# Promising Alloys for Hydrogen Storage in the Compositional Space of (TiVNb) 100– x (Cr,Mo) x High-Entropy Alloys

Andrei Agafonov, Nayely Pineda-Romero, Matthew Witman, Veronica Enblom, Martin Sahlberg, Vivian Nassif, Lei Lei, David Grant, Martin Dornheim, Sanliang Ling, et al.

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To cite this version:

Andrei Agafonov, Nayely Pineda-Romero, Matthew Witman, Veronica Enblom, Martin Sahlberg, et al. Promising Alloys for Hydrogen Storage in the Compositional Space of (TiVNb) 100– x (Cr,Mo) x High-Entropy Alloys. ACS Applied Materials & Interfaces, 2025, 17 (29), pp.41991-42003. 10.1021/acsami.5c08574 . hal-05268305

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Submitted on 19 Sep 2025

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Promising alloys for hydrogen storage in the
compositional space of (TiVNb)₁₀₀-x(Cr,Mo)ₓ high-
entropy alloys

Andrei Agafonov¹, Nayely Pineda-Romero¹, Matthew D. Witman², Veronica Enblom³, Martin Sahlberg³, Vivian Nassif⁴, Lei Lei⁵, David M. Grant⁵, Martin Dornheim⁵, Sanliang Ling⁵, Vitalie Stavila² and Claudia Zlotea¹*

¹Univ. Paris-Est Creteil, CNRS, ICMPE, UMR 7182, 2 Rue Henri Dunant, Thiais 94320, France

²Sandia National Laboratories, Livermore, CA 94551, United States

³Uppsala University, Department of Chemistry – Ångström Laboratory, Ångströmlaboratoriet,
Lägerhyddsvägen 1, Uppsala 751 20, Sweden

⁴CNRS, Université Grenoble Alpes, Institut Néel, Grenoble 38042, France

⁵Advanced Materials Research Group, Faculty of Engineering, University of Nottingham,
Nottingham NG7 2RD, UK
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ABSTRACT

This study reports on the search for the most promising alloys in the compositional space of (TiVNb)₈₀Cr₂₀-xMoₓ (x = 5, 10 and 15) and (TiVNb)₇₅Cr₂₅-xMoₓ (x = 5, 10, 15 and 20) high entropy alloys. Firstly, data-driven machine learning applied on these systems predicts that increasing Mo content destabilizes the enthalpy of the hydride phases. Second, experimental and density functional theory (DFT) validations were performed. The as-prepared alloys have single-phase bcc lattices and rapidly absorb hydrogen to form fcc-type hydrides with a high capacity between 1.6 and 2.0 H/M. Despite a positive effect on the thermodynamics of the hydride phases, increasing the Mo content in these alloys has a negative effect on the maximum capacity. The cycling experiments highlight the need to balance the reversible capacity, cycle life, and crystalline stabilities of these phases. Therefore, considering all these results, the most promising alloy with trade-off properties within the targeted compositional space has been identified to be (TiVNb)₇₅Cr₅Mo₂₀ that shows a maximum capacity of 2.6 wt. % (1.8 H/M), a reasonable enthalpy of hydride formation (-38.6 kJ/mol H₂), and a notable gravimetric reversible capacity of 1.42 wt. % at room temperature. To identify the most promising high entropy alloys for this application,
integrated machine learning predictions followed by experimental and DFT validations proved to
be an effective strategy.

KEYWORDS

High entropy alloys, Metal hydrides, Pair distribution function, Machine learning, Density
functional theory calculations
# 1. INTRODUCTION

Hydrogen is a versatile energy carrier that has the unique ability to connect various industries and support a more integrated energy system. It can be produced during periods of excess electricity generation, such as through electrolysis, stored for later use and then converted back into electricity during high-demand periods. This capability makes hydrogen valuable for long duration energy storage¹, particularly seasonal storage, where batteries suffer by self-discharge. However, the widespread adoption of hydrogen technologies remains constrained by the need for more efficient, cost effective, and sustainable solutions for its production, storage, and transportation. One of the key challenges is the storage and transportation of hydrogen.² Currently, the most common method for transport relies on storing it in high-pressure cylinders (typically 350 and 700 bar), but this remains expensive and falls short of future technical targets of both gravimetric and volumetric energy density. One promising solution, particularly in terms of volumetric energy density, is the solid-state storage and transportation of hydrogen in the chemically bound form. Among possible options, metal-hydrides (MH) are particularly promising, especially body-centred-cubic (bcc) alloys, which exhibit a high hydrogen per metal ratio (H/M).³ Among the cubic and hexagonal atomic packing arrangement, the bcc lattice has the most available interstitial sites. Thus, the bcc lattice can accommodate up to 2 H/M by transforming into a fcc structure with all tetrahedral interstitial sites occupied by hydrogen atoms.

Recent studies highlight the potential of bcc high-entropy alloys (HEAs) for hydrogen storage owing to their reversibility, favourable kinetics, and tuneable thermodynamics.¹,⁴⁻⁶ The widely accepted definition of HEAs describes them as solid solutions composed of at least five elements, each with a concentration ranging from 5 to 35 at. % and a mixing entropy ≥ 12.47 J/mol·K.⁷ Despite promising reports ⁷⁻⁹, these materials still have several drawbacks, including the formation
of stable hydrides (which require high temperature for hydrogen release) or insufficient hydrogen capacity. Efforts to destabilize high-entropy hydrides recognized that the addition of non-hydride forming elements generally results in more favourable thermodynamics. However, this is usually accompanied by a reduction in storage capacity.¹⁰⁻¹² Consequently, more pragmatic reports explore a trade-off between thermodynamics of the hydride phase and the hydrogen storage capacity in these materials.

Among many bcc HEAs reported, those containing Ti-V-Nb-Cr (Ti, V and Nb as metals with high affinity to hydrogen and Cr as a non-hydride forming element) have recently demonstrated promising properties for hydrogen storage, such as high capacities of up to 2 H/M.¹³,¹⁴ However, these benefits are often diminished due to too high thermodynamic stabilities of the respective hydrides (the enthalpy of hydride, ΔH<sub>abs</sub>, varies from -67 to -51.6 kJ/mol H<sub>2</sub>).¹² Increasing Cr content in TiVNbCr<sub>x</sub> can destabilize the hydride phase on the expense of capacity, especially for Cr contents exceeding 30-35 at. %.¹² One strategy to address this issue is to substitute small amounts of other non-hydride forming elements into the alloy, which can lead to further destabilization of the resulting hydride with limited loss in capacity only. For instance, efforts have been made to use elements such as Al¹⁵, Mo¹⁶ and Fe¹⁰. Each of these elements has demonstrated a destabilizing effect on the formed hydrides. However, adding new elements into these alloys introduces new challenges. For example, Al addition causes a significant decrease in the alloy's hydrogen capacity even at low concentrations (5-10 at. %)¹⁵, while the Fe addition leads to the formation of a secondary C14 Laves phase when its concentration exceeds 5 at. %, which also considerably reduces the alloy's hydrogen capacity¹⁰. Among the additional elements earlier proposed, Mo demonstrated relatively high solubility in TiVNb and TiVNbCr compositions without a significant tendency to form secondary phases¹⁷. Furthermore, Cheng et al.¹⁶ reported
promising results (around 2.2 wt. % reversible capacity and $ΔH_{abs}$ = -40 kJ/mol H₂) for a selection of Ti-V-Cr-Nb-Mo compositions (with maximum 6 at. % Mo content), making the Mo addition a particularly promising strategy to optimize HEAs performances. However, in this previous report absorption/desorption cycling has not been provided to confirm the stability of 2.2 wt.% reversible capacity over numerous cycles.

As discussed above, many studies have reported interesting results on HEAs containing refractory elements, but the compositional space is too large to be systematically investigated by common trial-and-error experimental methods.⁷,⁸ Therefore, the accelerated discovery of HEAs requires data-driven machine learning (ML) ¹⁸⁻²⁰ and/or first principles computational approaches to successfully target novel compositions in the vast compositional space with desired properties for hydrogen storage applications.¹⁰ Predictive ML methods are less computational expensive than *ab initio* modelling (DFT) approaches and are the preferred approach to identify the most effective compositions in terms of favourable thermodynamics and high capacity.¹⁰,¹²,¹⁷ In addition, ML methods not only help proposing novel interesting compositions but also emphasize trends and correlations between the numerous physicochemical descriptors and targeted properties of HEAs.¹⁰

In the present report, our approach is based on ML predictions in the Ti-V-Cr-Nb-Mo system followed by experimental and density functional theory (DFT) validations to investigate the impact of Cr substitution by Mo into (TiVNb)₈₀Cr₂₀-xMoₓ (x = 5, 10 and 15) and (TiVNb)₇₅Cr₂₅-xMoₓ (x = 5, 10, 15 and 20) alloys. This is a complete study based on ML predictions, DFT modelling and experimental validation loop to rationalize the effect of chemical substitution of Cr by Mo while keeping the ratio between Ti/V/Nb unchanged. The aim is twofold: to select the most promising composition with compromised but still advantageous performances for hydrogen storage in terms
of reversible capacity and cycle-life stability under ambient conditions, as well as to identify useful
correlations among relevant physicochemical descriptors (valence electron concentration, entropy
and enthalpy of mixing, Pauling electronegativity and unit cell volume of alloys) and targeted
performances (thermodynamics of hydride phase).

## 2. MATERIALS AND METHODS

**2.1. Alloy synthesis.** A total of seven novel alloys were prepared in the overall systems (TiVNb)₈₀Cr₂₀₋ₓMoₓ (x = 5, 10 and 15) and (TiVNb)₇₅Cr₂₅₋ₓMoₓ (x = 5, 10, 15 and 20) by electric arc-melting under Ar atmosphere (≈ 300 mbar). The samples were remelted around 10 times by flipping between each melting to achieve good homogeneity. High purity metals were used as feedstock materials: Ti (NEYCO titanium 99.99% pellets), V (NEYCO vanadium 99.9% pellets), Nb (NEYCO niobium 99.95% pellets), Cr (ChemPur chromium 99.99% pieces), Mo (NEYCO molybdenum 99.95% pellets). The total mass of each alloy sample was 3 g. The as-cast samples were cut by the help of a high-power precision saw (Buehler Isomet 4000), to ensure a flat surface for subsequent structural characterization.

**2.2. Laboratory X-ray diffraction.** The sample crystalline structures (as-cast alloys and powdered hydrides) were investigated by X-ray diffraction (XRD) using a D8 Advance Bruker diffractometer (Cu-Kα radiation λ = 1.5406 Å, Bragg-Brentano Geometry) in the 2θ range 20 - 90°. The XRD patterns were analysed using the fundamental parameters approach implemented in TOPAS Bruker software to calculate the lattice parameters and phase fractions.

**2.3. Synchrotron X-ray diffraction.** High-energy synchrotron X-ray diffraction (SR-XRD) measurements were carried out on the hydride phases at the Powder Diffraction and Total Scattering Beamline, P02.1, of PETRA III at Deutsches Elektronen-Synchrotron (DESY, Hamburg). High-resolution powder diffraction and total scattering data was collected
simultaneously, using a custom-made tandem detector setup consisting of two large area detectors, with a wavelength of 0.20737 Å.<sup>21,22</sup> Area detectors Varex (XRD 4343CT) and PerkinElmer (XRD1621) were used for the powder diffraction and total scattering measurements, respectively. The wavelength was refined using LaB<sub>6</sub> as a standard. Samples were packed in borosilicate capillaries with an inner diameter of 1.0 mm. G(r) profiles were obtained from the integrated patterns using pdfgetx3<sup>23</sup> with an upper Q-range cutoff (Q<sub>max-inst</sub>) at 22 Å<sup>-1</sup> and an r<sub>poly</sub> value set to 1.2 Å.<sup>23</sup> The structural analysis was carried out using the PDFgui free software.<sup>24</sup> The SR-XRD patterns were refined using the Rietveld method as implemented in the FullProf free software.<sup>25</sup>

**2.4. Scanning electron microscopy.** The microstructure was analysed by scanning electron microscopy (SEM) using a Zeiss Merlin instrument equipped with an EDS (energy-dispersive X-ray spectroscopy) detector. The samples, either in pieces or powdered form were placed in an epoxy resin, polished with various abrasive sizes (finally with 3 microns), and coated with a 1.5–2.5 nm Pd layer directly before the SEM analysis. For elemental analysis, an accelerated electron voltage of 10-15 keV was used and the element quantification was performed using Ti(K<sub>α1</sub>), V(K<sub>α1</sub>), Nb(L<sub>α1</sub>), Cr(K<sub>α1</sub>) and Mo(L<sub>α1</sub>) signals. The analyses were carried out for the as-cast, hydrogenated alloys and the materials after cycling.

**2.5. Hydrogen absorption and desorption measurements.** The hydrogenation process was carried out for all the alloys using a home-made Sieverts apparatus, which consisted of a manual manometric device with thermostatically calibrated volumes. The stainless-steel sample holder was filled with approximately 300 mg of the alloy, sealed using a metal gasket to prevent gas leakage and connected to the Sievert apparatus. Before starting the hydrogenation process, an activation procedure was carried out at 410 °C under vacuum (10<sup>-3</sup> mbar) for 3-10 hours. Three types of measurements were carried out: (1) absorption kinetics at 25 °C, (2) Pressure-
Composition-Isotherms (PCI) in a range of temperatures and (3) absorption/desorption cycling tests at 25 °C. For the absorption kinetics, the sample holder was placed in a water bath under H₂ pressure (~ 50-60 bar) and isothermal conditions (25 °C). For the acquisition of the PCIs, small H₂ doses were used up to maximum pressure of 100 bar while the temperature regulation was ensured by three different thermal devices: a refrigeration bath circulator (Huber CC-505) for temperatures below 25 °C, a thermostatic water bath for temperature slightly above ambient conditions (25-80 °C) or a furnace for higher temperature than 80 °C. The mass of the samples was measured before hydrogenation to calculate the storage capacity using the real gas state equation for H₂ from GASPAK Version 3.32 (Horizon Technologies). The cycling tests (2nd-20th cycles) were carried out under a final 35-40 bar H₂ pressure at 25 °C for the absorption step, while for desorption, the samples were exposed to dynamic vacuum at room temperature for 0.5-2 hours (until a base-level vacuum was achieved).

**2.6. Thermal desorption spectroscopy.** The hydrogen desorption properties from hydrogenated alloys were analysed by a home-made thermal desorption spectroscopy (TDS) using a quadrupole mass spectrometer (QMS). About 10 mg of the hydride sample was loaded into the sample holder each time and then connected to the QMS, working under secondary vacuum (10⁻⁶ mbar). The desorption profiles (partial pressures of released gases) were recorded by heating the sample at a constant rate of 5 °C/min up to 450 °C.

**2.7. Density functional theory (DFT) calculations.** Alloy structures with different Mo content in both *bcc* and *fcc* phases were generated with a supercell size of 3 × 3 × 3 (54 metal atoms) and 3 × 2 × 2 (48 metal atoms), respectively. For the hydride structures, only the *fcc* phase is calculated. All DFT calculations, including geometry relaxation and total energy calculations, were performed using the Vienna Ab initio Simulation Package ²⁶. For structure optimization, a plane-wave basis
set was used with a kinetic energy cutoff of 400 eV to expand the wave functions and used the Perdew-Burke-Ernzerhof (PBE) functional 27 with the projector augmented wave method 28,29 to solve the Kohn-Sham equations. A first-order Methfessel-Paxton smearing 30 with a width of 0.2 eV was used to improve the convergence of electronic self-consistent field calculations. A k-point mesh with a spacing of ca. 0.20 Å⁻¹ was used and the energy convergence threshold was set to 10⁻⁴ eV. Relaxation convergence was considered to be achieved for structural optimizations, including cell parameters and atomic positions, if the maximal forces felt by all atoms are less than 0.05 eV/Å.

To calculate the density of states (DoS) for both alloys and dihydrides, self-consistent field calculations were first conducted using a kinetic energy cutoff of 520 eV and an energy convergence threshold of 10⁻⁶ eV for the optimized geometry. The resulting charge densities were read, and DoS calculations were performed with 1500 bands. The tetrahedral holes in (TiVNb)₈₀Cr₅Mo₁₅ and (TiVNb)₇₅Cr₅Mo₂₀ were searched and identified as with or without Mo depending on whether the atoms locate at their vertices contains Mo. The *d*-orbital projected density of states for the vertices atoms for each tetrahedral site were extracted and the *d*-band centres (dbc) were calculated using the following equation: $dbc = \frac{\int \rho E dE}{\int \rho dE}$ where ρ is *d*-band density, E is the *d*-band energy, and ρdE is the number of states.
## 3. RESULTS AND DISCUSSION

### 3.1. Compositional ML model predictions

The ML-ready HydPARK database ³¹ (updated to v0.0.6 with recent literature data for close compositions) ⁷,¹⁵ was used to train/validate a gradient boosting tree regressor model for hydride thermodynamics ¹⁸,³² (see Section 1 in supplementary material). Magpie ³³ and custom properties derived solely from the nominal composition were used to generate feature vectors to represent each alloy composition, and to finally predict hydride thermodynamic properties of the Mo-substituted series (TiVNb)₇₅Cr₂₅₋ₓMoₓ and (TiVNb)₈₀Cr₂₀₋ₓMoₓ (0 < x < 20). The model predicts that increasing Mo content destabilizes the hydride phase by decreasing the enthalpy of hydride formation (ΔHₐbs), as shown in Figure 1a and listed in Table 1. For the Mo-substituted alloy predictions, Figure 1b summarizes the results of the model's Shapely Additive Prediction (SHAP) values ³⁴, i.e., the impact on the model's output (x-axis) attributed to each feature for a given prediction (scatter point). Only the top 4 most important features corresponding to composition-weighted averages of an elemental property, $\bar{p} = \sum_i x_i p_i$ ($x_i$ ≡ atomic fraction of element i, $p_i$ ≡ the elemental property) as quantified by the sum of absolute SHAP values, are shown in Figure 1b. These features include Magpie features: $r_c$ ≡ covalent radius, $T_m$ ≡ melting temperature, $\chi$ ≡ Pauling electronegativity and $\bar{v}_{pa}$ ≡ volume per atom in a crystal. Large variations in SHAP values of a given feature indicate a large impact on the predicted ΔHₐbs. SHAP values for only $\bar{\chi}$ and $\bar{v}_{pa}$ show variation > 1 kJ/molH₂, indicating that the model relies primarily on the change in the average electronegativity and the volume per atom to explain the increase in ΔHₐbs with increasing Mo substitution.
<figure><img src="image_4.png" /><figcaption>**Figure 1.** ML-predicted (a) absorption enthalpy and (b) SHAP values for the hydride enthalpy model.</figcaption></figure>

**3.2. HEAs synthesis and characterization**

To perform systematic experimental validation following the ML predictions of thermodynamic destabilization, the series $(\text{TiVNb})_{80}\text{Cr}_{20-x}\text{Mo}_x$ ($x = 5, 10$ and $15$) and $(\text{TiVNb})_{75}\text{Cr}_{25-x}\text{Mo}_x$ ($x = 5, 10, 15$ and $20$) were synthesized. Composition-derived parameters commonly used for HEAs such as, $\delta$ (mean square deviation of atomic size), $\Delta S_{\text{mix}}$ (mixing entropy), $\Delta H_{\text{mix}}$ (mixing enthalpy), $\Delta\chi$ (Pauling electronegativity mismatch) and VEC (valence electron concentration), are given in Table 1. The empirical guideline for substitutional solid solution formation in HEAs ($\delta < 6.6\%$)$^{35}$ is satisfied for all the compositions while bcc lattices are expected from the values of VEC being inferior to 5. Figure 2 shows the XRD of all compositions and the variation of the lattice parameters with Mo content in both series together with the DFT calculated lattice parameters.
<figure><img src="image_5.png" /><figcaption>**Figure 2.** XRD patterns of the as-synthesized $(\text{TiVNb})_{75}\text{Cr}_{25-x}\text{Mo}_x$ and $(\text{TiVNb})_{80}\text{Cr}_{20-x}\text{Mo}_x$ alloys with $x = 0-25$ (a); experimental lattice parameters $a_{bcc}$ as the function of Mo content (b), the values for $x = 0$ are shown as crossed diamonds and taken from references $^{12,17}$, the linear fits are guides for the eyes; DFT calculated lattice parameters of *bcc* phase $(\text{TiVNb})_{75}\text{Cr}_{25-x}\text{Mo}_x$ and $(\text{TiVNb})_{81.2}\text{Cr}_{18.8-x}\text{Mo}_x$ alloys, the values are an average of 100 configurations (c).</figcaption></figure>

All the alloys formed *bcc* solid solutions with *Im*3*m* space group (Figure 2a) without any detectable secondary phase which indicates high Mo solubility in the $(\text{TiVNb})_{100-x}\text{Cr}_x$ ($x = 20, 25$) compositions. Moreover, the $a_{bcc}$ lattice parameter linearly increases with Mo content (Figure 2b) which has a larger atomic radius compared to Cr ($r_{\text{Cr}} = 1.2491$ Å < $r_{\text{Mo}} = 1.3626$ Å)$^{35}$, in agreement with Vegard's law for substitutional solid solutions. Previously published lattice parameters for $(\text{TiVNb})_{100-x}\text{Cr}_x$ ($x = 20, 25$)$^{12}$ and TiVNbMo$^{17}$ are in excellent agreement with the present results.
Vegard's law is also observed in DFT-calculated average lattice parameters for *bcc* phase alloys with varying Mo content (Figure 2c), which is in good agreement with experiment (Figure 2b). The lattice parameters calculated by DFT are slightly smaller than the experimental results because these simulations are carried out at 0 K, whereas the experimental measurements are made at room temperature, where the thermal expansion contributes to the value of the lattice parameters. To account for random metal distributions in the alloys, 100 random configurations per composition were generated for $(TiVNb)_{81.2}Cr_{18.8-x}Mo_x$ and $(TiVNb)_{75}Cr_{25-x}Mo_x$, ensuring identical chemical compositions but differing metal distributions within the supercell used in DFT modeling. The small standard errors in the lattice parameters across these configurations indicate that the lattice parameter is largely insensitive to metal distribution.

The microstructure and chemical homogeneity of all as-synthesized alloys were verified by SEM-EDS. More details are given in section 2 in supplementary material (Figure S1, Table S1). No traces of secondary phase could be noticed in all as-synthesized alloys. The average chemical concentrations agree with the nominal values, irrespective of composition. Typical for refractory HEAs, dendritic/interdendritic microstructures are observed for all the samples, which can be attributed to the partitioning of high melting temperatures elements in the dendrites during the solidification process. This leads to slightly enriched dendrites in Nb and Mo, the highest melting point elements.
<table><caption>**Table 1.** Empirical physicochemical parameters (δ, VEC, ΔS<sub>mix</sub>, ΔH<sub>mix</sub> and Δχ), lattice type, crystalline lattice parameters (all the lattice parameters were fitted using the TOPAS software starting from the laboratory XRD data), storage capacity (as H/M and wt. %) and thermodynamic of hydrides formation (ΔH<sub>abs</sub> and ΔS<sub>abs</sub>); the main phase in multiphase materials is bolded.</caption><thead><tr><th rowspan="2">Composition</th><th rowspan="2">δ (%)</th><th rowspan="2">VEC</th><th rowspan="2">ΔS<sub>mix</sub> (J/mol·K)</th><th rowspan="2">ΔH<sub>mix</sub> (kJ/mol)</th><th rowspan="2">Δχ Pauling</th><th rowspan="2">Initial phase</th><th rowspan="2">a<sub>bcc</sub> (Å)</th><th rowspan="2">V<sub>bcc</sub>/Z (Å<sup>3</sup>)</th><th rowspan="2">Hydride phase</th><th rowspan="2">Phase fraction %</th><th rowspan="2">a<sub>fcc</sub> (Å) dihydride a<sub>bcc</sub> (Å) monohydride</th><th colspan="2">Max. H<sub>2</sub> capacity at 25°C</th><th rowspan="2">ΔH<sub>abs</sub> (ML) (kJ/molH<sub>2</sub>)</th><th rowspan="2">ΔH<sub>abs</sub> (exp) (kJ/molH<sub>2</sub>)</th><th rowspan="2">ΔS<sub>abs</sub> (exp) (J/K·molH<sub>2</sub>)</th><th rowspan="2">Ref.</th></tr><tr><th>H/M</th><th>wt. %</th></tr></thead><tbody><tr><td>TiVNb</td><td>4.4</td><td>4.7</td><td>9.13</td><td>-0.42</td><td>0.024</td><td>bcc</td><td>3.211</td><td>16.58</td><td>fcc</td><td>100</td><td>4.443</td><td>2.00</td><td>3.20</td><td>-58</td><td>-67</td><td>-157</td><td>11,17</td></tr><tr><td>(TiVNb)<sub>80</sub>Cr<sub>5</sub>Mo<sub>15</sub></td><td>4.65</td><td>4.93</td><td>12.23</td><td>-2.57</td><td>0.121</td><td>bcc</td><td>3.187(1)</td><td>16.19</td><td>fcc<br>bcc</td><td>94<br>6</td><td>4.410(1)<br>3.314(1)</td><td>1.91</td><td>2.80</td><td>-38.6</td><td>-39.2 (±2)</td><td>-128 (±4)</td><td>present</td></tr><tr><td>(TiVNb)<sub>80</sub>Cr<sub>10</sub>Mo<sub>10</sub></td><td>5.24</td><td>4.93</td><td>12.53</td><td>-2.94</td><td>0.105</td><td>bcc</td><td>3.171(1)</td><td>15.94</td><td>fcc</td><td>100</td><td>4.407(1)</td><td>1.97</td><td>2.98</td><td>-41.4</td><td>-42.4 (±1)</td><td>-129 (±1)</td><td>present</td></tr><tr><td>(TiVNb)<sub>80</sub>Cr<sub>15</sub>Mo<sub>5</sub></td><td>5.75</td><td>4.93</td><td>12.31</td><td>-3.28</td><td>0.076</td><td>bcc</td><td>3.165(1)</td><td>15.85</td><td>fcc</td><td>100</td><td>4.401(1)</td><td>1.97</td><td>3.09</td><td>-44.8</td><td>-50.6 (±1)</td><td>-143 (±2)</td><td>present</td></tr><tr><td>(TiVNb)<sub>80</sub>Cr<sub>20</sub></td><td>5.9</td><td>4.93</td><td>11.47</td><td>-3.70</td><td>0.027</td><td>bcc</td><td>3.156(3)</td><td>15.72</td><td>fcc</td><td>100</td><td>4.393(2)</td><td>1.93</td><td>3.13</td><td>-47.3</td><td>-54(5)</td><td>-149(9)</td><td>12</td></tr><tr><td>(TiVNb)<sub>75</sub>Mo<sub>25</sub></td><td>4.1</td><td>5.00</td><td>11.52</td><td>-2.65</td><td>0.141</td><td>bcc</td><td>3.189(1)</td><td>16.22</td><td>bcc<br>fcc</td><td>57<br>43</td><td>3.301(1)<br>4.405(1)</td><td>1.6</td><td>2.27</td><td>-</td><td>-27.3 (±6)</td><td>-117 (±21)</td><td>17</td></tr><tr><td>(TiVNb)<sub>75</sub>Cr<sub>5</sub>Mo<sub>20</sub></td><td>4.61</td><td>5.00</td><td>12.37</td><td>-2.84</td><td>0.132</td><td>bcc</td><td>3.183(1)</td><td>16.13</td><td>fcc<br>bcc</td><td>84<br>16</td><td>4.404(1)<br>3.303(1)</td><td>1.81</td><td>2.60</td><td>-38.0</td><td>-38.6 (±2)</td><td>-143 (±5)</td><td>present</td></tr><tr><td>(TiVNb)<sub>75</sub>Cr<sub>10</sub>Mo<sub>15</sub></td><td>5.19</td><td>5.00</td><td>12.79</td><td>-3.18</td><td>0.124</td><td>bcc</td><td>3.179(1)</td><td>16.07</td><td>fcc<br>bcc</td><td>88<br>12</td><td>4.397(1)<br>3.297(1)</td><td>1.89</td><td>2.80</td><td>-41.4</td><td>-41.1 (±2)</td><td>-140 (±6)</td><td>present</td></tr><tr><td>(TiVNb)<sub>75</sub>Cr<sub>15</sub>Mo<sub>10</sub></td><td>5.69</td><td>5.00</td><td>12.77</td><td>-3.51</td><td>0.097</td><td>bcc</td><td>3.160(1)</td><td>15.78</td><td>fcc<br>bcc</td><td>97<br>3</td><td>4.391(1)<br>3.277(1)</td><td>2.00</td><td>3.06</td><td>-41.3</td><td>-51.0 (±1)</td><td>-160 (±1)</td><td>present</td></tr><tr><td>(TiVNb)<sub>75</sub>Cr<sub>20</sub>Mo<sub>5</sub></td><td>6.13</td><td>5.00</td><td>12.54</td><td>-3.88</td><td>0.078</td><td>bcc</td><td>3.153(1)</td><td>15.67</td><td>fcc</td><td>100</td><td>4.385(1)</td><td>1.98</td><td>3.14</td><td>-43.1</td><td>-51.6 (±1)</td><td>-153 (±3)</td><td>present</td></tr><tr><td>(TiVNb)<sub>75</sub>Cr<sub>25</sub></td><td>6.11</td><td>5.00</td><td>11.53</td><td>-4.25</td><td>0.028</td><td>bcc</td><td>3.132(1)</td><td>15.36</td><td>fcc</td><td>100</td><td>4.378(2)</td><td>1.90</td><td>3.11</td><td>-47.0</td><td>-51.6</td><td>-129.3</td><td>12</td></tr></tbody></table>
### 3.3. Hydrogen absorption properties

As it was previously reported, TiVNbCr-based alloys absorb H₂ stepwise: first a solid solution of hydrogen in the alloy is formed (α-phase) with low hydrogen concentration; further absorption produces an intermediate phase (β-phase) called monohydride with a H/M ratio of about 1; full absorption leads to the formation of a dihydride phase (γ-phase) with the maximum 2 H/M.¹³,¹⁴

All the studied alloys rapidly absorb hydrogen at room temperature under 55 bar within less than 3 minutes (Figure S3 in section 3 of supplementary material). The SR-XRD patterns of the resulting hydrides are presented in Figure 3a. At low Mo concentrations (< 10 at. %), the hydrogenated materials are single-phase and exhibit an fcc lattice with $Fm\overline{3}m$ space group, in agreement with results previously reported for (TiVNb)₁₀₀-xCrx (x = 20, 25) alloys ¹⁴. However, as the Mo content increases (Mo > 10 at. %), the hydrogenated materials are multi-phased with an fcc lattice coexisting with a secondary bcc phase. The latter one can be attributed to the presence of a bcc-type monohydride, as demonstrated earlier.³⁶ This suggests the formation of unstable dihydride phases under STP conditions that spontaneously desorb hydrogen leading to coexistence of both dihydride and monohydride phases with increasing Mo content. As for the as-synthesized alloys, hydride lattice parameters (a<sub>fcc</sub>) increase with Mo content, which is in good agreement with previously published data for TiVNbMo ¹⁷ composition (Table 1).

The local structure of hydrogenated materials can be accessed from the analysis of PDF profiles shown in Figure 3b. Overall, all PDF profiles are similar with long-range structural correlations demonstrating good crystallinity of the hydrogenated materials. More details on PDF fitting and obtained results are given in section 4 of supplementary material. The fitting with PDFGui software is based either on a single fcc unit cell (for (TiVNb)₈₀Cr₁₅Mo₅, (TiVNb)₈₀Cr₁₀Mo₁₀ and (TiVNb)₇₅Cr₂₀Mo₅) or a mixture of bcc and fcc unit cells (for (TiVNb)₈₀Cr₅Mo₁₅,
(TiVNb)₇₅Cr₅Mo₂₀, (TiVNb)₇₅Cr₁₀Mo₁₅ and (TiVNb)₇₅Cr₁₅Mo₁₀), in agreement with SR-XRD data (Figure 3a). In the fitting unit cells, the atoms are randomly distributed in the unique crystallographic site of these lattices respecting the nominal compositions. The difference between the calculated PDF profiles and the experimental data is negligible (Figure S5) hinting to homogenous and random atoms distributions, irrespective of compositions and hydrogenated state (either bcc monohydride or fcc dihydride). Lattice parameters of both bcc and fcc lattices, along with the bcc phase fraction, increase with Mo content. Meanwhile, the isotropic atomic displacement (Uiso) and the parameter expressing experimental resolution effects, Qbroad (PDF peak broadening from increased intensity noise at high Q), are almost unchanged, within the error bars, and independent of composition (Table S2).

<figure><img src="image_6.png" /><figcaption>**Figure 3.** SR-XRD (λ=0.20737 Å) patterns (a) and related PDF profiles (b) of the (TiVNb)₈₀Cr₂₀-xMoₓ (x = 5, 10 and 15) and (TiVNb)₇₅Cr₂₅-xMoₓ (x = 5, 10, 15 and 20) hydrides from total X-ray scattering.</figcaption></figure>
Moreover, the compositions showing stable hydrides/deuterides (a total of 4 alloys: $(TiVNb)_{75}Cr_{25-x}Mo_x$ and $(TiVNb)_{80}Cr_{20-x}Mo_x$ with $x = 5$ and 10) have been studied by powder neutron diffraction to localize the deuterium atoms inside the fcc lattice. For more details see section 5 in supplementary material (Figure S6). As expected, the H/D atoms are found in the tetrahedral interstitial sites, in good agreement with previous results.$^{37}$

The maximum capacities of these alloys vary from 1.6 to 2.0 H/M or 2.2 to 3.3 wt. % (Table 1) and the gravimetric values are displayed in a ternary diagram in Figure 4. A marked decrease in capacity occurs when the Mo content exceeds 15 at.%.

<figure><img src="image_7.png" /></figure>

**Figure 4.** Ternary diagram of the maximum gravimetric capacity of $(TiVNb)_{80}Cr_{20-x}Mo_x$ ($x = 5, 10$ and 15) and $(TiVNb)_{75}Cr_{25-x}Mo_x$ ($x = 5, 10, 15$ and 20) alloys at 25 °C. Previously reported values were taken from the references $TiVNb^{11}$, $(TiVNb)_{80}Cr_{20}^{12}$, $(TiVNb)_{75}Cr_{25}^{12}$ and $TiVNbMo^{17}$.
### 3.4. Thermodynamics of high entropy hydride formation

As predicted by ML method (Figure 1a), a strong destabilization of the hydride phase is expected with increasing Mo content in both families of alloys. The results of the experimental absorption PCI measurements for all compositions are presented in Figures 5a and b for $(TiVNb)_{75}Cr_{25-x}Mo_x$ and $(TiVNb)_{80}Cr_{20-x}Mo_x$ series, respectively. More details are given in section 6 of supplementary material (Figures S7 and S8) including the PCI desorption curves and a comparison of absorption PCI curves in the series $(TiVNb)_{75}Cr_{25-x}Mo_x$ at 25 °C. Increasing the Mo content clearly destabilizes the dihydride phase, as evidenced by the rise in the equilibrium plateau pressures at the same temperature. Additionally, the equilibrium plateau becomes sloped with increasing Mo content, which complicates the use of the Van't Hoff approach to estimate the thermodynamic parameters for high Mo content compositions (Mo at. % ≥ 15). Despite this artifact, the Van't Hoff approach was applied to all compositions to evaluate the thermodynamics of hydride formation (Table 1). A summary of thermodynamic results is presented in the ternary diagram in Figure 6. A destabilization of dihydrides formation is thus evidenced experimentally by increasing Mo content: the greater the Mo content, the more destabilization can be achieved. The highest destabilization is observed in the $(TiVNb)_{75}Cr_5Mo_{20}$ composition where $\Delta H_{abs}$ changes from -67 kJ/mol for the ternary TiVNb alloy to -38.6 kJ/mol for $(TiVNb)_{75}Cr_5Mo_{20}$, with increasing sloped plateaus as Mo is added to this alloy.
<figure><img src="image_8.png" /><figcaption>**Figure 5.** The absorption PCI curves at several temperatures for (a) $(TiVNb)_{75}Cr_{25-x}Mo_x$ ($x$ = 5, 10, 15 and 20) and (b) $(TiVNb)_{80}Cr_{20-x}Mo_x$ ($x$ = 5, 10 and 15) alloys.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Figure 6.** Ternary diagram of the enthalpy of hydride formation in $(TiVNb)_{80}Cr_{20-x}Mo_x$ ($x$ = 5, 10 and 15) and $(TiVNb)_{75}Cr_{25-x}Mo_x$ ($x$ = 5, 10, 15 and 20) alloys.</figcaption></figure>
A comparison between the ternary diagrams of the capacity of the alloys (Figure 4) and their thermodynamics (Figure 6) allows to conclude that a compromise between compositions that demonstrate a high degree of hydride destabilization, an acceptable plateau slope, and a high hydrogen capacity must be searched for in this system.

### 3.5. DFT calculations

DFT calculations were conducted to gain insights into the hydride destabilization effect of Mo and corroborate the ML predictions. For each composition, four representative alloy configurations out of 100 are selected for hydrogenation: the one with the lowest formation energy, two with formation energy near the median value and the other with a high formation energy. All tetrahedral interstitial sites are identified and sorted ascendingly by the average electronegativity of the metal atoms at the vertices. Hydride structures with varying H/M ratios were generated by sequentially inserting hydrogen atoms to the sorted interstitial sites with a H-H distance constraint of ≥ 1.6 Å (the interstitial sites with an existing hydrogen atom within $d_{min}$ = 1.6 Å occupying its neighbour interstitial sites are skipped). The minimal H-H distance $d_{min}$ was chosen to be less than the Switendick criteria³⁸ while greater than experimentally measured exceptions to this rule³⁹. Once all the tetrahedral sites are exhausted, the same procedure is repeated for octahedral holes. The as-generated hydride structures were then relaxed. The hydrogenation enthalpy $\Delta H$ of a hydride configuration with N hydrogen atoms at 0 K can be calculated from the total energy of the hydride $E_{Hydride}$, the original alloy $E_{Alloy}$, and the gas-phase H₂ molecule, $E_{H₂}$:

$$ \Delta H = \frac{2}{N} E_{\text{Hydride}} - \frac{2}{N} E_{\text{Alloy}} - E_{\text{H}_2} \quad (\text{Eq. 1}) $$

The hydrogenation enthalpy of (TiVNb)₈₁.₂Cr₁₈.₈-xMoₓ and (TiVNb)₇₅Cr₂₅-xMoₓ, for H/M > 1, was calculated where the main hydride phase is the dihydride (γ) one. As shown in Figure 7, the absorption enthalpy of (TiVNb)₇₅Cr₂₅ is ca. 5 kJ/mol H₂ higher than that of (TiVNb)₈₁.₂Cr₁₈.₈,
which aligns with the experimental difference of 2.4 kJ/mol H₂. Both (TiVNb)₈₁.₂Cr₁₈.₈-xMoₓ and (TiVNb)₇₅Cr₂₅-xMoₓ exhibit an increasing trend in the absorption enthalpy with the increase of Mo content, showing a strong destabilization effect on the dihydride phase, which is in good agreement with ML prediction and experimental observations.

<figure><img src="image_10.png" /><figcaption>**Figure 7.** Average hydrogenation enthalpy of hydride structures obtained by DFT for (TiVNb)₈₁.₂Cr₁₈.₈-xMoₓ and (TiVNb)₇₅Cr₂₅-xMoₓ, four configurations (one with the lowest, two with medium and one with a high formation energy) were selected and their properties were averaged.</figcaption></figure>

To provide further insights on the destabilization effect of Mo on the dihydride phase, we calculated the average *d*-band centers of the metal atoms located at the vertices of tetrahedral interstitial sites in both (TiVNb)₈₀Cr₅Mo₁₅ and (TiVNb)₇₅Cr₅Mo₂₀. As shown in Figure 8, the average *d*-band centers for tetrahedral sites that include Mo are 1.19 and 1.13 eV above the Fermi level in (TiVNb)₈₀Cr₅Mo₁₅ and (TiVNb)₇₅Cr₅Mo₂₀, respectively. These values are 0.23 and 0.28 eV lower than those of tetrahedral sites without Mo. Tetrahedral sites with lower-lying *d*-band centers typically imply more occupied antibonding orbitals, which decrease the interactions between metal atoms and hydrogen and therefore weaker binding with hydrogen.⁴⁰,⁴¹ Thus, the incorporation of Mo tends to destabilize the corresponding hydrides.
<figure><img src="image_11.png" /></figure>

**Figure 8.** Projected density of states (pDoS) and average *d*-band centers for metal atoms at the vertices of tetrahedral interstitial sites (with and without Mo) in (TiVNb)₈₀Cr₅Mo₁₅ and (TiVNb)₇₅Cr₅Mo₂₀. The light blue and light red lines are *d* orbital pDoS and *d*-band centers for the metal atoms located at the vertices of individual tetrahedral sites, respectively, and the dark blue and dark red lines are the average values.

**3.6. Correlations between enthalpy of absorption and physicochemical factors**

Despite their simple crystalline structure, HEAs are complex materials, and their properties are affected by many entangled physicochemical factors. Thus, highlighting correlations among performances and simple physicochemical features are key to optimizing these materials. The SHAP analysis of ML predictions suggested that the enthalpies of hydrides in these alloys are mostly influenced by Pauling electronegativity and steric factors (Figure 1b). Based on the present experimental results and previous literature data ¹³,¹⁷, it is possible to highlight dependencies among the enthalpies of hydrides and most relevant physicochemical parameters such as, VEC, Δ*S*<sub>mix</sub>, Δ*H*<sub>mix</sub>, Δχ and V<sub>bcc</sub> (also listed in Table 1). Figure 9 presents the results of a multiple linear regression analysis (R² = 0.89) including a total of 22 compositions in the following families :
TiVNb ¹⁷, TiVNbAlₓ ¹⁷, TiVNbMoₓ ¹⁷, TiVNbCrₓ ⁴², TiVNbAlₓMoᵧ ¹⁷ and the present compositions.

<figure><img src="image_12.png" /><figcaption>**Figure 9.** The multiple regression results vs. experimental values of enthalpy of hydride formation in the family of alloys (TiVNb)Mₓ where M = Cr/Al/Mo/Al-Mo/Cr-Mo; additional data were taken from the earlier publications: (TiVNb)₁₀₀-xAlₓMoᵧ ¹⁷, (TiVNb)₁₀₀-xAlₓ ¹⁷, (TiVNb)₁₀₀-xMoₓ ¹⁷, (TiVNb)₁₀₀-xCrₓ ¹² and TiVNb ¹¹.</figcaption></figure>

The statistical analysis following the Prob>|t| value suggests two parameters with the most impact (values < 0.05) on the enthalpy of hydride: Δχ and ΔHmix. The destabilization of ΔHabs with the increase in Δχ is expected since it may be attributed to the less polar interaction of the Mo-H bond (Mo electronegativity is 2.16 and H one is 2.20 on Pauling scale) compared to the Cr-H bond (Cr electronegativity is 1.66) which makes the metal-H interaction weaker and, therefore, lowers the hydride phase stability. The correlation between ΔHabs and ΔHmix parameter translates Miedema's inverse stability rule ⁴³,⁴⁴, which predicts that more stable alloys form less stable hydrides and *vice versa*. Previously, Mo was demonstrated to stabilize bcc phase in Ti-Mo alloys.⁴⁵
Thus, it is expected that Mo addition in Ti-V-Nb-Cr compositions favours the formation of more stable alloys. Consequently, it can be reasonably expected that Mo destabilizes the hydride phases in agreement with Miedema's inverse stability rule.

The SHAP analysis also suggested that steric factor (volume) might be put forward to explain the thermodynamic change observed in these hydrides. This is in line with previous findings by ML approach applied on a large metal hydride data base that proposed a strong dependence of the metal hydride equilibrium H₂ pressure on the volume-based descriptor, $\bar{v}_{pa}$, that can be computed from just the elemental composition of the alloy.¹⁸ Recently, more complex correlations between hydrides performances and several empirical parameters were highlighted.⁷,¹⁷ For the (TiVNb)AlₓMoᵧ family, the strongest correlation with hydride's thermodynamic was shown by $\Delta\chi$ followed by $\Delta H_{mix}$ and $V_{bcc}/Z$. This places the volume-based descriptor on the third most relevant parameter for this series of alloys. In the present case, the multiple regression analysis based on experimental points excluded this feature as being important. This apparent contradiction can be understood by the fact that Mo substitution to Cr expands the initial bcc volume (Figure 2b), while steric factors are commonly invoked to explain thermodynamic destabilization in connection with an initial volume reduction: if the available interstitial volume diminishes, the required H₂ pressure to form a hydride phase increases. Thus, a decrease in the enthalpy of hydride formation is expected when a reduction of initial volume is noticed.

### 3.7. Reversibility and cycle-life properties

Other important properties of HEAs for their use in hydrogen storage are the cycle-life stability and reversibility of hydride formation at close to ambient conditions.⁴⁶ To verify the materials reversibility the TDS method was used by heating the hydride phases up to 450 °C under dynamic vacuum. During this analysis, the hydride material gradually desorbs hydrogen when heated at a
constant rate (Figure 10a). Accordingly, the more destabilized the hydride phase, the lower is the H₂ release temperature ($T_{onset}$) is expected to be. The experimental $T_{onset}$ decreases with increasing Mo content in both series of hydrides (Figure 10a), in line with the destabilization of the hydride phase. In addition, all desorbed materials revert to the initial *bcc* lattice, demonstrating good absorption-desorption reversibility (Figure 10b).

<figure><img src="image_13.png" /><figcaption>**Figure 10.** TDS curves for the (TiVNb)₈₀Cr₂₀-xMoₓ (x = 5, 10 and 15) and (TiVNb)₇₅Cr₂₅-xMoₓ (x = 5, 10, 15 and 20) hydrides recorded with 5 °C/min (a); XRD patterns of the desorbed materials after the TDS analysis (b).</figcaption></figure>

An in-depth investigation of the cycle-life stability was carried out only for 4 compositions: two alloys with maximum and minimum Mo contents have been chosen for each of the two series. Several absorption-desorption cycles were performed at 25 °C (absorption was done under 35-40 bar H₂ pressure and desorption was completed under dynamic primary vacuum). Thus, the present absorption ↔ desorption cycling concerns the phase transition *fcc* dihydride ↔ *bcc* monohydride under these conditions. Consequently, the gravimetric reversible capacity is smaller than the
maximum uptake reported in Table 1. The variations of the gravimetric reversible H₂ capacity during 20 cycles for the four selected compositions are presented in Figure 11a. The reversible capacity varies between 1.7 and 1.1 wt. % depending on the composition and number of cycles. The (TiVNb)₇₅Cr₂₀Mo₅ alloy shows the highest value of reversible capacity with 1.7 and 1.58 wt. % initial and final values, respectively. The next most elevated reversible capacity belongs to (TiVNb)₇₅Cr₅Mo₂₀, 1.43 wt. %, with good stability and negligible loss over 20 cycles. The capacity of (TiVNb)₈₀Cr₅Mo₁₅ varies between 1.4 wt. % to 1.33 wt. %, while (TiVNb)₈₀Cr₁₅Mo₅ shows a change between 1.38 wt. % to 1.12 wt. % during cycling. Among the four alloys, a capacity loss of 21, 9, 5 and almost 0 % is noticed between the first and last cycles for the (TiVNb)₈₀Cr₁₅Mo₅, (TiVNb)₇₅Cr₂₀Mo₅, (TiVNb)₈₀Cr₅Mo₁₅ and (TiVNb)₇₅Cr₅Mo₂₀ compositions, respectively. This finding might be related to the corresponding enthalpies of hydride phase that varies as follows, -50.6, -51.6, -39.2 and -38.6 kJ/mol H₂ (Table 1), for the above-mentioned series of alloys, suggesting that more destabilized hydride phases possess improved cycle-life stability albeit with reduced capacity.

<figure><img src="image_14.png" /><figcaption>**Figure 11.** The capacity variation during 20 absorption/desorption cycles at 25 °C for the (TiVNb)₈₀Cr₂₀-xMoₓ (x = 5 and 15) and (TiVNb)₇₅Cr₂₅-xMoₓ (x = 5 and 20) alloys (a) and XRD</figcaption></figure>
patterns of desorbed materials after 20 cycles under the vacuum at 25 °C (b); The *bcc* and *fcc* phases are marked with asterisk and triangle symbols, respectively.

To clarify this result, XRD experiments were carried out on the cycled materials desorbed under a primary dynamic vacuum at room temperature (Figure 11b). The desorbed samples exhibit mainly a *bcc* phase, as expected, with the presence of a secondary *fcc* phase with different degrees of intensity. The (TiVNb)₇₅Cr₂₀Mo₅ and (TiVNb)₈₀Cr₅Mo₁₅ compositions have only traces of secondary *fcc* hydride phases while (TiVNb)₈₀Cr₁₅Mo₅ clearly shows the coexistence of both *bcc* and *fcc* phases. This hints that the poor cycle-life stability of these three compositions can be explained by uncomplete hydride desorption, i.e. too stable thermodynamic of hydride phase and/or slow kinetics under these conditions. One notable exception is again the (TiVNb)₇₅Cr₅Mo₂₀ alloy that demonstrates a *bcc* single-phase after desorption, which might clarify the excellent cycle-life stability of this composition.

Another interesting feature from XRD patterns is the observation of smaller width of the diffraction peaks for the two highest Mo content alloys, (TiVNb)₈₀Cr₅Mo₁₅ and (TiVNb)₇₅Cr₅Mo₂₀ (the two compositions with minimum loss during cycling: 5 and ~0 wt. %) as compared to the other alloys showing rather large diffraction peaks. This suggests that preserving the crystallinity of the materials during cycling is key to maintaining their cycle-life stability.

Sections 7 and 8 in supplementary material contain more details, such as kinetics (Figure S9), structural (Figures S11-S14) and microstructural (Table S3, Figure S10) information related to cycling tests. Interestingly, when the desorption is performed at high temperature (410 °C under vacuum), all materials revert to a single-phase *bcc*-type lattice, demonstrating excellent reversibility after 20 cycles. All samples demonstrated fast absorption kinetics without obvious
kinetic degradation during cycling and 90 % of the capacity was reached in a few seconds,
irrespective of composition. The microstructure analysis of the desorbed alloys (SEM images)
reveals an expected decrepitation of initial bulk pieces into powder-like materials, while the
elemental compositions (SEM-EDS) are unchanged after cycling, irrespective of composition.

In the complex HEA systems, a compromise must be found between hydride destabilization,
acceptable plateau slope and high hydrogen capacity. Cycling experiments highlighted another
trade-off between high reversible capacity, excellent cycle life and crystalline stabilities, to
consider when selecting a promising composition. Therefore, we propose here that the most
promising alloy with interplay properties within the targeted compositional space is
(TiVNb)₇₅Cr₅Mo₂₀. This single-phase bcc alloy possesses a high maximum capacity of 2.6 wt. %
(1.8 H/M), a reasonable enthalpy of hydride formation of -38.6 kJ/mol H₂ and a notable reversible
capacity of 1.42 wt. % at room temperature.

4. CONCLUSIONS

A screening of the most promising compositions in the (TiVNb)₁₀₀-x(Cr,Mo)ₓ (x = 20 and 25) HEA system was performed by ML predictions, followed by experimental and DFT validations.

This study examined the effect of substituting Cr with Mo in two alloy series: (TiVNb)₈₀Cr₂₀-xMoₓ (x = 5, 10 and 15) and (TiVNb)₇₅Cr₂₅-xMoₓ (x = 5, 10, 15 and 20). The ML approach predicted a destabilization of the dihydride phases with increasing Mo content and identified average electronegativity as the most impactful parameter influencing the thermodynamic properties. All alloys are single-phased bcc latices and absorb hydrogen rapidly forming fcc-type hydrides with high capacity between 1.6 and 2.0 H/M (see Table 1 and Figure S15). Increasing the Mo content in these alloys has a negative effect on the maximum capacity, but at the same time has a positive effect on the thermodynamic properties of the hydride, in agreement with the ML predictions and
DFT simulations. It is therefore clear that a compromise must be found in this HEA compositional
space to select the alloy with the most interesting properties for hydrogen storage. In addition, a
multiple regression analysis of several experimental points suggested two most influential
parameters: the electronegativity mismatch, consistent with ML correlations, and the alloy mixing
enthalpy, consistent with Miedema's inverse stability rule.

The cycling experiments highlighted the need to balance the reversible capacity, cycle-life, and crystalline stabilities of HEA phases. Therefore, considering all these results, the most promising alloy with a balanced set of properties within the targeted compositional space is $(TiVNb)_{75}Cr_{5}Mo_{20}$ that shows promising hydrogen storage properties, including a maximum capacity of 2.6 wt. % (1.8 H/M), a reasonable enthalpy of hydride formation (-38.6 kJ/mol $H_{2}$), and a notable gravimetric reversible capacity of 1.42 wt. % at room temperature. The integrated approach based on ML prediction followed by experimental and DFT validations presents an effective strategy for identifying the most promising compositions for hydrogen storage in the vast compositional space of high entropy alloys.

**Supporting Information**

Section 1: machine learning details and validation;

Section 2: SEM-EDS results;

Section 3: absorption kinetics;

Section 4: PDF results;

Section 5: neutron diffraction studies;

Section 6: Pressure-Composition-Isotherms results;
Section 7: cycling tests;

Section 8: SEM-EDS and XRD results after cycling;

Section 9: ternary diagram of the hydrogen storage capacity (H/M).

**Corresponding author**

claudia.zlotea@cnrs.fr

**Author Contributions**

The manuscript was written through contributions of all authors. All authors have given approval
to the final version of the manuscript.

**Funding Sources**

AA, NPR and CZ acknowledge the French National Research Agency (ANR) for funding support
under France 2030 program, project reference ANR-22-PEHY-0007. VE and MS also want to
acknowledge funding for part of this research from ÅForsk (grant number 22-29). Work at the
University of Nottingham is supported by EPSRC (EP/V042556/1) and Leverhulme Trust (Grant
No. LIP-2021-018). The authors acknowledge the use of the ARCHER2 supercomputer through
membership of the UK's HPC Materials Chemistry Consortium, which is funded by EPSRC
(EP/X035859/1).

**ACKNOWLEDGMENT**

Valérie Lalanne, Fabrice Couturas, Olivier Rouleau and Rémy Pires Brazuna from ICMPE
(Institut de Chimie et des Matériaux Paris-Est, UMR 7182 CNRS-UPEC, Thiais, France) are
acknowledged for their help with hydrogenation, arc-melting, XRD, SEM-EDX experiments,
respectively. AA, NPR and CZ thank Faye Greaves from ICMPE and Laetitia Laversenne from
Institut Néel for help with neutron diffraction experiments and the ILL for the beam time
(http://doi.ill.fr/10.5291/ILL-DATA.5-22-832).

We acknowledge DESY (Hamburg, Germany), a member of the Helmholtz Association HGF,
for the provision of experimental facilities. Parts of this research were carried out at PETRA III
using the P02.1 beamline. Beamtime was allocated for proposal I-20231067.

Sandia National Laboratories is a multimission laboratory managed and operated by National
Technology \& Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell
International Inc., for the U.S. Department of Energy's National Nuclear Security Administration
(DOE/NNSA) under contract DE-NA0003525. This written work is authored by an employee of
NTESS. The employee, not NTESS, owns the right, title and interest in and to the written work
and is responsible for its contents. Any subjective views or opinions that might be expressed in the
written work do not necessarily represent the views of the U.S. Government. The publisher
acknowledges that the U.S. Government retains a non-exclusive, paid-up, irrevocable, world-wide
license to publish or reproduce the published form of this written work or allow others to do so,
for U.S. Government purposes. The DOE will provide public access to results of federally
sponsored research in accordance with the DOE Public Access Plan.
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