A series of “states” (points) in a complex system are connected by “transitions” (lines). Larger dots correspond to states where more time is spent during the simulation, and thicker lines indicate faster transitions. Investigating long trajectories with many jumps requires a large amount of computation. The machine learning model transforms this system (left) into an equivalent system (right) with the same diffusivity behavior. However, calculating diffusion is much simpler. In an uncorrelated system, each jump corresponds to a “kinoson”, which is a small contribution to the spread, and the sum of all kinosons gives the spreading rate.Credit: Granger Institute of Technology / University of Illinois at Urbana-Champaign
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A series of “states” (points) in a complex system are connected by “transitions” (lines). Larger dots correspond to states where more time is spent during the simulation, and thicker lines indicate faster transitions. Investigating long trajectories with many jumps requires a large amount of computation. A machine learning model transforms this system (left) into an equivalent system (left) with the same diffusivity behavior, but with a much simpler calculation of diffusion (right). In an uncorrelated system, each jump corresponds to a “kinoson”, which is a small contribution to the spread, and the sum of all kinosons gives the spreading rate.Credit: Granger Institute of Technology / University of Illinois at Urbana-Champaign
Researchers at the University of Illinois at Urbana-Champaign have recalculated diffusion in multicomponent alloys as a sum of individual contributions called “quinosons.” By using machine learning to calculate the statistical distribution of the individual contributions, they were able to model the alloy and calculate its diffusivity orders of magnitude more efficiently than calculating the entire trajectory.
This work is published in a magazine physical review letter.
“We discovered a more efficient way to calculate diffusion in solids. At the same time, we learned more about the fundamental process of diffusion in the same system,” said Professor of Materials Science and Engineering, who led the research. Dallas Trinkle says. With graduate student Soham Chattopadhyay.
Diffusion in solids is the process by which atoms move through a material. The production of steel, the movement of ions in batteries, and the doping of semiconductor devices are all controlled by diffusion.
Here, the research team modeled diffusion in a multicomponent alloy. Multicomponent alloys are metals that contain equal amounts of five different elements: manganese, cobalt, chromium, iron, and nickel in this study. These types of alloys are interesting. That's because one way to make strong materials is to add different elements together, much like carbon and iron are added to make steel.
Multicomponent alloys have unique properties such as good mechanical behavior and stability at high temperatures, so it is important to understand how atoms diffuse within these materials.
Long timescales are required to observe diffusion well because the atoms move around randomly and their displacement from the starting point increases over time. “When someone tries to simulate spread, it's tedious because they have to run the simulation for a very long time to get the full picture,” Trinkle said.
“This really limits a lot of the ways that we can study diffusion. A more accurate way to calculate transition rates is to take long-duration trajectories and find a reasonable value for diffusion.”
The atom might jump to the left, but then jump back to the right. In this case, the atoms are not moving anywhere. Now, let's say you jump to the left, then 1,000 other things happen, and then you jump to the right and back. It's the same effect.
“We call it a correlation, because at some point the atoms jump once, and then they jump back, and that's what complicates diffusion,” Trinkle said. When you look at how machine learning is solving problems, what machine learning is actually doing is changing.” The problem changes to one where these correlated jumps do not exist. ”
Therefore, the jump by the atoms contributes to the diffusion, making the problem much easier to solve. “We call these small jumps kinosons,” Trinkle says.
“We showed that you can extract their distribution, the probability of seeing a quinoson of a certain size, and add them all together to get the true diffusivity. You can see how it spreads in solids. “
Another advantage of using Kinoson and machine learning to model diffusion is that it is significantly faster than computing entire trajectories on long time scales. According to Trincle, this method allows him to run simulations 100 times faster than normal methods.
“I think this method is going to really change the way we think about proliferation,” he says. “This is a different way of looking at the problem, and I hope that within the next 10 years, this will become the standard way of looking at proliferation. To me, one of the exciting things is that it works faster. But it also means that users can learn more about what's going on inside the system. ”
For more information:
Soham Chattopadhyay et al., Contribution to the diffusion of complex materials quantified with machine learning; physical review letter (2024). DOI: 10.1103/PhysRevLett.132.186301.upon arXiv: DOI: 10.48550/arxiv.2401.06046
Magazine information:
physical review letter
,arXiv
