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 in the last decade, there has been renewed interest in its quantification, as decoding SRO is a crucial step toward developing tailored, high-performance alloys, such as stronger or heat-resistant materials.
Understanding how atoms organize themselves is not an easy task and must be verified using intensive laboratory experiments or computer simulations based on imperfect models. These obstacles have made it difficult 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 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. published in the Proceedings of the National Academy of Sciences.
Interest in understanding SRO is linked to the excitement about advanced materials called high-entropy alloys, whose complex compositions give them superior properties.
Typically, materials scientists develop alloys by using one element as a base and adding small amounts of other elements to improve certain properties. Adding chromium to nickel, for example, makes the resulting metal more resistant to corrosion.
Unlike most traditional alloys, high-entropy alloys contain multiple elements, from three to twenty, in nearly equal proportions. This provides a lot of leeway in design. “It’s like you’re making a recipe with a lot more ingredients,” Cao says.
The goal is to use SRO as a “knob” 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, hence the need to explore permutations and combinations of elements, Cao says.
Short Range Order Capture
Short-range order refers to the tendency of atoms to form chemical arrangements with specific neighboring atoms. While a cursory look at an alloy’s elemental distribution might indicate that its constituent elements are arranged randomly, this is often not the case. “Atoms have a preference for specific neighboring atoms to be arranged in particular patterns,” Freitas explains. “How often these patterns appear and how they are distributed in space define short-range order.”
Understanding SRO unlocks the keys to the kingdom of high-entropy materials. Unfortunately, not much is known about SRO in high-entropy alloys. “It’s like trying to build a huge Lego model without knowing what the smallest Lego piece we can have is,” Sheriff says.
Traditional methods for understanding spherical entropy involve small computer models or simulations with a limited number of atoms, which give 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 have to go a few length scales higher to capture the material accurately,” Sheriff says. “Otherwise, it’s like trying to understand your family tree without knowing any of the parents.”
The SRO has also been calculated using basic mathematics, by counting the immediate neighbors of a few atoms and calculating what this distribution might look like on average. Despite its popularity, this approach has its limitations, as it provides 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-ohAssistant Professor in the Department of Materials Science and Engineering at the University of Wisconsin-Madison and a former DMSE postdoctoral fellow, is excited to study SRO in more detail. 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 order, but calculating short-range order accurately has been nearly impossible,” Oh says.
A two-pronged machine learning solution
To study SRO using machine learning, it helps to think of the crystal structure of high-entropy alloys as a dot-to-dot game in a coloring book, Cao says.
“You have to know the rules for connecting the dots to see the model.” And you have to capture the atomic interactions with a simulation large enough to contain the entire model.
To understand the rules, they first had to reproduce the chemical bonds in high-entropy alloys. “There are small energy differences in chemical models 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, providing the researchers with the big picture, was more complex. High-entropy alloys can have billions of chemical “patterns,” or combinations of arrangements of atoms. Identifying these patterns from simulation data is difficult because they can appear in symmetrically equivalent forms (rotated, mirrored, or inverted). At first glance, they may look different, but contain the same chemical bonds.
The team solved this problem by employing 3D Euclidean Neural NetworksThese advanced computer models have allowed researchers to identify chemical patterns from high-entropy materials simulations 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 Pattern identification framework more accessible. “We have this sheet of all the possible permutations of [SRO] “We’ve already set up SROs and we know what number each of them got through this machine learning process,” Freitas says. “So later, when we run simulations, we can sort them to tell us what this new SRO will look like.” The neural network easily recognizes symmetry operations and marks 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 this for us very quickly and in a way that was inexpensive enough for us to apply in practice,” Freitas says.
Step inside the world’s fastest supercomputer
This summer, Cao, Sheriff and their team will have the opportunity to explore how SRO can perform under routine metal processing conditions, such as casting and cold rolling, through the U.S. Department of Energy program. INCITE Programwhich allows access to Borderthe world’s fastest supercomputer.
“If you want to know how short-range order evolves during real metal fabrication, you need a very good model and a very large simulation,” says Freitas. The team already has a robust model; they will now exploit INCITE’s computing facilities for the required robust simulations.
“With this, we hope to discover the kind of mechanisms that metallurgists could use to design alloys with predetermined SROs,” Freitas adds.
Sheriff is excited about the many promises of this research. One of them is the 3D information that can be obtained about chemical SROs. While traditional transmission electron microscopes and other methods are limited to two-dimensional data, physical simulations can fill in the dots and provide full access to 3D information, Sheriff says.
“We’ve put together a framework to start talking about chemical complexity,” Sheriff says. “Now that we can understand that, there’s a whole body of materials science on classical alloys to develop predictive tools for high-entropy materials.”
This could lead to the targeted design of new classes of materials instead of 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 under the MIT-Portugal Program.