A chef can spend a lifetime perfecting a recipe: adjusting the ingredients, creating the dish, sampling its flavors, making changes, and trying again. Similarly, a scientist can spend a lifetime perfecting a material. While the world can wait a few decades for the next groundbreaking risotto, the materials we need to solve today’s most pressing energy problems are required much sooner. A number of Energy Frontier Research Centers are exploring ways to leverage theory to create these material “recipes” faster.
What do we mean by “theory”? While it sounds esoteric, it’s not a tool reserved for scientists in a laboratory. In fact, you likely use theory every day. When you decide how far in advance you need to leave to get to work by 9 am, you probably have an idea of how the traffic and weather conditions will affect your commute. Once you’ve looked up the traffic report and poked your head outside to assess whether or not it’s raining, you can put those “parameters” into your “model” and solve for how much time you’ll need. Likewise, theorists begin with a set of equations that describes the system. Solving these equations allows theorists to compute the system’s properties. The equations that represent realistic systems are often too complex to be solved exactly, but fortunately for us, computers are able to help provide approximate solutions.
Theorists compare the calculated properties to the properties that experimental groups measure to further refine the theoretical model. Once the model predicts the properties of interest with reasonable accuracy, it becomes a new tool on the material scientist’s workbench.
Predicting stable materials by modeling electrons
A crucial tool for scientists who design novel materials is a phase diagram, a map showing which structures are most stable at a given set of conditions, such as temperature and pressure. Chemists and engineers use this map when they design reaction pathways and devices. Experiments can evaluate a material’s stability and thus can be used to generate phase diagrams, but the diagrams are limited to the small fraction of compounds that have been synthesized before, which means they could be missing the next breakthrough material. Computers, on the other hand, have the capacity to discover and analyze millions of compounds, whether or not the compounds have been experimentally synthesized. Therefore, an important question that scientists at both the Center for Next Generation of Materials Design (CNGMD) and the Center for Hierarchical Waste Form Materials (CHWM) are trying to answer is whether a material that currently only exists within a computer is stable enough to exist in the real world.
A material’s stability is related to its energy, so theorists need to be able to compute energies. Density functional theory (DFT) helps by relating the energy of a system to its electron density. A computer can then find the system’s ground-state energy by finding the electron density that minimizes the energy. By computing the energy of related, known compounds, scientists can predict how stable or unstable the new compound is relative to compounds that already exist. However, these calculations are very computationally expensive, and so previous calculations have only been performed at a limited set of conditions. Recently, however, theorists at CNGMD have used statistical learning methods to develop a prediction tool to enable the rapid extension of a large, database-scale number of existing DFT calculations to elevated temperatures, with an accuracy comparable to calculations from first principles, making DFT calculations even more relevant for materials discovery. “We have enough predictive accuracy to guide experiments in a meaningful way,” said Aaron Holder, a leader of theoretical work at CNGMD.
Theorists at CNGMD have already begun to do this. “What [the theorists] have been able to do is provide us a lot of guidance on where…there is the potential for new materials,” explained Laura Schelhas, a specialist in materials characterization with CNGMD. For instance, Wenhao Sun and others used these DFT capabilities along with other computational tools to discover 200 new ternary nitrides, compounds with nitrogen and two other elements. Sun, who led this effort along with Holder, created a map of this compositional space that illustrates where the groups of stable compounds are. “When you’re an experimentalist who goes into the lab, it’s kind of like searching in the dark. This map really helps to guide exploratory synthesis efforts,” said Sun. Based on these theoretical calculations, they synthesized a specific set of stable nitrides containing zinc and molybdenum. “It’s not just a material in a database,” said Sun. “It’s actually been made and I’ve held it in my hand.”
Designing systems to store nuclear waste
At CHWM, scientists also use DFT to predict the relative stabilities of specific compounds, but for a very different application. CHWM’s main goal is to investigate and design novel materials for managing nuclear waste, focusing on a class of materials called hierarchical materials. Just like a snowflake continues to exhibit interesting patterns even when you zoom in on it, these materials have interesting structures at various length scales. This hierarchy makes these materials especially promising for sequestering radioactive waste because it provides multiple spaces in which to incorporate the radionuclides as well as multiple layers of protection—a Russian nesting doll approach, as described by CHWM’s Deputy Director Theodore Besmann.
To model these larger systems, scientists at CHWM combine DFT with models more suitable for larger length scales, such as molecular dynamics simulations and phase-field modeling. Once theorists refine these models, they will use them to optimize the material’s capability to sequester radioactive waste. “We’ve got enough understanding now where we can try to be predictive,” said Besmann.
CHWM scientists were recently successful at modeling porous Na-LTA (sodium Linde Type A) zeolite structures, which collect radioactive strontium ions from a waste stream as the strontium ions replace the stable sodium ions in the structure. “The material structure is very complex, and there are a lot of opportunities to tune it to have better performance,” explained Shenyang Hu, the corresponding author of a recent paper in Computational Materials Science. Hu and others developed a series of equations to describe these multiscale structures and the movement of ions within them. Some of the parameters in these equations rely on models of the behavior of ions within the structures and are currently determined qualitatively based on experimental results, but could eventually require DFT calculations, according to Vancho Kocevski, another theorist at CHWM. “With DFT,” said Kocevski, “we can easily calculate the energy barrier [for diffusion]. The higher the barrier, the more energy required for the ion to move.”
The equations can be solved numerically to determine the concentrations of the ions within different parts of the Na-LTA structure over time. This procedure is repeated for different microstructures to understand how structural changes affect the mechanisms and efficiency of ion exchange. “We have developed the modeling capability. Now, we can guide the design of hierarchical waste form material microstructures,” said Hu.
Training a computer to be a scientist
Once you have a prediction for a novel, stable material, you still need to be able to synthesize it. Here, a computer can also lend a (robotic) hand. Led by John Parise, the team at A Next Generation Synthesis Center (GENESIS) aims to train a computer to take in data about how a reaction proceeds, determine which reaction conditions to change, and autonomously carry out those changes and monitor the results. The ultimate target is to let the computer do this without any human supervision, until arriving at the desired material.
Parise notes that this is a long-term goal, requiring both the computational infrastructure to make this process autonomous, as well as an understanding of the design space. “Before you start,” said Parise, “you have to have excellent knowledge of all the possible phases that might form in that reaction space.” That understanding is derived from existing theory and experiments on reaction pathways, and over the next few years, the GENESIS team will work to fill in the gaps.
Theory in practice
At these and other EFRCs, theory and synthesis have a symbiotic relationship—the models feed off of existing experimental results to develop and refine themselves and then drive the prediction and creation of novel and impactful materials. And maybe one day, they’ll design the perfect risotto!
