Researchers at the University of Illinois have developed a faster, more insightful way to model diffusion in alloys using 'kinothons' and machine learning, which could revolutionize how we understand and study this important process. Credit: SciTechDaily.com
Researchers at the University of Illinois at Urbana-Champaign have redefined diffusion in multi-component alloys by breaking them down into their individual components, which they call “quinons.” Machine LearningThey analyzed the statistical distribution of these elements, alloy This allows them to determine the rate of diffusion much more efficiently than calculating the entire trajectory. Their findings were recently published in the journal Nature. Physics Review Letter.
“We've found a much more efficient way to calculate diffusion in solids, and at the same time, we've learned much more about the fundamental process of diffusion in the same system,” said Dallas Trinkle, professor of materials science and engineering, who led the research with graduate student Soham Chattopadhyay.
Diffusion in solids is the process by which atoms move through a material. The making of steel, the movement of ions through batteries, and the doping of semiconductor devices are all controlled by diffusion.
Issues with diffusion simulation
Here, the research team modeled diffusion in multi-component alloys, which are metals that contain equal amounts of five different elements: in this study, manganese, cobalt, chromium, iron, and nickel. These types of alloys are interesting because one way to make stronger materials is to add different elements together, such as adding carbon and iron to make steel. Multi-component alloys have unique properties, such as good mechanical behavior and stability at high temperatures, so understanding how atoms diffuse within these materials is important.
A set of “states” (dots) connected with “transitions” (lines) in a complex system. Larger dots correspond to states that took a long time during the simulation, while thicker lines indicate faster transitions. Seeing long trajectories with many jumps requires a lot of computational work. A machine learning model transforms this system (left) into an equivalent system (right) with the same diffusive behavior but where the diffusion is much easier to calculate. In an uncorrelated system, each jump corresponds to a “kinoson”, with a small contribution to the diffusion and the sum of all the kinosons gives the diffusivity. Credit: Grainger School of Engineering, University of Illinois at Urbana-Champaign
To get a good look at diffusion, you need long timescales because atoms move around randomly, becoming more and more displaced from their starting point over time. “If someone tries to simulate diffusion, it's tedious, because they have to run the simulation for a very long time to get the whole picture,” Trinkle says. “This really limits a lot of the ways you can study diffusion. More accurate methods to calculate transition rates often can't be used because you can't run enough simulation steps to get long trajectories and get reasonable values for diffusion.”
Ann atom An atom might jump to the left, but then it might jump back to the right. In that case, the atom hasn't moved anywhere. Now say the atom jumps to the left, and then 1000 other things happen, and it jumps back to the right. It's the same effect. “We call this correlation because at some point the atom makes one jump and then it takes that jump back,” Trinkle says. “That's what makes it complicated over diffusion. When you look at how machine learning is solving the problem, it's actually turning it into a problem that doesn't have any correlated jumps at all.”
Simplifying Propagation with Machine Learning
So every jump that an atom makes contributes to diffusion, making the problem much easier to solve. “We call these jumps kinosons, which represent small movements,” says Trinkle. “We showed that we can extract the distribution of them, the probability of seeing a kinoson of a certain size, and then add them all up to get the true diffusivity. On top of that, we can tell how different elements are diffusing in the solid.”
Another advantage of using kinosons and machine learning to model diffusion is that it is significantly faster than calculating the entire trajectory over long time scales: Trinkle says that using this method they can run simulations 100 times faster than regular methods.
“I think this method really changes the way we think about diffusion,” he says. “It's a different way to look at the problem, and I hope that over the next decade this becomes the standard way of looking at diffusion. To me, one of the attractive things about this method is that not only does it allow us to work faster, but it also gives us much more insight into what's going on in the system.”
References: “Complex Materials Contributions to Diffusion Quantified with Machine Learning” by Soham Chattopadhyay and Dallas R. Trinkle, April 30, 2024; Physics Review Letter.
Article number: 10.1103/PhysRevLett.132.186301
This research was funded by the National Science Foundation under Program Number MPS-1940303.
