The concept of short-range order (SRO) in metallic alloys, i.e. the arrangement of atoms over short distances, has not been widely studied in materials science and engineering. However, over the past decade there has been renewed interest in quantifying SRO, as deciphering it is a key step towards developing customized high-performance alloys, including stronger and/or heat-resistant materials.
Understanding how the atoms arrange themselves is not easy and must be verified using exhaustive laboratory experiments or computer simulations based on imperfect models. These hurdles make it difficult to fully investigate SROs in metal alloys.
But Killian Sherif and Yifan Kao, graduate students in MIT's Department of Materials Science and Engineering (DMSE), are using machine learning to quantify, atom by atom, the complex chemical sequences that make up SRO. Under the guidance of Assistant Professor Rodrigo Freitas and in collaboration with Assistant Professor Tess Smit of the Department of Electrical Engineering and Computer Science, their work recently led to the discovery of a new material called a “single-atom-by-single-atom” that can measure the chemical structure of SRO. of Proceedings of the National Academy of Sciences.
Interest in understanding SROs is linked to an interest in advanced materials called high-entropy alloys, whose complex compositions give them superior properties.
Typically, materials scientists develop alloys by starting with one element and adding small amounts of other elements to enhance certain properties — for example, adding chromium to nickel makes the resulting metal more resistant to corrosion.
Unlike most conventional alloys, high-entropy alloys contain multiple elements, anywhere from three to as many as 20, in roughly equal proportions, providing more room for design. “It's like creating a recipe with more ingredients,” Cao says.
The goal is to use SROs as “knobs” to mix chemical elements in unique ways into high-entropy alloys to tune their material properties. This approach has potential applications in industries including aerospace, biomedical and electronics, where there is an increasing need to explore permutations and combinations of elements, Cao said.
Acquisition of short-range order
Short-range order refers to the tendency of atoms to form chemical arrangements with certain neighbors. If you look superficially at an alloy's elemental distribution, it might seem like its constituent elements are arranged randomly, but in reality, this is often not the case. “Atoms prefer to be arranged in certain patterns with certain neighbors,” Freitas says. “How often these patterns occur and how they are distributed in space defines the SRO.”
Understanding SRO unlocks the world of high-entropy materials. Unfortunately, not much is known about SRO, a high-entropy alloy. “It's like trying to build a giant Lego model without knowing what the smallest Lego piece is,” Sheriff says.
Traditional methods for understanding SROs involve small-scale computational models, or simulations using 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. To accurately capture the materials, you need to simulate them on scales several times longer than that,” Sheriff says. “Otherwise, it's like trying to understand a family tree without knowing either of the parents.”
SRO has also been calculated using basic mathematics by counting the atoms in a few atoms' immediate neighborhoods and calculating what that distribution looks like on average. Despite its popularity, this approach has limitations as it gives an incomplete picture of SRO.
Fortunately, researchers are leveraging machine learning to overcome shortcomings in traditional approaches to capturing and quantifying SROs.
Hyunseok Oh, an assistant professor in the Department of Materials Science and Engineering at the University of Wisconsin-Madison and a former DMSE postdoctoral researcher, is excited to explore SROs in more detail. Oh, who was not involved in the work, is studying how alloy compositions, processing methods, and their relationship to SROs can be leveraged to design better alloys. “The physical properties of alloys and the atomistic origins of those properties depend on short-range order, but precise calculations of short-range order have been nearly impossible,” Oh says.
Machine learning solutions from two perspectives
To study SROs using machine learning, Cao says it would be helpful to draw the crystal structures of high-entropy alloys like a connect-the-dots coloring book.
“To see the pattern, you need to know the rules that connect the dots.” And you need to capture the atomic interactions in a simulation large enough to fit the entire pattern.
First, to understand the rules, they needed to recreate the chemical bonds in high-entropy alloys. “There are small energy differences in the chemical patterns that lead to differences in short-range order, but we didn't have a good model to represent that,” Freitas says. The model the team developed is the first building block to precisely quantify SRO.
The second part of the challenge, helping researchers see the whole picture, was more complicated. High-entropy alloys can exhibit billions of chemical “motifs,” which are combinations of atomic arrangements. Identifying these motifs from simulation data is difficult because they can appear in symmetrically equivalent forms, such as rotations, mirror images and inversions. At first glance, they may look different, but they still contain the same chemical bonds.
The team employed 3D Euclidean neural networks to solve this problem. These advanced computational models allowed the researchers to identify chemical motifs in simulations of high-entropy materials in unprecedented detail, going atom by atom.
The final challenge was to quantify SRO. Freitas used machine learning to evaluate different chemical motifs and tag each one with a number. When researchers want to quantify the SRO of a new material, they run it through the model, which classifies it in its database and spits out an answer.
The team went further to make the motif identification framework more user-friendly. [SRO] “They’re already set up, and we know through this machine learning process what number each one got,” Freitas says, “so later when we run the simulation we can sort them out and know what the new SRO will look like.” The neural network easily recognizes symmetric operations, tagging equivalent structures with the same number.
“If you had to compile all the symmetries yourself, that would be a lot of work. Machine learning sorted this out very quickly and in a way that was cheap enough to actually be applied,” Freitas says.
The world's fastest supercomputer is here
This summer, through the U.S. Department of Energy's INCITE program, which gives them access to Frontier, the world's fastest supercomputer, Cao, Sherif and their team will have the opportunity to study how SRO changes under typical metal-processing conditions such as casting and cold rolling.
“If we want to understand how short-range order changes during the actual manufacturing of metals, we need very good models and very large-scale simulations,” Freitas says. The team already has powerful models and will now leverage INCITE's computing facilities to perform the robust simulations they need.
“We hope that this will uncover the sort of mechanisms that metallurgists can use to design alloys with predetermined SROs,” Freitas added.
Sherif is excited about the many possibilities this research opens up, one of which is the 3D information it could provide about chemical SROs. Traditional transmission electron microscopy and other methods are limited to two-dimensional data, but physical simulations can fill in the dots to fully access the 3D information, Sherif said.
“We've introduced a framework to start talking about chemical complexity,” Sherif explains. “Now that we can understand this, we have the whole of materials science on classical alloys to develop predictive tools for high-entropy materials.”
This could enable us to purposefully design new kinds of materials, rather than just blindly searching for them.
This 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 through the MIT–Portugal Program.
