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To meet the emerging engineering challenges posed by an evolving national security landscape, researchers need specially tuned materials to build new technologies. Few existing materials can withstand the extreme domains of hypersonics, stockpile science, and fusion energy inherent in Livermore’s deterrence and energy security mission areas. Supported by a Laboratory Directed Research and Development (LDRD) Strategic Initiative, Joseph McKeown, a group leader in the Materials Science Division, led an ambitious project to discover next-generation materials and to further transform and accelerate the materials discovery process. “Researchers have spent decades of trial and error to develop the range of materials presently available,” says McKeown. “Clearly, we don’t want to wait decades each time we need a new material with specific properties.”
By the conclusion of the three-year project, the team had developed and deployed the Materials Acceleration Platform (MAP), a design framework to computationally determine optimal alloy compositions and associated additive manufacturing (AM) process parameters to meet material performance targets. In addition, their project leveraged Laboratory investments in new experimental capabilities including a Directed Energy Deposition (DED) AM system and a high-temperature mechanical testing system—the MAP is already being applied to engineering challenges at Livermore and in collaboration with its partners.
Developing Alloy Recipes
Ensuring a brand-new alloy exhibits desired properties is a battle against combinatorics—the mathematics that describe the number of unique groupings achievable from a finite set of objects. For example, when designing a new alloy, selecting 10 elements from the periodic table to serve as the materials palette yields 1,023 possible systems with different combinations of those elements, each with their own compositional design space. High entropy alloys (HEAs), a new class of alloys that exhibit exceptional mechanical performance and thermal stability, are comprised of four elements or more, which can be discretized in increments of, for instance, 1 atomic percent. “The number of possible alloy compositions quickly becomes intractable to explore,” says project co-lead Aurélien Perron. “With 4.2 trillion options, nearly the number of cells in the human body, we could never tackle this problem through experiments alone.” When these atoms arrange into specific patterns, for instance, body-centered cubic (BCC) or face-centered cubic (FCC) crystal structures, they form distinct material phases with unique properties. This structural effect is clearly observed when comparing the softness of graphite (composed of stacked hexagonal carbon rings) to diamond (composed of FCC carbon lattices). Researchers must optimize alloys for phase stability to prevent their properties from unexpectedly changing in response to stresses. McKeown explains, “Ensuring phase changes don’t occur in typical operating temperatures is crucial. Otherwise, they could lead to a catastrophic engineering failure.”
Materials scientists turn to computational tools such as the Calculation of Phase Diagrams (CALPHAD) method to quantify the environmental conditions that result in phase changes and thereby estimate properties of new materials. While CALPHAD is the foundational tool of the MAP for designing new alloys, other computational tools were developed to efficiently search the vast design space and capture microstructure—the distribution of phases and defects throughout a material that greatly influences its macroscopic properties. “When we fabricate a material and test it, its properties can deviate from expectation. Strength relies on the underlying microstructure, which itself is impacted by the means of fabrication,” says McKeown. Properties of as-fabricated alloys are therefore challenging to accurately predict absent direct experimental testing, yet the design space for HEAs is too vast to cover experimentally.
Hacking the Design Lottery
The Livermore team developed the MAP to overcome limitations of existing alloy design methods, a capability they would demonstrate by developing new HEAs with improved mechanical properties and phase stability at high temperature (greater than or equal to 1,000ºC). The MAP is a flexible, agile framework consisting of materials property calculators, optimization engines, and storage backends that run on Livermore’s high-performance computing systems.
As the team identified promising alloy candidates, it produced them in the laboratory and used a host of characterization instruments to evaluate material properties, including compression and tensile testing; calorimetry; electron microscopy; x-ray diffraction; and Livermore’s new hypersonic capability, the Energy–Matter Interaction Tunnel (EMIT). (See S&TR, February 2024, Breaking Materials at Breakneck Speeds.) “We’re fortunate that Livermore has the resources to perform both the simulations to develop material models as well as the experimental work to fabricate those materials and validate our models,” says materials scientist Thomas Voisin. This empirical data feeds back into the MAP to refine its parameters and improve its predictive accuracy.
“Many materials science problems cannot be solved by theory alone. To create an alloy with a specific mass, heat resistance, and ductility, no mathematical formula exists that will specify exactly what composition is best,” says computer scientist Brian Gallagher, who led the team’s machine-learning (ML) work. “Machine learning is a great tool to lean on when such theory is lacking. Data-driven models have the advantages of speed and generality. As long as we have the data, we can apply it to any problem,” says Gallagher. However, not all data is created equal. Gallagher’s group had to determine how the MAP could make accurate predictions when combining the small amount of high-fidelity experimental data with hundreds of thousands of analytical predictions, which are inherently lower fidelity. To achieve this end, the team developed a novel data analysis framework, Bi-Level Regularized Pre-training and Transfer (Bi-RPT), which strategically combines multifidelity data using the ML technique of transfer learning (in which knowledge gained from training a model on one task is used to improve performance on a related but different task), enabling the MAP to accommodate fidelity differences and adjust its property predictions accordingly.
To probe the HEA design space, the team developed CALPHAD models of candidate alloys and used ML to accelerate their predictions. When the team trained ML surrogates on CALPHAD predictions generated from a set of nine elements, the model produced high-quality phase diagrams for previously untested element combinations. Even more impressively, it extrapolated these results, producing phase diagrams for alloys featuring elements outside of training data. Much of this predictive accuracy can be ascribed to the use of deep neural networks (DNNs). In contrast to the traditional ML technique of random forests (RF), which uses the most probable outcome of multiple decision trees to make predictions, DNNs are a modern ML technique using hidden layers between a neural network’s input and output layers, allowing it to ascertain certain features and trends in large datasets without being directed by researchers. “DNNs are data-hungry, and their performance is closely tied to design decisions. We spend considerable time tuning them to optimize their performance,” says Gallagher. Yet, once trained, the models are readily applied to any number of problems, and their performance does not slow as system complexity grows. “Our results bear this methodology out. RF performs better with less data, but DNNs perform better overall given sufficient data as well as in extrapolation scenarios,” says Gallagher.
Although the MAP could now draw from a more extensive database, the team still had to consider the effects of different manufacturing techniques on material properties. The properties of as-fabricated alloys often differ from predictions because of process conditions that influence how the material’s microstructure forms. The team was primarily focused on using arc-melt casting and directed-energy deposition (DED), a maturing AM technology for 3D-printing metal parts that fuses powders via laser. Better understanding of the relation between thermal history and DED process parameters, such as laser power and scan speed, was needed to predict microstructure. To avoid the computational burden of numerous high-fidelity DED simulations, the researchers developed a reduced order model (ROM), which parameterizes DED simulation. ROMs sacrifice some predictive accuracy, but reduce computational burden by orders of magnitude. The team’s purpose-built ROM, called Gaussian Process Latent Space Dynamics Identification, determines the time-dependent temperature field produced by DED operations roughly 1 million times faster than direct simulation and with a worst-case error of 8 percent. By integrating a thorough alloy composition database with the effects of manufacturing processes on resulting microstructure, the researchers could train ML models to generate material property predictions with greater accuracy, as verified by follow-on characterization testing. Saad Khairallah, who led the project’s Process Science thrust, says, “The final performance was unquestionable, as a single ROM simulation costs less than a millisecond on few processors, which is great for training machine learning models.”
Validation and Applications
To validate the platform’s capacity to support Livermore’s materials development efforts, the team tailored HEAs to maintain phase stability and yield strength at high temperature, while being ductile enough to process at room temperature. Prioritizing these parameters maximized the mechanical and thermal stress the material could bear before permanently deforming, enabling its use in the extreme environments for hypersonic, nuclear stockpile, and fusion energy applications. The team applied the MAP’s capabilities to search a nine-element design space for three-, four-, and five-element systems that boasted the greatest yield strength at high temperature, exhibited room-temperature ductility parameters, and could be easily fabricated, tested, and scaled for production. Comparing ductility parameters as reported in literature with BCC phase stability, they focused on systems containing hafnium, molybdenum, niobium, titanium, or vanadium because these HEAs’ yield strengths exceed that of conventional high-temperature engineering alloys.
Although the optimization effort prioritized mechanical properties, the MAP’s flexibility permits further parameters to guide material design. The optimal composition for a robust material might be susceptible to corrosion or might rely on scarce ingredients unobtainable in sufficient quantities. Aspects such as corrosion resistance, radiation response, machinability, carbon footprint, and cost of the raw materials all determine whether a simulated solution is a practical one for real-world applications. These factors impact the projects that the team’s new capability is supporting. “We are actively using the platform to design alloys that meet performance criteria for Laboratory programs,” says McKeown.
Among these projects is a multilaboratory LDRD effort with Los Alamos and Sandia national laboratories to design new refractory alloys and their AM production methods (such as DED and laser powder bed fusion) to assess their suitability as a stockpile material. Livermore is collaborating with Los Alamos on related discovery, design, and testing capabilities to support further national security efforts. In addition, in October 2024, the Advanced Research Projects Agency–Energy awarded $3.4 million in funding to a team led by Perron to pursue viable commercial fusion energy technologies. The researchers will apply Livermore’s materials discovery platform to develop new alloys to form fusion reactors’ first wall, which contains the extreme heat and radiation flux generated by fusion reactions. By developing the tools to rapidly discover and fabricate new alloys with targeted performance, the team is empowering engineering teams nationwide to address mission-relevant challenges.
—Elliot Jaffe
For further information contact Joseph McKeown (925) 422-1708 (mckeown3 [at] llnl.gov (mckeown3[at]llnl[dot]gov)).
