The concept of short-range order (SRO)—the arrangement of atoms at tiny distances—in metal alloys has been underexplored in materials science and engineering. However, the past decade has seen renewed interest in its quantification, as decoding SRO is a key step toward developing tailored high-performance alloys, such as stronger or heat-resistant materials.
Understanding how atoms arrange themselves is no effortless task and must be verified by intensive laboratory experiments or computer simulations based on imperfect models. These obstacles make it arduous to fully explore SRO in metal alloys.
But Killian Sheriff and Yifan Cao, graduate students in MIT’s Department of Materials Science and Engineering (DMSE), are using machine learning to quantify, atom by atom, the complicated chemical systems that make up SROs. Under the supervision of assistant professor Rodrigo Freitas and with the aid of assistant professor Tess Smidt in the Department of Electrical Engineering and Computer Science, their work was recently published IN .
The interest in understanding SRO is related to the excitement around advanced materials called high-entropy alloys, whose complicated compositions give them unique properties.
Typically, materials scientists develop alloys by using one element as a base and adding tiny amounts of other elements to enhance specific properties. For example, adding chromium to nickel makes the resulting metal more resistant to corrosion.
Unlike most established alloys, high-entropy alloys have several elements, from three to 20, in nearly equal proportions. That gives them a huge amount of design space. “It’s like creating a recipe with a lot more ingredients,” Cao says.
The goal is to utilize SRO as a “knob” to adjust material properties by mixing chemical elements in high-entropy alloys in unique ways. The approach has potential applications in industries such as aerospace, biomedicine and electronics, driving the need to explore element permutations and combinations, Cao says.
Compact-range command interception
Compact-range order refers to the tendency of atoms to form chemical arrangements with specific neighboring atoms. While a cursory glance at the elemental distribution of an alloy might suggest that its constituent elements are randomly arranged, that is often not the case. “Atoms prefer that specific neighboring atoms be arranged in specific patterns,” says Freitas. “How often these patterns form and how they are arranged in space defines the SRO.”
Understanding SRO unlocks the keys to the realm of high-entropy materials. Unfortunately, little is known about SRO in high-entropy alloys. “It’s like trying to build a giant Lego model without knowing what the smallest Lego piece you can have is,” Sheriff says.
Customary methods for understanding SROs involve tiny computational models or simulations with a narrow number of atoms, which provide an incomplete picture of complicated material systems. “High-entropy materials are chemically complex—you can’t simulate them well with just a few atoms; you really have to go several length scales beyond that to capture the material accurately,” Sheriff says. “Otherwise, it’s like trying to understand a family tree without knowing one of the parents.”
SRO has also been calculated using basic mathematics, counting the nearest neighbors for several atoms and calculating what this distribution might look like on average. Despite its popularity, this approach has limitations because it offers an incomplete picture of SRO.
Fortunately, researchers are using machine learning to overcome the shortcomings of established approaches to capturing and quantifying SROs.
Hyunseok Ohassistant professor in the Department of Materials Science and Engineering at the University of Wisconsin, Madison, and a former DMSE postdoc, is excited to explore SRO more deeply. Oh, who was not involved in the study, is investigating how to utilize alloy composition, processing methods, and their relationship to SRO to design better alloys. “The physics of alloys and the atomistic origin of their properties depend on short-term order, but it’s been nearly impossible to accurately calculate short-term order,” Oh says.
Two-track machine learning solution
To study the SRO phenomenon using machine learning, Cao says, it is helpful to imagine the crystal structure of high-entropy alloys as a connect-the-dots game in a coloring book.
“To see the pattern, you have to know the rules for connecting the dots.” And you have to capture the atomic interactions with a simulation that’s large enough to fit the entire pattern.
First, understanding the rules meant reproducing chemical bonding in high-entropy alloys. “There are small energy differences in the chemical patterns that lead to differences in short-range order, and we didn’t have a good model for doing that,” Freitas says. The model the team developed is the first building block for accurately quantifying SRO.
The second part of the challenge, providing researchers with the large picture, was more complicated. High-entropy alloys can exhibit billions of chemical “motifs,” combinations of atomic arrangements. Identifying these motifs from simulation data is arduous because they can appear in symmetrically equivalent forms—rotated, mirrored, or inverted. At first glance, they can look different but still contain the same chemical bonds.
The team solved this problem by hiring 3D Euclidean Neural NetworksThese advanced computational models allowed researchers to identify chemical motifs from simulations of high-entropy materials with an unprecedented level of detail, examining them atom by atom.
The final task was to quantify the SRO. Freitas used machine learning to evaluate the different chemical motifs and label each one with a number. When scientists want to quantify the SRO of a fresh material, they run it through a model that sorts it through its database and spits out an answer.
The team also put extra effort into improving their motif identification frame more accessible. “We have this card of all possible permutations [SRO] already set up and we know what number each one got from the machine learning process,” Freitas says. “So later, when we encounter simulations, we can sort them to tell us what this new SRO will look like.” The neural network easily recognizes symmetry operations and labels equivalent structures with the same number.
“If we had to compile all the symmetries ourselves, that would have been a lot of work. Machine learning organized that for us really quickly and in a way that was economical enough that we could do it in practice,” Freitas says.
Step inside the world’s fastest supercomputer
This summer, Cao, Sheriff and team will have the opportunity to study how SRO can change under routine metalworking conditions, such as casting and cold rolling, as part of a U.S. Department of Energy program INCITE Programwhich allows access to Borderthe world’s fastest supercomputer.
“If you want to know how the short-term order changes during actual metal production, you need a very good model and a very large simulation,” says Freitas. The team already has a robust model; it will now utilize INCITE’s computational backend to perform the required strong simulations.
“By doing this, we expect to uncover mechanisms that metallurgists could use to design alloys with a fixed SRO,” Freitas adds.
Sheriff is excited about the many promises of the research. One is the 3D information that can be extracted about the chemical SRO. While established transmission electron microscopes and other methods are narrow to two-dimensional data, physical simulations can fill in the gaps and provide full access to 3D information, Sheriff says.
“We put in place a framework to start talking about chemical complexity,” Sheriff explains. “Now that we can understand that, there’s a whole body of materials science out there on classical alloys to develop predictive tools for high-entropy materials.”
This could lead to the deliberate design of fresh classes of materials rather than acting blindly.
The research was funded by the MathWorks Ignition Fund, the MathWorks Engineering Fellowship Fund, and the Portuguese Foundation for International Cooperation in Science, Technology and Higher Education under the MIT–Portugal Program.