Tuning hydride stability in TiVZrNb high-entropy hydrogen storage alloys via alloy-hydrogen electronegativity difference

Sample preparation

The raw materials selected for this work (Ti, V, Zr, Nb) were small metal ingots, each with a purity better than 99.99 wt.% and purchased from Hebei Ancai New Material Technology Co., Ltd., China. Under an argon-protected atmosphere (99.999%, Linde Gas, China), a series of alloys with different compositions was prepared using the non-consumable vacuum arc melting method (SKY08K-102, Shenyang Scientific Instrument Research Center Co., Ltd., Chinese Academy of Sciences, China). To ensure compositional homogeneity, each ingot underwent at least four cycles of inversion and remelting. Subsequently, the as-cast alloy ingots were vacuum-sealed in quartz tubes, annealed at 1473 K for 2 h, and then water-quenched to obtain a uniform microstructure. The alloys are designated as HEA-1 to HEA-8 in descending order of their electronegativity difference. The physical parameters of the elements used in the calculations in this paper are shown in Supplementary Table 1^[32].

Microstructural characterization

The heat-treated samples were cut into 5 mm × 5 mm × 3 mm specimens, and the test surfaces were polished with sandpaper to remove the oxide layer. The crystal structure and lattice parameters of the alloy were analyzed using an X-ray diffractometer (Rigaku SmartLab SE, Cu Kα radiation, Japan) with a 2θ range of 20-90°. These XRD patterns were mainly used for phase identification and comparison of the overall phase constitution. For lattice-constant refinement of HEA-1 to HEA-8, additional XRD patterns were collected at a slower scan rate of 2°/min. The diffraction data collected at 2°/min were refined using GSAS-II software with Rietveld refinement, incorporating instrument parameters, lattice constants, and preferred orientations. The XRD patterns of the hydrogenated samples with different hydrogen contents were also collected at a scan rate of 2°/min. To further characterize the microstructure and composition distribution, the heat-treated specimens were hot-embedded and polished to a mirror finish. Subsequently, observation and analysis were performed using a scanning electron microscope (Sigma 300 Carl Zeiss Microscopy GmbH, Germany) equipped with an energy-dispersive spectrometer (EDS, Oxford Instruments, United Kingdom). Imaging employed a backscattered electron (BSE) detector at 20 kV acceleration voltage, 15 spot size, and 10 mm working distance to clearly reveal grains and grain boundaries.

Hydrogen storage measurements

The heat-treated samples were cut into 4 mm × 4 mm × 4 mm specimens and polished with sandpaper to remove the oxide layer, preparing them for subsequent hydrogen storage performance testing. High-purity H₂ gas (99.999%, Linde Gas, China) was used for all hydrogen absorption/desorption and pressure-composition isotherm (PCT) measurements. Alloy activation, hydrogen absorption/desorption kinetics, and PCT tests were conducted using a fully automated Sieverts-type apparatus (H2PCT-22101, GASTOUCH, Yangzhou University, China). The hydrogen uptake/release amount was calculated from the pressure-volume-temperature data obtained using the Sieverts-type apparatus. To improve the accuracy of the hydrogen capacity calculation, the system’s dead volume was calibrated before measurement, and the amount of hydrogen gas was calculated using the real-gas equation n = PV/(ZRT), where Z is the compressibility factor of hydrogen at the corresponding temperature and pressure. The specific experimental procedure is as follows: First, approximately 1.0 g of alloy sample was used for each PCT measurement. The sample was weighed and dynamically evacuated at 673 K for 2 h under a dynamic vacuum level of 10^-4 MPa (approximately 100 Pa) for activation. After cooling to 303 K, the initial hydrogen-uptake kinetics test was conducted at 5 MPa hydrogen pressure. Following hydrogen uptake, the sample was heated to 773 K for high-temperature dehydrogenation to prepare for subsequent PCT testing at different temperatures. To eliminate residual hydrogen effects on test results, the high-temperature dehydrogenation step was repeated before each PCT test. Due to significant variations in plateau pressure among different alloy samples and the difficulty of hydrogen desorption below 0.001 MPa, the PCT test temperature was controlled to maintain the hydrogen absorption/desorption plateau pressure within approximately 0.001-10 MPa for each sample, ensuring a complete PCT curve (actual test temperature was determined by the plateau region temperature due to potential fluctuations during testing). Additionally, a thermal desorption spectrometer (TDS: G8 GALILEO, Bruker, AXS GmbH, Germany) was used to perform programmed-temperature desorption tests on samples after the initial hydrogen-uptake kinetics. For each TDS measurement, approximately 0.1 g of hydrogenated sample was used according to the standard sample-mass requirement of the instrument. The heating rates were set at 5 K/min, 10 K/min, 15 K/min, and 20 K/min to analyze their hydrogen desorption behavior.

Alloy composition design based on the control of the electronegativity difference

The primary issue facing TiVZrNb-based hydrogen-storage HEAs is excessively high hydrogen-release temperatures, a problem fundamentally caused by the alloy’s hydrides’ high stability^[33]. Therefore, effectively regulating the thermodynamic behavior of hydrogen release is crucial for the practical application of these alloys. In hydrogen-storage HEAs, the equilibrium pressure for hydrogen absorption and desorption is a key parameter that describes the thermodynamic properties of hydrogen desorption. It is typically obtained by testing PCT curves at different temperatures. At a given temperature, a higher equilibrium pressure for hydrogen absorption and desorption indicates that the alloy is more difficult to hydrate and that the hydride is more prone to decomposition. However, for alloys with significant differences in hydrogen release thermodynamics, it is difficult to directly compare equilibrium pressures at the same temperature. Therefore, the relationship between temperature and decomposition pressure is typically derived by fitting the Van’t Hoff equation to equilibrium pressure data at different temperatures, which is then used to calculate the reaction entropy and enthalpy of hydride formation^[34]. The Van’t Hoff equation is given in^[22]:

where P is the equilibrium pressure for hydrogen absorption/desorption, T is the test temperature, R is the ideal gas constant [8.314 J/(mol·K)], and ΔS and ΔH are the reaction entropy and reaction enthalpy of the corresponding hydrogen absorption or desorption process, respectively. A larger absolute value of ΔH indicates that the hydride is more stable and that the energy required for dehydrogenation is higher. Therefore, ΔH can accurately reflect the thermodynamic performance of the alloy during hydrogen desorption. However, determining ΔH typically relies on lengthy PCT testing or complex theoretical calculations. Therefore, it is necessary to identify empirical parameters that predict thermodynamic trends in hydrogen release as a function of alloy composition to guide the design of hydrogen-storage HEAs with a BCC structure.

Previous studies have shown that several key parameters of high-entropy alloys, such as electronegativity difference^[21], VEC^[35], lattice constants^[21], and lattice distortion (δ)^[36], are closely related to their thermodynamic properties of hydrogen release. Among these, the average electronegativity difference between the alloy and hydrogen can be used to describe the average electronic interaction between them. EDV_alloy can be calculated using^[21]:

where c_i is the concentration of element i in the alloy, and EV_i and EV_H are the Pauling electronegativities of element i and hydrogen, respectively. Since the electronegativities of the elements in this study are all lower than that of hydrogen, a larger EDV_alloy value indicates a greater average electronegativity difference between the alloy and hydrogen. VEC is the average valence electron count of each element, calculated as follows^[35]:

The lattice distortion (δ) is calculated as given in^[36]:

where r_i is the atomic radius of element i, and is the average atomic radius. To investigate the relationship between the above parameters and the thermodynamics of hydrogen release, this section performs a statistical analysis of 14 hydrogen-storage HEAs previously reported by our research group. The selection criteria are as follows: (1) The alloy must have a single-phase BCC structure to eliminate the interference of multi-phase structures on the thermodynamics of hydrogen release; (2) Alloys previously reported by our research group were selected to ensure consistency in preparation processes and testing conditions, thereby reducing the impact of experimental errors on the correlation of parameters.

Based on the above selection criteria, the compiled data were plotted with the key parameters on the x-axis and the thermodynamic parameter ΔH_des on the y-axis. Linear fitting was then performed to quantitatively assess the correlations between different descriptors and ΔH_des; the results are shown in Figure 1. In Figure 1A, no clear pattern is observed in the variation of ΔH_des with lattice parameters. Figure 1B shows that lattice distortion exhibits a relatively weak correlation with ΔH_des compared with VEC and EDV_alloy. This indicates that lattice parameters or lattice distortion cannot accurately describe the thermodynamic changes in hydrogen release for these alloys. Figure 1D shows that ΔH_des decreases with increasing VEC. This suggests that a higher VEC reduces hydride stability to some extent, a trend consistent with the findings of Nygård et al.^[20]. However, for some alloys, such as 3, 6, 7, and 8, the VEC values are all 5.1, yet the measured ΔH_des values differ significantly; similarly, alloys 9 and 13 both have a VEC of 5.25, yet their ΔH_des values differ. This indicates that a single global VEC parameter is insufficient to fully describe the thermodynamic differences in hydrogen release among alloys. This is because VEC is essentially the component-weighted average of the total valence-electron counts of the alloy’s elements, primarily reflecting the alloy’s overall average electron concentration. For hydrogen storage HEAs, even if different alloys have the same or similar global VEC values, their local chemical environments and d-orbital distributions may still differ significantly. Particularly in transition metal hydrides, the hybridization between the H 1s state and the metal d states has a significant impact on the M-H bond strength. In contrast, the global VEC struggles to distinguish the contributions of localized d states from different elements to hydrogen-occupancy stability^[21,29,37]. Therefore, relying solely on the global VEC makes it difficult to accurately describe the thermodynamics of hydrogen release in alloys.

Figure 1. Correlation between the ΔH_des of single-phase BCC alloys reported in the literature and (A) lattice constants, (B) δ, (C) corresponding alloy composition, (D) VEC, and (E) EDV_alloy; (F) design strategy. The linear fitting results, including R² and P-values, are shown in the corresponding panels. VEC: Valence electron concentration; ΔH_des: desorption enthalpy; EDV_alloy: electronegativity difference value of the alloy; HEA: high-entropy alloy; δ: lattice distortion; BCC: body-centered cubic.

In contrast, as shown in Figure 1E, ΔH_des increases almost monotonically with EDV_alloy and exhibits a higher correlation with the fitting than with the lattice constant, δ, and VEC. This quantitative comparison further indicates that EDV_alloy is more effective than the other descriptors in explaining alloys with similar VEC values but different hydride stability. The underlying physical mechanism can be explained in terms of charge transfer and M-H bonding: during hydrogen absorption and desorption, hydrogen interacts electronically with surrounding metal atoms, leading to partial charge transfer from the metal to hydrogen and the formation of M-H bonds that exhibit both ionic and covalent character. The greater the EDV_alloy, the stronger the driving force for electron transfer from the metal to hydrogen, the stronger the average M-H interaction, and the more stable the hydride; conversely, a smaller EDV_alloy indicates that the alloy’s average electronegativity is closer to that of hydrogen, weakening the driving force for electron transfer from the metal to hydrogen and reducing the average M-H bond strength, thereby promoting hydride destabilization^[21,38,39]. Furthermore, hydrogen has an electronegativity of 2.2, while transition metals generally have electronegativities lower than 2.2; even among elements with the same VEC (such as V and Nb, both with VEC = 5), there are subtle differences in electronegativity^[40]. Therefore, EDV_alloy can serve as an effective empirical parameter for describing the thermodynamic trends in hydrogen release in BCC hydrogen-storage HEAs. The phase structures, key parameters, and ΔH_des values of the 14 compiled alloys are summarized in Table 1.

Based on the above analysis, thermodynamic control of BCC hydrogen storage HEAs in the TiVZrNb system was further conducted using EDV_alloy composition design parameters. The design objective was to moderately reduce the stability of alloy hydrides while maintaining a single-phase BCC structure and high hydrogen storage capacity, thereby improving hydrogen release performance. In the TiVZrNb quaternary system, the Pauling electronegativities of the elements are, in order: Zr = 1.33, Ti = 1.54, Nb = 1.60, and V = 1.63, all of which are lower than the electronegativity of H (2.20). Among these elements, Zr and Ti have relatively lower electronegativities and therefore contribute to a larger average electronegativity difference between the alloy and H. In contrast, Nb and V have relatively higher electronegativities, and increasing the Nb content raises the alloy’s average electronegativity and reduces EDV_alloy [Figure 1F]. Therefore, this study employs a method to reduce the Ti/Zr content and increase the Nb content, thereby continuously regulating the EDV_alloy composition_. Concurrently, the V content was fixed at 30 at. % in all alloys to minimize the impact of V content variations on the stability of the BCC phase and hydrogen storage capacity. The specific compositions and key parameters are shown in Table 2. As the Ti and Zr contents decrease, the alloy’s electronegativity difference gradually decreases; it is anticipated that the stability of the alloy hydrides will consequently weaken, thereby improving hydrogen desorption performance. Since the second phase significantly affects the hydrogen storage plateau and thermodynamic parameters - for example, the C14 Laves phase, Zr-rich phase, or other intermetallic compounds may introduce additional hydrogen absorption and desorption reaction processes - this study first requires the designed alloys to possess a stable single-phase BCC region during the composition design stage. To this end, the TCHEA6 database in Thermo-Calc software was used to predict the equilibrium phase compositions of HEA-1 to HEA-8. The calculation results are shown in Figure 2, indicating that all alloys exhibit a wide single-phase BCC temperature range near 1,473 K. Therefore, in this study, the as-cast alloys were subjected to homogenization annealing at 1,473 K followed by water quenching to obtain a single-phase BCC solid solution with uniform composition, thereby eliminating the interference of the second phase on the subsequent thermodynamic analysis of hydrogen release and further verifying the regulatory effect of EDV_alloy on the thermodynamics of hydrogen release in TiVZrNb BCC hydrogen-storage HEAs.

Figure 2. Phase diagrams for HEA-1 to HEA-8 alloys calculated using Thermo-Calc software: (A) HEA-1, (B) HEA-2, (C) HEA-3, (D) HEA-4, (E) HEA-5, (F) HEA-6, (G) HEA-7, and (H) HEA-8. BCC_B2#1 and BCC_B2#2 denote two distinct composition sets of the BCC/B2 thermodynamic phase model generated by Thermo-Calc; HCP_A3 denotes the hexagonal close-packed solid-solution phase; and LIQUID denotes the liquid phase. BCC: Body-centered cubic; HCP: hexagonal close-packed; HEA: high-entropy alloy.

Phase structure and microstructure

Figure 3 and Supplementary Figures 1 and 2 show the X-ray diffraction (XRD) spectrum of alloys HEA-1 to HEA-8. As shown in the Figure 3A, all alloys exhibit only characteristic diffraction peaks of the BCC structure. The peaks at approximately 2θ = 40°, 56°, and 71° correspond to the (110), (200), and (211) crystal planes of the BCC structure, respectively; no diffraction peaks from a second phase were observed. The lattice parameters of the alloys were refined using the Rietveld method with GSAS-II software, and the results are listed in Supplementary Table 2. As the Nb content increased, and the Zr and Ti contents decreased, the lattice parameter a of the alloy decreased from 3.2594 Å to 3.2458 Å. This is because Nb partially substitutes for Zr and Ti, and the atomic radius of Nb (1.429 Å) is smaller than that of Zr (1.603 Å) and Ti (1.462 Å), resulting in a decrease in the average atomic radius of the alloy and a more compact lattice packing, thereby reducing the lattice parameters.

Figure 3. (A) XRD patterns of HEA-1 to HEA-8 collected at a scan rate of 2°/min; (B) corresponding lattice parameters obtained by GSAS-II refinement. Error bars in (B) represent the standard uncertainties obtained from GSAS-II refinement. BCC: Body-centered cubic; HEA: high-entropy alloy; XRD: X-ray diffraction; GSAS-II: General Structure Analysis System II.

To further characterize the microstructure of the alloys, BSE and energy-dispersive X-ray spectroscopy (EDS) analyses were performed on the heat-treated alloys; the results are shown in Figure 4. The microstructure of all alloys (HEA-1 to HEA-8) exhibited an approximately equiaxed grain structure. Due to differences in crystal orientation between grains, distinct contrast differences were observed in the backscattered electron images, allowing for clear identification of grain boundaries. No second phase was detected, further confirming that the alloys have a single-phase BCC structure, consistent with the XRD results. The corresponding EDS results [Figure 4A’-H’] show that various elements are uniformly distributed within the alloys, with no regional compositional segregation observed. Furthermore, the alloy compositions determined by EDS are nearly consistent with the designed nominal values. Higher-magnification BSE images and the corresponding EDS elemental maps of HEA-1 to HEA-8 are shown in Supplementary Figure 3, and EDS line-scan results of the representative HEA-8 alloy across the grain boundary and grain interior regions are shown in Supplementary Figure 4. These results show no obvious secondary phase contrast or elemental enrichment/depletion at the SEM-EDS detection scale, further supporting the chemical homogeneity of the alloys.

Figure 4. The BSE images (A-H) and the corresponding EDS maps (A’-H’) of HEA-1 to HEA-8 alloys. HEA: High-entropy alloy; BSE: backscattered electron; EDS: energy-dispersive X-ray spectroscopy.

Hydrogen absorption kinetics

To investigate the alloy’s hydrogen storage capacity, hydrogen absorption kinetics tests were conducted on heat-treated samples. Figure 5 shows the hydrogen absorption kinetics curves for the activated samples at 303 K and 5 MPa hydrogen pressure. As shown in the figure, all samples exhibited rapid hydrogen absorption kinetics, reaching their saturated hydrogen storage capacity within 150 s. Among them, HEA-8 demonstrated the most outstanding hydrogen absorption kinetics, reaching its saturated hydrogen storage capacity in just 75 s. It is worth noting that no significant correlation was observed between hydrogen absorption kinetics and the electronegativity difference, indicating that, within the composition range studied, reducing the EDV_alloy did not have a significant adverse effect on the alloy’s rapid hydrogen absorption behavior. Although some fluctuations were observed among the intermediate alloys, the gravimetric hydrogen storage capacity showed an overall decreasing trend from 3.12 wt.% for HEA-1 to 2.86 wt.% for HEA-8 as EDV_alloy decreased. This trend is primarily attributed to differences in the relative atomic masses of the elements. When the mass hydrogen storage capacity is converted to the hydrogen-to-metal atomic ratio (H/M), the H/M values for HEA-1 to HEA-8 were 2.00, 2.01, 2.01, 2.01, 2.02, 2.01, 2.02, and 2.02, respectively. The repeated initial hydrogen absorption measurements used to calculate the standard deviations of the H/M values in Figure 5B are shown in Supplementary Figure 5. These values are significantly higher than the H/M value (1.75) reported by Montero et al.^[16] for the Ti_0.325V_0.275Zr_0.125Nb_0.275 alloy, reaching the theoretical maximum H/M value for high-entropy alloys with a BCC structure, indicating that the optimized alloys in this series possess excellent hydrogen storage capacity.

Figure 5. (A) Initial hydrogen absorption kinetics curves for activated alloys HEA-1 to HEA-8 at 303 K and 5 MPa hydrogen pressure, along with (B) their mass hydrogen storage capacity and H/M values. Error bars in (B) represent the standard deviations obtained from repeated Sievert measurements (n = 3 for HEA-1-HEA-5 and n = 2 for HEA-6-HEA-8). HEA: High-entropy alloy; H/M: hydrogen-to-metal atom ratio.

Hydrogen storage thermodynamics

To further investigate the thermodynamic properties of the alloy, PCT curves were measured at various temperatures [Figure 6] to verify whether EDV_alloy can effectively regulate hydride stability. Detailed thermodynamic parameters for hydrogen absorption and desorption are summarized in Supplementary Table 3. The PCT curves reveal that the thermodynamic behavior of the TiVZrNb alloy system is consistent with that of typical BCC hydrogen storage alloys, specifically exhibiting two plateau regions, indicating the presence of two hydrogen-induced phase transformations^[11]. During the initial hydrogen absorption stage, hydrogen exists in the alloy’s interstitial sites in the form of a solid solution (α phase). When the hydrogen concentration reaches the alloy’s solubility limit, a hydrogen-induced phase transformation occurs, forming the β₁ phase; at this point, the alloy enters the first plateau region (where the α phase and β₁ phase coexist). Since the plateau pressure in this region is extremely low, exceeding the detection range of the instrument’s pressure accuracy, its plateau characteristics are not observed in Figure 6. As the hydrogen absorption process continues, the β₁ phase gradually transforms into the β₂ phase. Once the β₁ phase has completely converted to the β₂ phase, a further increase in hydrogen concentration initiates the formation of the γ phase, at which point the alloy enters the second plateau region (where the β₂ and γ phases coexist)^[45]. This plateau primarily reflects the alloy’s thermodynamic properties. It can also be observed that as the temperature rises, the alloy’s plateau pressure increases accordingly. This is because the hydrogen absorption process is exothermic, while the hydrogen desorption process is endothermic. The hydrogen absorption and desorption reactions are reversible; increasing temperature favors hydrogen desorption but hinders absorption. Therefore, for hydrogen absorption, a higher hydrogen pressure is required to drive the reaction forward, resulting in a higher plateau pressure. For hydrogen desorption, high temperatures are favorable, promoting hydride decomposition and hydrogen release^[22,46]. Meanwhile, the absorption and desorption plateau pressures are clearly separated, indicating pronounced absorption-desorption hysteresis in this alloy series. This hysteresis is mainly associated with the β monohydride-γ dihydride transformation, which involves the structural transition between the BCC-type monohydride-related state and the hydrogen-rich face-centered cubic (FCC) dihydride state. During forward and reverse transformations, lattice expansion/contraction, lattice mismatch, elastic strain, interfacial energy, and distinct nucleation/interface migration barriers can lead to distinct driving forces for hydrogen absorption and desorption, resulting in separate absorption and desorption plateau pressures^[47,48]. In addition, local lattice distortion and heterogeneous hydrogen site energies in the TiVZrNb solid solution may also contribute to plateau slope and hysteresis^[49]. Additionally, the PCT curves show that the maximum hydrogen storage capacity (H/M) for all alloys is 2, consistent with the results of kinetic tests.

Figure 6. Complete hydrogen absorption-desorption PCT curves of (A) HEA-1, (B) HEA-2, (C) HEA-3, (D) HEA-4, (E) HEA-5, (F) HEA-6, (G) HEA-7, and (H) HEA-8 at different temperatures, together with (I) the Van’t Hoff fitting results obtained from the hydrogen absorption plateau pressures. HEA: High-entropy alloy; PCT: pressure-composition isotherm.

Due to significant differences in the thermodynamic parameters across all alloys, it is difficult to directly compare their pressure parameters at a given temperature. To more reasonably compare the relative stability of alloy hydrides, the enthalpy change (ΔH) and entropy change (ΔS) during the hydrogen absorption/desorption reactions were calculated using the Van’t Hoff equation (Equation 1). The actual PCT temperatures used for the Van’t Hoff analysis are listed in Supplementary Table 3 for each alloy. The 303 K curves shown in Figure 6 were used to illustrate the initial hydrogen absorption behavior and were not included in the Van’t Hoff fitting. Only the plateau pressures measured at the temperatures listed in Figures 6I and 7A show the Van’t Hoff fitting results for the hydrogen absorption and desorption processes, respectively. The entropy and enthalpy changes for the hydrogen absorption and desorption reactions were obtained from the slopes and intercepts of the linear fits [Supplementary Table 3]. Figure 7B further illustrates the relationship between the ΔH_des values of the HEA-1 to HEA-8 alloys and EDV_alloy. As EDV_alloy decreases from 0.6420 to 0.6195, ΔH_des decreases from 230.3 kJ/mol H₂ to 97.3 kJ/mol H₂, demonstrating a clear positive correlation between the two. Figure 7C summarizes the corresponding enthalpy changes for hydrogen absorption and desorption. This trend indicates that as the alloy composition is adjusted, hydride stability gradually decreases, the heat required for hydride decomposition decreases, and hydrogen desorption becomes increasingly thermodynamically favorable. This result is consistent with the earlier composition design prediction based on the electronegativity difference: reducing the average electronegativity difference between the alloy and H weakens the average M-H interaction, thereby reducing the thermodynamic stability of the hydride. From a compositional perspective, the Ti/Zr content gradually decreases from HEA-1 to HEA-8, while the Nb content gradually increases. Since Nb has a higher Pauling electronegativity than Ti and Zr, increasing the Nb content raises the alloy’s average electronegativity, thereby reducing the average electronegativity difference between the alloy and H. A smaller EDV_alloy value indicates a weakened driving force for average charge transfer from the metal to hydrogen and reduced M-H bond strength; consequently, the hydrogen-rich hydride phase decomposes more readily, as evidenced by a lower ΔH_des. To further compare the influence of different descriptors within the designed HEA-1 to HEA-8 series, the correlations between ΔH_des and EDV_alloy, VEC, lattice constant, and δ were analyzed by linear fitting, as shown in Figure 8. The corresponding R² and p values were added to each panel to provide a quantitative comparison rather. Compared to VEC, lattice constant, and δ, EDV_alloy exhibits a clearer positive correlation with ΔH_des. This indicates that the alloy-hydrogen average electronegativity difference can effectively reflect the trend in the average M-H interaction strength in single-phase BCC alloys and serves as an effective empirical parameter for guiding the thermodynamic regulation of hydrogen release in BCC high-entropy hydrogen storage alloys. However, it must be noted that hydride stability is not determined solely by the EDV_alloy factor. In the HEA-1 to HEA-8 series, EDV_alloy changes together with VEC, δ, lattice parameter, Ti/Zr content, and Nb content, indicating that the effect of EDV_alloy is inevitably coupled with compositional and structural factors. In particular, the alloy’s lattice parameters can influence ΔHdes by affecting the interstitial space available for hydrogen occupation, the stability of hydrogen in interstitial sites, and the repulsive interactions between neighboring hydrogen atoms. In both the statistical data and the experimental results for HEA-1 to HEA-8 in this study, ΔH_des shows the strongest monotonic correlation with EDV_alloy. Meanwhile, the strong correlation between lattice constant and ΔH_des in Figure 8 also indicates that the lattice-size effect cannot be ignored in this composition series. Therefore, EDV_alloy is more suitable as a first-order empirical descriptor in composition design than as the sole parameter to completely replace structural and electronic factors. A more rigorous distinction between the contributions of EDV_alloy and lattice-related factors requires the design of control alloy series with decoupled electronegativity and lattice-size parameters. This will be an important direction for future work to further clarify the relative contribution of EDV_alloy to hydride stability.

Figure 7. Van’t Hoff fitting of the hydrogen desorption process (A), the correlation between ΔH_des and EDV_alloy (B), and the corresponding enthalpy changes for hydrogen absorption and desorption (C) for alloys HEA-1 to HEA-8. Error bars represent the uncertainties calculated from the standard errors of the Van’t Hoff linear fittings. EDV_alloy: Electronegativity difference value of the alloy; HEA: high-entropy alloy; ΔH_des: desorption enthalpy.

Figure 8. Correlation between the ΔH_des in HEA-1 to HEA-8 alloys, and their EDV_alloy (A), VEC (B), lattice constants (C), and δ (D). The linear fitting results, including R² and P-values, are shown in the corresponding panels. HEA: High-entropy alloy; ΔH_des: desorption enthalpy; EDV_alloy: electronegativity difference value of the alloy; VEC: valence electron concentration; δ: lattice distortion.

Analysis of alloy dehydrogenation behavior

To further verify the influence of EDV_alloy on actual dehydrogenation behavior, TDS curves for alloys HEA-1 through HEA-8 were measured at a heating rate of 5 K/min [Figure 9], and all results were subjected to Gaussian peak deconvolution analysis. The results show that the TDS curves of all alloys can be decomposed into three hydrogen desorption peaks: a low-temperature peak (Peak 1) and high-temperature peaks (Peak 2 and Peak 3). This indicates that HEA-1 to HEA-8 exhibit similar multi-stage dehydrogenation processes, corresponding to the gradual decomposition of different hydride phases or distinct hydrogen-occupation states following hydrogen absorption.

Figure 9. TDS of alloys HEA-1 to HEA-8 at a heating rate of 5 K/min: (A) comparison of TDS curves for different alloys; (B-I) peak fitting analysis of hydrogen desorption peaks. The curves in (A) are vertically offset for clarity. HEA: High-entropy alloy; TDS: thermal desorption spectroscopy.

It should be noted that the three-peak deconvolution was applied to the entire HEA-1 to HEA-8 alloy series, rather than being established solely from the hydrogen-content-dependent analysis of HEA-8. Since these alloys share the same constituent elements and differ primarily in their relative compositions, their principal hydrogen-induced phase transformations and dehydrogenation processes are expected to be similar, whereas hydride stability varies systematically with composition. The small sharp features observed near the low-temperature peak in HEA-5 to HEA-8 were not treated as independent desorption peaks. Since the TDS signal reflects the hydrogen release rate, these features may be related to transient fluctuations in the desorption rate caused by reduced hydride stability and accelerated low-temperature dehydrogenation. Therefore, the deconvolution focuses on the main desorption contributions rather than on every minor local fluctuation. As EDV_alloy decreases, the peak temperature of Peak 1 gradually decreases from 632 K in HEA-1 to 509 K in HEA-8, and the peak temperature of Peak 2 decreases from 681 K (HEA-1) to 533 K (HEA-8). This indicates that reducing EDV_alloy can significantly lower the dehydrogenation temperature of the main hydride phase, consistent with the observed reduction in ΔH_des in the Van’t Hoff analysis. In other words, as the average electronegativity difference between the alloy and H decreases, the average M-H interaction weakens, making the hydride more prone to decomposition during heating. In contrast, the peak temperature of Peak 3 shows little change from HEA-3 to HEA-8, indicating that the hydrogen release process corresponding to this peak is relatively insensitive to EDV_alloy.

To further clarify the structural transformation processes corresponding to each dehydrogenation peak in the TDS, HEA-8 - which exhibits the lowest thermodynamic stability for hydrogen release and the lowest dehydrogenation peak temperature - was selected as the representative sample for stepwise dehydrogenation analysis. Figure 10A shows the PCT curve of HEA-8 at 453 K. By controlling the cutoff hydrogen pressure during PCT testing, samples with hydrogen contents of 2.83, 1.88, 1.32, and 1.18 wt.% were obtained. TDS measurements determined the actual hydrogen content of the samples at each stage [Supplementary Figure 6], with the vertical axis representing the hydrogen release rate (ppm/s) and the horizontal axis representing time. By integrating over time, the actual hydrogen contents of the samples at each stage were determined to be 28,340, 18,840, 13,230, and 11,750 ppm (weight ppm, unless otherwise mentioned), with corresponding H/M atomic ratios of 2.00, 1.31, 0.92, and 0.81. At a heating rate of 5 K/min, TDS testing and Gaussian peak deconvolution were performed on samples with varying hydrogen content, and the results are shown in Figure 10B. The TDS curve of the MH_2.00 sample can be decomposed into three hydrogen release peaks with peak temperatures of 509, 533, and 723 K; the MH_1.31 sample also exhibits three hydrogen release peaks with peak temperatures of 551, 570, and 721 K; the MH_0.92 sample decomposed into two hydrogen release peaks with peak temperatures of 586 and 725 K; the MH_0.81 sample also exhibited two hydrogen release peaks with peak temperatures of 598 and 723 K. It can be seen that as the hydrogen content decreases, the peak hydrogen release rates gradually decrease. The areas of the hydrogen release peaks correspondingly shrink.

Figure 10. Analysis of the hydrogen absorption and desorption behavior of the HEA-8 alloy: (A) PCT curve at 453 K, (B) TDS spectra at different hydrogen contents, (C) corresponding XRD patterns, and (D) proposed hydrogen desorption processes corresponding to the different fitted peaks. HEA: High-entropy alloy; FCC: BCC: body-centered cubic; PCT: pressure-composition isotherm; TDS: thermal desorption spectroscopy; XRD: X-ray diffraction.

To further establish the correlation between the dehydrogenation peak and structural transitions, XRD measurements at a scan rate of 2°/min were performed on samples with different hydrogen contents, and the results are shown in Figure 10C. The diffraction pattern of the MH_2.00 sample exhibits a single FCC structure with a lattice constant a = 4.464 Å, indicating that the sample is a dihydride (γ phase), consistent with previous reports^[50]. Upon dehydrogenation to MH_1.31, the sample exhibited coexistence of FCC and BCC phases, with the BCC phase having a lattice constant of 3.388 Å and the FCC phase’s lattice constant decreasing slightly to 4.461 Å. For BCC-based hydrogen storage alloys, the stability of the dihydride (FCC) is typically much lower than that of the monohydride (BCC); therefore, Peak 1 can be attributed to the dehydrogenation peak of the dihydride to the monohydride. Upon further hydrogen release to MH_0.92, the sample’s FCC diffraction peak completely disappeared, transforming into a single BCC structure corresponding to the monohydride phase (β phase), with a lattice constant of a = 3.368 Å. At this point, Peak 1 completely disappeared, further confirming that it corresponds to the dehydrogenation of the dihydride. When hydrogen was released to MH_0.81, the sample retained a single BCC structure, but the lattice constant decreased from 3.368 Å to 3.357 Å, due to lattice contraction caused by hydrogen release. By subjecting the sample to dynamic vacuum pumping at 773 K, a fully dehydrogenated sample can be obtained [Supplementary Figure 7], which reversibly recovers to the initial BCC structure, with a lattice constant similar to that of the original, hydrogen-unabsorbed sample. Based on the above results, Peak 2 is primarily attributed to hydrogen desorption from the monohydride (β phase). In contrast, Peak 3 may be associated with the further release of more stable residual hydrogen from the β phase and/or the BCC solid-solution α phase. Combining the above analyses, the hydrogen release pathway of the HEA-8 alloy can be qualitatively described as shown in Figure 10D: the low-temperature Peak 1 is mainly associated with the transformation of the FCC hydride (γ phase) to the BCC-type intermediate hydride (β phase), while the higher-temperature Peaks 2 and 3 are related to the further dehydrogenation of the β phase and/or BCC α phase^[13]. This interpretation is consistent with the typical stepwise dehydrogenation behavior of BCC hydrogen storage alloys and related BCC high-entropy hydrides, in which the dehydrogenation process proceeds from a hydrogen-rich FCC dihydride to an intermediate monohydride and finally to a BCC structure. However, conventional ex-situ XRD cannot accurately quantify the hydrogen content or phase fraction in each phase, nor can it directly determine hydrogen occupation. Therefore, the present peak assignment should be regarded as a qualitative interpretation based on ex-situ XRD, TDS peak evolution, and reported in-situ results, rather than a definitive phase-resolved quantification. Further in situ XRD or neutron diffraction would be required to directly validate the high-temperature desorption contribution, especially for Peak 3.

Combining the changes in TDS peak temperatures for HEA-1 to HEA-8 reveals that the reduction in EDV_alloy primarily affects Peak 1 and Peak 2, corresponding to the stability of the hydrogen-rich FCC dihydride and BCC intermediate hydride phases. This indicates that reducing the average electronegativity difference between the alloy and hydrogen primarily weakens the average M-H interactions in high-hydrogen-content hydride phases, thereby increasing their susceptibility to dehydrogenation and decomposition. In contrast, the effect of EDV_alloy on Peak 3 is relatively weak. To further analyze the influence of EDV_alloy on the dehydrogenation process from a kinetic perspective, TDS curves for alloys HEA-1 to HEA-8 were measured at different heating rates, and the corresponding Gaussian deconvolution results are shown in Supplementary Figures 8-15, respectively. The apparent dehydrogenation activation energies were calculated using the Kissinger method, and the corresponding peak temperatures and activation energies are summarized in Supplementary Table 4. The Kissinger equation is as follows^[44]:

where T_m is the peak temperature, θ is the heating rate, E_a is the dehydrogenation activation energy, and R is the ideal gas constant. Figure 11 shows the TDS curves for HEA-1 to HEA-8 at different heating rates, along with the corresponding Kissinger fitting results. As the heating rate increases, Peak 1 consistently shifts toward higher temperatures for all alloys, while Peaks 2 and 3 generally exhibit an overall shift toward higher temperatures, with minor deviations for individual samples. This behavior is characteristic of a thermally activated dehydrogenation process. The Kissinger fitting results indicate that as the EDV_alloy decreases, the apparent dehydrogenation activation energy corresponding to Peak 1 gradually decreases. This suggests that the kinetic resistance to the transition from the FCC dihydride γ phase to the BCC intermediate hydride phase decreases, consistent with the aforementioned trend of decreasing Peak 1 temperature and ΔH_des in the PCT. Therefore, TDS and Kissinger analyses further support, from a kinetic perspective, the regulatory role of EDV_alloy on hydride stability. As EDV_alloy decreases, the average electronegativity difference between the alloy and hydrogen decreases, and the average M-H bond strength decreases, making the hydrogen-rich FCC dihydride phase more prone to decomposition, as evidenced by the decrease in the Peak 1 dehydrogenation peak temperature and the apparent dehydrogenation activation energy. Combined with the decrease in ΔH_des obtained from the PCT/Van’t Hoff equation, this indicates that composition regulation based on EDV_alloy not only reduces the thermodynamic stability of the hydride but also lowers the kinetic resistance of the primary dehydrogenation process, thereby improving the hydrogen release performance of high-entropy BCC hydrogen storage alloys in the TiVZrNb system.

Figure 11. TDS curves for HEA-1 to HEA-8 alloys at different heating rates (5, 10, 15, 20 K/min) (A-H), corresponding Kissinger fitting results (I), the correlation between hydrogen release temperature and EDV_alloy (J), and the relationship between E_a and EDV_alloy (K). The TDS curves in (A-H) are vertically offset for clarity. HEA: High-entropy alloy; EDV_alloy: electronegativity difference value of the alloy; TDS: thermal desorption spectroscopy.

EDV_alloy as a thermodynamic descriptor for single-phase BCC hydrogen-storage HEAs

TiVZrNb-based BCC high-entropy hydrogen storage alloys possess high hydrogen storage capacity; however, the key issue limiting their practical application is their excessively high hydride stability. Therefore, it is crucial to reduce hydride stability while maintaining a single-phase BCC structure and a high H/M ratio. The results of this study indicate that, compared to VEC, lattice parameters, and δ, EDV_alloy shows a stronger correlation with ΔH_des. This suggests that EDV_alloy can more directly reflect the trend in hydride stability in single-phase BCC high-entropy hydrogen storage alloys. Furthermore, in the HEA-1 to HEA-8 series of alloys designed in this study, ΔH_des decreases correspondingly as EDV_alloy decreases. This result further validates the effectiveness of EDV_alloy as a thermodynamic control parameter: reducing the average electronegativity difference between the alloy and hydrogen can significantly lower the enthalpy of hydrogen desorption from hydrogen-rich hydrides, thereby thermodynamically destabilizing the hydrides. Existing first-principles calculations indicate that chemical contributions primarily govern changes in the dehydrogenation enthalpy of TiVZrNb-based hydrides; that is, the metal matrix’s affinity for H is a key factor determining hydride stability, while structural and elastic contributions have a relatively minor impact on the differences in dehydrogenation enthalpy among various hydrides^[39]. Therefore, the decrease in ΔH_des observed in this study, driven by the reduction in EDV_alloy, is likely primarily due to weakening of metal-hydrogen chemical interactions. From a bonding perspective, the electronegativity of Ti, V, Zr, and Nb is lower than that of H. After hydrogen absorption, H atoms enter the interstitial sites of the metal lattice and form a local M-H coordination environment with surrounding metal atoms. Existing first-principles studies of TiVZrNb-based hydrides further indicate that hybridization occurs between the H s state and the metal sp/d states, forming M-H bonding states. Meanwhile, Bader charge analysis reveals charge transfer from metal atoms to H atoms, suggesting that M-H interactions exhibit charge-transfer characteristics and ionic components^[39]. Based on the above understanding, the results of this study can be interpreted from the perspective of electronegativity differences: a larger EDV_alloy corresponds to a stronger trend of charge transfer from the metal to H and a stronger average M-H interaction, making H more stable at the interstitial sites, thus resulting in a higher ΔH_des. Conversely, when EDV_alloy decreases, the alloy’s average electronegativity approaches that of H, the average charge-transfer driving force may weaken, and the M-H bond strength decreases accordingly, thereby reducing the energy required for hydride decomposition.

It should be noted that EDV_alloy is an average composition descriptor whose validity depends on a single-phase BCC structure and a relatively uniform elemental distribution. For alloy systems containing a second phase, significant segregation, or complex multi-phase reactions, local hydrogen-occupancy environments and hydrogen absorption/desorption reactions involving the second phase may weaken the correlation between EDV_alloy and ΔH_des. Therefore, EDV_alloy is more suitable as an effective empirical descriptor for regulating the thermodynamic stability of hydrogen desorption in single-phase BCC hydrogen storage HEAs, rather than as the sole parameter independently determining all hydrogen storage behavior.

Microscopic dehydrogenation behavior regulated by EDV_alloy

The decrease in ΔH_des indicates a decline in the overall thermodynamic stability of the hydride; however, it is difficult to determine which stage of the dehydrogenation process EDV_alloy affects solely from a Van’t Hoff analysis. Based on the aforementioned multi-peak characteristics observed in the TDS and XRD analyses of samples with different hydrogen contents, it can be concluded that the dehydrogenation process of TiVZrNb-based alloys is not a single-step reaction. Specifically, hydrogen-rich FCC dihydrides first decompose and transform into BCC-type intermediate hydrides; subsequently, the intermediate hydrides undergo further dehydrogenation, ultimately reverting to a low-hydrogen BCC solid solution or the initial BCC alloy structure. Therefore, the different dehydrogenation peaks in the TDS do not merely reflect hydrogen released at different temperatures, but rather correspond to the gradual release of hydrogen from different hydride phases, hydrogen occupation states, or local binding strengths. As EDV_alloy decreases, the main dehydrogenation peaks shift toward lower temperatures overall, indicating that the stability of hydrogen-rich hydrides and some intermediate hydrides is weakened. In particular, the low-temperature dehydrogenation peaks are relatively sensitive to changes in EDV_alloy, suggesting that electronegativity-driven regulation primarily acts on the hydrogen-rich dihydride phase. In this phase, H atoms extensively occupy interstitial sites in the metal lattice, and M-H interactions significantly contribute to the stability of the hydrides. As EDV_alloy decreases, the average M-H bond strength weakens, and the ability of FCC hydrides to maintain a high hydrogen content declines, increasing the likelihood of decomposition at lower temperatures. From a microscopic perspective, the hydrogen occupancy environment in high-entropy alloys exhibits significant diversity. Even when the alloy as a whole consists of a single-phase BCC solid solution, the coordination environments of Ti, V, Zr, and Nb around different interstitial sites vary, leading to a distribution of local M-H bond strengths and hydrogen-occupancy stabilities. A decrease in EDV_alloy does not imply that all local M-H bonds weaken proportionally; rather, it is more likely to manifest as a shift in the overall distribution of hydrogen binding energies toward lower stability. Specifically, this involves a reduction in the proportion of strongly bound H sites or a decrease in H stability in Ti/Zr-rich local environments. This overall decline in local stability can explain why the TDS main peak temperature shifts toward lower values as EDV_alloy decreases.

Furthermore, some high-temperature dehydrogenation peaks exhibit a relatively weak response to EDV_alloy, suggesting that this stage may be governed not only by average M-H bonding but also by factors such as residual hydrogen in low-hydrogen BCC solid solutions, the local interstitial environment, H diffusion pathways, lattice contraction, and defect confinement. Consequently, the influence of EDV_alloy on dehydrogenation pathways exhibits phase selectivity: it is more sensitive to the decomposition processes of hydrogen-rich hydrides and major intermediate hydrides, while local structural factors may limit its ability to describe low-hydrogen residual states.

Thermodynamic and kinetic effects of EDV_alloy

Both thermodynamic and kinetic factors govern the hydrogen release process. As the EDV_alloy content decreases, the alloy’s ΔH_des drops significantly, indicating reduced thermodynamic stability of the hydride and making the hydrogen release reaction thermodynamically more favorable. Concurrently, the main dehydrogenation peak in the TDS curve shifts toward lower temperatures, and the apparent activation energy for the decomposition of hydrogen-rich dihydrides obtained from the Kissinger fit also decreases. This indicates that the reduction in EDV_alloy not only weakens the equilibrium stability of the hydrides but also reduces the kinetic resistance during the actual dehydrogenation process.

This simultaneous thermodynamic and kinetic change may stem from the weakening of the average M-H interaction. When EDV_alloy is high, the average electronegativity difference between the alloy and H is large, the driving force for electron transfer from the metal to H is strong, and H atoms are more strongly bound by M-H bonding at interstitial sites. Consequently, hydride decomposition requires overcoming a larger thermodynamic energy difference, reflected in a higher ΔH_des; simultaneously, when H atoms detach from their local coordination environment to participate in subsequent diffusion, phase transition, and desorption processes, they must also overcome a higher energy barrier, reflected in a higher E_a. When EDV_alloy is reduced, the alloy’s average electronegativity becomes closer to that of H, the average charge transfer driving force weakens, and the M-H bond strength decreases, reducing the stability of H atoms in hydrogen-rich hydrides. Consequently, the heat required for hydride decomposition decreases, and the combined kinetic energy barrier that must be overcome for H to escape interstitial sites and for the hydrogen-rich phase to decompose decreases as well.

From the perspective of dehydrogenation pathways, the decrease in E_a primarily reflects the improved kinetics of the decomposition process of the hydrogen-rich dihydride. In hydrogen-rich FCC dihydrides, the high hydrogen content causes H atoms to occupy a large number of interstitial sites in the metal lattice, making their stability highly sensitive to M-H interactions. When EDV_alloy decreases, the local confinement of H in the hydrogen-rich phase weakens, making it easier for the FCC dihydride to transform into intermediate hydrides or low-hydrogen BCC solid solutions. Consequently, the low-temperature dehydrogenation peak in the TDS shifts toward lower temperatures, and the corresponding apparent activation energy decreases. This indicates that the reduction in EDV_alloy not only lowers the thermodynamic stability of hydrogen-rich hydrides but also reduces the kinetic resistance to their decomposition and phase transformation.

CONCLUSION

In this study, based on the EDV_alloy, we designed and prepared TiVZrNb-based BCC hydrogen storage HEAs. We systematically investigated their phase structure, hydrogen storage capacity, hydrogen release thermodynamics, and dehydrogenation kinetics. The main conclusions are as follows:

(1) EDV_alloy shows a clearer correlation with ΔH_des than VEC, lattice parameters, and δ do for single-phase BCC hydrogen storage HEAs, indicating that EDV_alloy is more suitable as a first-order empirical descriptor for describing the variation trend of hydride stability in BCC hydrogen storage HEAs, rather than as the only parameter that completely replaces lattice structure, compositional effects, and electronic-structure factors.

(2) By reducing the Ti/Zr content and increasing the Nb content, the EDV_alloy of the HEA-1 to HEA-8 alloys decreased from 0.6420 to 0.6195. All alloys maintained a compositionally homogeneous single-phase BCC structure and exhibited high hydrogen storage capacities approaching H/M = 2, indicating that this compositional control strategy did not compromise the alloys’ phase stability or high-capacity hydrogen storage characteristics.

(3) As EDV_alloy decreased, the alloy’s ΔH_des decreased from 230.3 kJ/mol H₂ to 97.3 kJ/mol H₂, and the main dehydrogenation peak shifted to lower temperatures. This indicates that reducing the average electronegativity difference between the alloy and hydrogen weakens M-H interactions, thereby destabilizing hydrogen-rich hydrides thermodynamically.

(4) TDS, structural analysis of samples with different hydrogen contents, and Kissinger analysis indicate that the reduction in EDV_alloy primarily affects the dehydrogenation behavior of hydrogen-rich FCC dihydrides and certain BCC intermediate hydride phases, while also lowering the apparent activation energy of the hydrogen-rich dihydride decomposition process. This suggests that it not only reduces the thermodynamic stability of the hydrides but also decreases the kinetic resistance of the main dehydrogenation stages. The above results provide an effective design strategy for reducing the stability of hydrides in TiVZrNb-based BCC hydrogen storage HEAs while maintaining high hydrogen storage capacity.