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Machine learning prediction of hydrogen sorption properties of zirconium-titanium based C14 Laves phase AB 2 alloy from chemical composition

This study demonstrates that machine learning models trained on elemental atomic percentages can effectively predict key hydrogen sorption properties of Zr–Ti-based C14 Laves phase AB2 alloys, achieving high accuracy for unit cell volume and moderate accuracy for equilibrium pressure, thereby accelerating the design of hydrogen storage materials.

Original authors: Suwarno Suwarno, Mohammad Ismail, witantyo Witantyo, Ivan Tolj

Published 2026-11-02

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Suwarno Suwarno, Mohammad Ismail, witantyo Witantyo, Ivan Tolj

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Hydrogen is a clean fuel that burns without pollution, but storing it is a tricky engineering problem. Because hydrogen is the lightest element in the universe, it takes up a huge amount of space unless it is squeezed tightly together. One way to solve this is to trap hydrogen atoms inside the crystal structure of a metal, creating a solid material that holds the gas safely. These materials, called metal hydrides, can absorb hydrogen like a sponge soaks up water and release it again when needed. Among the many types of metals being studied, a specific group known as AB2 alloys has shown great promise. These are mixtures of two different metals that form a rigid, repeating pattern called a crystal lattice. When hydrogen enters this lattice, it changes the size of the pattern and the energy required to hold the gas. Scientists need to know exactly how these changes happen to design better batteries and fuel tanks, but testing every possible combination of metals in a laboratory is slow, expensive, and often impossible to do for every theoretical mix.

To speed up this discovery process, researchers from Indonesia, Malaysia, and Croatia turned to a different kind of tool: machine learning. Instead of melting metals in a furnace for every experiment, they taught a computer to predict the behavior of these alloys based on their chemical makeup. The team focused on a specific family of alloys made primarily from zirconium and titanium, which are known to form a hexagonal crystal structure called the C14 Laves phase. They gathered a massive collection of data from previous scientific studies, compiling information on 244 different alloy recipes. For each recipe, they knew exactly which elements were present and in what amounts, as well as the resulting physical properties: how much the crystal structure expanded when it absorbed hydrogen, how much heat was released during the process, how much disorder was created, and the pressure at which the hydrogen would settle.

The researchers wanted to see if they could predict these four key outcomes just by looking at the list of ingredients. They tested two different ways of feeding this information to the computer. The first method used the raw percentages of each element, such as "10 percent titanium" or "5 percent manganese." The second method used calculated physical properties derived from those ingredients, such as the average size of the atoms, the density of the material, and the ratio of the two main metal types. They trained five different types of computer algorithms on this data, splitting the information so that the computer learned from most of the examples and was tested on the ones it had never seen before. This approach allowed them to judge how well the computer could guess the properties of a new, unseen alloy.

The results showed a clear winner in how to describe the ingredients. The computer performed significantly better when it was given the simple list of element percentages rather than the calculated physical properties. When predicting the size of the crystal unit cell—the tiny box that repeats to form the metal—the model using element percentages was remarkably accurate. One simple linear model, which looks for straight-line relationships between data points, achieved a score of 0.955 on the test set, meaning it could predict the crystal size with very high precision. This suggests that the size of the crystal is largely determined by a straightforward average of the sizes of the atoms inside it. In contrast, the models using the more complex physical properties struggled to reach the same level of accuracy, indicating that those calculated numbers might hide some of the specific details the computer needs.

However, the story was different for the other properties. Predicting the heat released when hydrogen is absorbed proved much harder. Even the best models could only capture about half of the variation in the data, suggesting that the heat of absorption depends on subtle electronic and structural factors that a simple list of ingredients cannot fully explain. The prediction of entropy, which measures the disorder or randomness created when hydrogen enters the metal, was the most difficult task of all. Most of the computer models performed worse than simply guessing the average value for every new alloy, indicating that the current data does not contain enough information to understand the complex vibrations and arrangements that govern this property.

The equilibrium pressure, which is the force at which the hydrogen sits comfortably inside the metal, showed moderate success. The computer could predict this value reasonably well, especially when using the element percentages. Interestingly, the researchers found a strong link between the pressure and the size of the crystal cell: as the crystal box got larger, the pressure needed to hold the hydrogen dropped. This makes physical sense because a larger space inside the metal makes it easier for hydrogen atoms to fit in, requiring less pressure to force them there. The study concludes that while machine learning is a powerful tool for designing these hydrogen storage materials, it works best for structural properties like size. For the more complex thermodynamic behaviors like heat and disorder, scientists will need to develop smarter ways to describe the materials before computers can reliably predict them. This work provides a clear path forward, showing that knowing the exact recipe of an alloy is often more useful than knowing its derived physical traits when trying to forecast how it will store energy.

Technical Summary: Machine Learning Prediction of Hydrogen Sorption Properties in Zr-Ti Based C14 Laves Phase AB2 Alloys

Problem Statement
The design of metal hydrides for solid-state hydrogen storage and battery applications requires precise control over thermodynamic and structural properties. Specifically, Zr-Ti based C14 Laves phase $AB_2$ alloys are of significant interest due to their high hydrogen capacities and activation properties. However, experimentally determining key hydrogen sorption parameters—such as unit cell volume ( $V_{14}$ ), enthalpy of hydrogen absorption ( $\Delta H$ ), entropy of hydrogen absorption ( $\Delta S$ ), and equilibrium plateau pressure ( $P_{eq}$ )—is resource-intensive. While machine learning (ML) has been applied to metal hydride prediction, existing databases are often outdated, and the optimal input features for predicting specific Laves phase properties remain under-explored. This study addresses the need to develop robust ML models that predict these sorption properties directly from chemical composition, comparing two distinct feature engineering approaches.

Methodology
The researchers constructed a curated dataset comprising 244 entries of Zr-Ti based $AB_2$ alloys, extracted from academic literature. The dataset was filtered to include only alloys with identified C14 Laves phases, removing entries with only C15 phases or insufficient variance in elemental composition.

Two categories of independent variables (features) were systematically compared:

Element Atomic Percent: Direct representation of the alloy's chemical composition.
Properties-Based Variables: Derived physical descriptors calculated from the composition, including molar mass, bulk density, molar volume, atomic radius ratio, bulk modulus, electron density, and the B/A site ratio.

Five machine learning algorithms were evaluated: Multivariate Linear Regression (LR), Random Forest (RF), Ridge Regression, k-Nearest Neighbors (KNN), and Extreme Gradient Boosting (XGBoost). The workflow involved:

Preprocessing: Removal of low-variance elements (e.g., Ho, Sn, Al) and handling of high correlations (e.g., between Ti and Zr, which were retained due to their critical role in A-site substitution). Data was scaled using Min-Max normalization.
Feature Selection: Forward feature selection was employed to identify the most informative subsets of variables for each target and algorithm.
Model Training and Validation: The dataset was split into 80% training and 20% testing sets. Performance was rigorously assessed using 5-fold cross-validation.
Evaluation Metrics: Models were evaluated based on the coefficient of determination ( $R^2$ ), Mean Absolute Error (MAE), and Root Mean Squared Error (RMSE).

Key Results
The study yielded distinct performance outcomes depending on the target variable and the feature type used:

Unit Cell Volume ( $V_{14}$ ): This was the most successfully predicted variable. Models using element atomic percent features significantly outperformed those using properties-based features. Notably, a simple Linear Regression model achieved the highest test set accuracy with an $R^2$ of 0.955, surpassing complex ensemble methods like XGBoost and RF. This suggests a predominantly linear relationship between elemental composition and unit cell volume. In contrast, properties-based features yielded a lower test $R^2$ of 0.670 for LR, though RF achieved 0.931.
Enthalpy ( $\Delta H$ ) and Entropy ( $\Delta S$ ): Prediction of thermodynamic properties proved challenging.
- For $\Delta H$ , the best validation $R^2$ was moderate at 0.561 (RF with properties-based features) and 0.531 (KNN with element-based features).
- For $\Delta S$ , performance was poor; most models resulted in negative validation $R^2$ values, indicating they performed worse than a simple mean prediction. The best validation $R^2$ was only 0.218 (KNN with element-based features).
Equilibrium Pressure ( $P_{eq}$ ): This variable showed moderate prediction accuracy. The best validation $R^2$ reached 0.739 (achieved by both KNN and XGBoost using element-based features). A significant finding was the observed linear correlation between $P_{eq}$ and $V_{14}$ , consistent with the van't Hoff equation, where larger unit cell volumes correlate with lower equilibrium pressures.

Contributions and Significance
The paper demonstrates that machine learning can effectively accelerate the design of $AB_2$ hydrogen storage alloys, particularly for predicting structural properties like unit cell volume directly from chemical composition.

Feature Efficacy: The study establishes that raw elemental atomic percentages are superior to derived physical properties for predicting $V_{14}$ , likely because they provide a more granular representation of composition-dependent variations.
Algorithm Selection: The results highlight that model complexity does not always equate to better performance; for $V_{14}$ prediction, linear models outperformed non-linear ensemble methods, suggesting the underlying physics is largely linear regarding atomic radii.
Limitations and Future Directions: The authors modestly conclude that while structural properties are predictable, thermodynamic properties ( $\Delta H$ , $\Delta S$ ) remain difficult to model with current descriptors. The low accuracy for entropy suggests that current bulk property descriptors fail to capture the complex configurational, vibrational, and electronic contributions governing these values. The paper posits that more advanced feature engineering is required to improve the prediction of thermodynamic sorption properties.

In summary, this work validates the utility of data-driven approaches for the rapid screening of Zr-Ti based Laves phase alloys, offering a reliable pathway for predicting structural parameters while identifying specific gaps in current feature sets for thermodynamic prediction.

Technical Summary: Machine Learning Prediction of Hydrogen Sorption Properties in Zr-Ti Based C14 Laves Phase AB2 Alloys

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