Predicting Entropy-Enthalpy Compensation in Metal Hydrides Using Machine Learning

Metal hydrides are among the most promising materials for hydrogen storage because of their high gravimetric and volumetric energy density. In some cases, the volumetric capacity is higher than even liquid hydrogen. This makes them attractive for transportation applications, where minimizing storage system volume is paramount. The primary challenge to implementing metal hydrides is a “Goldilocks” tradeoff between the thermodynamics of H₂ release and the reversible capacity.¹ One strategy to surmount this challenge is to reduce (i.e., make more negative) the free energy of dehydrogenation (<i>ΔG</i>^°(dehyd)) by maximizing the dehydrogenation entropy (<i>ΔS</i>^°(dehyd)) and minimizing the corresponding enthalpy change (<i>ΔH</i>^°(dehyd)). However, entropy-enthalpy compensation,^2-3 in which a reduced <i>ΔH</i>^°(dehyd) is counteracted by a smaller <i>ΔS</i>^°(dehyd), could defeat this strategy. Therefore, understanding the extent to which <i>ΔH</i>^° and <i>ΔS</i>^° can be independently controlled is crucial to designing strategies for tailoring the thermodynamics of metal hydrides.<br/> <br/>Here, we discuss our recent use of a machine learning model to identify features correlated with <i>ΔS</i>^°(dehydr) and <i>ΔH</i>^°(dehydr) for metal hydrides.⁴ For intermetallic (interstitial) metal hydrides, our results indicate that the material features that best predict <i>ΔH</i>^°(dehydr) can differ from those for <i>ΔS</i>^°(dehydr). In particular, <i>ΔS</i>^°(dehydr) is most strongly correlated with the corresponding volume change upon dehydrogenation, whereas <i>ΔH</i>^°(dehydr) is strongly correlated with the mean ground-state atomic volume, which depends only on composition and not structure. For several other classes of metal hydrides, including high entropy alloys (HEA),⁵ metal-substituted TiFe, and AB₂ (Laves-type) hydrides,⁶ we find entropy-enthalpy compensation effects are present to varying degrees, but these correlations are rather weak, suggesting that independent <i>ΔS</i>^° tuning may be possible.<br/> <br/>Finally, we report a statistical analysis of entropy-enthalpy compensation effects in metal hydride nanoparticles. Uncoupling <i>ΔS</i>^°(dehyd) of nano-MH from <i>ΔH</i>^°(dehyd) may be possible using material formats that strongly immobilize nanoclusters, thereby reducing <i>S</i>^°(nanocluster) and increasing <i>ΔS</i>^°(dehyd). Data for hydride nanoparticles are much more limited than for the bulk counterparts, but our statistical analysis of the available nanohydride data suggests that <i>ΔS</i>^°(dehyd) and <i>ΔH</i>^°(dehyd) are correlated for MgH₂ and PdH_x and this is dependent on particle size. The results suggest a structure-property correlation indicating that uncoupling <i>ΔS</i>^°(dehyd) from <i>ΔH</i>^°(dehyd) may be possible for nanoscale hydrides using material formats that strongly immobilize nanoclusters, thereby lowering <i>S</i>^°(nanocluster) and increasing <i>ΔS</i>^°(dehyd).<br/> <br/>1. Allendorf, M. D.; Stavila, V.; Snider, J. L.; Witman, M.; Bowden, M. E.; Brooks, K.; Tran, B. L.; Autrey, T., Challenges to developing materials for the transport and storage of hydrogen. <i>Nature Chemistry </i><b>2022,</b> <i>14</i>, 1214.<br/>2. Pasquini, L., The Effects of Nanostructure on the Hydrogen Sorption Properties of Magnesium-Based Metallic Compounds: A Review. <i>Crystals </i><b>2018,</b> <i>8</i>, 106.<br/>3. Yartys, V. A.; Lototskyy, M. V., Laves type intermetallic compounds as hydrogen storage materials: A review. <i>Journal of Alloys and Compounds </i><b>2022,</b> <i>916</i>, 165219.<br/>4. Witman, M.; Ling, S.; Grant, D. M.; Walker, G. S.; Agarwal, S.; Stavila, V.; Allendorf, M. D., Extracting an empirical intermetallic hydride design principle from limited data via interpretable machine learning. <i>J. Phys. Chem. Lett. </i><b>2020,</b> <i>11</i>, 40.<br/>5. Witman, M.; Ek, G.; Ling, S.; Chames, J.; Agarwal, S.; Wong, J.; Allendorf, M. D.; Sahlberg, M.; Stavila, V., Data-Driven Discovery and Synthesis of High Entropy Alloy Hydrides with Targeted Thermodynamic Stability. <i>Chemistry of Materials </i><b>2021,</b> <i>33</i> , 4067.<br/>6. Witman, M.; Guan, P.; Stavila, V.; Allendorf, M. D., Towards Pareto optimal high entropy hydrides via data-driven materials discovery. <i>ChemRxiv </i><b>2022</b>, DOI: 10.26434/chemrxiv-2022-wktf4.