations, the alloy was modified by adding a 0.7 wt%, 1.2 wt%. and 2.0 wt% of Mn. The phase formation and morphology of iron-rich compounds was systematically studied and correlated by different microstructural characterization techniques. The experimental results showed that the detrimental β-Fe phase can be avoided by adding at least 1.2 wt % of Mn at the studied cooling rates. Finally, the effect of different holding temperatures in the sedimentation of Fe-rich compounds also was studied. Hence, the gravitational sedimentation experiments at different holding times and temperatures were conducted to validate the feasibility of the methodology in different processing conditions. The experimental results showed a high Fe removal efficiency up to 64% and 61%, after a holding time of 30 min at 600 °C and 670 °C, respectively. The addition of Mn improved the Fe removal efficiency but not gradually, as the best results were obtained in the alloy containing 1.2 wt % Mn.

Composition-dependent shuffle-shear coupling and shuffle-regulated strain glass transition in compositionally modulated Ti-Nb alloys

Athermal pure shuffle O′ nanodomains have been reported as a common structural state in metastable β-Ti alloys. In this study, by integrating thermodynamic databases, first-principles calculations, phase field simulations, and experiments, we reveal the coupling between the shuffle (O′) and shear (α″, orthorhombic martensite) nanodomains as a function of Nb concentration in Ti-Nb alloys. In particular, our first-principles calculations suggest a change in the phase transformation path from β → α″ to β → O′ as the Nb concentration increases, and our CALPHAD calculations based on the available thermodynamic database show a large metastable miscibility gap in Ti-Nb. Informed by these findings, our phase field simulations demonstrate how the O′ and α″ nanodomains form and evolve upon cooling in compositionally modulated Ti-Nb alloys produced by spinodal decomposition and the corresponding transformation behavior. Finally, our experimental characterization shows a continuous change of the shuffle component across the O′/α″ nanodomain boundaries. The novel microstructural states and their unique phase transformation path lead to an unprecedented continuous transformation behavior accompanied by superelasticity with almost zero hysteresis and small residual strain over a wide temperature range, all of which have been observed in the experiments. This unique transformation behavior upon cooling can be well characterized as a shuffle-regulated strain glass transition. This study could provide new insight in alloy design by utilizing composition-dependent shuffle-shear coupling during a structural phase transformation.

Generalized method of sensitivity analysis for uncertainty quantification in Calphad calculations

Calculation of Phase Diagrams (Calphad) is a method of using thermodynamic models obtained from experimental data to perform thermodynamic calculations. The next step to advancing this methodology is to account for the inconsistency or lack of data when assessing thermodynamic systems. A generalized method of propagating uncertainty through Calphad calculations by local expansion is proposed such that any type of Gibbs free energy model or number of components can be used. This method is faster than Monte Carlo approaches as only a single equilibrium calculation is needed for uncertainty propagation and also improves upon previous approaches to uncertainty propagation by its generalization to any thermodynamic system. As a case study, the Mg–Si system was assessed using a Bayesian approach and various thermodynamic calculations were performed comparing uncertainty quantification by Monte Carlo and the method in this work. Sensitivities (derivatives with respect to model parameters) were calculated on the Fe–Cr–Ni system and compared with sensitivities determined by finite different method.

Machine learning prediction of the mechanical properties of refractory multicomponent alloys based on a dataset of phase and first principles simulation

In this work, a dataset including structural and mechanical properties of refractory multicomponent alloys was developed by fusing computations of phase diagram (CALPHAD) and density functional theory (DFT). The refractory multicomponent alloys, also named refractory complex concentrated alloys (CCAs) which contain 2–5 types of refractory elements were constructed based on Special Quasi-random Structure (SQS). The phase of alloys was predicted using CALPHAD and the mechanical property of alloys with stable and single body-centered cubic (BCC) at high temperature (over 1,500°C) was investigated using DFT-based simulation. As a result, a dataset with 393 refractory alloys and 12 features, including volume, melting temperature, density, energy, elastic constants, mechanical moduli, and hardness, were produced. To test the capability of the dataset on supporting machine learning (ML) study to investigate the property of CCAs, CALPHAD, and DFT calculations were compared with principal components analysis (PCA) technique and rule of mixture (ROM), respectively. It is demonstrated that the CALPHAD and DFT results are more in line with experimental observations for the alloy phase, structural and mechanical properties. Furthermore, the data were utilized to train a verity of ML models to predict the performance of certain CCAs with advanced mechanical properties, highlighting the usefulness of the dataset for ML technique on CCA property prediction.

Numerical Design of CoNi-Base Superalloys With Improved Casting Structure

Numerical methods can accelerate the design of alloys with improved material properties. One approach is the coupling of multi-criteria optimization with CALPHAD-based models of alloy properties. While this technique has already yielded promising new Nickel-base superalloys, the applicability to CoNi-base alloys has not yet been investigated. These alloys show promising properties for application as wrought high-temperature materials. We designed three CoNi-base superalloys, which were optimized for either high strength or high chemical homogeneity. The alloys were cast, and mechanical and thermophysical properties were characterized. The alloy optimized for strength showed creep performance inferior to a conventionally designed CoNi-alloy but had a much lower density. For developing highly homogeneous alloys, Scheil calculations were implemented in the optimization routine to quantify the severity of segregation. Non-equilibrium phases could be predicted successfully, resulting in a degree of homogeneity that rivaled that of a low-segregation ternary Co-base alloy. A comparison of elemental partitioning behavior and phase transition temperatures with CALPHAD calculations showed that trends are well represented for the most part. Finally, the applicability of the alloy design approach for Co-rich superalloys is evaluated, and possible applications for the optimized alloys are discussed.

Effects of Ni and Cr on the high-temperature oxidation behavior and mechanisms of Co- and CoNi-base superalloys

The high-temperature oxidation behaviors of Co- and CoNi-base alloys with different Ni and Cr additions were investigated by isothermal oxidation in air at 900 and 1000 °C. The structure, composition, and element distribution in the three layers within the oxide scales in different alloys have been explored in detail by electron microscopy, especially with regard to the fine oxide particles in the intermediate layer. Based on the microstructure and phase constitution of the oxide scales, the synergetic effects of alloying elements on the oxidation mechanisms and resistance have been elucidated in detail with the aid of CALPHAD calculation.

CALPHAD informed design of multicomponent CoNiCr-based superalloys exhibiting large lattice misfit and high yield stress

Usually, Co-based superalloys contain a high fraction of W and/or Mo. The refractory elements stabilize the precipitate phase, but cause a high density. In this work, new L12-phase hardened, low-density CoNiCr-based superalloys were developed with the assistance of CALPHAD calculations. Several alloys were studied experimentally and their microstructures, elemental distributions, lattice parameters and the lattice misfit between the γ and γ′ phases were evaluated using scanning electron microscopy, transmission electron microscopy, atom probe tomography and high energy X-ray diffraction. The alloys exhibit a very high misfit, good phase stability and excellent mechanical strength. It was found by hardness tests that a two-step heat treatment improves the strength of the new alloys even further. In comparison with conventional Co-based superalloys, Co–Al–W based superalloys and Co–Ti based superalloys, as well as Ni-based superalloys, i.e. Udimet 720Li, they have a low mass density and high yield stress. They also overcome the problem of a generally low lattice misfit of previous L12-phase hardened CoNiCr-based superalloys with high Ni and Cr contents. As a result, they show cuboidal-shaped precipitates similar to Co–Al–W and Co–Al–Mo based superalloys.

Critical Evaluation and Thermodynamic Modeling of the Li-Se and Na-Se Binary Systems Using Combined CALPHAD and First-Principles Calculations Method

This work presents a complete review of the literature on and a critical evaluation and thermodynamic optimization of the Li-Se and Na-Se binary systems. The modified quasi-chemical model in the pair approximation (MQMPA) was employed to describe the liquid solution exhibiting a high degree of short-range ordering behavior of atoms. The thermodynamic properties of the compounds Li2Se (cF12_Fm3¯m), Na2Se (cF12_Fm3¯m), NaSe (hP8_P63/mmc), and NaSe2 (tI48_I4¯2d) were also calculated by using first-principles density functional theory (DFT) calculations to assist the thermodynamic description of these two binary systems. All the available and reliable experimental data are reproduced within experimental error limits. Moreover, the phase equilibria of these two systems at low total pressure were analyzed by using the developed thermodynamic model.

Design and preparation of aluminum alloy with high thermal conductivity based on CALPHAD and first-principles calculation

To obtain the aluminum alloy with high thermal and mechanical properties, the effects of alloying elements and the second phases on the thermal conductivity of Al alloys were investigated by CALPHAD and first-principles calculation, respectively. The properties of the second phases, including Young’s modulus, Poisson’s ratio and minimum thermal conductivity, were systematically studied. Results show that the ranking order of the effects of the alloying elements on the thermal conductivity is Mg>Cu>Fe>Si, and for Al-12Si alloys, the mathematical model of the relationship between the alloying elements and the thermal conductivity can be expressed as λ=ax2-bx+c when the second phase precipitates in the matrix. All kinds of ternary phases of Al-Fe-Si have higher deformation resistance, rigidity, theoretical hardness, Debye temperature and thermal conductivity than the other phases which possibly exist in the Al-12Si alloys. Based on the guidance of CALPHAD and first-principles calculation, the optimized chemical composition of Al alloy with high conductivity is Al-11.5Si-0.4Fe-0.2Mg (wt.%) with a thermal conductivity of 137.50 Wm−1·K−1 and a hardness of 81.3 HBW.

Oxidation resistance of ZrB2‐based monoliths using polymer‐derived Si(Zr,B)CN as sintering aid

AbstractThe focus of the present work is the investigation of the influence of polymer‐derived ceramics, used as sintering aids for preparing ZrB2‐based monoliths, on their high‐temperature oxidation behavior. For the preparation of the monoliths, ZrB2 powder was coated with polymer‐derived SiCN, SiZrCN, or SiZrBCN and subsequently densified via hot‐pressing at temperatures as low as 1800°C. To investigate the oxidation kinetics, thermogravimetric analysis (TGA) was performed at 1300°C in synthetic air with exposure times of 50 and 100 h. A detailed study of the materials oxide scale and subsurface microstructure was conducted using optical microscopy, electron probe microanalysis, scanning electron microscopy, and X‐ray diffraction. The experimental findings were compared to thermodynamic equilibrium calculations using the CALPHAD method, which led to a better understanding of the oxidation mechanism. In comparison to the literature data of ZrB2–SiC, the results show improved oxidation resistance for all three investigated materials. The formation of gaseous species during oxidation, in particular CO, CO2, B2O3, and SiO, within the oxide scale of the monoliths was rationalized via CALPHAD calculations and used to explain the oxidation behavior and kinetics and also the formation of bubbles in the subsurface region of the oxidized specimens.

Multiscale simulation of powder-bed fusion processing of metallic alloys

We present a computational framework for the simulations of powder-bed fusion of metallic alloys, which combines: (1) CalPhaD calculations of temperature-dependent alloy properties and phase diagrams, (2) macroscale finite element (FE) thermal simulations of the material addition and fusion, and (3) microscopic phase-field (PF) simulations of solidification in the melt pool. The methodology is applied to simulate the selective laser melting (SLM) of an Inconel 718 alloy using realistic processing parameters. We discuss the effect of temperature-dependent properties and the importance of accounting for different properties between the powder bed and the dense material in the macroscale thermal simulations. Using a two-dimensional longitudinal slice of the thermal field calculated via FE simulations, we perform an appropriately-converged PF solidification simulation at the scale of the entire melt pool, resulting in a calculation with over one billion grid points, yet performed on a single cluster node with eight graphics processing units (GPUs). These microscale simulations provide new insight into the grain texture selection via polycrystalline growth competition under realistic SLM conditions, with a level of detail down to individual dendrites.

The AlMo0.5NbTa0.5TiZr refractory high entropy superalloy: Experimental findings and comparison with calculations using the CALPHAD method

Detailed microstructural characterization of the AlMo0.5NbTa0.5TiZr refractory high entropy superalloy in the as-cast state is reported for first time and compared with the state annealed at 1400 °C for 24 h. The former shows a dendritic structure, with a mixture of A2/B2 phases < 20 nm in both the dendritic and interdendritic regions. A mostly amorphous phase, rich in Al and Zr, is found within the interdendritic region. The annealed state reproduced the combination of A2/B2/Al-Zr-rich phases reported previously. Calculations from two relevant ThermoCalc databases were compared with the experimental results. Equilibrium calculations were compared with results for the annealed alloy, whereas solidification paths calculated using Scheil-Gulliver model were used for comparison with the as-cast alloy. A previously hypothesized spinodal decomposition during cooling as the mechanism responsible for the patterned A2/B2 microstructure is confirmed via the CALPHAD calculations, pointing to its use as an efficient design tool for such alloys. Finally, the comparison between the experimental and computational findings allowed better understanding the solidification path and equilibrium stability of this alloy, giving a base to make better decisions on the field of new refractory superalloy design.

Critical Evaluation and Thermodynamic Modeling of the Li-Se and Na-Se Binary Systems Using Combined Calphad and First-Principles Calculations Method

Critical Evaluation and Thermodynamic Modeling of the Li-Se and Na-Se Binary Systems Using Combined Calphad and First-Principles Calculations Method

Towards a better understanding of the high-temperature oxidation of MAX phase Cr2AlC

High-temperature oxidation of bulk single crystal, fine and coarse grained polycrystals of Cr2AlC has been performed from 800 °C to 1500 °C. In the temperature range T = [800;1400] °C, an α-Al2O3 scale with a Cr7C3 subscale are in-situ formed independently of the initial microstructure on top of the bulk Cr2AlC. CALPHAD calculations were performed to explain the formation of Cr7C3 instead of the expected mixture of carbides, indicating a favourable driving force for Cr7C3 formation. The kinetic study of the oxidation is consistent with previous works with an activation energy of about 400 kJ.mol−1. Oxidizing for a longer time (1000 h) or at higher temperature (1500 °C) leads to the formation of chromia in the former alumina scale, which correspond to the calculated equilibrium phases.

On the phase constituents of three CoCrFeNiX (X = B, Al, Ga) high-entropy alloys after prolonged annealing

Equilibrium or near-equilibrium phase data are crucial to the development and application of high entropy alloys (HEAs). However, the vast majority of published HEA phase data are based on as-cast or shortly annealed conditions. Here, the phase constituents and microstructures in three equimolar CoCrFeNiX alloys (X = B, Al, Ga) after prolonged annealing at 500–1100 °C have been investigated. The CoCrFeNiB alloy was comprised of a dominating FCC phase and various boride phases [(Cr, Fe)2B, (Fe, Co, Ni)3B, Cr2B-tI12] at all annealing temperatures. Annealing at 700 °C led to the additional formation of CrB. The CoCrFeNiAl alloy was comprised of B2, BCC, and FCC phases at 1100 and 500 °C. The BCC phase transformed to the sigma phase at 700 and 900 °C. The CoCrFeNiGa alloy was comprised of BCC and FCC phases at all annealing temperatures, with additional sigma phase formation at 700 °C and 500 °C. The experimental results were compared with CALPHAD predictions. Depending on the alloy system, the accuracy of CALPHAD calculations varied significantly. The accuracies are well-related to the fraction of assessed systems of each alloy. These data here are not only useful as individual alloys. Together with previous parts of this systematic study, which investigated X elements from groups IVB, VB, and VIB (Y, Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W), the holistic dataset offers the basis for new analysis and interpretations when looked at in its totality. We expect that this dataset will be valuable for future studies on the phase formation and other aspects of HEAs.

Experimental determination of enthalpies of formation of Li17Si4, Li16.42Si4 and Li13Si4

The hydrogen absorption equilibria have been investigated to determine the enthalpy of formation of the lithium rich silicides Li17Si4, Li16.42Si4 and Li13Si4. For the corresponding experiments, two different sample types of Li17Si4: pure silicide and a stoichiometric mixture of lithium hydride and silicon (ratio 17:4), as well as Li16.42Si4 were used. The measurements were performed at three different temperatures (450 °C, 475 °C, 500 °C). The calculation of the enthalpies of formation by using the slopes of the classical van´t Hoff plot resulted in uncertainties of at least 10%. Due to this unsatisfying large error an alternative evaluation method was applied linking up the hydrogen equilibrium pressure peq(H2) from the sorption measurements and our recently published precise heat capacity and entropy data of the lithium silicides. The values obtained in this manner for the standard enthalpies of formation (Li17Si4 - (mol atom)−1; Li13Si4 = -24.4 ± 0.3 kJ (mol atom)−1 and Li16.42Si4 = -22.2 ± 0.5 kJ (mol atom)−1 show strongly reduced uncertainties that are acceptable for CALPHAD calculations to obtain a largely improved phase diagram description completely based on an experimental thermodynamic dataset.

A new class of light-weight metastable high entropy alloy with high strength and large ductility

The strength-ductility (or density, or thermal conductivity) trade-off is unavoidable in most conventional alloys due to the limited composition space. Herein, we developed a new class of light-weight metastable high entropy alloy (LW metastable HEA) with high specific strength and large ductility. Firstly, a property-targeted alloy design to develop the LW TRIP-assisted dual-phase HEA was performed based on CALPHAD calculation by constituting the alloy with a higher fraction of LW elements in 3d transition metal elements and having the extremely low stacking fault energy. Secondly, we systematically add Al (low density, large atomic size misfit, and Ferrite stabilizer) up to 5 at.% in the non-equiatomic Cr24Mn6Fe40Co24Ni6 HEA developed through the first step. As a result, we confirmed that the phase constitution is changed with increasing Al contents from (FCC+HCP) dual-phase to FCC single phase to (FCC+BCC (B2)) dual-phase. In particular, the FCC single-phase HEA exhibits (1) a relatively low density (∼10% reduction compared to Cantor alloy), (2) an abnormally large lattice distortion (3 times greater atomic size mismatch compared to Cantor alloy), which can be confirmed by extremely low thermal conductivity as well as large lattice parameter; (3) a large solid solution strengthening, which can be confirmed by a significant Hall-Petch coefficient (∼50% increase compared to Cantor alloy); (4) TRIP/TWIP complex deformation mechanisms (large ductility over ∼40%). Thus, it can be understood that the developed single- phase FCC HEAs can provide exceptional combinations of density, strength, and ductility in the trade-off relationship through the confusion effect by the microstructural complexity as well as the chemical complexity. Consequently, these results provide a guideline on how to design a new class of LW metastable HEA with promising properties as a new generation of structural material.