The concept of short-range order (SRO)—the arrangement of atoms over small distances—in metal alloys has not been sufficiently explored in materials science and engineering. But the past decade has seen renewed interest in quantifying it, as deciphering short-range order is a crucial step toward developing tailor-made high-performance alloys, such as stronger or heat-resistant materials.
Understanding how atoms arrange themselves is not an easy task, and must be verified using extensive laboratory experiments or computer simulations based on incomplete models. These obstacles have made it difficult to fully explore SRO in metallic alloys.
But Kilian Sherif and Yifan Cao, graduate students in MIT’s Department of Materials Science and Engineering, are using machine learning to measure the complex chemical arrangements that make up SRO atom by atom. Their work, led by Assistant Professor Rodrigo Freitas and with the help of Assistant Professor Tess Smidt in the Department of Electrical Engineering and Computer Science, was recently published. Published in the Proceedings of the National Academy of Sciences.
Interest in understanding SRO is linked to the excitement surrounding advanced materials called high-entropy alloys, whose complex compositions give them superior properties.
Materials scientists typically develop alloys using one element as a base and adding small amounts of other elements to enhance certain properties. For example, adding chromium to nickel makes the resulting metal more corrosion resistant.
Unlike most conventional alloys, high-entropy alloys contain several elements, from three to 20, in roughly equal proportions. This provides a wide design space. “It’s like making a recipe with a lot of ingredients,” says Cao.
The goal is to use SRO as a “switch” to customize the properties of materials by mixing the chemical elements in high-entropy alloys in unique ways. The approach has potential applications in industries such as aerospace, biomedicine and electronics, Cao says, driving the need to explore permutations and combinations of the elements.
Short term system capture
Short-range order refers to the tendency of atoms to form chemical arrangements with specific neighboring atoms. While a superficial look at the distribution of elements in an alloy might suggest that the elements are arranged randomly, this is often not the case. “Atoms prefer to have specific neighboring atoms arranged in specific patterns,” Freitas says. “How often these patterns occur and how they are distributed in space is what determines short-range order.”
Understanding SRO unlocks the realm of high-entropy materials. Unfortunately, we don’t know much about SRO in high-entropy alloys. “It’s like trying to build a giant Lego model without knowing what the smallest Lego piece is that you can get,” Sherif says.
Traditional approaches to understanding SRO involve small computational models, or simulations with a limited number of atoms, which provide 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 higher length scales than that to capture the material accurately,” Sharif says. “Otherwise, it’s like trying to understand your family tree without knowing which parent.”
The SRO has also been calculated using basic mathematics, counting the immediate neighbors of a few atoms and calculating what this distribution might look like on average. Despite its popularity, this approach has limitations, as it gives an incomplete picture of the SRO.
Fortunately, researchers are leveraging machine learning to overcome the shortcomings of traditional methods for capturing and measuring SRO.
Hyunsuk OhOh, an assistant professor in the Department of Materials Science and Engineering at the University of Wisconsin-Madison and a former postdoctoral researcher at DMSE, is excited to investigate SRO more thoroughly. 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 atomic origin of their properties depend on short-range order, but accurate calculation of short-range order has been nearly impossible,” says Oh.
Two-pronged machine learning solution
To study SRO using machine learning, it is useful to visualize the crystal structure in high-entropy alloys as a connect-the-dots game in a coloring book, Kao says.
“You need to know the rules for connecting the dots so you can see the pattern.” And you also need to capture the atomic interactions using a simulation large enough to fit the entire pattern.
First, understanding the rules meant 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 step toward accurately quantifying SRO.
The second part of the challenge, which involved the researchers getting the full picture, was more complicated. High-entropy alloys can display billions of chemical “patterns,” which are collections of atomic arrangements. Identifying these patterns from simulation data is difficult because they can appear in symmetrical equivalent shapes—rotated, mirrored, or upside down. At first glance, they may look different, but they still contain the same chemical bonds.
The team solved this problem by using 3D Euclidean Neural NetworksThese advanced computational models have allowed researchers to identify chemical elements from simulations of high-entropy materials in unprecedented detail, examining them atom by atom.
The final task was to determine the amount of SRO. Freitas used machine learning to evaluate different chemical elements and label each one with a number. When the researchers wanted to determine the amount of SRO for a new substance, they ran it through the model, which sorted it through its database and came up with an answer.
The team also put extra effort into making Ornamental selection frame “More accessible. “We have this sheet that has all the possible permutations of [SRO] “They’re already set up, and we know what number each one got through this machine learning process,” Freitas says. “So later, when we come across simulations, we can sort through them to tell us what the new SRO will look like.” The neural network easily recognizes the symmetries and labels equivalent structures with the same number.
“If you had to assemble all the symmetries yourself, that would be a lot of work,” Freitas says. “Machine learning organized this for us very quickly and cheaply enough that we could implement it in practice.”
Enter the world’s fastest supercomputer
This summer, Kao, Sharif, and their team will have the opportunity to explore how SRO can change under routine metal processing conditions, such as casting and cold rolling, through a U.S. Department of Energy program. INCITE Programallowing access to borderthe world’s fastest supercomputer.
“If you want to know how the short-range order changes during actual metal fabrication, you need a very good model and a very large simulation,” says Freitas. The team already has a powerful model; they will now take advantage of INCITE’s computing facilities to run the powerful simulations needed.
“We expect to discover what kind of mechanisms metallurgists can use to design alloys with a pre-defined metabolic response rate,” Freitas adds.
Sharif is excited about the many promises of the research. One of them is the 3D information that can be obtained about a chemical reaction. While conventional transmission electron microscopes and other methods are limited to 2D data, physical simulations can fill in the dots and provide full access to 3D information, Sharif says.
“We’ve provided a framework to start talking about chemical complexity,” Sherif explains. “Now that we can understand this, we have a whole suite of materials science working on classical alloys to develop predictive tools for high-entropy materials.”
This could lead to the purposeful design of new classes of materials rather than just imaging 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.
