Amid nearly endless recipes for metal alloys, pinpointing the alloy that best satisfies an engineering challenge is a painstaking process. Most common alloys consist of one primary element mixed with traces of one or two other elements. Specialized alloys such as those found in engines or heat shields may contain significant fractions of four or more elements. This expanding palette of elemental ingredients causes the number of potential alloy formulations to grow exponentially.
However, scientists cannot evaluate every formulation in the laboratory. (See S&TR, March 2025, Accelerating Materials Discovery.) Sophisticated computational and machine learning–assisted methods are accelerating engineering workflows by estimating the material properties for hundreds or thousands of alloys en masse and shrinking the number of candidates for laboratory testing.
An Established Method
Alloys must often satisfy conflicting material requirements, such as retaining strength at high temperature or ensuring machinability while remaining stiff. These macroscopic properties derive from crystal structures (or phases) formed at the atomic level. For example, atoms arranged into the body-centered cubic (BCC) phase tend to offer higher strength while the face-centered cubic (FCC) phase usually increases ductility.
To determine the best alloy for a task, researchers consult phase diagrams that capture how materials form distinct phases over a range of temperatures. Comparing phase information between materials enables scientists to determine which will fare best in the anticipated operating conditions and which could jeopardize performance. However, designing a new alloy by direct experimentation is laborious and time consuming.
Turning to computational means, scientists today integrate physics models with data from decades of alloy research to predict the properties of increasingly complex, yet-to-be-tested alloys. This field of computational materials design first surged during the 1970s with the introduction of the calculation of phase diagrams (CALPHAD) method, which has grown ever more sophisticated. Using CALPHAD, scientists can predict what phase or mixtures of phases will form (such as BCC or FCC) and their respective fraction (amount) and constitution (chemical composition) as functions of the material’s composition and temperature. Carrying out this method over a range of temperatures and material compositions estimates its full phase diagram and permits the design of new alloys with tailored properties.
CALPHAD is a phase-based method in which the Gibbs energy of each phase is modeled using power series expansion. Scientists construct this energy function using many information sources including direct thermodynamic property measurements, such as enthalpy of formation and/or mixing and heat capacity; phase-equilibrium measurements (curves demarcating regions of a phase diagram); and computational inputs from other methods such as density functional theory (DFT). (See Cracking Quantum Mechanics with Code) For a given initial chemical composition, CALPHAD minimizes the total Gibbs energy of the system at a specified temperature and pressure to determine the phase or phases the material will form and their respective fraction and constitution.
Overcoming Data Gaps
While DFT calculations are useful to parametrize CALPHAD models, real-world measurements are still required to validate material phases (and their properties) using the CALPHAD method. The method’s accuracy depends on data availability for the pure elements, binary systems (mixture of two elements), and ternary systems (mixture of three elements). Once the models are parametrized up to the ternary systems, predictions can be made in the multicomponent space followed by experimental validation. Given the vast alloy design space, experimental data for ternary, quaternary (four elements), and more complex systems are sparse. Livermore materials scientist Kate Elder explains, “The materials science community has compiled large amounts of data concerning binary alloy systems tested under different conditions, but we have far less experimental data concerning ternary systems and more complex alloys. In other words, we have ample experimental data for alloys composed of elements A and B in different concentrations, as well as those composed of elements B and C, but not nearly as much data for alloys containing all A, B, and C.”
Alloys containing the same elements can exhibit wildly different properties depending on the relative concentration of each ingredient. Researchers may begin evaluating complex alloys assuming an equal mixture of ingredients, but optimizing an alloy for strength, resilience, corrosion resistance, hardness, or temperature stability, for instance, usually involves a nonequiatomic formula. “CALPHAD entails extrapolation in the composition space of multiple elements, but interpolation in the phase space. Therefore, the validity of CALPHAD predictions depends on how well we understand constituent alloys of two or three elements,” says Aurélien Perron, a computational materials scientist at Livermore. “Experimental data is the ground truth. As computational materials scientists, we do our best to parametrize models based on experimental data, but when we extrapolate into multicomponent phase space, these predictions need validation.” For instance, researchers could use CALPHAD to extrapolate models from binary and ternary systems and predict the phase diagram for a quaternary system. However, if the quaternary system were to form a distinct material phase not already captured in the ternary system’s phase diagram, CALPHAD will not predict this quaternary phase.
Further complicating the discovery process, materials’ properties vary with their means of fabrication. Performing metal casting versus additive manufacturing can produce different microscale structures, such as dendrites and columnar grains, which influence the resulting mechanical properties. “The CALPHAD methodology will provide scientists with predicted phase information, but the only way to validate this prediction and test the impact of processing conditions on properties is to fabricate and test the alloy firsthand,” says Livermore scientist Jibril Shittu.
Perron, Elder, and Shittu each encountered this obstacle while investigating an alloy destined for jet turbine blades, which demand a mix of strength, flexibility, and thermal stability. The team fabricated and then characterized three alloys composed of chromium (Cr), molybdenum (Mo), niobium (Nb), and vanadium (V)—one using an equiatomic composition while the other two formulas included more or less of each element. Although the researchers found the equiatomic formula to exhibit the highest yield strength, the alloy incorporating less Cr and Mo offered greater structural stability up to 1,400 ºC. High yield strength is important for this application, yet the equiatomic mixture could eventually fail over multiple temperature cycles, indicating another composition is preferable for real-world use. Alloy optimization clearly requires predictive methods working in tandem with experimental validation.
Optimization through Computation
Computational tools can identify promising alloy compositions for a specific engineering application. Fabricating and characterizing this small set of candidates in the laboratory then becomes logistically feasible. However, computational optimization can pose a high barrier to entry both in computational cost and code complexity. For instance, seamlessly integrating CALPHAD calculations and other material property models into an engineering workflow can prove challenging. Nonspecialists may be unfamiliar with the coding practices necessary to move beyond CALPHAD-based phase prediction and applying machine-learning models, among others, to predict alloy properties.
Given these limitations, Perron headed several projects with Livermore colleagues Nicholas Ury, Brandon Bocklund, and Vincenzo Lordi to create a software that accelerates and democratizes alloy design. The result is TAOS (the alloy optimization software). “We set out to develop a user-friendly software to empower researchers who are not CALPHAD or computational materials experts to perform alloy optimization themselves,” says Perron.
Ury and Bocklund were instrumental in programming for the platform. “TAOS not only leverages the phase-prediction abilities of CALPHAD—doing so through the open-source PyCalphad thermodynamics library—it also allows researchers to interface with their proprietary data as well as apply custom property models to provide deeper insights into how a candidate material might behave once fabricated,” says Bocklund. “TAOS runs on commodity computers instead of expensive supercomputers, and the software is highly modular, allowing users to couple their own data and property models,” notes Ury. Adds Perron, “TAOS’s capabilities now go far beyond our initial vision, approaching an all-in-one solution that unifies materials databases.”
By prioritizing usability, TAOS simplifies alloy development for materials science experts and nonexperts alike. “TAOS runs directly on a laptop, meaning the customer could be a small company, even a single researcher, and TAOS will work for them because of the few resources needed,” says Lordi. To identify optimal alloy compositions, TAOS users define their preferences in terms of models, objectives, and constraints. First, users import open-source or proprietary thermodynamic databases and property models for materials in their chosen design palette (as in the Cr–Mo–Nb–V system investigated for jet turbine blades). Next, they set the objective(s) function to identify the property(ies) TAOS will optimize by maximizing or minimizing factors such as element concentration, phases present at a certain temperature, liquidus and/or solidus temperatures, or sensitivity to cracking. Users can also define constraints to further restrict the design space such as a composition range in which a particular element does not exceed 10 percent of the overall concentration. In other scenarios, users can prioritize compositions that form a specific phase in a defined temperature range or those that avoid certain phases altogether. Once the alloy optimization problem is set up, TAOS rapidly assesses different alloy compositions to return those that meet defined objectives while satisfying the specified constraints. The most recent release of TAOS can provide alloy compositions that satisfy two optimization objectives (bi-objective) for unconstrained and constrained problems. In the case of bi-objective searches, TAOS returns a Pareto front, which indicates the set of compositions that balance the tradeoff of the two objectives. Finally, TAOS offers post-optimization data analysis features to help users downselect the best alloy candidates for experimental validation.
TAOS returns promising alloy candidates in minutes to hours, enabling researchers to fabricate and test relevant candidate alloys much faster than through standard design workflows and to rapidly iterate on their alloy design criteria—objective(s) and constraint(s)—to meet application-specific requirements. The TAOS development team estimates that researchers using the software would halve the expected time-to-market of their final product and reduce overall alloy discovery cost by 90 percent.
As engineering demands become increasingly exacting, computational tools ensure researchers can deliver improved materials for critical systems that help build and maintain economic competitiveness and national security assuredness. In addition, the ability to design new alloys rapidly and provide agile materials solutions is crucial to address issues in the materials supply chain. Scientists continue to enhance the CALPHAD methodology with increasingly powerful modeling capabilities, machine-learning processes, and an ever-growing base of experimental data. Through TAOS, Livermore researchers bring the speed and predictive power of modern alloy discovery methods to a wider user community to rapidly iterate and deliver optimal materials. For manufacturers, TAOS offers a secure path toward ensuring competitive and lasting products, while for the national laboratories and collaborating institutions, TAOS stands to compress the alloy design cycle and quickly deliver high-performance materials demanded by national security-driven activities.
—Elliot Jaffe
For further information contact Aurélien Perron (925) 423-0285 (perron1 [at] llnl.gov (perron1[at]llnl[dot]gov)).
