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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Thermodynamics and its prediction and CALPHAD modeling: Review, state of the art, and perspectives

Thermodynamics is a science concerning the state of a system, whether it is stable, metastable, or unstable, when interacting with its surroundings. The combined law of thermodynamics derived by Gibbs about 150 years ago laid the foundation of thermodynamics. In Gibbs combined law, the entropy production due to internal processes was not included, and the 2nd law was thus practically removed from the Gibbs combined law, so it is only applicable to systems under equilibrium, thus commonly termed as equilibrium or Gibbs thermodynamics. Gibbs further derived the classical statistical thermodynamics in terms of the probability of configurations in a system in the later 1800's and early 1900's. With the quantum mechanics (QM) developed in 1920's, the QM-based statistical thermodynamics was established and connected to classical statistical thermodynamics at the classical limit as shown by Landau in the 1940's. In 1960's the development of density functional theory (DFT) by Kohn and co-workers enabled the QM prediction of properties of the ground state of a system. On the other hand, the entropy production due to internal processes in non-equilibrium systems was studied separately by Onsager in 1930's and Prigogine and co-workers in the 1950's. In 1960's to 1970's the digitization of thermodynamics was developed by Kaufman in the framework of the CALculation of PHAse Diagrams (CALPHAD) modeling of individual phases with internal degrees of freedom. CALPHAD modeling of thermodynamics and atomic transport properties has enabled computational design of complex materials in the last 50 years. Our recently termed zentropy theory integrates DFT and statistical mechanics through the replacement of the internal energy of each individual configuration by its DFT-predicted free energy. The zentropy theory is capable of accurately predicting the free energy of individual phases, transition temperatures and properties of magnetic and ferroelectric materials with free energies of individual configurations solely from DFT-based calculations and without fitting parameters, and is being tested for other phenomena including superconductivity, quantum criticality, and black holes. Those predictions include the singularity at critical points with divergence of physical properties, negative thermal expansion, and the strongly correlated physics. Furthermore, those individual configurations may thus be considered as the genomic building blocks of individual phases in the spirit of the materials genome®. This has the potential to shift the paradigm of CALPHAD modeling from being heavily dependent on experimental inputs to becoming fully predictive with inputs solely from DFT-based calculations and machine learning models built on those calculations and existing experimental data through newly developed and future open-source tools. Furthermore, through the combined law of thermodynamics including the internal entropy production, it is shown that the kinetic coefficient matrix of independent internal processes is diagonal with respect to the conjugate potentials in the combined law, and the cross phenomena that the phenomenological Onsager flux and reciprocal relationships are due to the dependence of the conjugate potential of a molar quantity on nonconjugate molar quantities and other potentials, which can be predicted by the zentropy theory and CALPHAD modeling.

42 ENGINEERING↗
DOE OSTI2025

Analytical gradient-based optimization of CALPHAD model parameters

The calibration of CALPHAD (CALculation of PHAse Diagrams) models involves the solution of a very challenging high-dimensional multiobjective optimization problem. Traditional approaches to parameter fitting predominantly rely on gradient-free methods, which while robust, are computationally inefficient and often scale poorly with model complexity. In this work, we introduce and demonstrate a generalizable framework for analytic gradient-based optimization of the parameters of the CALPHAD model enabled by the recently formalized Jansson derivative technique. This method allows for efficient evaluation of gradients of thermodynamic properties at equilibrium with respect to model parameters, even in the presence of arbitrarily complex internal degrees of freedom. Leveraging these semi-analytic gradients, we employ the conjugate gradient (CG) method to optimize thermodynamic model parameters for four binary alloy systems: Cu-Mg, Fe-Ni, Cr-Ni, and Cr-Fe. Across all systems, CG achieves comparable or superior optimality relative to Bayesian ensemble Markov Chain Monte Carlo (MCMC) with improvements in computational efficiency ranging from one to three orders of magnitude. Furthermore, our results establish a new paradigm for CALPHAD assessments in which high fidelity data-rich model calibration becomes tractable using deterministic gradient-informed algorithms.

CALPHAD↗
DOE OSTI2026

Gradient-informed Hamiltonian Monte Carlo for multicomponent CALPHAD model optimization and uncertainty quantification

CALPHAD model parameter optimization is inherently challenging due to non-smooth objective functions, high-dimensional parameter spaces, and the need for uncertainty quantification (UQ). Traditional weighted nonlinear least squares approaches are computationally efficient but local, whereas black-box global optimizers and ensemble Markov Chain Monte Carlo (MCMC) methods provide broader exploration at substantial computational cost. The objective of this work is to combine the global exploration capability of gradient-informed Hamiltonian Monte Carlo – specifically the No-U-Turn Sampler (NUTS) – with local deterministic refinement using BFGS to efficiently optimize multicomponent CALPHAD models with minimal manual intervention. Analytic gradients are computed via the Jansson derivative framework. The methodology is demonstrated on the Cr—Fe binary system and extended to the Cr—Fe—Ni ternary system with 32 degrees of freedom. For Cr—Fe, NUTS achieves comparable or superior optimality relative to ensemble MCMC while requiring over an order-of-magnitude fewer likelihood evaluations. Parameter uncertainties are quantified through NUTS sampling and propagated to thermodynamic observables using local expansion, demonstrating a novel modular approach that combines binary and ternary parameter subsets without requiring global relaxation. These results establish gradient-informed exploration as a scalable strategy for multicomponent CALPHAD optimization and provide a practical route towards efficient higher-order database development with quantified uncertainty.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Predictive modeling of Néel temperature in austenitic alloys using CALPHAD and data analytics

The Néel temperature is a crucial yet often overlooked parameter in calculating the stacking fault energy (SFE) of austenitic alloys. Several empirical equations have been proposed to estimate the Néel temperature of austenitic alloys, which are then used to calculate the SFE and explain deformation mechanisms. However, these empirical equations, typically derived using linear regression algorithms, are often simplistic and may fail to capture the complex interactions among multiple alloying elements that influence the Néel temperature. Moreover, their applicability is usually limited to specific compositional ranges. In this study, we propose a CALPHAD based approach and develop a surrogate decision tree based regression model capable of capturing the interactions among multiple alloying elements to predict the Néel temperature. Predictions from both the CALPHAD approach and the regression model show close agreement with experimental measurements reported in the literature. In conclusion, the implications of accurate Néel temperature predictions on the calculated SFE and deformation mechanisms are also discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2025

LASSO for CALPHAD Model Selection Enables Data-Efficient Thermodynamic Modeling: An Application in Thermochemical Hydrogen Production Materials

Phenomenological CALPHAD (CALculation of PHAse Diagrams) models, widely used for multicomponent materials, often contain a considerable number of parameters and require fitting using data from a relatively small number of experimental measurements or theoretical calculations. Sometimes these parameters are introduced for the purpose of improving model fits but without clear physical justification, which leads to overparametrized models with poor generalization performance. Automated approaches for optimal model selection based on the available data therefore become critical. Here, in this work, a least absolute shrinkage and selection operator (LASSO)-based approach is developed for model selection by leveraging the linearity of the CALPHAD model with respect to its parameters to convert the model selection and fitting to a LASSO minimization problem. We demonstrate its utility for thermodynamic modeling of thermochemical hydrogen (TCH) production materials using lanthanum strontium manganite (LSM) as an example. Various TCH-relevant properties, including oxygen stoichiometry as a function of oxygen partial pressure, enthalpy of reduction, and entropy of reduction, are successfully predicted with reasonable accuracy using a minimal set of model parameters. Importantly, the model selection and fitting involve minimal human decision; it can therefore be applied to high-throughput DFT defect calculations and yield efficient workflows for TCH material modeling and optimization.

CALPHAD↗
DOE OSTI2025

CALPHAD-based ICME design of single-step aging to enhance mechanical strength of WAAM Haynes 282

To match the strength of wire-arc additive manufactured Haynes 282 to its wrought counterpart via a single-step aging heat treatment, the CALPHAD (Calculation of Phase Diagrams) method is integrated with physics-based process-structure-property models and experimental validation. The integrated computational materials engineering (ICME) framework simulates the effects of aging on γ′ and M 23 C 6 precipitation and the resulting yield strength. To improve simulation reliability, the interfacial energies between γ/γ′ and γ/M 23 C 6 carbides were estimated by comparison with precipitation kinetic modeling and measured precipitate sizes. γ′ and M23C6 were found to precipitate simultaneously between 640 and 860 °C, producing microstructures similar to those produced by two-step aging. The optimal γ′ size for peak yield stress was calculated to be 20–23 nm. WAAM Haynes 282 aged at 780 °C for 50 h exceeded the mechanical performance of its wrought counterpart subjected to two-step aging, though desired properties can also be achieved at 800 °C for 16 h or less. The error in yield strength is less than 20 MPa, demonstrating good agreement between the modeling framework and experiments. Creep studies showed that WAAM Haynes 282 exceeded the calculated rupture time, reaching 481 h. This proposed methodology can accelerate the design of aging heat treatments for any γ′-strengthened nickel-base alloy, minimizing the resources required for trial-and-error experiments.

CALPHAD↗
DOE OSTI2026

Predicting the High-Temperature Oxidation Response of Nickel Superalloys Using CALPHAD-Enhanced Machine Learning

Structural materials such as Ni-based superalloys used in high-temperature power cycles are routinely exposed to toxic environments including high temperature and pressure, aqueous and gas corrosion, etc. Here, we present a physics-informed machine learning approach to predict the oxidation response of diverse Ni-superalloys. First, a high-fidelity experimental dataset is curated from typical oxidation mass-change experiments in air, covering 25+ elements and different physical behavior such as parabolic growth, non-parabolic growth, and oxide spallation. Second, the dataset is featurized using thermophysical, chemical, and mechanical properties obtained from high-throughput CALPHAD calculations. Third, several machine learning models are developed to identify key features related to mass-change characteristics and model the mass-change curve for various alloys. Finally, the model is deployed to rapidly screen over a new composition space and down-select candidate alloys with high oxidation resistance for experimental validation.

CALPHAD↗
DOE OSTI2025

CALPHAD-based Bayesian optimization to accelerate alloy discovery for high-temperature applications

Two crucial properties influencing the performance of high-temperature alloys are coefficient of thermal expansion (CTE) and phase constitution. It is desirable to have alloys with low CTE, which reduces CTE mismatch with the surface oxide and the likelihood of oxide spallation. Reducing the amount of brittle intermetallic phases such as Sigma (σ) enhances alloy ductility and processability. Here, we propose a multi-objective Bayesian Optimization (BO) model to simultaneously minimize CTE (at an operational temperature of 1150 °C) and T σ (temperature when the Sigma phase completely dissolves in the metal matrix), properties which are obtained from high-throughput CALculation of PHAse Diagrams (CALPHAD). The model successfully identifies several alloys with CTE ≤ 2 × 10 –5 /K and T σ ≤ 500 °C by exploring just 7% of the nickel–chromium–cobalt–aluminum–iron (Ni–Cr–Co–Al–Fe) composition space. Such multi-objective alloy design frameworks can be used to inform additive manufacturing experiments and accelerate alloy discovery for high-temperature energy applications.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Model form and sensitivity analysis of CALPHAD-based nucleation models in b-stabilized Ti alloys

Accurate prediction of α-phase nucleation and growth in β-stabilized titanium alloys is crucial for designing heat treatments to optimize mechanical properties in additively manufactured lightweight components. Ideally, predictions of nucleation and growth would incorporate both top-down observations of past experimental heat treatments and bottom-up modeling of phase transformations; however, the appropriate method of combining these information sources is not self-evident. Combining top-down and bottom-up information requires a unified form of model that can connect between spatiotemporal scales, as well as sets of fitting parameters that can be identified by each data source. The selection of which parameters to fit to which data source can be made based on expert opinion, or by performing a sensitivity analysis. In solid-solid nucleation, direct observation of the nucleation and growth process is challenging. Most data on the heat treatment-controlled phase transformations are not in-situ. To predict the process and outcome of the nucleation, growth and coarsening of precipitates, theoretical models of the nucleation pathway are used to bridge the gap. Many sources of uncertainty affect the modeling of this nucleation process. It can be influenced by small variations in the thermomechanical processing history, chemical composition, and initial microstructure. If molecular dynamics (MD) simulations are used to determine thermodynamic quantities and inform CALPHAD modeling, additional uncertainty can be introduced and accounted for using Bayesian methods. Top-down uncertainties require additional steps to quantify. The influence of nucleation model form on the sensitivity of predictions to input parameters and physical conditions is the focus of this study. Classical nucleation theory (CNT) allows modeling to formulate the nucleation as homogeneous or, more commonly, heterogeneous. Non-classical nucleation models are also increasingly explored as a means of reconciling top-down and bottom-up data. In this study, the sensitivity of the intragranular nucleation of α in a β-annealed, slow-cooled aging (BASCA) heat treatment of β-stabilized Ti5553 alloy is explored using CNT and both heterogeneous and homogeneous assumptions. The Kampmann-Wagner Numerical model of precipitate nucleation and growth is employed. Using open-source tools (pyCalphad and thermodynamic modeling of TiMo as a surrogate system, a sensitivity analysis is performed to measure variations in key parameters, including chemical driving force, interfacial energy, and diffusivity, as they relate to predictions of precipitate number density. The inclusion of top-down and bottom-up data in selection of nucleation model form is discussed.

Rodriguez Negron, A. M.↗
DOE OSTI2025

Design of novel refractory equiatomic multi-principal elemental alloys based on Mo-Nb-Ti system for Gen IV reactor applications

Excellent irradiation damage resistance demonstrated by multi-principal elemental alloys (MPEAs) has sparked significant interest among researchers, prompting exploration into their vast compositional space, to validate their suitability for nuclear applications. A combined approach of thermodynamic and empirical parameters calculations alongside CALPHAD (CALculation of PHAse Diagrams) for phase formation predictions enable high-throughput material selection for sophisticated applications like nuclear, overcoming laborious and time-consuming experiments. Key thermodynamic and empirical parameters for eight novel equiatomic MPEAs, based on seven low thermal neutron cross section refractory elements, for predicting phase formation were calculated, and equilibrium and non-equilibrium simulations in CALPHAD were employed to comprehensively model the systems. Pseudo binary phase diagram simulations showed that Zr, V or equiatomic CrV additions to the base MoNbTi alloy (MoNbTi-Zr, MoNbTi-V and MoNbTi-CrV alloys) favor the formation of isomorphous body-centered cubic (BCC) phase at high temperatures, while Cr, Al, equiatomic ZrV, or equiatomic CrAl additions (MoNbTi-Cr, MoNbTi-Al, MoNbTi-ZrV or MoNbTi-CrAl alloys) limit the solubility of them. Equilibrium CALPHAD simulations at 750 oC were consistent with XRD results on MoNbTi, MoNbTiZr and MoNbTiCr alloys, and partially for others. Notably, elemental segregation observed in the backscattered electron (BSE) scanning electron microscopy (SEM) images of the alloys was accurately simulated through non-equilibrium Scheil solidification calculations in CALPHAD, further verified by experiments. The precipitation of TiCr2 Laves phase in Cr containing MoNbTiCr and MoNbTiCrAl was accurately predicted while discrepancies were noted in MoNbTiCrV. The equilibrium simulations also provided insights into phase compositions at specific temperatures offering a pathway for tailoring the desired microstructure and properties of these systems. Empirical parameters calculations successfully predicted random solid solution in the base MoNbTi alloy, and with an exception in MoNbTiV and MoNbTiAl, predicted intermetallic precipitation in the rest, especially, Laves phase precipitation in Cr containing alloys.

36 - MATERIALS SCIENCE↗
DOE OSTI2024

Computational thermodynamics-guided alloy design and phase stability in CoCrFeMnNi-based medium-and high-entropy alloys: An experimental-theoretical study

A computational thermodynamics approach has been employed to design CoCrFeMnNi-based medium- and high-entropy alloys (M/HEAs) with systematically varied compositions (Co(( 80-X )/ 2 )Cr(( 80-X )/ 2 )Fe X Mn 10 Ni 10 with x = 30, 40, and 50 at.%) and phase stability. Since the formation of sigma phase, usually brittle and undesirable, is a common concern, when this class of alloys is subjected to elevated temperatures (600–1000 °C), predicting its formation becomes essential. Thus, its formation and the phase equilibria were studied using the CALPHAD method, and two empirical methods, namely, valence electron concentration (VEC) and paired sigma-forming element (PSFE). Isothermal aging treatments at 900–1100 °C for 20 h were performed, since CALPHAD and VEC/PSFE predictions diverged. Both prediction methods were compared with experimental characterization by a combination of scanning electron microscopy and high-energy synchrotron X-ray diffraction. In conclusion, the predictions from the VEC/PSFE and CALPHAD calculations (depending on the database used) were shown to be quite accurate.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Microstructural, Oxidation, and Mechanical Behavior of NbTi-Based Refractory Alloys with 5 to 10 Pct Co, Cr, and Ni Additions

NbTi-based refractory alloys with additions of Co, Cr, and Ni represent an interesting medium-entropy alloy system with potential for protective oxide film formation, high strength, and ductility. This study investigates the microstructural evolution, oxidation behavior, and mechanical properties of NbTi-based alloys containing 5 to 10 at. pct Co, Cr, and Ni. CALPHAD predictions suggest that this composition range can be heat treated to obtain a predominantly body-centered cubic matrix phase. Mechanical properties, including microhardness, yield strength, maximum strength, and specific strength are evaluated through isothermal compression tests conducted between room temperature and 800 °C. The oxidation kinetics of these alloys are assessed through discontinuous oxidation tests. Parabolic oxidation kinetics were observed for NbTi–10Ni and NbTi–5Co, while linear oxidation kinetics were found for NbTi–10Cr and NbTi–10(CoCrNi). Microstructures and oxide layers are characterized using X-ray diffraction, electron backscatter diffraction, energy-dispersive X-ray spectroscopy, and scanning electron microscopy. All alloys exhibit significant mechanical softening between room temperature and 800 °C, with elastic-perfectly plastic flow observed at 800 °C. The addition of 10 pct Cr to NbTi resulted in two BCC phases up to 1050 °C, conflicting with CALPHAD predictions of a single-phase solid solution at this temperature, and resulting in higher flow stress at 800 °C. NbTi–10(CoCrNi) exhibited the lowest flow stress at 800 °C despite having more ‘cocktail effect’ potential and insufficient molar fractions of Co, Cr, or Ni to form a desirable protective oxide film.

36 MATERIALS SCIENCE↗
DOE OSTI2026

High-throughput validation of phase formability and simulation accuracy of Cantor alloys

High-throughput methods enable accelerated discovery of novel materials in complex systems such as high-entropy alloys, which exhibit intricate phase stability across vast compositional spaces. Computational approaches, including Density Functional Theory (DFT) and calculation of phase diagrams (CALPHAD), facilitate screening of phase formability as a function of composition and temperature. However, the integration of computational predictions with experimental validation remains challenging in high-throughput studies. In this work, we introduce a quantitative confidence metric to assess the agreement between predictions and experimental observations, providing a quantitative measure of the confidence of machine learning models trained on either DFT or CALPHAD input in accounting for experimental evidence. The experimental dataset was generated via high-throughput in-situ synchrotron X-ray diffraction on compositionally varied FeNiMnCr alloy libraries, heated from room temperature to ~1000 °C. Agreement between the observed and predicted phases was evaluated using either temperature-independent phase classification or a model that incorporates a temperature-dependent probability of phase formation. This integrated approach demonstrates where strong overall agreement between computation and experiment exists, while also identifying key discrepancies, particularly in FCC/BCC predictions at Mn-rich regions to inform future model refinement.

36 - MATERIALS SCIENCE↗
DOE OSTI2026

An Integrated Computational Materials Engineering (ICME) Approach to Design Nonlinear Transition Zones Between Dissimilar Metals

Current approaches to designing graded transition joints (GTJs) between dissimilar metals often rely on linear changes in both composition profiles and thickness of each sublayer. This increases fabrication cost and may not be optimal with respect to residual stress or the formation of undesirable phases. Here, in this study, GTJs between P91 ferritic/martensitic steel and 347H austenitic stainless steel were designed using Integrated Computational Materials Engineering (ICME) principles with nonlinear composition and length profiles. Guided by inputs from classical mechanics and CALPHAD predictions of carbon chemical potential, a novel transition zone consisting of five discrete compositions was proposed, with the thickness of each sublayer varying according to a brachistochrone-inspired distribution. In addition to carbon potential gradients, CALPHAD was used to predict coefficients of thermal expansion, which were incorporated into finite element models to evaluate stress evolution. The proposed nonlinear design resulted in a smoother carbon potential gradient, lower carbon depletion at the P91 interface, and a comparable residual stress under long-term thermal exposure, compared to a conventional linear design using ten sublayers with equal thickness. This work introduces a brachistochrone-inspired distribution for GTJ design, offering a general framework for optimizing graded interfaces between dissimilar metals.

Directed Energy Deposition↗
DOE OSTI2024

Effect of Si impurities on microstructure and tensile properties of a cast Al-Mg-Fe alloy

Al-Mg alloys are attractive for structural castings owing to their superior strength and ductility in the as-cast state. However, given the tight tolerance for impurities, Al-Mg alloys produced from secondary sources still face multiple challenges. Here, we report the effect of increased Si impurity (0.05–1.6 wt%), which is commonly found in secondary Al sources, on microstructure and tensile properties of a cast Al-4.3Mg-1.6Fe (wt%) alloy, commercially referred to as Castaduct-42 alloy. Microstructural characterization revealed that Si addition increased the volume fraction, size, and aspect ratio of primary Al13Fe4 intermetallic particles as well as the volume fraction of other binary and ternary eutectic phases. Tensile testing results demonstrated that increasing Si impurities from 0.05 to 1.6 wt% reduced ductility from 14.3 ± 1.4 % to 2.2 ± 1.0 %. A particle cracking damage accumulation model coupled with failure analysis indicated primary Al13Fe4 intermetallic particles to be the major contributing factor to the deterioration in ductility with increasing Si content. Additionally, the stabilizing effect of Si on primary Al 13 Fe 4 was inconsistent with the CALPHAD calculation results based on existing CALPHAD databases which predict a slightly decreasing primary Al13Fe4 phase fraction with increasing Si concentration. This work provides new insights into the phase stability and mechanical behavior of the lesser studied Al-Mg-Fe-Si alloy system that will contribute to the development of sustainable cast Al-Mg based alloys.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Rapid Bayesian High Entropy Alloy Designs Fabricated via Wire Arc Additive Manufacturing

Purpose: This project seeks to demonstrate a new high-throughput (rapid) alloy design technique applied to creating new high entropy alloys (HEAs) for extreme environments. High entropy alloys shift the design paradigm from being focused on a single principal element (e.g. nickel-based alloys) to target alloys that include high atomic fractions (X >10%) of multiple elements. These HEA materials can exhibit sluggish diffusion and enhanced corrosion resistance, ideal for potential applications in advanced ultra supercritical (A-USC) steam cycles for power generation. Scope: The addition of multiple elements in high atomic fractions creates an enormous design space that cannot easily be investigated by traditional material design strategies such as designed of experiments (DOE). This project utilizes a Bayesian machine learning algorithm that has been modified to work with calculation of phase diagrams (CALPHAD) software. This Bayesian algorithm reduces manual inputs and increase the likelihood of achieving an optimal solution. Compositional inputs to this algorithm will be assessed using existing material property models for high temperature strength and corrosion resistance. The target for alloy performance will be a 15% (~100 ⁰C) increase in allowable service temperature beyond heat-resistant stainless steels while maintaining or improving alloy cost and corrosion resistance. Haynes 230 was selected as a baseline, which is 57 wt% Ni with 22 wt% Cr 14 wt% W, and 2 wt% Mo as solid solution strengtheners. In addition to rapid design via Bayesian machine learning, the alloys were rapidly fabricated using a multi-wire arc additive manufacturing (mWAAM) technique which allows for precise control of alloy composition and assessing of alloy design “windows” to study composition effects. Build speeds for wire-arc additive processes are among the highest for additive technologies enabling rapid and reliable sample fabrication when compared to conventional methods such as arc button melting. The mWAAM samples will be rapidly characterized via instrumented indentation for room temperature modulus and strength and for elevated temperature strength via hot hardness tests. After being screened with hardness testing, potential alloys will be further evaluated with conventional microscopy techniques including scanning electron microscopy (SEM) and transmission electron microscopy (TEM) to assess agreement with modeling results. The most promising compositions will also be evaluated by printing full sized tensile specimens for mechanical behavior tests at elevated temperatures. Results: Bayesian machine learning of a single performance function was initially used to optimize five performance metrics: 1) single phase stability, 2) yield strength, 3) creep resistance (low diffusion coefficient), 4) freezing range (weldability), and 5) material cost. The single performance function was suboptimal as assumptions had to be made about the results while formulating the optimization. A goal-oriented Bayesian optimization strategy (Hanaoka, 2021) was implemented with CALPHAD for use with the five metrics above. This multi-objective Bayesian optimization (MOBO) enabled the design of NiCrCoFe alloys with V and W additions. A base composition of NiCoCr was selected as Ni provides a stable FCC matrix, Cr aids corrosion/oxidation resistance, and Co is a solid-solutions strengthener that also improves creep by increasing the activation energy. Fe helps reduce diffusion coefficients and cost. Finally, V and W were selected for their reasonable solubility and high atomic misfit to aid in solid solution strengthening. Cracking of the mWAAM specimens was an early issue, and the Easton solidification cracking model (Easton et al., 2014a) was selected for addition to the MOBO function. High performing alloys fabricated by mWAAM included Ni 28 Cr 25 Co 26 Fe 15 V 8 and Ni 62 Cr 18 Co 1 Fe 3 W 15 . It was observed that even after adapting the mWAAM process for W, the W did not fully dissolve. To fully evaluate the Ni 62 Cr 18 Co 1 Fe 3 W 15 composition, a cored wire (80-20 NiCr sheath/powder core) was manufactured and printed via WAAM, and HIP’ing was utilized to homogenize and densify the printed alloy. The V and W alloys produced met metrics 1 (solid solution), 4 (solidification cracking), and 5 (cost). However, an unmodeled mechanism of thermal stress cracking was identified in the WAAM produced materials, perhaps exacerbated by the lack of grain boundary strengthening elements (B, C). Conclusions & Recommendations: A high-throughput (rapid) alloy design technique was applied to designing and manufacturing new high entropy alloys (HEAs) for extreme environments utilizing MOBO and mWAAM. The developed process was rapid and effective in addressing the mechanisms included in the model. The lack of grain boundary strengthening element additions (e.g., B, C) was a simplification that likely produced thermal stress cracking that turned into a large part of the investigation. Additions on the order of 0.005 wt% B and 0.05 wt% C likely would have minimized thermal stress grain boundary cracking. Overall, the high throughput design strategy is promising for rapid design of metrics-driven alloys for advanced ultra supercritical (A-USC) steam cycles for power generation. The MOBO and mWAAM process could be commercialized to accelerate metrics-driven alloy design. In addition, the cored-wire process utilized for scale-up is a promising high-volume process for WAAM alloy development and scale-up.

36 MATERIALS SCIENCE↗