The concept of short-range order (SRO)—the arrangement of atoms over small distances—in metallic alloys has been little explored in materials science and engineering. But over the past decade, there has been renewed interest in quantifying it, as deciphering SRO is a crucial step toward developing tailored high-performance alloys, such as stronger or more heat-resistant materials.
Understanding how atoms are organized is not an easy task and must be verified by intensive laboratory experiments or computer simulations based on imperfect models. These obstacles have hampered the full exploration of 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 complex chemical arrangements that make up SRO. Under the supervision of Assistant Professor Rodrigo Freitas, and with the help of Assistant Professor Tess Smidt in the Department of Electrical Engineering and Computer Science, their work was recently published in He proceedings of the National Academy of Sciences.
Interest in understanding SRO is linked to enthusiasm surrounding advanced materials called high-entropy alloys, whose complex compositions give them superior properties.
Typically, materials scientists develop alloys using one element as a base and adding small amounts of other elements to improve specific properties. Adding chromium to nickel, for example, makes the resulting metal more resistant to corrosion.
Unlike most traditional alloys, high-entropy alloys have multiple elements, from three to 20, in nearly equal proportions. This offers a lot of scope for design. “It’s like you’re making a recipe with a lot more ingredients,” Cao says.
The goal is to use SRO as a “button” to tailor material properties by mixing chemical elements into high-entropy alloys in unique ways. This approach has potential applications in industries such as aerospace, biomedicine and electronics, driving the need to explore permutations and combinations of elements, Cao says.
Capturing short range order
Short-range order refers to the tendency of atoms to form chemical arrangements with specific neighboring atoms. While a cursory look at the elemental distribution of an alloy might indicate that its constituent elements are arranged randomly, this is often not the case. “Atoms have a preference for having specific neighboring atoms arranged in particular patterns,” Freitas says. “How often these patterns arise and how they are distributed in space is what defines the SRO.”
Understanding SRO allows us to tap into the realm of high-entropy materials. Unfortunately, not much is known about SRO in high-entropy alloys. “It’s like we’re trying to build a huge Lego model without knowing what the smallest Lego piece we can have is,” Sheriff says.
Traditional methods for understanding SRO involve small computational models or simulations with a limited number of atoms, providing an incomplete picture of complex material systems. “High-entropy materials are chemically complex – you can’t simulate them well with just a few atoms; you really need to go to a few length scales above that to capture the material accurately,” Sheriff says. “Otherwise, it’s like trying to understand your family tree without knowing one of the parents.”
The SRO has also been calculated using basic mathematics, by counting the immediate neighbours of a few atoms and calculating what that distribution might look like on average. Despite its popularity, the method has limitations, as it gives an incomplete picture of the SRO.
Fortunately, researchers are leveraging machine learning to overcome the shortcomings of traditional approaches to capturing and quantifying SRO.
Hyun Seok OhOh, an assistant professor in the Department of Materials Science and Engineering at the University of Wisconsin-Madison and a former DMSE postdoc, is excited to further investigate SRO. Oh, who was not involved in this study, is exploring how to leverage 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-range ordering, but accurate calculation of short-range ordering has been nearly impossible,” Oh says.
A two-pronged machine learning solution
To study SRO using machine learning, it's helpful to imagine the crystal structure in high-entropy alloys as a connect-the-dots game in a coloring book, Cao says.
“You need to know the rules for connecting the dots to see the pattern.” And you need to capture the atomic interactions with a simulation that’s big enough to fit the whole pattern.
First, understanding the rules involved reproducing the chemical bonds 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 to do that,” Freitas says. The model the team developed is the first building block for accurately quantifying SRO.
The second part of the challenge — ensuring that researchers get the full picture — was more complex. High-entropy alloys can exhibit billions of chemical “motifs” — combinations of arrangements of atoms. Identifying these motifs from simulation data is difficult because they can appear in symmetrically equivalent forms (rotated, mirrored or inverted). At first glance, they may appear different, but they still contain the same chemical bonds.
The team solved this problem by using 3D Euclidean Neural NetworksThese advanced computational models allowed researchers to identify chemical motifs from simulations of high-entropy materials in unprecedented 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 the researchers want to quantify the SRO of a new material, they run it through the model, which sorts it through its database and generates an answer.
The team also invested extra effort in making their framework for identifying motives more accessible. “We already have this sheet set up of all the possible permutations of (SRO) and we know what number each of them got through this machine learning process,” says Freitas. “So later, when we come across simulations, we can sort them to tell us what that new SRO will look like.” The neural network easily recognizes symmetry operations and labels equivalent structures with the same number.
“If you had to compile all the symmetries yourself, it would be a lot of work. Machine learning organized all of this for us very quickly and in a way that was cheap enough that we could apply it in practice,” Freitas says.
Enter the world's fastest supercomputer
This summer, Cao, Sheriff and their team will have the opportunity to explore how SRO can change in routine metal processing conditions, such as smelting and cold rolling, through the U.S. Department of Energy. INCITE Programwhich allows access to Borderthe world's fastest supercomputer.
“If you want to know how the short-term order changes during real metal fabrication, you need a very good model and a very large simulation,” Freitas says. The team already has a solid model; now they will take advantage of INCITE’s computing facilities to run the necessary robust simulations.
“With this, we hope to discover the type of mechanisms that metallurgists could employ to design alloys with predetermined SRO,” Freitas adds.
Sheriff is excited about the many promises of the research. One of them is the 3-D information that can be obtained about the chemical ORS. While traditional transmission electron microscopes and other methods are limited to two-dimensional data, physical simulations can fill in the blanks and provide full access to 3-D information, Sheriff says.
“We’ve introduced a framework to start talking about chemical complexity,” Sheriff explains. “Now that we can understand this, there’s a whole body of materials science on classical alloys to develop predictive tools for high-entropy materials.”
That could lead to the targeted design of new classes of materials rather than just shooting in the dark.
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 at MIT-Portugal Program.