Exploring the electrocatalytic performance of PdIrSnZnMo high entropy alloy (HEA) towards the hydrogen evolution reaction in an acidic medium: a theoretically supported approach

Abstract

High entropy alloys (HEAs) are a versatile class of electrocatalysts with tunable surface properties, compositions, and synergistic elemental effects, notably enhancing the hydrogen evolution reaction (HER). Herein, we report the development of PdIrSnZnMo HEAs with varying Pd loadings (0.01–0.05 M) using a facile solvothermal method. The structural features and composition of the prepared PdIrSnZnMo HEA nanostructures were characterized using X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), field emission scanning electron microscopy (FESEM), and high-resolution transmission electron microscopy (HR-TEM). Systematic electrocatalytic studies revealed a remarkable HER performance even at a low Pd loading (0.01 M). Notably, the PdIrSnZnMo HEA with 0.05 M Pd exhibited an ultra-low overpotential of 17 mV to achieve a current density of −10 mA cm⁻² in an acidic medium, surpassing the conventional Pt/C electrocatalyst. The electrocatalyst also demonstrated outstanding durability and maintained its stability without decomposition during prolonged operation. Density functional theory (DFT) calculations elucidated the surface atomic configurations of the PdIrSnZnMo HEA, highlighting the role of Pd active centers coordinated by Ir, Sn, Zn, and Mo. This study presents versatile nanostructured HEA systems and a straightforward synthetic strategy with broad implications for catalysis in energy conversion applications.

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1 Introduction

Global energy demand continues to rise due to the increasing consumption, depletion of fossil fuels, and greenhouse gas emissions associated with conventional energy sources.^1,2 To address the challenges of sustainable energy development, hydrogen has emerged as a promising alternative to prospective energy solutions owing to its high energy density and zero carbon emissions.^3,4 Electrochemical water splitting is an effective method for hydrogen production, involving the oxygen evolution reaction (OER) at the anode and the hydrogen evolution reaction (HER) at the cathode.^5–7 Among water electrolysis technologies, proton exchange membrane water electrolyzers (PEMWEs) have gained significant attention for producing ultra-pure hydrogen. PEMWEs offer multiple advantages, including zero carbon emissions, high current densities (up to 2 A cm⁻²), high efficiency (80–90%), and rapid response to load fluctuations.^8–10 However, challenges such as electrocatalyst leaching and degradation limit the catalytic performance and long-term durability.^11,12

To date, Pt is regarded as a state-of-the-art electrocatalyst for the HER in acidic media, but it suffers from corrosion under acidic conditions, and its scarcity motivates the development of cost-effective alternatives by alloying with cheaper elements without compromising activity.^13–15 Therefore, developing robust, stable, and cost-effective electrocatalysts that can operate under harsh acidic conditions is critical for the commercialization of PEM water electrolyzers. The performance of an electrocatalyst is largely determined by the surface adsorption energies of the reaction intermediates, which are strongly influenced by the electronic structure of the active species.¹⁶

Recently, high entropy materials (HEMs) have attracted considerable attention for electrocatalysis due to their configurational entropy arising from multiple metal species in equi- or near-equiatomic fractions. This high entropy enhances entropic contributions, reducing the overall free energy and stabilizing complex structures.²⁰ HEMs encompass a wide range of materials, including high-entropy oxides, carbides, hydroxides, metal–organic frameworks (MOFs), and fluorides.²³ Among them, high-entropy alloys (HEAs) have garnered particular interest due to their unique synergistic effects, which stem from high entropy, lattice distortion, sluggish diffusion, and the so-called cocktail effect, enabling enhanced catalytic activity and stability.^17,18 HEAs are composed of five or more metal elements that are randomly distributed to form a single solid-solution phase and are characterized by high configurational entropy (>1.5 R). Due to this intrinsic feature, structural stability is improved, thereby enhancing the material's resistance to degradation during electrochemical reactions and facilitating long-term electrocatalyst durability. In addition, lattice distortion suppresses atomic diffusion, which prevents surface reconstruction and further improves corrosion resistance. The high mixing entropy (ΔS_mix) reduces the Gibbs free energy (ΔG_mix = ΔH_mix − TΔS_mix), enhancing material stability, particularly at elevated temperatures.^21,22 Fabricating single-phase HEAs is highly desirable, as they often exhibit amorphous-like features with abundant catalytically active sites and surface defects induced by lattice strain, which collectively improve the HER kinetics. Additionally, the electronic structures of HEAs can be effectively tuned to facilitate charge transfer and promote the adsorption of reaction intermediates by modifying the overlap of atomic orbitals, thereby further promoting the HER activity in acidic media.^19,24,25 These intrinsic properties endow HEAs with superior electrocatalytic performance, remarkable stability, structural tunability, and excellent corrosion resistance. The diverse elemental compositions of HEAs also enable the rapid adsorption of reaction intermediates, supporting efficient hydrogen evolution at low overpotentials.²⁶ Considering the intrinsic advantages of HEAs and the exceptional performance of state-of-the-art catalysts, such as Pt, the development of new catalysts based on Pt-based HEAs for the HER in acidic media has garnered significant interest, offering high efficiency and reducing the required Pt content through high-entropy alloy formation. However, most reported HEA-based HER electrocatalysts still include Pt as a constituent metal to enhance their stability. To address this limitation, the present study focuses on developing HEA electrocatalysts without Pt. Therefore, developing a Pt-free electrocatalyst is the primary objective of this study, which is achieved by incorporating other metals without compromising the catalytic activity. The combination of multiple elements, including earth-abundant non-noble metals, together with small amounts of PGMs in an alloy, enables high catalytic performance while significantly reducing the total PGM content. As alternatives, other PGMs, such as Pd and Ir, were combined with low-cost transition metals (Sn, Mo, and Zn), and their electrocatalytic performance was evaluated in acidic media. The specific choice of Pd is mainly due to its high activity, similar to platinum properties, and high hydrogen adsorption energy, which is second only to that of Pt. In addition, Ir can effectively tune the electron environment and thus enhance the intrinsic catalytic activity by adjusting the adsorption of active H species.^69,70 For example, Fu et al. reported Pt-free PdMoGaInNi HEA nanosheets for HER in an acidic medium that achieved a current density of −10 mA cm⁻² at an overpotential of only 13 mV, maintaining exceptional durability of over 200 h.⁶⁰ Similarly, Jeong and coworkers demonstrated that AuPdFeNiCo HEA nanoparticles (NPs) delivered −10 mA cm⁻² at 45 mV under acidic conditions.⁶¹ In addition, the synthesis strategy for HEAs plays a significant role in modulating electronic structures, tuning morphology, and creating adsorption sites that are favorable for electrochemical activity.^24,27

Solvothermal synthesis offers a facile and effective route for fabricating nanostructured HEAs, avoiding harsh conditions and requiring sophisticated instrumentation. Selecting an appropriate solvent ensures uniform precursor dispersion, effective alloying, and suppression of phase separation. By carefully controlling the reaction parameters and accounting for the differing reduction rates of the metallic species, solvothermal synthesis promotes the formation of abundant active sites through strong chemical interactions and lattice strain arising from atomic size differences.^28,29 For instance, Zhao et al. synthesized PtPdRhRuCu HEA nanoparticles via a solvothermal process and achieved a uniform single-phase structure without phase separation. These HEA nanoparticles exhibited remarkable electrocatalytic activity, requiring an overpotential of only 23.3 mV to reach a current density of 10 mA cm⁻² in an alkaline medium. DFT calculations attributed this enhanced performance to synergistic interactions among the active sites.³⁰ In the present study, PdIrSnZnMo HEAs were synthesized using a simple solvothermal method. The atomic radii of the constituent elements (Pd, Mo, Sn, Zn, and Ir) are 0.137, 0.139, 0.162, 0.132, and 0.135 nm, respectively. Notably, Sn has the largest atomic radius, which increases its propensity to oxidize. This enhanced oxidation tendency promotes stronger interactions with other metal species, facilitating alloy formation and generating numerous catalytically active sites. HER electrocatalytic performance is closely related to these atomic arrangements and the resulting electronic structure. DFT calculations were carried out to explore the structural diversities of the PdIrSnZnMo HEA and to evaluate its thermodynamic and kinetic favorability for the HER in H₂SO₄. In addition, the d-band properties, including HOMO–LUMO positions relative to the Fermi level, were analyzed, and the density of states (DOS) was examined to identify active sites, investigating the availability of electronic states and their orbital contributions from different elements near the Fermi level.

2 Materials and methods

The precursors used for the preparation of alloys included tetraamminepalladium (II) acetate (Pd(NH₃)₄(CH₃CO₂)₂), iridium (III) acetylacetonate (C₁₅H₂₁IrO₆), tin (II) chloride dihydrate (SnCl₂·2H₂O), zinc sulphate heptahydrate (ZnSO₄·7H₂O), molybdic acid (MoO₃·H₂O), and Nafion 117 were purchased from Sigma Aldrich Pvt. Ltd. Ethylene glycol (EG, (CH₂OH)₂), isopropyl alcohol (IPA, CH₃CH(OH)CH₃), and methanol (CH₃OH) were procured from Ensure Chemicals. Graphite foil (thickness 0.4 mm, (0.015 in), 99.8%) was purchased from Thermo Fischer Scientific.

2.1 Solvothermal synthesis of PdIrSnZnMo HEA

To synthesize PdIrSnZnMo HEA, nearly equimolar ratios of the respective precursors were dispersed in organic solvents. The precursors for Sn, Zn, Mo, and Pd were dissolved in ethylene glycol to form solution 1, while the Ir precursor was dissolved separately in methanol to form solution 2. After achieving a homogeneous suspension of solution 1, solution 2 was added, and the mixture was magnetically stirred for 4 h to ensure complete blending. The resulting suspension was then transferred to a Teflon-lined stainless steel autoclave and heat-treated at 200 °C for 18 h. After the reaction, the autoclave was allowed to cool naturally.³¹ The obtained product was thoroughly washed with deionized water and ethanol to remove residual impurities, followed by drying at 70 °C for 5 h to yield the final PdIrSnZnMo HEA. To prepare PdIrSnZnMo HEAs with varying Pd concentrations (0.01–0.05 M), the same procedure was followed while keeping the concentrations of Ir, Sn, Mo, and Zn constant (0.05 M). The resulting samples were labeled Pd_0.01IrSnZnMo, Pd_0.02IrSnZnMo, Pd_0.03IrSnZnMo, Pd_0.04IrSnZnMo, and Pd_0.05IrSnZnMo HEA. A schematic illustration of the synthesis procedure is shown in Scheme 1.

Scheme 1 Schematic of the synthesis of PdIrSnZnMo HEA using the solvothermal technique.

2.2 Characterization techniques

X-ray diffraction (XRD) analysis was performed using a Rigaku XRD diffractometer with Cu-K_α radiation (λ = 1.5406 Å). The diffraction patterns were collected over a 2θ range of 5–90° at a scan rate of 5° per min. Microstructural and elemental analyses were carried out using a field emission scanning electron microscope (FESEM, Hitachi S-4700, Japan) equipped with an energy-dispersive X-ray spectroscopy (EDS) system (Noran System 7). High-resolution transmission electron microscopy (HR-TEM) was conducted using a Tecnai Osiris microscope operating at an accelerating voltage of 200 kV. HR-TEM equipped with EDS and high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) was used to examine the morphology, elemental composition, and spatial distribution of the prepared nanostructures. The atomic concentrations of Pd, Ir, Sn, Zn, and Mo were determined using inductively coupled plasma mass spectrometry (ICP-MS, Agilent). The valence states of the elements in the HEAs were analyzed by X-ray photoelectron spectroscopy (XPS, Microlab 350, Thermo Electron) with peak fitting performed using an asymmetric Gaussian/Lorentzian mixed function. All recorded binding energies were calibrated with reference to the C 1s peak at 284.7 eV.

2.3 Electrochemical techniques

The electrochemical hydrogen evolution reaction (HER) performance was evaluated in a standard three-electrode setup using a Biologic VMP-300 electrochemical workstation in an acidic medium. Graphite foil (thickness ∼0.4 mm) modified with the electrocatalysts was used as the working electrode. A graphite rod served as the counter electrode, while a saturated calomel electrode (SCE) was used as the reference electrode. To investigate the redox behavior of the electrocatalysts and ensure the stability of the catalyst layer, cyclic voltammograms (CVs) were recorded in the potential range from 0.8 to −0.8 V vs. SCE at a scan rate of 10 mV s⁻¹ in a 0.5 M H₂SO₄ electrolyte. These measurements were conducted for all samples prepared with varying Pd contents (Pd_0.01IrSnZnMo, Pd_0.02IrSnZnMo, Pd_0.03IrSnZnMo, Pd_0.04IrSnZnMo, and Pd_0.05IrSnZnMo). The overpotential required to achieve a current density of −10 mA cm⁻², as well as the onset potential for hydrogen evolution, was determined from polarization curves obtained by linear sweep voltammetry (LSV) in 0.5 M H₂SO₄ (pH ∼0) at ambient temperature. LSV was carried out in the potential range from 0 to −0.8 V vs. SCE at a scan rate of 1 mV s⁻¹. The reaction kinetics were analyzed by extracting Tafel slopes from Tafel plots, which were obtained by refitting the polarization data with the logarithm of the current density plotted on the x-axis and overpotential on the y-axis. The measured potentials were converted to the reversible hydrogen electrode (RHE) scale using the following equation (eqn (1)):

E_RHE = E_SCE + E_SCE⁰ + 0.059 × pH (E_SCE⁰ = 0.241, pH = 0). (1)

The electrochemically active surface area (ECSA) was estimated from the double layer capacitance (C_dl). To determine C_dl, CV measurements were performed at different scan rates (20–200 mV s⁻¹) within the non-faradic potential region from −0.1 to −0.2 V vs. SCE, which displayed a characteristic rectangular profile (Fig. S1, SI). The current density at a fixed potential (−0.15 V vs. SCE) was determined, and a plot of current density versus scan rate was constructed. The slope of the resulting linear fit corresponds to the C_dl value (Table S1, SI). The roughness factor (R_f) is another parameter that influences the electrocatalytic performance. R_f was determined as the ratio of the ECSA to the geometric surface area of the electrode (1 cm²). The calculated values are listed in Table S1 (SI).

The turnover frequency (TOF), which reflects intrinsic HER activity, was calculated using the following expression (eqn (2)):

where J represents the current density at the overpotential value (17 mV), F is the faraday constant (96 485.4 C mol⁻¹), and n is the number of moles of the catalyst. The long-term durability of the electrocatalysts in an acidic medium was evaluated using chronopotentiometry (CP) at constant current densities.

2.4 Catalyst ink preparation and electrode modification

The electrocatalyst ink was prepared by dispersing 5 mg of the synthesized electrocatalysts (PdIrSnZnMo HEAs with varying Pd concentrations) in a mixture of 5 µL of Nafion 117 and 20 µL of isopropyl alcohol (IPA). The resulting slurry was ultrasonicated for a few minutes to obtain a homogeneous suspension. Prior to the electrocatalyst loading, the graphite foil working electrode (2 cm × 1 cm) was polished with sandpaper to roughen the surface, thereby improving catalyst adhesion. The graphite foil was subsequently washed with acetone and dried to ensure a clean substrate. The catalyst ink was then drop-cast onto the cleaned graphite foil over an active area of 1 cm × 1 cm and dried at 70 °C for 5 h, yielding a well-adhered catalyst-modified electrode that was used for all electrochemical measurements.

3 Results and discussion

3.1 Structural and composition analyses

The XRD patterns of the Pd_0.01IrSnZnMo, Pd_0.02IrSnZnMo, Pd_0.03IrSnZnMo, Pd_0.04IrSnZnMo, and Pd_0.05IrSnZnMo HEAs are shown in Fig. 1(a). With an increasing Pd concentration from 0.02 M to 0.05 M, the intensity of the diffraction peaks increased, indicating improved crystallinity. Moreover, a noticeable shift in peak positions along with peak broadening was observed, as highlighted in the extended XRD view (Fig. 1(b)). This shift may arise from lattice contraction or overlapping of multiple metallic species during alloy formation. The prominent diffraction peaks at 2θ of 39.8°, 46.2°, 67.5°, 81.3°, and 85.7° corresponded to the (111), (200), (220), (311), and (222) planes of Pd (ICDD, PDF No. 00-005-0681), respectively.³² These indexed planes confirmed the formation of a single-phase, face-centered cubic (fcc) structure. The broad peak observed at ∼42° may originate from the combination of the IrPdZn alloy, which is consistent with ICCD PDF No. 00-060-0156. Furthermore, it was evident that with increasing Pd concentration, the peak intensity increased. For the sample with 0.05 M Pd (Pd_0.05IrSnZnMo), the peak position was slightly shifted toward higher angles, which might have resulted from lattice strain or structural changes induced by the strong bonding of additional Pd atoms. Importantly, no additional diffraction peaks corresponding to the crystalline phases of the individual elements were detected, strongly confirming the formation of a nanostructured alloy through high entropy mixing.

Fig. 1 XRD patterns of Pd_0.01IrSnZnMo, Pd_0.02IrSnZnMo, Pd_0.03IrSnZnMo, Pd_0.04IrSnZnMo, Pd_0.05IrSnZnMo HEAs, and IrSnZnMo. (b) Enlarged view of the XRD pattern (Fig. 1(a)) in the range of 39–45°. (c) Raman spectra of Pd_0.01IrSnZnMo, Pd_0.02IrSnZnMo, Pd_0.03IrSnZnMo, Pd_0.04IrSnZnMo, Pd_0.05IrSnZnMo HEAs, and IrSnZnMo.

Raman spectra of Pd_0.01IrSnZnMo, Pd_0.02IrSnZnMo, Pd_0.03IrSnZnMo, Pd_0.04IrSnZnMo, and Pd_0.05IrSnZnMo HEAs and the IrSnZnMo reference are presented in Fig. 1(c). The Pd_0.05IrSnZnMo sample exhibited a Raman band at 621.9 cm⁻¹, which can be attributed to the B_1g vibrational mode of Pd and/or the A_1g mode of Sn.^57,58 In samples with lower Pd concentrations, this peak displayed a blue shift (toward lower wavelengths), suggesting changes in chemical bond length or electronic structure caused by the intercalation of multiple elements. Additionally, weak and broad bands at ∼273.6 and 320.3 cm⁻¹ were ascribed to second order scattering or possibly a resonance effect, respectively.^33,34 A less intense Raman band at 422 cm⁻¹ in the Pd_0.05IrSnZnMo sample was associated with the E_g vibrational mode of Pd and/or nanoscale effects of Sn.^33,58 Furthermore, a broad band at 861.3 cm⁻¹ was attributed to the A_1g/B_g vibrational modes of Mo.⁵⁹ Overall, the absence of prominent or sharp Raman peaks across all samples suggests strong interaction and lattice distortion among the constituent elements in the HEAs. Elemental analysis by EDS during HRTEM and FESEM confirmed the presence of Ir, Sn, Zn, Mo, and Pd without detectable impurities, further verifying the successful synthesis of the designed HEAs (Fig. S3(a) and (b), SI). From the ICP-MS data, the elemental compositions of Pd_0.01IrSnZnMo, Pd_0.02IrSnZnMo, Pd_0.03IrSnZnMo, Pd_0.04IrSnZnMo, and Pd_0.05IrSnZnMo HEAs were determined, as summarized in Table S2 (SI). Among the elements, Mo and Sn were present in the highest amounts, followed by Pd, whereas Zn and Ir contents were the lowest.

3.2 Morphological analysis

FESEM images of the Pd_0.05IrSnZnMo sample at different magnifications are shown in Fig. 2(a and b), while the corresponding TEM images are presented in Fig. 2(c–e). Small nanostructures attached to bulk spherical structures were observed. The bulk spheres formed by the aggregation of Ir, Sn, Zn, Mo, and Pd are largely amorphous, whereas the smaller spherical nanostructures bonded to the bulk are crystalline and primarily composed of Pd and Sn. The bonding between Pd and Sn is primarily facilitated by electronic interactions: Pd possesses an electron-rich d-band, while Sn readily undergoes oxidation, giving it a strong tendency to selectively coordinate to Pd sites rather than to other metals. In addition, electron transfer from Sn to Pd occurs due to the lower electronegativity of Sn relative to Pd.^66,67 These electronic interactions favor the formation of a well-crystallized core–shell structure. In contrast, the bulk regions exist in an amorphous phase composed of all the metal components. The major factors influencing amorphous phase formation in HEAs include mixing entropy, mixing enthalpy, and the atomic size differences among the constituent elements.⁶⁸ These factors collectively result in the structural heterogeneity observed in the prepared HEAs. The regions marked in Fig. 2(c) are magnified in Fig. 2(d and e). These images reveal that small spherical nanostructures resemble core–shell structures consisting of Pd and Sn species. A significant feature of core–shell structures is their high surface area, which can facilitate electron transfer. The HRTEM image in Fig. 2(f) shows well-resolved lattice fringes, with corresponding (hkl) planes identified using ImageJ by processing fast Fourier transform (FFT) and inverse FFT images (Fig. 2(g–i)). In the FFT image (Fig. 2(g)), the three highlighted spots correspond to the (111), (220), and (200) planes of Pd. These planes were attributed to the fcc phase, which is consistent with the XRD results. The inverse FFT image depicted in Fig. 2(h) highlights lattice fringes corresponding to the Pd (111) plane, while Fig. 2(i) shows overlapping fringes, indicating possible bonding between Pd and Sn. This also highlights the lattice distortion resulting from the random distribution of atoms with varying atomic sizes within the crystal structure. The selected area diffraction (SAED) pattern shown in Fig. 2(j) confirms the crystalline growth of Pd nanoparticles, as evidenced by the bright dotted ring corresponding to the (111) plane of Pd, indicating an fcc structure. The randomly distributed ring pattern further demonstrates the polycrystalline nature of the HEA, where differently oriented single crystals coexist within a single phase. The HAADF-STEM image (Fig. 2(k1)) and the corresponding EDS elemental maps of Pd_0.05IrSnZnMo presented in Fig. 2(k2–k7) confirm the homogeneous distribution of all constituent elements within the HEA.

Fig. 2 Morphology of Pd_0.05IrSnZnMo HEA: (a and b) FESEM images, (c–e) TEM images, (f) corresponding HRTEM image, (g) FFT pattern, (h and i) inverse FFT patterns, (j) SAED pattern, and (k1) high-resolution HAADF–STEM images and (k2–k7) the corresponding EDS elemental maps revealing the distribution of elements.

3.3 Electronic structure analysis

X-ray photoelectron spectroscopy (XPS) was performed to determine the surface oxidation states of the five elements constituting the alloy, as shown in Fig. 3. The survey spectrum (Fig. S2, SI) confirmed the presence of the constituent elements, thereby verifying the successful formation of the PdIrSnZnMo HEA synthesized with different Pd concentrations. The strong bonding among the metallic components stabilizes the high entropy alloy as a single-phase structure. The high-resolution spectrum of Pd (Fig. 3(a)) displays two prominent peaks at binding energies of ∼336 eV (Pd 3d_5/2) and 343.1 eV (Pd 3d_3/2), which are characteristics of metallic Pd. The deconvolution of the spectrum reveals additional peaks at about 336.1 and 341.2 eV, corresponding to Pd (0) (metallic) and Pd (II) species associated with oxidized Pd.^35,36 The approximation (∼) notation for binding energies is used because peak positions shift across samples with varying Pd concentrations. This shift is likely caused by strong interactions with other metal species, which induce electron transfer and modify the electronic structure due to the influence of neighboring atoms or ions.⁵⁶ As illustrated in Fig. 3(a), the peaks corresponding to the Pd 3d_5/2 and Pd 3d_3/2 oxidation states shifted toward higher binding energies with increasing Pd concentration, which might be attributed to the partial oxidation of Pd, facilitating strong chemical bonding with other metal species.⁶⁴ The core-level spectrum of Ir 4f (Fig. 3(b)) exhibits two asymmetric spin–orbit doublets observed at binding energies of 61.8 and 64.2 eV, which are attributed to the Ir 4f_7/2 and Ir 4f_5/2 states, respectively.³⁸ These features indicate the coexistence of metallic Ir and hydrated iridium oxyhydroxide species (IrO_y·nH₂O)₇.³⁷ The XPS core-level spectrum of Mo shown in Fig. 3(c) displays two prominent peaks at binding energies of 235.2 and 232.2 eV, which correspond to Mo 3d_3/2 and Mo 3d_5/2 levels, respectively, in the 0.01 M Pd-loaded alloy (Pd_0.01IrSnZnMo).³⁹ In samples with higher Pd loading (Pd_0.02IrSnZnMo, Pd_0.03IrSnZnMo, Pd_0.04IrSnZnMo, and Pd_0.02IrSnZnMo), these peaks shift to higher binding energies. The dominant peak observed at ∼235 eV is assigned to the Mo⁶⁺ oxidation state (Mo 3d_3/2), while a less intense peak at ∼234 eV corresponds to the Mo⁴⁺ oxidation state of the Mo 3d_3/2 level.⁴⁰ Additionally, the peak at ∼231 eV is attributed to the Mo⁵⁺ oxidation state of the Mo 3d_5/2 level.^40,41 The high-resolution spectrum of Sn 3d shown in Fig. 3(d) exhibits one main peak at a binding energy of ∼495.5 eV, ascribed to the Sn 3d_5/2 level.⁴² The deconvolution of the Sn 3d_5/2 peak reveals a component at 486.6–486.8 eV in all samples (Pd_0.01IrSnZnMo, Pd_0.02IrSnZnMo, Pd_0.03IrSnZnMo, Pd_0.04IrSnZnMo, and Pd_0.05IrSnZnMo), which is attributed to the Sn⁴⁺ oxidation state.⁶⁵ In addition, a weaker peak at 485.1 eV, detected in Pd_0.02IrSnZnMo, Pd_0.03IrSnZnMo, Pd_0.04IrSnZnMo, and Pd_0.05IrSnZnMo, is assigned to the Sn⁰ (metallic Sn) oxidation state of the Sn 3d_5/2 level. Notably, the intensity of this peak, corresponding to the Sn⁰ state, increased significantly from 5% to 60%, as the Pd loadings increased from 0.02 M to 0.05 M. This clearly indicates that higher Pd concentrations promote the formation of Sn⁰, driven by the strong electronic interaction between Pd and Sn, which is favored due to the lower electronegativity of Sn relative to Pd. This effect can be attributed to interactions or bonding between Sn and Pd species.⁶⁶ The core-level XPS spectrum of Zn 2p shown in Fig. 3(e) exhibits a prominent peak at 1021.9 eV, corresponding to the Zn 2p_3/2 level.⁴³ No peak shift is observed, corroborating that the Zn component does not undergo any oxidation process, while its incorporation confirms successful bonding within the alloy structure. The O 1s core-level XPS spectrum of the Pd_0.01IrSnZnMo sample displayed in Fig. 3(f) reveals three deconvoluted peaks at 531.9, 532.3, and 534.1 eV, attributed to O=C (doubly bonded oxygen to carbon), O–C (singly bonded oxygen to carbon), and adsorbed/chemisorbed water molecules, respectively.⁴⁴ In HEAs with higher Pd loadings (Pd_0.02IrSnZnMo, Pd_0.03IrSnZnMo, Pd_0.04IrSnZnMo, and Pd_0.05IrSnZnMo), the peaks at 532.3 and 534.1 eV shift toward lower binding energies, indicating the creation of oxygen vacancies due to lattice distortion.⁷

Fig. 3 XPS core-level spectra of (a) Pd 3d, (b) Ir 4f, (c) Mo 3d, (d) Sn 3d, (e) Zn 2p, and (f) O 1s.

3.4 Electrochemical HER studies in acidic medium

To assess the catalytic performance of the fabricated HEA-based electrocatalysts, hydrogen evolution reaction (HER) tests were conducted in an acidic medium using a standard three-electrode cell. Prior to HER evaluation, the electrode–electrolyte interface of the catalyst-coated electrode was activated by multiple (20 cycles) potential cycles using cyclic voltammetry. After multiple cycling tests, the CV curves were recorded again, as shown in Fig. 4(a). The obtained CV curves displayed a sharp and intense cathodic peak, indicating the strong hydrogen evolving capability of the prepared electrocatalysts. Notably, the sample without Pd (IrSnZnMo) exhibited a relatively low current density of −4.9 mA cm⁻², while all Pd-containing samples demonstrated significantly higher current densities. Specifically, the current density values for Pd_0.01IrSnZnMo, Pd_0.02IrSnZnMo, Pd_0.03IrSnZnMo, Pd_0.04IrSnZnMo, and Pd_0.05IrSnZnMo HEAs were found to be −32.3, −65.5, −104.2, −76.0, and −98.0 mA cm⁻², respectively. It is evident that with increasing Pd content, the crystallinity of the materials improved, which in turn enhanced electron transfer and accelerated electrocatalytic activity. Among the investigated samples, Pd_0.03IrSnZnMo exhibited the highest current density, whereas Pd_0.05IrSnZnMo exhibited a lower onset potential for HER. This suggests that the Pd_0.05IrSnZnMo HEA possesses superior catalytic activity and efficiency toward HER. This improved performance can be attributed to the increased number of electroactive surface sites available for proton adsorption, followed by electrochemical discharge, leading to H₂ evolution.

Fig. 4 CVs recorded in the potential range from −0.8 to 0.8 V vs. SCE in 0.5 M H₂SO₄, (b) linear polarization curves obtained at the scan rate of 1 mV s⁻¹, (c) the corresponding Tafel plots, and (d) comparison of overpotential as a function of Pd concentration in the catalyst.

To further evaluate the intrinsic catalytic efficacy of the fabricated electrocatalysts, polarization curves were recorded using linear sweep voltammetry (LSV). The effectiveness of the electrocatalysts was assessed based on the overpotential required to achieve a current density of −10 mA cm⁻², which is widely regarded as a standard benchmark for the solar-to-fuel conversion process. This overpotential serves as a key parameter in determining the catalytic activity toward HER. As shown in Fig. 4(b), the Pd_0.05IrSnZnMo HEA catalyst exhibited the lowest overpotential of 17 mV to reach a current density of −10 mA cm⁻², significantly outperforming the other compositions. In contrast, the overpotentials required for Pd_0.01IrSnZnMo, Pd_0.02IrSnZnMo, Pd_0.03IrSnZnMo, and Pd_0.04IrSnZnMo to achieve the same current density were 293, 162, 80, and 202 mV, respectively, as shown in the comparison plot (Fig. 4(d)). The Pd_0.04IrSnZnMo HEA electrocatalyst revealed a comparatively higher overpotential, which might be attributed to the lower number of available active sites, thereby suppressing the adsorption of H* intermediates and hindering the subsequent desorption of H₂ molecules, ultimately resulting in increased overpotential. The results also clearly showed the poor activity of the IrSnZnMo catalyst, which delivered only low current densities and exhibited no observable hydrogen evolution up to −0.4 V vs. RHE, indicating its inferior catalytic performance. This strongly confirms that Pd is the primary contributor to facilitating HER.

This outstanding activity of the Pd_0.05IrSnZnMo HEA can be primarily attributed to the presence of Pd, which possesses a hydrogen adsorption free energy (ΔG*) equal to zero, which is widely considered the key descriptor for efficient HER catalysts.^45,47 Additionally, Ir contributes substantially to catalytic activity, while the synergistic effects of other alloying elements, each with distinct adsorption energies, further enhance performance in acidic media. The HER process begins with the adsorption of H⁺ ions from the electrolyte onto the catalyst surface, followed by the discharge of H₂O molecules and the formation of hydrated protons (H₃O⁺). Subsequently, various hydrogen containing intermediates (H*, , or H⁻) are formed, which participate in the reduction pathways leading to H₂ molecules.^46,48 The kinetics of the electrochemical HER were further elucidated by analyzing the Tafel slope values. These were obtained by plotting the log of the current density (x-axis) against the overpotential (η, y-axis), as presented in Fig. 4(c). The slope of the linear fit corresponds to the Tafel equation (eqn (3)):

From the above relation, it is evident that the Tafel slope is inversely proportional to the charge transfer coefficient, confirming that a lower Tafel slope corresponds to a more efficient charge transfer across the electrode–electrolyte interface during the electrocatalytic reaction.⁴⁹ Furthermore, the faster formation of hydrogen intermediates from H₃O⁺, compared to H₂O, explains the enhanced catalytic activity observed in acidic media. It is well established that hydrogen evolution on the cathode surface proceeds through a multi-step electrochemical pathway. Specifically, in acidic electrolytes, the HER mechanism can be described by the following sequential steps (eqn (4)–(6)):^50,51

M − H₃O⁺ + e⁻ + M → M − H + H₂O (volmer step – electrochemical hydrogen adsorption) (4)

M − H + H₃O⁺ + e⁻ → M + H₂ + H₂O (Heyrovsky step – electrochemical desorption) (5)

2M − H → 2M + H₂ (Tafel step – chemical recombination). (6)

The calculated Tafel slope values for Pd_0.01IrSnZnMo, Pd_0.02IrSnZnMo, Pd_0.03IrSnZnMo, Pd_0.04IrSnZnMo, and Pd_0.05IrSnZnMo HEAs were 106.2, 93.3, 60.3, 101.6, and 52.7 mV per dec. respectively. These results suggest that the reaction kinetics of HER on these electrocatalysts in an acidic medium follow the Volmer-Heyrovsky mechanism.⁴⁹ In this pathway, the evolution of an H₂ molecule is facilitated by the adsorption and electrochemical discharge of a proton onto an H atom previously adsorbed and discharged at the same active site. To further probe the intrinsic catalytic activity, the electrochemically active surface area (ECSA) was determined for each catalyst from the ratio of the electrochemical double-layer capacitance (C_dl) to the specific capacitance value. The C_dl values were derived from CV measurements recorded in the non-faradaic potential region at different scan rates. For the Pd_0.01IrSnZnMo, Pd_0.02IrSnZnMo, Pd_0.03IrSnZnMo, and Pd_0.04IrSnZnMo HEAs, CV curves were recorded at different scan rates in the non-faradaic potential region from −0.1 to −0.2 V vs. SCE (Fig. S1(a–d), SI), while for the Pd_0.05IrSnZnMo HEA, CV curves were recorded in the potential region from 0 to −0.1 V vs. SCE (Fig. S1(e), SI). The corresponding linear plots of current density vs. scan rate are shown in Fig. S1(f) and (g) (SI). The calculated C_dl, ECSA, and roughness factor (R_f) values are summarized in Table S1 (SI). The obtained results showed that the Pd_0.05IrSnZnMo HEA exhibited the highest ECSA and R_f values, confirming that the catalyst possesses numerous active sites, most likely originating from its core–shell structures. The significant importance of core shell architectures in catalysis can be attributed to three main effects: (i) ligand effect – influenced by the adsorption behavior of the catalyst surface due to the presence of multiple atomic groups; (ii) ensemble effect – arising from the interactions between the core and shell, which alter charge transfer between the components depending on atomic proximity, thereby affecting the electronic band-structure; and (iii) structural effect – caused by 3D structural constraints, leading to variations in surface atomic activity.^62,63 Additionally, TOF, which reflects the intrinsic catalytic rate of HER per active site, was calculated using the expression described in Subsection 2.3. The TOF value for the best-performing Pd_0.05IrSnZnMo HEA electrocatalyst was determined to be 9.02 × 10⁻⁴ s⁻¹, whereas the other catalysts revealed lower values, as summarized in Table S1 (SI). The higher TOF observed for the Pd_0.05IrSnZnMo HEA confirms that it possesses numerous catalytically active sites that facilitate the rapid evolution of H₂ molecules. The electrochemical performance of the Pd_0.05IrSnZnMo HEA toward HER electrocatalysis in acidic medium was compared with other high entropy Pd-based electrocatalysts reported in the literature, as summarized in Table S5 (SI).

3.5 Stability studies

Stability is a crucial parameter in evaluating the practical applicability of electrocatalysts, particularly under harsh acidic conditions. To assess durability, CP measurements were carried out at different current densities, as shown in Fig. 5. At a constant current density of −5 mA cm⁻² (Fig. 5(a)), the Pd_0.01IrSnZnMo, Pd_0.02IrSnZnMo, Pd_0.03IrSnZnMo, Pd_0.04IrSnZnMo and Pd_0.05IrSnZnMo HEA samples revealed robust stability, showing negligible changes in overpotential even after 20 h of continuous electrochemical activity. Similarly, when tested at a higher current density of −10 mA cm⁻² (Fig. 5(b)), all HEAs, including Pd_0.05IrSnZnMo, maintained a stable performance without any obvious potential decay over 25 h. To further assess long-term durability, CP measurements were extended to 100 h (4 days and 4 h) at −10 mA cm⁻² (Fig. 5(c)). The catalysts demonstrated excellent stability although minor fluctuations were observed due to electrolyte evaporation and continuous gas bubbling. Importantly, replenishing electrolytes restored performance, confirming that these disturbances were not related to catalyst degradation. A decrease in overpotential was also observed compared to the value recorded during the initial 25 h CP test at −10 mA cm⁻² (Fig. 5(b)). This decrease may be attributed to the renewal of active sites, which facilitates the rapid adsorption of H* species and the efficient desorption of H₂ molecules. Finally, to verify the structural and electrochemical integrity of the best-performing Pd_0.05IrSnZnMo HEA, polarization curves were recorded after 100 h of continuous operation at a fixed current density of −10 mA cm⁻², as shown in Fig. 5(d). The results confirmed stable activity, with only a negligible increase in overpotential, underscoring the outstanding durability of this electrocatalyst in acidic media.

Fig. 5 Chronopotentiometric analysis at −5 mA cm⁻² for the Pd_0.01IrSnZnMo, Pd_0.02IrSnZnMo, Pd_0.03IrSnZnMo, Pd_0.04IrSnZnMo and Pd_0.05IrSnZnMo HEAs over 20 h; (b) chronopotentiometric analysis at −10 mA cm⁻² for the Pd_0.01IrSnZnMo, Pd_0.02IrSnZnMo, Pd_0.03IrSnZnMo, Pd_0.04IrSnZnMo, and Pd_0.05IrSnZnMo HEAs over 25 h; (c) long-term chronopotentiometric analysis of the Pd_0.05IrSnZnMo HEA at −10 mA cm⁻² for 100 h; and (d) LSV curves of the Pd_0.05IrSnZnMo HEA recorded before and after 100 h stability test in the acidic medium.

3.6 Structural and compositional characterizations of the electrocatalyst after HER

To gain deeper insight into the performance of the Pd_0.05IrSnZnMo electrocatalyst, a series of characterizations, including XPS, FESEM, EDS, and elemental mapping, were carried out to probe the oxidation states, morphology, and elemental distribution of the constituent metals.

The XPS core-level spectra (Fig. 6(a–d)) reveal significant insights into the electronic structure of the catalyst. The Pd 3d spectrum (Fig. 6(a)) shows a clear shift of the Pd 3d_3/2 and Pd 3d_5/2 peaks to higher binding energies after HER, indicating changes in the electronic environment of the Pd atoms, likely due to chemical interactions or variations in the oxidation state. Similarly, the Mo 3d, Ir 4f and O 1s spectra (Fig. 6(b)–(d)) exhibit shifts toward higher binding energies, revealing changes in peak positions that can be attributed to variations in electronegativity, chemical bonding with neighboring species, and oxidation state modifications during electrochemical operation. These shifts suggest that the catalyst surface actively participates in electron transfer processes, consistent with its enhanced HER activity. FESEM images of the Pd_0.05IrSnZnMo post-tested electrocatalyst-coated electrode surface (Fig. 6(e) and (f)) were taken to investigate morphological variations. Distinct nanostructures were not observed likely due to the preparation method, where the catalyst was mixed with the binder and solvent to form a slurry, followed by ultrasonication to ensure homogeneity. However, the coating remained uniform, providing sufficient surface coverage for electrocatalysis. Elemental composition and distribution were further examined using EDS and elemental mapping. The EDS spectrum (Fig. 6(g)) confirms the presence of Pd, Mo, Ir, and Sn with no detectable impurities. The Zn signal was not observed possibly due to its lower bonding contribution or low concentration with the HEA. Elemental mapping (Fig. 6(h1–h6)) demonstrates a uniform distribution of Pd, Ir, Sn, Mo, O, and C across the electrode surface, confirming successful incorporation and homogeneous dispersion of all metal components. Collectively, these structural and compositional analyses indicate that the Pd_0.05IrSnZnMo catalyst possesses well-dispersed active sites, favorable electronic configurations, and uniform elemental distribution. These features are consistent with its HER performance, as the material facilitates efficient adsorption of reaction intermediates and accelerates electron transfer.

Fig. 6 XPS core-level spectra of (a) Pd 3d, (b) Mo 3d, (c) Ir 4f, and (d) O 1s; (e and f) FESEM images of the post-test catalyst-coated electrode surface at different magnifications; (g) the corresponding EDS spectrum, and (h1–h6) elemental mappings showing the distribution of Pd, Ir, Sn, Mo, O, and C.

3.7 DFT calculations

This subsection presents theoretical studies on the conformational dependence of the thermodynamic and electronic properties of five distinct conformations of the PdIrSnZnMo HEA for HER electrocatalysis. Understanding the thermodynamics of high-entropy metal alloys at the quantum level is important because it provides insight into how the structural and electrochemical properties depend on the quantum conformational states present in the bulk material. Exploring the intrinsic physical properties of these conformational states is particularly important for designing HEA catalysts, as they directly influence the thermodynamic feasibility and kinetic accessibility of hydrogen evolution reaction (HER) pathways.⁵²

In this study, the structural, electronic, and thermodynamic properties of selected conformations of metal alloys composed of d-block heavy metals, namely Ir, Zn, Sn, Pd, and Mo, were investigated at the quantum level. Such an analysis also offers deeper insights into the possible structural diversities present in bulk alloys. Fig. 7 depicts the optimized geometries of five distinct conformations of the PdIrSnZnMo alloy obtained via full geometry optimization at the B3LYP/LANL2DZ level of theory: (A) ring, (B) trigonal bipyramidal with Mo at the vertex, (C) square pyramidal, (D) trigonal bipyramidal with Zn at the vertex, and (E) one-atom bound tetragonal configuration. These optimized structures serve as the basis for the subsequent analysis of the electronic properties and thermodynamic stability relevant to HER catalysis.

Fig. 7 Optimized structures of the (a) ring, (b) trigonal bipyramidal (with Mo at the vertex), (c) square pyramidal, (d) trigonal bipyramidal (with Zn at the vertex), and (e) one-atom bound tetragonal configuration at the B3LYP/LANL2DZ level of theory.

All five conformations shown in Fig. 7 were fully optimized in both the gas and solvent phases using the B3LYP functional with the LANL2DZ pseudo-core potential basis set. Sulphuric acid was used as a solvent and modeled via the conductor-like polarizable continuum model (CPCM). To evaluate the electronic properties, the HOMO–LUMO energy gaps of the systems were analyzed, where HOMO represents the highest occupied molecular orbital and LUMO represents the lowest unoccupied molecular orbital. A higher HOMO level enhances the electron-donating ability, which is critical for proton reduction, while a lower LUMO facilitates electron acceptance and stabilizes the adsorbed hydrogen intermediate.⁵³ Thermodynamic properties and redox potentials were assessed through calculations of solvation free energies, determined from the Gibbs free energy differences between geometries optimized in the gas and solvent phases. These redox potentials provide insights into the electron-transfer capacity of each conformer, which is directly related to suitability as HER electrocatalysts. Comparing the redox potential across different conformers further reveals how conformational variations can tune catalytic activity and influence HER performance.⁵⁴ Additionally, density of states (DOS) analysis was performed to identify potential active sites by examining the availability of electronic states near the Fermi level and their elemental orbital contributions. This analysis provides a deeper understanding of the individual contribution of metal components to electron transfer and catalysis, aiding in the rational design of high-entropy alloy catalysts for the HER.

To evaluate the HER performance of the five conformations, descriptors including the HOMO–LUMO energy gap (E_g), solvation free energy, and redox potential were calculated (Tables S1 and S2). From Table S3 (SI), conformers C and D exhibit the narrowest energy gaps in the solvent (1.568 and 1.582 eV, respectively), indicating higher chemical reactivity and more favorable H* adsorption for HER. In the solvent phase, these conformations also displayed the highest HOMO energies among all the structures analyzed (C: −3.326 eV and D: −3.494 eV). The relatively lower negative HOMO values suggest a stronger tendency to donate electrons, enhancing the proton reduction process. Table S4 (SI) presents the calculated solvation free energies, showing that conformations C (−28.650 kcal mol⁻¹) and D (−29.565 kcal mol⁻¹) have significantly less negative values compared to the other conformers. Higher solvation free energy reduces the energy activation barrier, improves reaction kinetics, and thus enhances HER efficiency. Additionally, the calculated redox potentials for C (0.478 V) and D (0.484 V) are among the highest in the series, indicating that these conformations require lower overpotentials to drive HER. These results are consistent with literature reports, where small-metal clusters typically exhibit redox potentials ranging from 0.2 to 1.6 V.⁵⁵ Overall, the electronic structure, solvation behavior, and redox properties of conformations C and D highlight their superior potential as effective HER electrocatalysts.

The calculated total density of states (TDOS), representing the overall distribution of electronic states, and the projected density of states (PDOS), showing the contributions of specific metal fragments, in the solvent phase are presented in Fig. 8 and 9. From the TDOS of the ring, trigonal bipyramidal with Mo at the vertex, square pyramidal, trigonal bipyramidal with Zn at the vertex, and one-atom bound tetragonal configurations shown in Fig. 8(a, d and g) and Fig. 9(a and d), it is evident that the TDOS near the highest occupied molecular orbital (HOMO) is primarily dominated by the d-electron orbitals of the constituent elements (Pd, Ir, Sn, Zn, and Mo), indicating strong electronic interactions between individual metallic sites. The PDOS plots (Fig. 8 and 9) provide further insight into the contributions of individual metal fragments, showing the occupancies of the molecular orbitals for Ir-5d, Mo-4d, Zn-3d, Pd-4d, and Sn-4d relative to the HOMO level. From the TDOS plots (Fig. 8(a, d and g) and Fig. 9(a and d)), the energy gaps of conformers C (1.475 eV) (Fig. 8(g)) and D (1.423 eV) (Fig. 9(a)) are smaller than those of the other structures, which is consistent with the frontier molecular orbital analysis. Furthermore, the PDOS analysis reveals that the d-orbitals of Sn-4d, Ir-5d, and Mo-4d contribute most significantly at the HOMO level, creating electron depletion centers favorable for HER. In contrast, the Pd-4d orbitals are located slightly below the HOMO and act as electron reservoirs during the reduction process. This indicates that the most favorable site for proton adsorption is Sn, which facilitates electron depletion, while Pd serves as an electron reservoir to drive hydrogen evolution. Overall, the smaller energy gaps of conformers C and D imply higher chemical reactivity, enhancing their suitability as active sites for HER and correlating well with their predicted superior catalytic performance.

Fig. 8 Total density of states (TDOS) for (a) ring, and projected density of states (PDOS) for (b and c) p and d orbitals of the ring structure, (d) TDOS for the trigonal bipyramidal structure (with Mo at the vertex), (e and f) PDOS for p and d orbitals of the trigonal bipyramidal structure (with Mo at the vertex), (g) TDOS for the square pyramidal structure, and (h and i) PDOS for p and d orbitals of the square pyramidal structure (with Zn at the vertex). The dashed vertical line represents the position of the highest occupied molecular orbital (HOMO).

Fig. 9 (a) TDOS for the trigonal bipyramidal structure (with Zn at the vertex), (b and c) PDOS for the p and d orbitals of the trigonal bipyramidal structure (with Zn at the vertex), (d) TDOS for the one-atom bound tetragonal conformation, and (e and f) TDOS for the p and d orbitals of the one-atom bound tetragonal structure.

4 Conclusions

In summary, a novel high entropy stabilized single-phase PdIrSnZnMo HEA was successfully synthesized using a facile solvothermal method. To elucidate the role of Pd species, the Pd concentration varied from 0.01 to 0.05 M, and the resulting electrocatalysts were evaluated for HER. Among the tested compositions, Pd_0.05IrSnZnMo (0.05 M Pd) exhibited the best HER performance in an acidic medium (0.5 M H₂SO₄), requiring only 17 mV overpotential to achieve −10 mA cm⁻², with the reaction mechanism proceeding via the Volmer-Heyrovsky pathway. Remarkably, the electrocatalyst also demonstrated excellent durability, retaining activity without noticeable degradation. The superior performance was attributed to synergistic multielement interactions stabilized by the high entropy effect, along with the near-zero hydrogen adsorption free energy (ΔG* ≈ 0) of Pd, which promotes rapid adsorption and dissociation of hydrogen intermediates. DFT calculations provided further insight into the structure–activity relationship. Among the five evaluated conformations, conformers C (square pyramidal) and D (trigonal bipyramidal with Zn at the vertex) exhibited the narrowest energy gaps (1.568 and 1.582 eV, respectively) in the acidic medium, indicating enhanced reactivity and favourable H* binding. PDOS analysis confirmed that Sn-4d, Ir-5d, and Mo-4d orbitals contributed significantly at the HOMO level, which served as electron depletion centers for HER, while Pd-4d orbitals functioned as electron reservoirs, facilitating the reduction process. Overall, both experimental and theoretical results establish PdIrSnZnMo HEA as an efficient and durable electrocatalyst for HER in an acidic medium.

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have influenced the work reported in this paper.

Data availability

The data supporting this article have been included as part of the supplementary information (SI) and are available from the corresponding author upon reasonable request. Supplementary information: CV curves recorded at different scan rates in the non-Faradaic potential region for Pd_0.01IrSnZnMo, Pd_0.02IrSnZnMo, Pd_0.03IrSnZnMo, and Pd_0.04IrSnZnMo HEAs (from −0.1 to −0.2 V vs. SCE) and for the Pd_0.05IrSnZnMo HEA (from 0 to −0.1 V vs. SCE); linear fit of the difference between anodic and cathodic current densities at −0.15 V vs. SCE as a function of scan rate and the corresponding linear plot for the Pd_0.05IrSnZnMo electrocatalyst; XPS survey spectra; EDS spectra recorded during HRTEM and FESEM analyses; tabulated values of C_dl, ECSA, R_f, and TOF (Table S1); atomic percentage of elements in Pd_0.01IrSnZnMo, Pd_0.02IrSnZnMo, Pd_0.03IrSnZnMo, Pd_0.04IrSnZnMo, and Pd_0.05IrSnZnMo HEAs determined by ICP-MS (Table S2); HOMO–LUMO energy gaps and redox potentials (Table S3); and total energy, Gibbs free energy, and solvation free energy derived from DFT calculations (Table S4); and comparison of the catalytic performance of the outperformed Pd_0.05IrSnZnMo HEA with the existing high entropy stabilized Pd-based electrocatalysts in an acidic medium (Table S5). See DOI: https://doi.org/10.1039/d5ta08468g.

Acknowledgements

R.A. gratefully acknowledges the financial support from the Polish National Agency for the Academic Exchange (NAWA) under the Ulam Program (grant no. BPN/ULM/2021/1/00101). The study was partially carried out using research infrastructure funded by the European Union under the framework of the Smart Growth Operational Programme, Measure 4.2 (Grant No. POIR. 04.02.00-00-D001/20), “ATOMIN 2.0–Center for materials research on ATOMic scale for the INnovative economy”. The authors also acknowledge the Laboratory of Field Emission Scanning Electron Microscopy and Microanalysis at the Institute of Geological Sciences, Jagiellonian University, Krakow, Poland, for providing the FESEM instrumentation facility.

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