Forging ahead in alloy design using machine learning
Predicting atomic behavior in advanced alloys paves the way for targeted material design.
Jieruei Chang–The Tech
In 3500 BC, a metalsmith in ancient Persia is smelting copper. He’s made a mistake — the ore he’s using is impure. When it comes out of the forge, the metal has strange properties. It is stronger than normal copper and easier to cast. The smith has discovered humanity’s earliest alloy: arsenic bronze.
Mixing metals together often results in alloys with better properties than their constituent parts. But alloys today are almost always composed of one or two elements with small amounts of other substances mixed in. Bronze is 88% copper and 12% tin. Steel is 98% iron and 2% carbon. What would happen if many more metals were mixed together?
The answer lies in high-entropy alloys. Theorized in the 1980s and first synthesized in 2004, they are considered an entirely new class of material. High-entropy alloys are made of up to twenty different elements, mixed together in more even proportions. When they come out of the forge, they have unique properties. They’re strong. Hard. Heat-resistant. Corrosion-resistant. High-entropy alloys are already starting to be used in aerospace, nuclear reactors, and biomedical devices.
However, they’re hard to design: there are too many variables to tune. Trying all possible combinations experimentally is infeasible. Instead, researchers have been turning to computational models that simulate material systems starting from pure physics. In a paper published last June in The Proceedings of the National Academy of Sciences, researchers in MIT’s Materials Science and Engineering (DMSE) and Electrical Engineering and Computer Science (EECS) departments used simulations with machine learning to predict how atoms arrange themselves in alloys.
“This work is making two messages: here's one way we could accurately simulate on a computer high-entropy materials, and here's how we could start making sense of the information that we have from atomistic simulations,” says Killian Sheriff, PhD candidate in DMSE and the lead researcher on the work. Sheriff first became interested in high-entropy alloys while studying physics as an undergraduate. He speaks excitedly in a French accent, waving his hands in the air. Four times during our conversation, he runs to the whiteboard at the other side of the room and starts drawing diagrams.
Unlike most metals, high-entropy alloys have no clear repeating crystal structure. They appear to be haphazard lattices of atoms, like randomly colored balls in a ballpit; the apparent disorder in their atomic arrangement is what gives high-entropy alloys their name. For a long time, people modeled these alloys as if their elements were randomly distributed. However, it turns out that atoms in a high-entropy alloy form small local patterns, called short-range order (SRO). Some of these local patterns appear a thousand times more often in real life than if the atoms were truly arranged randomly, which means they have a significant effect on how a material behaves.
(1) Unlike regular alloys with relatively well-defined crystal patterns, atoms in high-entropy alloys fill a lattice grid seemingly (but not at all) randomly.
“The physics of alloys and the atomistic origin of their properties depend on short-range ordering, but the accurate calculation of short-range ordering has been almost impossible,” said Hyunseok Oh, an assistant professor in materials science at the University of Wisconsin-Madison, in an interview with MIT News. Oh was not involved in the study.
But accurately simulating atoms on the length scales necessary to capture SRO is difficult. “If you want to try to do the most accurate simulations you can on supercomputers, you're limited to 100 to 200 atoms,” Sheriff says.
Because SRO is so complex, the simulations need a length scale that is orders of magnitude greater than what is possible with traditional physics-based simulations. This is where machine learning comes in. Using smaller traditional simulations as training data, the researchers taught a computer how different atoms behave around each other. They created a model called a machine learning potential, which predicts the energy of interactions between atoms but much more efficiently than the traditional simulations.
The simulation returns an enormous list of the position and velocity of every virtual atom. Like a real high-entropy alloy, it looks like a random jumble, far too large and complex to analyze by eye. “How do we actually make sense of the information that is hidden in those systems?” asks Sheriff.
(2) The result of an atomistic simulation, and the process of extracting local patterns from it. (Credit: Freitas Research Group)
SRO was previously modeled by counting the percentage of other elements that appeared next to an atom.
Consider a copper atom. Maybe chromium appears half the time, and nickel a third of the time. But that’s not the full picture. As it turns out, how they’re arranged around that copper atom ― called the chemical motif ― is also important. In a common five-element system, there are 9,100 types of chemical motif compositions, but 100 million chemically distinct motifs. That’s four orders of magnitude of chemical complexity that was previously ignored.
(3) Different motifs can have the same compositions, but different chemical properties.
But trying to identify these motifs from an atomistic simulation result is difficult. Inside a simulation, the motifs might be rotated or distorted in different ways, while still being the same motif. Testing if an arrangement of atoms is indeed a certain motif would typically require the solution to a problem for which there is no known efficient algorithm, the graph isomorphism problem. Instead, the researchers sidestepped the problem with machine learning. A Euclidean neural network, designed to have some built-in mathematical understanding of symmetry, takes in a group of atoms and spits out a “fingerprint,” or a unique identifier. These fingerprints can be easily compared, so it’s easy to classify a group of atoms by comparing its fingerprint to that of a known motif.
(4) How do you match a jumble of atoms to a motif?
However, neural networks can be unpredictable. How do you know that the fingerprints are actually unique ― that two fingerprints produced by the network are only similar if the original input motifs are the same? To solve this, Sheriff used a math concept called Pólya’s theorem.
Suppose you want to paint a cube, and you have two different colors you can use. How many ways can you paint it? The problem is a little tricky because cubes are symmetric ― two different colorings might actually be the same if you rotate the cube. Pólya’s theorem counts the number of colorings without double-counting those that are symmetric to each other.
(5) The first two cubes are rotationally equivalent, but the third is not.
It turns out that a chemical motif is a lot like the painted cube, with different colors representing different elements surrounding a central atom. Sheriff used Pólya’s theorem to count how many possible unique motifs could exist without double-counting ― the various distortions and rotations ― and then showed that it matched the number of fingerprints generated by the neural network.
With a description of all the different motifs present inside the simulation, the researchers then turned to identifying how these motifs themselves were arranged in relation to each other. They found that SRO could be efficiently characterized by two numbers: one that quantifies how “ordered” the system is, and one that describes the effective size of an SRO.
The researchers compared their two calculated numbers to those from a known alloy, and found that indeed, they did match. “Thanks to those numbers, we know that it's physically accurate,” says Sheriff. “So, that's step one.” Step two is to look at how different material properties and processing conditions correlate with the characterized SRO: how does SRO relate to alloy strength? How does the annealing temperature change the SRO? What about the cooling rate? It has been shown that properties such as stress-strain curves have a dependence on SRO, but Sheriff is still working on testing these relationships.
“We can't really go into a lab and decide where we put atoms in those materials,” says Sheriff. But it is possible to change the synthesis steps. “And so, we went and ran the simulations and then computed how much short-range ordering changes.”
If researchers could identify the associations between the processing conditions and SRO, as well as the associations between SRO and material properties, then they would have a much better understanding of how to tune the processing steps to affect the resulting material.
Chi-Ken Lu, an assistant professor at Rutgers University who studies physics-based machine learning, is optimistic. Lu, who was not involved in the study, believes that this approach could assist in streamlining the discovery and design of new alloys. “This is of great help for people who are looking for one best material out of a sea of choices.”
The researchers’ end goal is to use computational tools to design fully custom alloys. The holy grail, according to Sheriff, is to look at a list of required material properties and immediately answer the question: “What elements of the periodic tables do I need ― and how do I synthesize them?”
“I really like this project because it mixes a little bit of computer science, a little bit of pure math, a little bit of material science, and tries to make a story all together,” says Sheriff.