Session 3: AI-Guided Predictions of Metastable Materials

Evaluating the Synthesizability of Predicted Metastable Materials Beyond the DFT Convex Hull

Wenhao Sun of the University of Michigan spoke about the synthesizability of metastable materials beyond the DFT convex hull. In particular, he focused on distinguishing between metastable materials that are predicted hypothetically and those that can actually be synthesized. 

As context, he pointed to several papers that predicted a large number of stable and metastable materials, including some that used AI for their predictions. However, he added, while many hypothetical materials can be generated in a computer, not all of them are synthesizable. Indeed, when researchers have tested a collection of hypothesized materials, they have often found that they can synthesize only a tiny portion, if any, of them. He called this the “overprediction problem.”

Furthermore, he continued, when one is searching for materials with properties, there will always be far more predicted metastable materials than stable materials since there is only one equilibrium phase but potentially an infinite number of possible computationally generated metastable structures. So materials with the most desirable properties will often be in the metastable space.

Sun offered three questions for analyzing this issue: Which metastable materials can form? Which metastable materials will form under particular synthesis conditions? And, how can one keep (or get rid of) metastable materials that have formed?

The first screening criterion for which materials can form is stability, which is evaluated in terms of the convex hull (Figure 2). “The convex hull is a plot of the energy versus composition,” Sun explained, “and we see that the stable phases fall upon this convex envelope that connects the elemental reference states. Materials that have an energy that is above the convex hull we call metastable.”

In general, Sun said, the assumption in his community has been that materials that lie on the convex hull are stable and should be synthesizable, while metastable materials that fall within some energy range of the hull are probably synthesizable and metastable materials that have an energy far above the convex hull probably are not synthesizable. “What I want to show you today,” he said, “is that this assumption needs revision.”

The assumption, Sun said, is due in large part to a paper he published in 2016 that concluded that 90 percent of known metastable materials have an energy above the convex hull that is less than 70 meV per atom. This led many to believe that computed metastable materials whose energy is within 70 meV/atom of the hull are probably synthesizable, but that is not correct, Sun said, and the paper did not make that claim. Indeed, he continued, his paper showed that in the case of five well studied binary oxides, there are many possible crystal structures within 70 meV/atom of the convex hull that have never been synthesized and probably cannot be synthesized.

Exploring metastability in more detail, Sun first observed that the thermodynamic scale of metastability—about 100 meV/atom—is much smaller than the energy scale of formation, which is usually 1–5 eV per atom. He characterized the former as the energy scale of crystal structure for metastability and the latter as the energy scale of chemical bonds. 

“So what’s so special about this number, 100 meV per atom?” he asked. He examined temperature-driven phase transitions, pressure-driven phase transitions, and size-driven phase transitions and showed that they all point to 100 meV/atom being roughly the enthalpy scale of metastability.

“So then we came up with this hypothesis called ʻremnant metastability,’” he said. “The idea of remnant metastability is that observed metastable phases are generally remnants of thermodynamic conditions where they were once the equilibrium phase.” Although this is only a hypothesis, he said, his group believes that which metastable materials can form is informed by this principle of remnant metastability.

Moving on to his second question—Under what conditions will a given metastable material form?—Sun emphasized that when researchers talk about stability and equilibrium, it is much more complicated in modern materials than it was in the past because in the past researchers worked basically with the variables of temperatures and pressure, but there are now many more variables that play a role in how a material is created. In creating multiferroic thin films, for instance, one may control the partial pressure of gases, biaxial strain, electric polarization, and the magnetic field in addition to temperature and other variables. Making high-entropy alloys involves keeping track of multiple elements in the composition, reactions with reservoir elements such as oxygen or sea water, nuclear radiation, and so forth. “So these are very, very complicated systems for us to even talk about things like stability and metastability and equilibrium,” Sun said.

He then offered several examples of the complexity of making modern materials. “What I want to emphasize to you in all of this” he said, “is that the thermodynamic potential that nature uses is much bigger than the one that we in material science usually use. We usually use temperature, pressure and composition, but there are many other forms of thermodynamic work, and these different forms of thermodynamic work are applied by different synthesis methods.” So, he concluded, a researcher who is deciding which synthesis method to use to make a particular material should make the decision based on what forms of thermodynamic work are available in those particular methods to help access that material.

Concerning the third question of how to kinetically keep or get rid of a metastable phase, he noted that there are not that many possible mechanisms in kinetics. Loosely, they can be broken down into diffusion, nucleation, and growth. And he offered one example of each mechanism that can block the formation of an equilibrium phase. 

For diffusion-limited processes, he offered an example of powder reactions, where the proper choice of precursor powders can influence the amount of reaction energy available for a reaction. For nucleation-limited processes, he described how changing the solution conditions in solution synthesis could drive the reaction down different pathways. And to illustrate growth-limited processes, he described how the mineral dolomite grows in nature. In normal lab growth, it forms defects which block crystal growth, but in nature the system is sometimes undersaturated, which selectively removes the defective regions first because they are higher energy and more soluble, allowing the crystals to form.

Discussion

Raja opened the discussion period with three questions, one about dealing with high-dimensional phase diagrams, a second about knowing the difference between a failure to synthesize a material and a material that cannot be synthesized, and a third about dark data, or information collected by organizations that is never actually used or shared. 

All three of the panelists addressed the question about high-dimensional phase diagrams. Sun pointed out that there are mathematical formalisms for dealing with such high-dimensional spaces and mentioned a paper his group published on the geometry of high-dimensional phase diagrams where they discuss how to construct, navigate, and interpret them. Beaucage said that soft matter systems inevitably have high-dimensional phase spaces, but the dimension can generally be greatly reduced with physics and other considerations. And Sankaranarayanan commented that AI should be able to help with navigating and interpreting a high-dimensional phase diagram.

Sun addressed the second question about synthesizing materials by saying that it is useful to reframe the issue from how to synthesize a target material to how to avoid synthesizing all of the materials that are not desired. “Once you shift your frame of thinking to that,” he said, “. . . you will start to look for all the things that are competing in your chemical space that really want to form.” This in turn leads to a different approach to synthesis where one designs algorithms “to avoid those really deep thermodynamic sinks in high-dimensional space.”

Concerning the issue of dark data, Beaucage said he has a depressing take on the topic. “User facilities have these massive lakes of data with largely 1 percent or 5 percent of it [that] is published,” he said. “I think the odds of recovering the balance of that data are really low, and the best that we can do is to ensure really good tagging moving forward and ensure really robust reproducible synthesis.” Sankaranarayanan emphasized the need for more AI-ready datasets so that a larger percentage of the data can be used in the future. And Sun questioned the value of much of the dark data, saying he was part of a research project that text-mined historical literature on synthesis reactions, “and we found that we could get tens of thousands of recipes, but we found that they were all basically the same recipe for a material.” Thus he said he suspected that dark reaction data wouldn’t be as diverse or as effective in training AI algorithms as one would hope. Given that, he echoed Beaucage in saying that the focus should be on collecting plenty of good data going forward. 

Next, workshop co-chair Raymundo Arroyave commented about the difficulty of making the sorts of calculations necessary to figure out which metastable states in a complex system are synthesizable, and he asked Sun to comment. Sun said that he prefers to calculate what is easy to calculate and to measure what is easy to measure experimentally. Thus in the case of trying to synthesize a new metastable material, rather than attempting to calculate a solution, the better approach is to try to synthesize the desired material and see what happens. “The easiest way to figure out what you don’t want to make is to try making it and then get something else, get the impurity phase,” he said. “Once you get the impurity phase you don’t know precisely what kinetic mechanism drove that impurity phase, but at least you know that that is the material that you’re fighting against.” The result of using the information from the experiment is that one does not have to map out the entire phase diagram but only a small part of it that involves avoiding the impurity. That is a much more tractable problem, he said.

Sankaranarayanan agreed but added that there is a need to change the whole synthesis hardware in order to increase the volume of data being generated to the point that it is useful for training AI. Raja added that it is not just the volume of data that is important; it is also crucial to generate highly diverse synthesis data. And Sun said that data science refers to the “four V’s”—volume, variety, velocity, and veracity. “Historically, we haven’t done a great job at sampling all four of those V’s,” he said, “and right now I think we have the opportunity to be smarter about doing that,” in part by using AI and agentic reasoning in the planning.

In answer to a question from Dennis Zhao, a Ph.D. student at the University of Maryland, Sun said that being reductionist is not a particularly useful approach in learning which materials are synthesizable. Instead, one should embrace the complexity for what it is and not, for example, try to reduce the problem to two or three dimensions.

In response to a question from William Ratcliff of NIST, Sun offered an illustration of the importance variety in synthesis. The standard approach to making the yttrium barium copper oxide (YBCO) involves using barium carbonate as a precursor along with yttrium oxide and copper oxide. Experimentalists like barium carbonate because it is shelf-stable. But since barium carbonate decomposes at a temperature higher than the melting temperature of YBCO, Sun thought it would not be a good precursor and tried using barium peroxide (which is not shelf stable but made more sense for the reaction) instead. He found that he could make YBCO in 25 minutes, phase-pure, and in one shot, with no regrinding or re-annealing needed. “Reactions are better done from weird, unusual places than they are from the common places,” he concluded.