Data-driven multi-element substitution of TiFe alloys for tunable thermodynamics and enhanced activation behaviour for hydrogen storage

Abstract

Due to their high volumetric hydrogen storage capacity under moderate storage conditions, TiFe alloys have been widely investigated as candidates for practical solid-state hydrogen storage. Partially substituting Ti or Fe sites can improve the key characteristics of TiFe alloys, such as the first hydrogen absorption step (activation) and the equilibrium hydrogen pressure (thermodynamic properties). However, the selection of substitution elements has heavily relied on intuition and trial-and-error. Also, conventional substitution strategies have mainly focused on single-element substitution within the TiFe alloy, limiting the design space and tunability for target applications. To address this limitation, we report a multi-element substitution strategy motivated by an efficient, data-driven machine learning (ML) approach combined with corroborating density functional theory (DFT) calculations. Our models successfully predict experimentally measured hydride stability in five selected alloys using only compositional descriptors. Most importantly, the multi-element substitution leads to enhanced activation properties compared to pure TiFe, achieving near room-temperature activation behaviour. This work provides a method for on-demand tuning of hydrogen storage and activation properties, which may have broad implications for data-driven discovery of energy storage materials.

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1. Introduction

Despite extensive research efforts on practical applications of solid-state hydrogen storage materials, identifying a reversible storage platform with desired properties has proven challenging.¹ TiFe intermetallics are among the viable candidates for practical hydrogen storage due to their mild operating conditions, excellent volumetric capacity (up to 105 kg H₂ m⁻³), and cost effectiveness of constituent elements.² However, the as-prepared pure TiFe alloy is known to have a thick passivation layer on the surface that can block the alloy from hydrogenation. The presence of this passivation layer presents difficulties for the initial hydrogenation step, also referred to as activation, and is one of the main challenges for achieving cost-efficient practical applications.² A variety of studies have investigated the mechanism of activation, and it has been shown that the activation behaviour of TiFe can be controlled by variables such as the elemental substitution and the resulting evolution of secondary phases,^3,4 the formation of surface oxide layers,^5,6 and the exertion of mechanical force.^7,8 For example, the addition of Mn or Cr to TiFe can lead to the formation of Laves phases, and such secondary phases can play an important role in facilitating the activation.⁹

In addition to the activation behaviour, tunable hydrogen uptake and release pressure is another important factor for future hydrogen storage platforms across various applications.^10,11 The equilibrium pressure and the shape of hydrogen isotherm curves along with the resulting thermodynamic properties can be also significantly affected by the type of substitution elements and their concentrations.² For instance, the addition of V equalizes first and second desorption plateaus, enabling an increased working capacity for a smaller pressure swing.^12,13 Therefore, substituting Ti or Fe sites with alternative elements is a compelling method to simultaneously induce composition-dependent alterations in the thermodynamic properties and activation behaviour of TiFe.^2,14

Previous research on elemental substitutions of TiFe alloys has primarily focused on the substitution with a single element by varying its concentration. The question naturally arises if more compositionally complex substitution profiles can be leveraged to more finely tune TiFe hydride thermodynamics than can be achieved with single-element substitution, as may be needed for maximizing efficiency in specific use-case scenarios.¹⁵ It has been reported that the substitution of TiFe with two or more elements can additionally alter the hydrogen sorption properties of the alloy compared to the single element-substituted counterpart in terms of plateau pressure,¹⁶ shape and hysteresis of the plateau,¹⁷ activation properties,^18,19 and hydrogen storage capacity.²⁰ However, relying only on experimental intuition to target new substitutions for fine-tuning TiFe alloys is inefficient, especially given the massive exploration space when one considers 3, 4, or even more elements for substitution from the pool of known candidates.²¹ A preferred approach is to derive quantitatively accurate models to predict the effect of multi-element substitution on TiFe hydride stability and, ideally, elucidate explainable composition design rules that dictate this stability. This would enable much more efficient and rapid targeting of novel substituted TiFe alloys with desired hydride stability.²²

Therefore, this study aims to further diversify and increase the number of substitution combinations considered for fine-tuning of TiFe hydride thermodynamics. We accelerate the exploration of 4-element equimolar substitution combinations by using a data-driven machine learning (ML) model based on gradient boosting tree regressors and trained on the hydride thermodynamic properties contained in the ML-ready hydrogen storage materials database (HydPARK database).²³ Importantly, the features in this approach are derived from only the nominal composition, permitting reasonably accurate inference predictions without prior knowledge of the phase formation behaviour (which must be obtained from costly material characterization and is not readily amenable to high-throughput approaches). Previous works have shown that ML models can predict the thermodynamics of high-entropy metal hydrides with reasonable accuracy and can be used to target novel high-capacity, destabilized hydride phases.^24,25 Furthermore, interpretability of these ML models can elucidate underlying composition–property relationships of metal hydrides, highlighting that individual thermodynamic properties (e.g. ΔH, ΔS, and plateau pressure) carry different dependencies on physics-based features within the models (e.g. composition-weighted mean or deviation of constituent elements' properties).^11,25

We propose that the thermodynamic properties of TiFe-based alloys can be specifically tailored by changing the combinations of four substitution elements predicted by high-throughput screening enabled by the ML model. Based on the reported substitution elements for TiFe, five different multi-element-substituted TiFe samples—TiFe_0.8(X)_0.2: TiFe_0.8(CrMnCuSn)_0.2, TiFe_0.8(CrMnNiCu)_0.2, TiFe_0.8(MnCoNiCu)_0.2, TiFe_0.8(CrCoNiCu)_0.2, and TiFe_0.8(VCoNiCu)_0.2—were selected and synthesized, and the phase formation behaviours and thermodynamic properties were evaluated. Concurrently with ML, thermodynamic assessments and DFT calculations are also utilized for computing phase-formation behaviours and enthalpy, respectively. The ML-predicted ΔH shows a reasonable match with the experimentally obtained and DFT-calculated values, implying that the high-throughput ML model effectively predicts compositions with tailored thermodynamic properties of TiFe-based alloys. Furthermore, these results can establish a general design rule for multi-element-substituted TiFe alloys with desirable properties for specific hydrogen use cases.¹⁵

2. Methods

2.1. Materials

TiFe-based alloys were prepared using vacuum arc remelting (VAR) equipment (H-PAM-40, SAMVAC, Korea). A water-cooled copper crucible was employed during sample preparation to prevent contamination from the crucible. First, the constituent elements were placed in the crucible, and the VAR chamber was evacuated to a pressure of 3.76 × 10⁻⁴ torr using rotary and oil diffusion pumps. After evacuation, the VAR chamber was backfilled with high-purity Ar gas to a pressure of 600 torr. The samples were melted using arc melting with a tungsten electrode at a power of 20 kW. To ensure compositional homogeneity, the samples were remelted five times with flipping between each melting step. Finally, the molten alloys were cast into a disc shape with a diameter of 87 mm and a height of 10 mm.

2.2. Characterization and instrumentation

Powder X-ray diffraction (XRD) patterns were collected with a SmartLab high-resolution powder X-ray diffractometer (Rigaku, KAIST Analysis Center for Research Advancement (KARA)). Prior to XRD data collection, the ingot samples were crushed in air using stainless steel mortar and pestle. The crushed powder was sieved through a 625 mesh stainless steel sieve to obtain a randomly distributed fine powder with particle sizes less than 20 microns. Cu K-alpha radiation was used as the X-ray source (λ = 0.154 nm) with a step size of 0.01°, and the scan rate was 1.3° min⁻¹. Lattice parameters of the samples were calculated using Cohen's method.²⁶ Elemental quantifications of the alloy samples were carried out using ZSX Priums II X-ray fluorescence spectrometer (Rigaku, KARA). Scanning electron microscopy (SEM) was performed with an SU8230 instrument (Hitachi, KARA) using crushed ingot samples mounted on the carbon tape. X-ray photoelectron spectroscopy (XPS) data were collected using a K-alpha X-ray photoelectron spectrometer (Thermo VG Scientific, KARA) using Al X-ray source (1486.7 eV) under ultra-high vacuum (<10⁻⁹ torr). Spectra were calibrated to adventitious C 1s peak at 285 eV. As-prepared ingot samples were transferred into the XPS instrument after exposing in air. In the case of activated samples, the samples were loaded on a vacuum transfer module in an Ar-filled glove box. Hydrogen absorption and desorption kinetic curves and pressure–composition–temperature isotherms were recorded on a Sieverts-type PCT-Pro instrument (SETARAM) and HPVA II (Micromeritics). Approximately 1 g of TiFe alloy samples were crushed in an Ar-filled glove box, and then placed in a stainless-steel sample holder for measurements. In the case of the activation experiments, the samples were first crushed in the Ar-glove box, then either transferred under Ar conditions or exposed to air for 1 hour before hydrogen pressurization. Absorption and desorption temperatures were kept constant with a PID-controlled heating jacket. Volume calibrations were carried out at each reaction temperature.

2.3. Machine learning details

Matminer²⁷ was used to derive Magpie features for the alloy compositions. A set of elemental properties, p (electronegativity, covalent radius, etc.) and the molar fractions (f) in a given composition are combined in various operations, such as mean , average deviation , max({p_i}), min({p_i}), etc. In addition to the standard elemental properties covered in Matminer, we supplement p with domain specific features such as ΔH_b (each element's binary hydride formation enthalpy) which were taken from computed entries in materials project²⁸ since these experimental values for most non-hydriding elements are not readily available.

Gradient boosting tree regression (GBTR) models have previously been found to be high-performing models for predicting hydride thermodynamics.^{23–25,29,30} We utilized scikit-learn³¹ to train GBTR models for hydride thermodynamic properties available in v0.0.6 of the ML-ready HydPARK database (https://zenodo.org/records/10680097), which consists of training data for ∼700 distinct alloy compositions. This includes the enthalpy and entropy of desorption (ΔH and ΔS, respectively) and room temperature equilibrium plateau pressure, , with reference pressure of P_o = 1 bar. Hyperparameters were tuned to minimize over-fitting by minimizing the average K = 10-fold cross validation test set errors (n_estimators = 1500, max_depth = 4, learning_rate = 0.005, alpha = 0.99, subsample = 0.75).

2.4. Calculation of hydride reaction enthalpy (ΔH) for TiFe_0.8(X)_0.2

First-principles density functional theory (DFT) calculations were performed using the Vienna Ab initio Simulation Package (VASP).^32–34 The projector-augmented wave (PAW) method³⁵ within the Perdew–Burke–Ernzerhof (PBE)³⁶ generalized gradient approximation was employed to describe the exchange-correlation energy. A plane-wave cutoff energy of 400 eV and the Methfessel-Paxton smearing method with a width of 0.1 eV were used. The Brillouin zone was sampled using Γ-centred k-point meshes of 5 × 3 × 5 for the TiFeH monohydride structure, which contains 120 atoms per supercell (Ti: 40, Fe: 40, H: 40), and for the B2 TiFe structure without hydrogen (Ti: 40, Fe: 40). The selection of the cutoff energy and k-point values was based on convergence tests. All supercells achieved convergence within an energy difference of 1 meV per atom, confirming that the selected parameters are sufficient for accurate calculations of the target properties. Ionic relaxations were carried out using the conjugate gradient algorithm, with convergence criteria set to 10⁻⁶ eV for total energy and 10⁻² eV Å⁻¹ for forces.

The hydride reaction enthalpy (ΔH) for the TiFe-based monohydride, per one mole of H₂ gas, was estimated as the hydrogenation reaction energy (ΔE_r) at 0 K, calculated using the following equation:

−ΔH ≈ ΔE_r(TiFeH) = 2E_TiFeH − 2E_TiFe − 1E_H2 (1)

Due to the limited size of the DFT supercell, partial atomic disorder within a given sublattice was approximated using special quasi-random structures (SQS), generated via the Monte Carlo algorithm implemented in the MCSQS code of the Alloy Theoretic Automated Toolkit (ATAT).^37,38 Based on the chosen supercell sizes—80 atoms for the B2 structure and 120 atoms for the monohydride structure—the compositional resolution for the B2 structure was 1.25 at% (1/80). DFT calculations were performed using supercells representing partially disordered monohydride [Ti₁Fe_0.8(X)_0.2H₁] and B2 [Ti₁Fe_0.8(X)_0.2] structures, where alloying elements (V, Cr, Fe, Co, or Ni) were randomly mixed within the Fe sublattice (Table S1). To mitigate the stochastic nature of the calculations, six independent SQS supercells were generated for each target composition using different sets of correlation functions (pair and/or triplet) over varying interaction ranges, following the methodology of a previous study.³⁹ The hydrogenation reaction energy was obtained by averaging the results from these independent SQS calculations for each composition.

3. Results and discussion

3.1. Machine learning predictions of TiFe-X hydriding enthalpies

Compositional machine learning models⁴⁰ have enabled computationally cheap and sufficiently accurate predictions for thermodynamic properties of metal hydrides to elucidate explainable design rules⁴¹ and facilitate discovery of new hydride phases with desired properties. An alloy's feature vector is generated by simple mathematical operations (mean, deviation, etc.) applied to various elemental properties and molar fractions of the composition, denoted the “Magpie” features.⁴⁰ Following this featurization approach and subsequent metal hydride thermodynamic ML model development, extensively detailed in previous work and summarised in the SI (Note S1, Fig. S1, and Table S2),²⁴ we trained a gradient boosting tree model on v0.0.6 of the ML-ready HydPARK database,²³ which contains the hydride reaction enthalpy, ΔH_exp, among other target properties. Fig. 1a shows the density parity plot of the K = 10-fold cross validation test set predictions, ΔH_ML, for the ML-ready HydPARK data, with expected mean absolute error (MAE) of 4.2 kJ mol⁻¹ H₂. K-fold cross-validation is a resampling technique to evaluate predictive performance of an ML model that (1) splits the dataset into K groups (folds), (2) trains a model on K-1 folds and tests on the remaining fold, and (3) repeats this process K times with each fold as a test set. Expected MAE is the average of the MAE's of all K test sets. To validate this model's ability to predict ΔH_exp trends across substituted TiFe-X hydrides, we next compare ΔH_ML to experimental values aggregated from the literature by Dematteis et al. in Fig. 1b.² For alloy compositions with both absorption and desorption enthalpies reported, represents their average. Note that a small number of alloy compositions in the Dematteis review already existed in the HydPARK training data, and model prediction errors for such materials are the lowest for these hydrides, as expected. Compositions from the Dematteis review that do not exist in HydPARK training data (blue and orange stars in Fig. 1) are better indicators of the model's true predictive accuracy; for this subset of predictions, the model's MAE ∼ 3 kJ mol⁻¹ H₂ is still less than the expected error of the model, as derived from the K-fold cross validation.

Fig. 1 (a) Parity plot of HydPARK experimental values vs. ML test set predictions from a K = 10-fold cross-validation (log-scale color bar corresponds to the number of alloy compositions in a given bin). Cyan circles represent ML predictions for the TiFe-X compositions, ΔH^TiFe-X, aggregated by Dematteis et al. (b) Parity plot of ML predictions vs. ΔH^TiFe-X, i.e., the cyan circles in (a), delineated by whether they already existed in the HydPARK training data, or represent new compositions or even chemical systems not in HydPARK (MAE in parentheses). (c and d) Global SHAP summary for all HydPARK compositions vs. TiFe-X compositions, respectively. The following appear in five most important features: v_pa ≡ volume per atom of elemental solid, χ ≡ Pauling electronegativity, r_c ≡ covalent radius, ΔH_b ≡ binary hydride formation enthalpy, N_v ≡ valence electron number, SG# ≡ space group number of the elemental solid.

Fig. 1c and d visualize the SHAP explainability analysis⁴² for the ΔH_ML model for predictions of the entire HydPARK dataset (Fig. 1c) and just the TiFe-X dataset (Fig. 1d). At the highest level, SHAP values indicate the contribution of each feature to the final prediction, and overall feature importance (row ordering) is ranked by the sum of the absolute SHAP values per feature, while feature effects (i.e., SHAP values' dependence on the feature values) can yield interpretable material design rules. Among the 145 Magpie features⁴⁰ used to describe a given composition, the 5 most overall important features are shown in Fig. 1c and d. For example, the dominant feature contribution to ΔH_ML across the entire HydPARK dataset (a much wider chemical/structural space of interstitial hydrides than TiFe-X) is the composition-weighted, mean volume per atom of the elemental solids, (Fig. 1c). However, in the narrower chemical/structural space of TiFe-X hydrides, ν_pa is no longer a useful feature for differentiating the hydriding enthalpy and instead the composition-weighted, mean binary hydride formation, , primarily determines the model's predictions for ΔH_ML (Fig. 1d). Note that we used Materials Project to extract the feature (i.e., it is not a default elemental property by which Magpie features are derived). This points to the importance of adding non-standard, domain specific features if possible (i.e., for hydrides, features derived from elemental properties related to metal–hydrogen interactions). These SHAP insights provide a useful first approximation to rationally design complex doping strategies in TiFe-X, i.e. doping profiles that maximize or minimize the compositions are the tuning knob most likely to respectively increase or decrease ΔH_ML.

3.2. Selection and synthesis of multi-element-substituted TiFe-X

To generate candidate compositions of multi-element-substituted TiFe, we limit ourselves to the 8 substituent elements (E = {Al, V, Cr, Mn, Co, Ni, Cu, and Sn}) found in Dematteis et al.² We then enumerated all possible 4 component equimolar combinations, , and predicted ΔH_ML for each (Scheme 1a). Five representative compositions were chosen (TiFe_0.8(CrMnCuSn)_0.2, TiFe_0.8(CrMnNiCu)_0.2, TiFe_0.8(MnCoNiCu)_0.2, TiFe_0.8(CrCoNiCu)_0.2, and TiFe_0.8(VCoNiCu)_0.2), spanning a wide range of predicted ΔH_ML values. First, two compositions—TiFe_0.8(CrMnCuSn)_0.2 and TiFe_0.8(VCoNiCu)_0.2—with minimum and maximum |ΔH| values are included: the other three compositions were selected to have similar ΔH value intervals. However, Al was excluded due to the large hysteresis reported previously,⁴³ which could possibly compromise the accuracy of the ΔH calculation.

Scheme 1 (a) A scheme of multi-element-substituted TiFe system predicted by ML. (b) The ML-predicted ΔH values of TiFe_0.8(X)_0.2 samples.

The predicted enthalpy values are indicated in Scheme 1b. The substituted TiFe samples with selected compositions were prepared by VAR technique, and the XRD patterns of each alloy suggest that the B2 TiFe phase is the major phase, accompanied by secondary phases originated from the introduction of substitution elements (Fig. 2a and S2). However, in the case of multi-element-substituted TiFe-X system, the measured unit cell volumes do not correlate well with the ΔH_ML, additionally supporting that the is no longer a primary feature for predicting ΔH values of TiFe-X system (Fig. 2b). All samples exhibit larger lattice parameters compared to the that of reported TiFe, indicating lattice expansion due to substitution (Fig. 2c).⁴⁴ Such lattice expansion is mainly due to the larger atomic radii (r_Cr = 0.12491 nm, r_Mn = 0.135 nm, r_Co = 0.1251, r_Ni = 0.12459 nm, r_Sn = 0.162 nm, r_Cu = 0.1278 nm, r_V = 0.1316 nm) of the substitution elements compared to that of the substituted Fe (r_Fe = 0.12412 nm).² Also, the average atomic radii of the samples were evaluated based on the quantification results of B2 TiFe phases; however, no significant correlation with the cell volume is observed (Fig. S2b).

Fig. 2 (a) Powder XRD patterns of TiFe_0.8(X)_0.2 samples. The parentheses are the indices of B2 (TiFe) phases. (b) Correlation between enthalpy changes predicted by ML (ΔH_ML) and cell volumes of TiFe_0.8(X)_0.2 samples. (c) A table of lattice parameters of TiFe_0.8(X)_0.2 samples.

3.3. Secondary phase formation behaviours of multi-element-substituted TiFe alloys

The phase formation behaviours and elemental compositions of prepared TiFe alloy samples were evaluated by SEM coupled with energy dispersive X-ray spectroscopy (EDS) and X-ray fluorescence spectroscopy (XRF) (Fig. 3a–e and S3). The overall elemental contents measured by both SEM-EDS and XRF are close to the intended synthetic compositions of each sample. Among the samples, TiFe_0.8(MnCoNiCu)_0.2 and TiFe_0.8(CrCoNiCu)_0.2 show comparatively little formation of secondary phases. In contrast, the SEM-EDS maps and backscattered electron (BSE) images of other compositions reveal the formation of significant secondary phases accompanied by the segregation of specific elements—particularly noticeable within TiFe_0.8(CrMnCuSn)_0.2 and TiFe_0.8(VCoNiCu)_0.2. This segregation is evident in the BSE images, where Sn-rich and V-rich regions are distinguished as brighter and darker areas, respectively (Fig. S3a and e). The SEM-EDS mappings and quantification results show that the Sn- and V-rich signals are associated with high Ti concentration. By calculating the defect formation energies of the substitution elements at different sites, the preferences for Ti-site or Fe-site substitutions can be quantified (Table S3 and Note S2).⁴⁵ Also, the effect of Ti-rich or Fe-rich B2 compositions are taken into account, by averaging the cases for Ti-rich and Fe-rich B2 phases.^46–48 The calculated defect formation energies suggest that the V and Sn strongly favour substitution at Ti sites over Fe sites. It is difficult to form single phase Fe-substituted TiFe alloys while keeping the original synthetic ratios of TiFe_0.8(CrMnCuSn)_0.2 and TiFe_0.8(VCoNiCu)_0.2, which leads to the formation of segregated areas with V or Sn.

Fig. 3 SEM-BSE images and EDS mappings of (a) TiFe_0.8(CrMnCuSn)_0.2, (b) TiFe_0.8(CrMnNiCu)_0.2, (c) TiFe_0.8(MnCoNiCu)_0.2, (d) TiFe_0.8(CrCoNiCu)_0.2, and (e) TiFe_0.8(VCoNiCu)_0.2 samples. The scale bars on the elemental mappings of the samples are 10 μm.

Thermodynamic assessments also show similar trends as the DFT calculations for predicting preferences of substitution elements for Ti or Fe sites (Fig. S4, Table S4, and Note S3). Specifically, the unfavourable substitution of Fe-sites with V or Sn is also confirmed by the thermodynamic calculations showing high concentrations of these elements in the secondary phases despite the overall Fe-deficiency. For the thermodynamic calculation results, while TiFe_0.8(MnCoNiCu)_0.2 shows single-phase behaviour for most of the temperature range, the other alloys show some degree of secondary phase formation. In accordance with the XRD patterns and SEM-EDS mappings, the secondary phase is less likely formed in TiFe_0.8(CrCoNiCu)_0.2, TiFe_0.8(MnCoNiCu)_0.2, and TiFe_0.8(CrMnNiCu)_0.2 than in TiFe_0.8(CrMnCuSn)_0.2 and TiFe_0.8(VCoNiCu)_0.2, in which the segregation of Sn- and V-containing compounds is detected, respectively. In particular, the thermodynamic assessment of TiFe_0.8(CrMnCuSn)_0.2 sample predicts the formation of Ti- and Sn-rich AlTi₃-like phase, which is in good agreement with the experimental results (Fig. S3). However, the prediction for TiFe_0.8(VCoNiCu)_0.2 does not show a good match in terms of the elemental compositions of secondary phases. While the secondary phase observed in SEM-EDS is rich in Ti and V, the thermodynamic assessment indicates no inclusion of V in the Ti-rich NiTi₂-type phase. This discrepancy may imply that the thermodynamic assessment has lost some accuracy due to the increased number of constituent elements.⁴⁶

3.4. Thermodynamic parameters of multi-element-substituted TiFe alloys

To experimentally determine thermodynamic parameters (ΔH and ΔS) of the TiFe alloy samples, PCT hydrogen isotherms at 4 different temperatures (30, 50, 70, and 90 °C) were obtained (Fig. 4). Compared to the isotherms of pure TiFe in Fig. S5, the substituted alloys show sloped isotherms, consistent with previous studies of substituted TiFe alloys.^14,47 TiFe_0.8(MnCoNiCu)_0.2 shows much flatter isotherm curves compared to the other samples, possibly due to the absence of V and Cr, which have been reported to make the plateau region sloped.^17,48 In addition to the impact of V or Cr individually incorporated into the alloys, the sloped plateau may also result from the broad size distribution of octahedral interstices due to the multi-element substitution, which creates a dispersion of local binding energetics.⁴³ To account for the sloped isotherms, the P_eq values were selected as the inflection points of the curves or midpoint of linear plateau regions and fitted using van't Hoff plot to calculate the ΔH and ΔS values (Fig. S6, and Tables 1, S5). However, despite the observed lattice expansion of the samples, their gravimetric hydrogen storage capacities decrease compared to the non-substituted TiFe. This reduction in capacity mainly arises from the formation of secondary phases that either do not absorb hydrogen or absorb it only minimally. In particular, the formation of the suboxide Ti₄Fe₂O_x phase may contribute to the reduction in the hydrogen capacity, particularly for Fe-deficient TiFe systems.⁴⁹ However, it is challenging to detect such phase due to the overlap with main reflections in the XRD patterns and its presence on the outer surface of the ingot.¹⁰ The ΔH value representing each sample is determined from the geometric mean of P_eq values for absorption and desorption, which is equivalent to averaging ΔH values calculated from absorption and desorption.⁵⁰ Considering that substitution of non-hydride-forming B elements can contribute to the stabilization of hydride phases, the higher enthalpy values versus pure stoichiometric TiFe (24.1 kJ mol⁻¹ H₂, Fig. S5c) are attributed to the major substitution of the B element (Fe).²

Fig. 4 Hydrogen pressure-composition isotherms (PCI) of (a) TiFe_0.8(CrMnCuSn)_0.2, (b) TiFe_0.8(CrMnNiCu)_0.2, (c) TiFe_0.8(MnCoNiCu)_0.2, (d) TiFe_0.8(CrCoNiCu)_0.2, and (e) TiFe_0.8(VCoNiCu)_0.2 samples. The isotherms were measured at 30, 50, 70, and 90 °C.

Table 1 The experimentally obtained ΔH and ΔS values of TiFe_0.8(X)_0.2 samples

	ΔHabs (kJ mol^−1 H2)	ΔHdes (kJ mol^−1 H2)	ΔSabs (J mol^−1 H2 K^−1)	ΔSdes (J mol^−1 H2 K^−1)
TiFe0.8(CrMnCuSn)0.2	29.8	35.4	98.7	112
TiFe0.8(CrMnNiCu)0.2	28.3	35.7	86.7	105
TiFe0.8(MnCoNiCu)0.2	28.7	31.6	93.9	97.1
TiFe0.8(CrCoNiCu)0.2	33.6	35.1	103	102
TiFe0.8(VCoNiCu)0.2	30.2	36.6	91.4	107

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To predict ΔH values from ML, gradient boosting tree (GBT) regressor models were trained, similarly to previous studies focused on data-driven prediction of thermodynamic properties of metal hydrides.^23–25 Concurrently with the ML model, the enthalpy ΔH values were also estimated from DFT.³⁹ In both sets of calculations, the synthetic compositions were used to yield the ΔH values (Fig. S7). As a benchmark to evaluate predictive accuracy, the absolute values of the differences from the experimentally measured ΔH values were obtained (Fig. 5a). As indicated in Fig. 5b–d, the predicted values from ML show similar (or even superior) accuracy versus DFT with respect to the measured experimental values. Note that although DFT is an accurate first-principles approach, the configurational sampling of the alloy presents some difficulty (see Section 2.4. for details of how this was done). In contrast, the ML model can give reasonable predictions without any prior information regarding the local atomic configurations and at a small fraction of the computational cost. Additionally, it should be noted that many of the previous prediction studies on hydrogen storage alloys primarily focused on varying the compositions with fixed types of elements,^51–53 while this study also demonstrates flexibility in selecting the constituent elements. In this sense, we suggest that the high-throughput ML models are generally highly efficient to screen multi-atom-substituted TiFe alloys for on-demand tuning of thermodynamic properties.

Fig. 5 (a) A table of ΔH_exp, ΔH_ML and ΔH_DFT. Parity plots of experimentally obtained, ML-predicted and DFT-calculated ΔH values (ΔH_exp, ΔH_ML and ΔH_DFT, respectively); (b) ΔH_exp and ΔH_ML, (c) ΔH_exp and ΔH_DFT, and (d) ΔH_ML and ΔH_DFT. The star symbols denote averaged enthalpy values of absorption and desorption for each sample.

All five samples exhibit significantly lower plateau pressures compared to stoichiometric TiFe. While the lowered plateau pressures are beneficial to low-pressure operation of hydrogen storage systems, TiFe alloys with higher plateau pressures also need to be tested to increase the working capacity at low temperatures. To examine the samples with higher plateau pressures, two more systems were devised to destabilise the hydrides: (i) additional A-site (Ti) substitution with Mo and (ii) a lower level of B-site (Fe) substitution. For each of these, the enthalpy values were likewise predicted from ML.

In the case of Ti-site substitution with Mo, we find that the ML model significantly underpredicts the measured ΔH: the alloy composition with Ti_0.95Mo_0.05Fe_0.8(MnCoNiCu)_0.2 is predicted by the ML model to have ΔH = 22.2 kJ mol⁻¹ H₂, whereas our prepared sample was measured to have ΔH = 31.4 and 34.1 kJ mol⁻¹ H₂ for absorption and desorption, respectively (Fig. S8)—an average of ∼10.6 kJ mol⁻¹ H₂ higher than predictions. It is speculated that this anomaly can be mainly attributed to the substitution of Fe sites by Mo, as the formation of an Fe-rich secondary phase containing Mo is observed in SEM-EDS, which suggests a larger degree of substitution of Fe than Ti (Fig. S9). Given that the substitution of Fe sites with Mo is reported to stabilise hydrides compared to pure TiFe,⁵⁴ this discrepancy likely arises from the incorporation of Mo into the B (Fe) sites.

Also, another alloy with the composition of TiFe_0.9(MnCoNiCu)_0.1 was examined as a proxy for reduced substitution of Fe-sites to achieve higher plateau pressure, since the TiFe_0.8(MnCoNiCu)_0.2 sample exhibits a flatter plateau compared to other samples with single-phase behaviour (Fig. S10a–c). TiFe_0.9(MnCoNiCu)_0.1 shows a significantly increased plateau pressure compared to TiFe_0.8(MnCoNiCu)_0.2, implying a destabilising effect for less substitution. Nevertheless, the ΔH values of TiFe_0.9(MnCoNiCu)_0.1 and TiFe_0.8(MnCoNiCu)_0.2 are very similar, contrary to their significantly different plateau pressures (Fig. S10d). Notably, this small difference was also correctly predicted by the ML model to be only 0.3 kJ mol⁻¹ H₂. Instead, such large difference in plateau pressure is mainly attributed to the difference in ΔS, which is larger for TiFe_0.9(MnCoNiCu)_0.1, in contrast to the reported case of TiFe_1−xNi_x.¹⁰ This distinct behaviour is strongly influenced by the specific substitutional compositions rather than the degree of substitution, particularly in multi-element substitution system. The strong dependence on the composition is also corroborated by the significant variation in |ΔS| values, ranging from 86.7 to 112 J mol⁻¹ H₂ K⁻¹. Overall, the examples of Ti_0.95Mo_0.05Fe_0.8(MnCoNiCu)_0.2 and TiFe_0.9(MnCoNiCu)_0.1 lead us to assume that upon varying the base TiFe_0.8(X)_0.2 composition, the predictive capability of the ML model remains more consistent when considering only B-site substitution.

3.5. Activation behaviour of TiFe alloys

One of the primary challenges in the practical use of TiFe-based alloys for various hydrogen use cases is the difficulty associated with the first hydrogen absorption, which is also referred to as activation. The activation properties of TiFe alloys are influenced by a variety of contributing factors including the types of secondary phases, the amount of secondary phases, the thickness of the passivation layer, the composition of the passivation layer, and even the atmosphere in which samples were treated.^4,5,9 To evaluate the impact of oxidised surfaces, activation behaviours under two conditions were examined for each alloy: (i) samples were crushed in Ar-filled glovebox and transferred without air exposure, and (ii) samples were similarly crushed under Ar but subsequently exposed to air to form an oxidised layer on the surface (Fig. 6a and b, respectively). For the samples transferred without air exposure, hydrogen is immediately absorbed for all of the substituted alloys, in contrast to the pure TiFe sample which shows only limited hydrogen absorption with the same process (Fig. 6a). Such immediate hydrogen absorption can primarily be attributed to the protected clean surface by inert atmosphere during the transfer, which limits oxide formation. However, note that the pure TiFe does not show similarly rapid activation kinetics, even under protective atmosphere. Hence, the substitution elements must also contribute to the activation behaviour; this is consistent with previously reports of TiFe alloys showing short incubation times when crushed under protective atmosphere.^55,56

Fig. 6 First hydrogenation (activation) kinetics under 40 bar H₂ at 30 °C of TiFe_0.8(X)_0.2 samples with pure TiFe: (a) transferred under Ar and (b) exposed in air for 1 hour. (c) Fe 2p and (d) Ti 2p XPS spectra of air-exposed TiFe_0.8(X)_0.2 samples.

In contrast to the case without air exposure, the air-exposed samples exhibit very different shapes of the absorption curves, presenting a slow absorption region at the initial stage, also known as the incubation time (Fig. 6b). Such behaviour is primarily attributed to the formation of a passivating oxide layer on the surface of alloys when exposed to air, which is known to hinder activation.^57,58 Despite such air exposure, all of the modified samples show hydrogen uptake at near-room temperature (30 °C), while pure TiFe does not absorb hydrogen at all under these conditions. The morphological change of alloys upon the activation was also investigated with SEM (Fig. S11). After activation, cracks are known to develop on the surface of TiFe powders due to volume expansion upon hydrogenation.^59,60

In the case of the air-exposed samples, the activation ability exhibits notable variations among the samples, and identifying the primary factors contributing to these differences remains challenging. The incubation times of the samples vary in the following order: TiFe_0.8(CrMnNiCu)_0.2 > TiFe_0.8(CrCoNiCu)_0.2 > TiFe_0.8(MnCoNiCu)_0.2 > TiFe_0.8(CrMnCuSn)_0.2 > TiFe_0.8(VCoNiCu)_0.2. In this system, upon the introduction of substitution elements, two primary factors can potentially affect the activation properties of the samples: (i) change in surface structure or oxide thickness; and (ii) secondary phases formed depending on the introduction of substituent elements. To observe the surface structures and compositions of the alloys, X-ray photoelectron spectra (XPS) of the air-exposed samples prior to activation were collected (Fig. 6c, d and Table S6). Although a significant amount of oxygen is observed, each of the samples exhibits Fe⁰ and Ti⁰ signals in the Fe 2p and Ti 2p spectra, with the relative intensities of the metallic peaks differing depending on the sample. Several studies have reported that the emergence of a metallic Fe peak is observed after activation, which may relate to the exposure of metallic Fe component itself⁶¹ or the evolution of metallic Fe protected by thin oxidised layers of other oxyphilic elements that may aid activation by facilitating dissociation of H₂ molecules on the surface. However, in our case, the different intensities of metallic peaks among the samples curiously show little correlation to the observed activation behaviour or incubation time. In addition, the Ti/Fe ratio of the surface, which reflects the change in surface structure arising from Ti and Fe-related secondary phases and was reported to affect activation behaviour,⁶² likewise exhibits poor correlation with the relative activation abilities of the samples in this study (Table S6). Another key factor in predicting activation abilities of the alloy samples is the degree of formation of secondary phases upon the introduction of substitution elements. However, TiFe_0.8(CrMnCuSn)_0.2, which shows the most prominent secondary phases, including Laves phases as observed in XRD and SEM-EDS, exhibits similar or longer incubation time compared to the other samples. Also, the potential presence of the aforementioned Ti₄Fe₂O_x phase may facilitate the activation behaviour.^49,63

In this regard, neither the surface structures nor the formation of secondary phases can solely explain the trend in the activation behaviour of the alloys. Consequently, it can be concluded that in this system, both factors must contribute somehow to the observed activation behaviour, making it challenging to predict activation outcomes when considering only one contributing factor.

While it is challenging to establish a general explanation for the activation behaviours of multi-element-substituted TiFe samples, it can be deduced that the distinctly short incubation time of TiFe_0.8(VCoNiCu)_0.2 can be partially explained by the presence of V, an element not present in the other samples. Indeed, a previous study of single-substituted TiFe_0.9M_0.1 (M = V, Cr, Fe, Co, Ni) alloys also revealed that TiFe_0.9V_0.1 exhibits the best activation performance among the tested samples by forming the thinnest Ti-oxide layer to aid the activation.⁵ Therefore, it also can be deduced that the introduction of V may affect the surface structure to form thin Ti-oxides compared to the other samples, which is also consistent with the smaller Ti/Fe ratio compared to the other samples (0.78, Table S6). However, the negligible surface fraction of V (0.1 at%) from XPS quantification further suggests that the influence of V incorporation is primarily indirect, affecting the relative compositions and growth rates of Ti-oxides and Fe-oxides on the surface rather than directly facilitating hydrogen transport.

4. Conclusion

We demonstrated that data-driven predictions can be used to guide multi-element substitution strategies in TiFe and target finely tuned hydride thermodynamic stability. ML models were used to predict thermodynamic properties (specifically hydride reaction enthalpy) of TiFe substituted with four elements, and five compositions were selected for subsequent experimental validation. DFT calculations were also utilized to predict hydride reaction enthalpy for comparison with the experimental and ML-predicted values. The enthalpy values predicted by ML (and DFT) show generally good agreement with the experimental values with only minor exceptions, indicating that ML-based screening models using features derived only from the nominal composition^24,25 are generally effective for predicting the thermodynamic properties of multi-element-substituted TiFe materials.

In addition to the thermodynamic properties, activation behaviours of the TiFe alloys were also evaluated, revealing that all of the samples show near-instant activation during the first hydrogenation step under Ar. Similarly, the samples exposed to air show facile activation near room temperature, with the incubation time significantly influenced by the sample composition. This behaviour contrasts sharply with that of pure TiFe, which is essentially inert under these same conditions. The alloy samples exhibit significant variation in incubation time, but no single factor could be discerned as dominantly correlated to the activation properties. Hence, we conclude that the variability is likely attributable to a subtle combination of multiple factors, including (i) formation of different surface structures by substitution elements,⁵ and (ii) formation of secondary phases such as C14 Laves phases.⁶⁴ We suggest that a deeper understanding of the interplay among these factors—particularly in the case of complex, multi-element-substituted alloys—would be a fruitful avenue for further investigation. Leveraging the predictive power of high-throughput ML models combined with multi-element substitution, we further suggest that other hydrogen storage alloys (e.g. AB₂, AB₅) could also be tuned to achieve tailored properties with diversified elemental compositions, reducing the dependency on any particular element, and potentially enabling the use of recycled or scrap metal alloys.⁶⁵

Author contributions

YongJun Cho: conceptualization, methodology, investigation, validation, writing – original draft, visualization. Matthew D. Witman: conceptualization, formal analysis, software, investigation, writing – original draft, investigation, formal analysis, conceptualization. Hyung-Ki Park: formal analysis, investigation, resources. Won-Seok Ko: methodology, formal analysis, resources, writing – review & editing. Brandon C. Wood: writing – review & editing, supervision. Vitalie Stavila: conceptualization, methodology, resources, writing – review & editing, supervision, project administration, funding acquisition. Eun Seon Cho: conceptualization, methodology, resources, writing – review & editing, supervision, project administration, funding acquisition.

Conflicts of interest

There are no conflicts to declare.

Data availability

The authors will supply the relevant data in response to reasonable requests. The data supporting this article have been included as part of the SI.

The supplementary information contains the following contents: (1) details of ML, DFT, and thermodynamic calculations; (2) hydride thermodynamic properties in the dataset; (3) magnified XRD patterns and the correlation between cell volumes and average atomic radii; (4) SEM-BSE images, SEM-EDS quantifications, and XRF elemental quantifications; (5) temperature-dependent thermodynamic calculations; (6) hydrogen PCT isotherms of pure TiFe, van't Hoff plots, and thermodynamic parameters; (7) van't Hoff plots; (8) the atomic structure used in the DFT calculations; (9) the hydrogen PCT isotherms of Ti_0.95Mo_0.05Fe_0.8(MnCoNiCu)_0.2, van't Hoff plots, and thermodynamic parameters; (10) SEM-BSE images and elemental compositions of phases of Ti_0.95Mo_0.05Fe_0.8(MnCoNiCu)_0.2; (11) a SEM-BSE image, elemental mappings, hydrogen PCT isotherms, van't Hoff plots, and thermodynamic properties of TiFe_0.9(MnCoNiCu)_0.1; (12) SEM images of air-exposed TiFe_0.8(X)_0.2 samples before and after activation; (13) site prefernces of alloying elements predicted by DFT; (14) elemental XPS quantification of air-exposed samples. See DOI: https://doi.org/10.1039/d5ta04389a.

Acknowledgements

This work was supported by National R&D Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (RS-2022-NR066812) and by the Trilateral Research Program through the National Research Council of Science & Technology (NST) funded by the Ministry of Science & ICT, Republic of Korea (Grant #. Global-24-005). This research was partially supported by the U.S. Department of Energy's National Nuclear Security Administration (NNSA) under the Trilateral Framework on Cooperation in Science and Innovation among the NNSA, the Cabinet Office of Japan, and the Ministry of Science and ICT of the Republic of Korea. We also gratefully acknowledge research support from the U.S. Department of Energy (DOE), Office of Energy Efficiency and Renewable Energy (EERE), Hydrogen and Fuel Cell Technologies Office through the Hydrogen Materials Advanced Research Consortium (HyMARC). A portion of this work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory (LLNL) under Contract DE-AC52-07NA27344. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC (NTESS), 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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