Advances in CALPHAD Methodology for Modeling Hydrides: A Comprehensive Review

J. Phase Equilib. Diffus. https://doi.org/10.1007/s11669-024-01113-y REVIEW Advances in CALPHAD Methodology for Modeling Hydrides: A Comprehensive Review M. Palumbo1 M. Baricco1 • E. M. Dematteis1 • L. Fenocchio2 • G. Cacciamani2 • Submitted: 28 December 2023 / in revised form: 16 April 2024 / Accepted: 18 April 2024 Ó The Author(s) 2024 Abstract Hydrides enable handling hydrogen at low pressure and near room temperature, offering higher volumetric densities than compressed or liquid hydrogen and enhancing safety. The CALPHAD method, rooted in the principles of thermodynamics, offers a systematic approach for predicting phase equilibria and thermodynamic properties in multicomponent materials. This comprehensive review paper aims to provide a detailed overview of the application of the CALPHAD method in the realm of metallic and complex hydrides. After an introduction to the fundamental thermodynamic aspects of hydrides, key elements of applying the CALPHAD method to model metalhydrogen systems and complex hydrides are discussed. Subsequently, recent publications are reviewed, highlighting key findings and recent progresses in the field. Finally, the challenges that must be overcome to achieve further progress in this area are explored. Keywords CALPHAD  hydrides  hydrogen storage  thermodynamics This invited article is part of a special tribute issue of the Journal of Phase Equilibria and Diffusion dedicated to the memory of Thaddeus B. ‘‘Ted’’ Massalski. The issue was organized by David E. Laughlin, Carnegie Mellon University; John H. Perepezko, University of Wisconsin–Madison; Wei Xiong, University of Pittsburgh; and JPED Editor-in-Chief Ursula Kattner, National Institute of Standards and Technology (NIST). & M. Palumbo 1 Department of Chemistry and NIS- INSTM, University of Turin, V. P. Giuria 7, 10125 Turin, Italy 2 Dipartimento di Chimica e Chimica Industriale, Università di Genova, Genoa, Italy 1 Introduction To effectively limit the rise in global temperatures from climate change, it is essential to find alternatives to fossil fuels in transportation and energy production. Renewable energy sources like solar, wind, and water are promising, especially if we can store their energy efficiently. Hydrogen, as an energy carrier, offers several benefits. It is a secondary energy vector, because it is produced from primary energy sources and can be stored for extended periods. Hydrogen is appealing because it reacts with oxygen to produce only water, releasing a significant amount of energy. For instance, 1 kg of hydrogen has the same energy content as 2.4 kg of methane or 2.8 kg of gasoline.[1] This makes hydrogen more energy-dense by weight compared to other fuels. However, its energy density by volume is lower, as evidenced by liquid hydrogen, which contains 8.5 MJ/L compared to 32.6 MJ/L for gasoline. This means a larger volume of hydrogen is needed to match the energy provided by most fossil fuels. Green hydrogen can be produced through various methods, such as electrolysis, biogas reforming, or photoelectrochemical processing. It can be converted back into energy using fuel cells or internal combustion engines. Utilizing hydrogen as an energy carrier requires the development of a suitable infrastructure for its handling, including purification to remove contaminants, transportation, storage, and compression. Typically, hydrogen is stored as a compressed gas or cryogenic liquid, technologies which require substantial energy for compression and cooling, making them economically challenging. Alternatively, suitable carriers allow for handling hydrogen at low pressure and near room temperature, offering higher volumetric densities than compressed or liquid hydrogen and enhancing safety.[2] For 123 J. Phase Equilib. Diffus. example, metallic hydrides are promising materials that can reversibly uptake and release hydrogen and possess a great potential for a wide range of applications.[3–5] Research in the hydrogen sector aims to increase energy density while limiting system volume. To harness the full potential of metallic hydrides, a deep understanding of their thermodynamic and kinetic properties is essential.[3,6–8] In this context, the CALPHAD (Calculation of Phase Diagrams) method has emerged as a powerful and suitable tool for modeling and predicting the behaviour of hydride systems.[9,10] The CALPHAD method, rooted in the principles of thermodynamics, offers a systematic approach to the prediction of phase equilibria and thermodynamic properties in multicomponent materials.[11,12] Originally developed in the 1970 s for applications in metallurgy, CALPHAD has since evolved and found wide-ranging utility in diverse fields, including the study of hydrides.[9,10] By combining thermodynamic databases, experimental data, and computational techniques, the CALPHAD approach allows researchers to unravel the complex interplay of phases and reactions that occur during hydrogen absorption and desorption in metallic systems. This comprehensive review paper aims to provide a detailed overview of the application of the CALPHAD method in the realm of metallic and complex hydrides. We will explore the fundamental concepts behind CALPHAD and its adaptation to address the unique challenges posed by hydride systems. Furthermore, we will delve into the critical contributions of CALPHAD in elucidating the thermodynamics of hydrogen absorption and desorption processes and the design of new hydride materials. Additionally, we will highlight recent advances and future prospects in the field, showcasing the continuous evolution of CALPHAD as an indispensable tool for advancing the science and technology of hydrides. Through this review, we hope to offer researchers, engineers, and materials scientists a comprehensive resource for understanding the state-of-the-art in CALPHAD-based modeling of metallic hydride systems and inspire further advancements in this field. 2 Hydrogen Absorption Solid hydrogen carriers need to have a substantial mass and volume capacity, along with rapid gas absorption and release rates. Moreover, the hydrogenation reaction should ideally occur near ambient pressures and temperatures. Achieving these characteristics requires appropriate thermodynamic and kinetic properties, as well as optimal gravimetric and volumetric densities for the hydrogen carrier. 123 On the one hand, the interaction between hydrogen gas (H2) and a solid-phase carrier (M), typically a metal, can lead to the formation of a solid solution M(H). This process is described by the following reaction: x M þ H2  M ðH Þ ðEq 1Þ 2 In this case, the process is driven by the Sievert law: H ¼ Ks p1=2 M ðEq 2Þ where H/M is the ratio between hydrogen and the metal M in the solution, Ks is a constant and p is the pressure. The dependence of Ks on the temperature, T, can be expressed as: lnKs ¼ DHmix DSmix þ RT R ðEq 3Þ where R is the gas constant and DHmix and DSmix are the p (...truncated)