Synergistic Effects of Mixing and Strain 
in High Entropy Spinel Oxides for Oxygen Evolution Reaction

doi:10.21203/rs.3.rs-1879578/v1

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Synergistic Effects of Mixing and Strain in High Entropy Spinel Oxides for Oxygen Evolution Reaction

https://doi.org/10.21203/rs.3.rs-1879578/v1

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published 23 Sep, 2023

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Designing electrochemically active, stable, and earth-abundant electrocatalysts is essential for boosting oxygen evolution reaction (OER) rates for sustainable hydrogen production. High entropy oxides (HEOs) consist of five or more metal cations, offering ample opportunities to tune their catalytic properties toward high OER efficiency. In this work, we combine theoretical and experimental studies to scrutinize the OER activity and stability for spinel-type HEOs. Our density functional theory calculations unequivocally confirm that randomly mixed metal sites are more thermodynamically stable, while we also show that adsorption energies of the intermediates display widening distributions accompanied by the equatorial strain of active metal-oxygen bonds under mixing. The rapid sol-flame method was successfully employed to synthesize spinel oxides up to five third-row metal cations (Co, Fe, Ni, Cr, and Mn) with high degree of entropy. Such catalyst exhibits the highest OER activity of 309 mV at 10 mA cm^− 2 and prolonged durability up to 168 hours under alkaline conditions over less complex mixtures despite partial formation of surface oxyhydroxide. The high-entropy model developed in this work identifies mixed Co³⁺ active site as the most active center of this system. Overall, this work reveals that a key feature controlling the enhanced activity of high-entropy oxides is related to mixing and resulting strain near the active site.

The transition from fossil fuel-based to renewable energy-based society requires efficient and clean energy carriers, such as electrons and hydrogen.^1,2 Electrochemical water splitting, i.e., water electrolysis, converts electricity to hydrogen and oxygen,^3,4 but its efficiency is hampered by the slow kinetics of oxygen evolution reaction (OER) at the anode, which calls for efficient and stable electrocatalysts to reduce the reaction barrier for OER.⁵ To date, the most active and stable catalysts for OER are noble metal-based oxides, such as IrO₂ and RuO₂.^6–10 However, the scarcity and high cost of Ir and Ru have limited the scalable adoption of water electrolysis, and the search for noble-metal-free OER electrocatalysts is being actively pursued. Many strategies have been suggested to improve OER activity for non-noble metal-based electrocatalysts,¹¹ including the modification of chemical composition,¹² nano/microstructure,¹³ phase distribution,¹⁴ or alloying.¹⁵ Among those non-noble metal-based catalysts, the 3d transition metal oxides with different phases (rock-salt, perovskite, or spinel) and (oxy)hydroxide show low overpotential at the desired current densities (> 10 mA cm^− 2) in alkaline electrolyte.^16–23

A new class of material, i.e., high-entropy materials (HEMs), such as high-entropy oxides (HEOs), has emerged as a new class of electrocatalysts. HEMs, consisting of five or more equimolar cations in a single phase,²⁴ have already attracted great interest in energy storage,^25,26 fuel cell,^27,28 and catalysis,^15,29,30 due to their excellent tunability from mixing different species and the concentration of constituents^31–35 as well as the physical and chemical stability from the large entropy of mixing.^35,36 HEOs are particularly of interest as OER electrocatalysts. Indeed, different crystal structures of HEOs, such as rock-salt,^37,38 perovskite (ABO₃),³⁹ spinel-type (AB₂O₄),^40,41 and (oxy)hydroxide (MOOH)⁴² have been evaluated as OER catalysts. Zhang et al. reported that the entropy-engineered rock-salt (CoNiMnZnFe)₃O_3.2 shows an overpotential of 336 mV at 10 mA cm^− 2 and good stability (retained 86.9% of current density for 20 h) for OER.³⁸ Nguyen et al. studied La-based perovskite HEO with different B site cations (Cr, Mn, Fe, Co, and Ni) for OER. It shows an overpotential of 325 mV at 10 mA cm^− 2 and stability for 50 hours without apparent degradation.³⁹ Zhang et al. investigated spinel-based HEO (Co_0.2Mn_0.2Ni_0.2Fe_0.2Zn_0.2)Fe₂O₄ for OER, exhibiting an overpotential of 326 mV at 10 mA cm^− 2 and maintaining 89.4% of current density after 10 hours.⁴¹ In addition to the experimental efforts, various computational techniques have been utilized to understand the thermodynamic stability and the surface catalytic processes for HEOs.⁴³ In another recent computational work, Anand et al. optimized the lattice configurations of cations and anions to examine how the elemental composition of HEO (NiMgCoCuZn)O affected enthalpy and configurational entropy.⁴⁴ More recently, Rossmeisl et al. computationally predicted oxygen reduction reaction (ORR) electrochemical activity via calculating O* and OH* binding energy distributions for different active sites of HEAs.⁴⁵ By use of DFT's adsorption energies prediction, Svane et al. theoretically optimized the composition of rutile HEO (110) surface based on Ir, Ru, Ti, Os, and Rh for OER.⁴⁶ These pioneering studies suggest that randomly mixed cations modulate their valence states, electronic structure, and adsorption energies of the intermediate species, e.g., *O, *OH, and *OOH, offering the possibility to tune and improve their catalytic properties towards OER.^12,46,47 However, a thorough investigation of the catalytic properties of HEOs for OER is still deficient both experimentally and theoretically due to the complication involved in the synthesis and the lack of a proper computational model to describe stability and OER activity. Moreover, identifying active sites for OER in HEOs and their activity origin is still unrevealed.

Here, we study spinel structure HEOs for OER as they have tunable physicochemical properties from different cation arrangements in the tetrahedral and octahedral sites, which affects catalytic properties. To examine the OER activity and stability for spinel HEOs comprising Co, Fe, Ni, Cr, and Mn, we first computationally develop a HEO impurity model. Then, we evaluate the HEO stability for various active sites by calculating mixing entropies and enthalpies of a homogenous mixtures. Guided by the theory results, we experimentally synthesize spinel HEO (Co, Fe, Ni, Cr, and Mn) by the sol-flame method.^48,49 The morphological and structural properties of the synthesized HEO are characterized via X-ray diffraction (XRD), scanning transmission electron microscopy (STEM), and energy-dispersive X-ray spectroscopy (EDS) elemental mapping. X-ray photoelectron spectroscopy (XPS), X-ray absorption spectroscopy (XAS), and electron energy loss spectroscopy (EELS) are further used to investigate the surface and bulk oxidation states of the HEO constituents. Moreover, we evaluate and compare the OER performance for HEO to those of the lower entropy oxides ranging from binary to quinary in alkaline electrolytes. Further, we use our HEO impurity model to predict OER activity for various metal active sites via calculating O* and OH* adsorption energies and overpotentials and their connection to contraction and expansion of metal-oxide bonds. Finally, we discuss overall OER activity trends and further optimization routes.

HEO impurity model. The initial studies of unary, binary and ternary mixtures of Cr, Mn, Fe, Co and Ni are described in the Methods Section,. In the case of more complex metal oxides, rather than constructing the fully periodic bulk model of an arbitrary mixture, it is more computationally feasible to study the HEO effect via local mixing near the active site. As schematically illustrated in Fig. 1a, we select a central metal site and allow neighboring metals (or ligands) to be interchanged. Such an approach can be extended to the next-neighbor shells and beyond while also being site-specific and computationally tractable. This approach can be used to develop both bulk and surface impurity models. The surface model is applied to extract the mixing enthalpy and study the catalytic properties, such as OER, as discussed later.

For the equimolar HEO surface systems, we purposely choose Co₃O₄(N) as it forms a stable normal spinel structure with high cubic symmetry (see Table S1). Arguably, some other systems or volume-averaged spinel models could also have been used. Here, we choose the (100) facet terminated with the octahedral site (100)-A type surface of Co₃O₄ from the literature.⁵² (see Methods Section). In this setting, each active site at the top-most layer is surrounded by five nearest elements (< 3.5 Å) (A-E, Fig. 1a), and these five neighboring sites can be occupied by Cr, Co, Mn, Ni, and Fe in any arrangements, which leads to 120 distinct permutations per active site. Similar to approach by Rossmeisl et al. for high entropy alloys,⁴⁵ this strategy allows the local, tractable treatment of the HEO catalytic effects at the surface. Including the next-neighbor shells (within 6.6 Å) in our model would result in a 100-fold increase of distinct permutations. However, based on few cases, we determined that this effect is less than 0.3 eV per adsorption energy. Moreover, we limit our study to Co, Cr, and Fe as active sites because both Co and Cr pure spinel oxides show the best activity in pure form for OER, while Fe active sites represent weak binding limits (Fe, Mn, Ni) (discussed later). The likelihood that Fe-site behaves similarly in Fe-doped NiOOHx⁶² and related HEO systems¹² is also relevant factor.

Stability of HEO. The feasibility of successful HEO formation is estimated thermodynamically by calculating the Gibbs free energy of mixing (${\varDelta G}_{mix}$) using Eq. (1) as a more negative value of ${\varDelta G}_{mix}$ indicates a more stable and homogenous mixing.

$${\varDelta G}_{mix}={\varDelta H}_{mix}-{T\varDelta S}_{mix} \left(1\right)$$

We evaluated the theoretical configurational entropy of mixing ${\varDelta S}_{mix}$ for an equimolar 5-metal system by using the following formula as

$${\varDelta S}_{mix}=-R{\sum }_{i=1}^{M}{x}_{i} ln \left({x}_{i}\right)$$

where R is the ideal gas constant (0.0000862 eV K^− 1 metal^− 1); M is the number of metal cations in HEOs;${x}_{i}$is the molar fraction of each metal cation. For a 5-component (M = 5) equimolar system, ${\varDelta S}_{mix}=1.6R$ and the calculated configuration mixing entropy at the flame annealing temperature of 1000 K is ${-T\varDelta S}_{mix}$~ -0.14 eV/metal. We used our surface HEO impurity model to evaluate the enthalpy of mixing, ${\varDelta H}_{mix}$ per metal referenced to pure Co₃O₄ (100) surface simply as

$${\varDelta H}_{mix}=\left[{E}_{HEO\left(100\right)}^{slab}-{E}_{C{o}_{3}{O}_{4}\left(100\right)}^{slab}-{\sum }_{i=1}^{M}{E}_{i}^{bulk}\left({M}_{3}^{i}{O}_{4}\right)+M{\bullet E}^{bulk}\left({Co}_{3}{O}_{4}\right)\right]/M$$

where ${E}_{HEO\left(100\right)}^{slab}$ and ${E}_{C{o}_{3}{O}_{4}\left(100\right)}^{slab}$ are the DFT total energies for the HEO and Co₃O₄ (100) slabs, respectively. In Eq. (3), the spinel bulk energies for individual mixing metals (M = Co, Fe, Ni, Cr, Mn) are labeled as ${E}_{i}^{bulk}\left({M}_{3}^{i}{O}_{4}\right)$. Because surface energies of the HEO (100) model and Co₃O₄ (100) approximately cancel out, the mixing enthalpy of this surface model is also a reasonable estimation of the bulk HEO mixing.

Figure 1b plots the distribution of the resulting mixing enthalpies for the Co, Cr, and Fe active sites. The distribution of ${\varDelta H}_{mix}$ per metal for all three active sites is rather symmetric around the mean value and spans up to 0.5 eV, which is much larger than that of the rated HEA study (~ 0.06 eV)⁵³ by considering an equimolar five elements system. Moreover, over 85% of combinations have a negative ${\varDelta H}_{mix}$. Since the ${-T\varDelta S}_{mix}$ is also negative (-0.14 eV/metal), ${\varDelta G}_{mix}$ will be mostly negative, indicating the formation of HEOs is thermodynamically favorable.

Synthesis and characterization of HEOs. Figure 2a illustrates the sol-flame process^48,49 of synthesizing spinel HEO (Co, Fe, Ni, Cr, Mn) as described in the Experimental section. It entails precursor mixing in the liquid phase, followed by spin coating and rapid high-temperature flame annealing and quenching. The high-temperature annealing and subsequent quenching process are crucial to preventing the formation of intermetallic phases.^15,54 The X-ray diffraction (XRD) of the resulting HEO in Fig. 2b shows a pure spinel Fd-3m (227) crystal structure with ICDD 00-01-0325. The in-situ XRD results (Fig. S5) show that the pure spinel structure starts to appear at 400 ˚C and is prominent at the flame treatment temperature of 1000 ˚C, indicating that the sol-flame temperature is high enough to synthesize the spinel structure of HEO. Moreover, the transmission electron microscopy (TEM) (Fig. 2c) and scanning electron microscopy (SEM) (Fig. S6) images show that the as-synthesized HEO consists of interconnected nanoparticles (tens of nm in diameter) that are uniformly coated on the FTO/glass substrate. In addition, the high-resolution TEM image (Fig. 2d) and the selected area electron diffraction (SAED) pattern (Fig. 2e) reveal that those nanoparticles are the polycrystalline phase of spinel oxide, mainly indexed to (311), (220), and (222), corresponding to the d-spacings of 0.252, 0.240, and 0.290 nm, respectively. The d-spacing values slightly deviate from the reference NiFe₂O₄ (00-010-0325), 0.251, 0.241, and 0.294 nm for (311), (220), and (222), which is probably attributed to the atoms with different ionic radius in the lattice. The fast Fourier transform (FFT) image (Fig. 2d, inset) further confirms that the lattice fringes agree well with the XRD and scanning transmission electron microscopy (STEM) results. Figure 2f shows the dark-field STEM and energy dispersive X-ray spectroscopy (EDS) elemental mapping images, verifying the homogeneous mixing of each element (Co, Fe, Ni, Cr, Mn, and O).

The X-ray photoelectron spectroscopy (XPS) (Fig. S7) quantification analysis shows that the HEO surface has a near-equimolar concentration of each metal cation. Detailed elemental XPS analysis in Fig. S8 shows that Cr only exists as Cr³⁺ and other elements (Mn, Fe, Co, and Ni) have both divalent and trivalent oxidation states. The O 1s spectra were also deconvoluted to three different peaks; M-O at 529.8 eV, M-OH at 531.2 eV, and adsorbed H₂O at 532.5 eV, suggesting that the synthesized HEO particle surface contains hydroxide or oxyhydroxide species as well. For binary oxides to HEO, we deconvoluted the detailed Fe 2p_3/2 and Co 2p_3/2 XPS spectra to see the different ratios of divalent and trivalent oxidation states, as shown in Fig. S9. They exhibit different Fe²⁺/Fe³⁺ and Co²⁺/Co³⁺ at the surface where HEO shows the lower Fe²⁺/Fe³⁺ and higher Co²⁺/Co³⁺ than the lower entropy oxides. This implies that HEO has more Fe³⁺ and Co²⁺ at the surface, elaborated by electron energy loss spectroscopy (EELS) later. Thus, the different ratios of divalent and trivalent states in Co and Fe 2p_3/2 influence the OER activity. Also, the concentration of trivalent and divalent states of all elements for different spinel oxides is summarized in Table S2.

Furthermore, the X-ray absorption spectroscopy (XAS) measurements (Fig. S10) show that the bulk valence states of Co and Fe in HEO contain divalent and trivalent states. In detail, the slope of X-ray absorption near-edge structure (XANES) profiles for both Co and Fe K-edge show that HEO exhibits the higher bulk Co³⁺ than Co²⁺ and lower Fe²⁺ than Fe³⁺ overall throughout the particles, compared to those of the lower entropy oxides, which is consistent with the XPS results. A detailed description of XANES is also shown in Supplementary information (caption in Fig. S10).

The electron energy loss spectroscopy (EELS) analysis (Fig. 2g to 2k, 80 nm distance, spacing roughly 16 nm) was performed on the HEO particle to quantify its chemical composition. The EEL spectra (Fig. 2h) show the presence of the L_2,3-edges of all five metal elements (Cr, Mn, Fe, Co, Ni) at six positions in Fig. 2g. Moreover, Figs. 2i and 2j plot the L₃/L₂ white-line intensity ratio for Co and Fe at those six positions. As the L₃/L₂ white-line intensity ratio was reported to be closely associated with the orbital occupancy of the 3d transition metal elements and their oxidation states,^55–58 the results suggest that the HEO has more Fe³⁺ and Co²⁺ on the surface and more Fe²⁺ and Co³⁺ in the center of the HEO particle (80 nm). Figure 2k shows the energy separation between O K-edge pre-peak to the main peak, and its larger values near the surface indicate the higher oxidation states of overall elements on the surface.⁵⁹

Electrochemical performance of high-entropy spinel oxides. Comparisons of the polarization curves of different spinel oxides containing one to five metal cations in a 1 M KOH electrolyte are shown in Fig. 3a. Among them, the HEO (CoFeNiCrMn) has the lowest overpotential of 309 mV at 10 mA cm^− 2, in comparison to the other spinel oxides: CoFeNiCr (327 mV) < CoFeNiMn (379 mV) ~ CoFeNi (351 mV) < CoFe (418 mV) ~ Co (433 mV), and < Fe (522 mV) (Fig. S11). Starting from Co, adding Fe is negligible for the activity improvement, while adding Ni lowers the overpotential. Combining Mn to CoFeNi degrades the performance, while adding Cr is hugely beneficial. Interestingly, HEO (CoFeNiCrMn) shows the highest performance even though it contains Mn, which probably stems from the tuned adsorption energies discussed later. The HEO also has the smallest Tafel slope (30 mV dec^− 1) than other spinel oxides (Fig. 3b). In addition, the electrochemical impedance spectroscopy (EIS) measurement shows that HEO has both the lowest charge transfer resistance inside the bulk material and across the interface between the catalyst and electrolyte (Fig. S12 and Table S3). It suggests that HEO has higher electrical conductivity than the lower entropy oxides. For HEOs, we also fixed the four metal cations of CoFeNiMn and varied the fifth one from Cr to V, Cu, Zn, and W (Fig. S13). Among them, the inclusion of Cr exhibits the lowest onset potential, which is consistent with the report that Cr (oxide or oxyhydroxide) is active for OER.⁶⁰ Fig. 3c summarizes the activity trend for all the overpotential values of the different spinel oxides, showing that the OER activity is improved with increasing the number of the metal cations. Also, the HEO (CoFeNiCrMn) displays nearly 95% of Faradaic efficiency (FE) at 1.54 V vs. RHE, demonstrating great selectivity (Fig. S14).

The stability of HEO (CoFeNiCrMn) was further evaluated by chronopotentiometry and cyclic voltammetry tests. The chronopotentiometry measurement under 10 mA cm^− 2 shows that the overpotential for HEO increases by ~ 12% for 168 hours (7 days) (Fig. 3d). It should be noted that part of the charge is related to surface coverage by generated oxygen bubbles that were not entirely removed during the measurement. In comparison, spinel oxides with three and four metal cations show a pronounced 27% and 22% increase in overpotentials within 2 hours (Fig. 3d, inset). The trend demonstrates that the stability is improved with the larger degree on mixing. Furthermore, the cyclic voltammetry test of HEO shows that the oxidation peak at approximately 1.4 V vs. RHE gradually increases during the 1000 cycles (scan rate of 100 mV s^− 1) (Fig. S15), suggesting that the surface oxidation states were altered during the OER. The OER activity and stability values for different HEMs, binary spinel oxides, and binary layered double hydroxides (LDH) from other literature are also summarized for comparison in Table S4. Here, we conducted the durability test for the longest time among the catalysts in the table, and HEO shows comparable stability and activity compared to the reported materials, even though we simply synthesized it as a thin film, not including complex synthesis and engineering. In addition, time-dependent ex-situ XPS analysis was performed to analyze the surface state change of HEO. Figure 3e shows that the ratio of trivalent state in Fe and Ni and divalent state in Mn increase within a couple of hours of the test. The O 1s XPS spectra in Fig. 3f show that the surface OH out of (OH + O) became dominant with time. Detailed XPS analysis in Fig. S16 indicates that the Fe³⁺ and Ni³⁺ and OH concentrations were increased at the surface for 5 hours. This result demonstrates that the surface Fe-NiOOH was formed during the EC measurement, which influenced the slight change of overpotential (Fig. 3e). Although it is well known that the surface oxyhydroxide is also a promising OER catalyst,⁶⁰ HEO still plays an important role as support contributing to the great stability. Thus, we also evaluated the surface oxidation OER activity on oxyhydroxide by the DFT calculation that will be elaborated on in the later section.

Theoretical investigation of OER activity. After experimental synthesis and OER activity/stability measurements, we found that the spinel HEO shows lower overpotential than lower entropy oxides. To interpret the experimental activity, we calculated the O* and OH* binding energies for three different active sites using the HEO impurity model (see Fig. 1), along with the pure spinel systems. The results are summarized in a 2D volcano (O*-OH*, OH* descriptors) overpotential heat map (Fig. 4a), developed previously^10,47,60,61 and based on scaling in Fig. S1. By considering only the octahedral (+ 3) active sites at the (100) facets, our calculations show that the Co₃O₄ spinel has the smallest overpotential of 0.63 V among all pure spinel oxides. The trends of overpotential for various pure spinel oxides are: Co₃O₄ (0.63 V) < Cr₃O₄ (0.64 V) < Mn₃O₄ (0.91 V) < Ni₃O₄ (1.25 V) < Fe₃O₄ (1.76 V). The binding energy for all adsorbates and their corresponding overpotentials are tabulated in Table S5 and plotted in Fig. 4a. Next, we introduce the O* and OH* binding energies from the HEO impurity model (see Fig. 1) for Cr, Co, and Fe active sites. The predicted more than one thousand binding energies and their corresponding overpotentials were grouped for each active site (Fig. 4a). The distributions of overpotentials (and their corresponding descriptor values) for Co (light blue) and Cr (orange) sites in HEO are densely packed, while Fe (light green) sites is widespread. The arrows represent the changes in the activity trends compared to their respective pure spinel overpotentials. In all three tested active metal types, DG_O* - DG_OH* OER descriptor values are moved from right to left side towards region of stronger adsorption, and Cr shows the smallest while Fe shows the largest shift.

The overall OER activity for HEO depends strongly on the active sites. The Co active site in HEO shows a minimum overpotential of 0.29 V, while both Cr and Fe result in a minimum overpotential of 0.34 V for the OER activity. Figure 4b shows the OER activity distribution as a function of overpotential, extracted from the 2D volcano plot (Fig. 4a). It shows that less than 5% of the active sites are activated below 0.4 V applied overpotential and the majority contribution to activity comes from the Co active sites. Nearly 25% of the sites are active when the overpotential is less than 0.5 V, and Co sites continues to dominate in terms of activity. Next, several Cr active sites were activated within the region of intermediate overpotential of 0.5–0.8 V. More Cr active sites are activated as the overpotential increases. Unlike Co and Cr, only a few Fe active sites are found bellow 0.7 V overpotential. We also compared the OER activity on the Fe-NiOOH oxyhydroxide system calculated previosly⁶² to the spinel systems. The theoretical activity Fe-NiOOH (0.37 V) is slightly worse than the most active Fe site in HEO (0.34 V) and overall active site Co site in HEO (0.29 V).

To analyze the activity trend results obtained in the experiment, we compared the OER activity of HEO with that of other spinel oxides, such as ternary and quaternary with various elemental combinations, along with Fe-NiOOH (see Fig. 4c). We predicted that the combination of 5 elements in HEO has the lowest calculated overpotential of 0.29 V. The calculated overpotential trends for these oxide systems are as follows: HEO (CoFeNiCrMn) (0.29 V) < Fe-NiOOH (0.37 V) < CoFeNiCr (0.49 V) < CoFeNi (0.52 V) < CoFeNiMn (0.69 V), which shows good overall consistency with experimental finding, justifying the applicability of the HEO impurity model. Finally, we also analyzed the evolution of board adsorption energy distributions for O* and OH* descriptors, as discussed in detail next.

The role of local strain on HEO activities. The HEO DG_O* - DG_OH* OER descriptor values are generally shifted towards the region of stronger adsorption (Fig. 4a and S17). However, the individual distributions of O* and OH* binding energies are more complex. The Cr active sites move to the left (stronger ads.), while Co and Fe move to the right (weaker ads.) (Fig. S18). We attempted to investigate the possible reason for these changes considering two limiting cases having either strong or weak adsorption energies relative to the pure system using the Co active site (Figs. S19 and S20). The major finding here is that the local expansion (contraction) to equatorial Co-O bonds causes the stronger (weaker) O* and OH* binding. The presence of Fe as a surface neighbor strongly attracts oxygen, causing an expansion of these lateral Co-O bonds. In contrast, when the surface neighbor is Mn, and the sub-surface neighbor is Cr, these Co-O bonds contract, resulting in a weaker O* and OH* adsorption. The charge density difference analysis clearly shows that such expansion of Co-O bonds creates electron depletion along Co sites causing strong O* and OH* adsorption compared to pure and contraction cases. Finally, the equatorial expansion-contraction is also compensated by the axial sub-surface oxygen M-O bond to shorten-elongate, respectively (Figs. S21 and S22).

In summary, we developed a computationally feasible HEO impurity model to describe the stability and OER activity of any metal-oxide HEO. The model can be easily formed by local mixing near the active site instead of constructing a completely periodic bulk model of an arbitrary mixture. The mixing enthalpy calculations using this model demonstrate that the spinel HEO (CoFeNiCrMn) system is thermodynamically stable at 1000 ˚C. We further experimentally synthesized the HEO (CoFeNiCrMn) and spinel oxides with one to four metal cations at 1000 ˚C using the sol-flame method. Our electrochemical characterization shows that the HEO (CoFeNiCrMn) has the lowest overpotential of 309 mV to reach 10 mA cm^− 2, the smallest Tafel slope (30 mV dec^− 1), and the best stability (~ 12% increment of the overpotential over 168 hrs) compared to oxides with a smaller number of metal cations. The interaction among metal cations for OER activity is rather complex. Starting from the Co binary oxide, adding Fe was negligible for the activity improvement, while Ni significantly enhanced the activity. For the quinary oxides, combining Mn with CoFeNi degraded the performance, while Cr was hugely beneficial. Moreover, our model also predicts that the HEO (CoFeNiCrMn) has the highest activity due to the tunable adsorption energies with major active sites of Co, followed by Cr. The high OER activity in the HEO (CoFeNiCrMn) originated from the broader OER activity distributions due to a large number of stable local bonding configurations. The mean values of these distributions are controlled by the local strain in the active metal site-oxygen bonds, where equatorial contraction (expansion) leads to weaker (stronger) OER surface thermodynamics. This study demonstrates the promise of HEO as a material with tunable properties due to the abundance of stable thermodynamic configurations and local strain effects that result in a wide range of active sites.

Author Information

Corresponding Author

Xiaolin Zheng − Department of Mechanical Engineering, Stanford University, Stanford, California 94305, United States; orcid.org/0000-0002-8889-7873

Email: [email protected]

Michal Bajdich − SUNCAT Center for Interface Science and Catalysis, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, United States; orcid.org/0000-0003-1168-8616

Email: [email protected]

Authors

Jihyun Baek – Department of Mechanical Engineering, Stanford University, Stanford, California 94305, United States; orcid.org/0000-0002-1917-759X

Md Delowar Hossain – SUNCAT Center for Interface Science and Catalysis, Department of Chemical Engineering, Stanford University, Stanford, CA 94305, United States. SUNCAT Center for Interface Science and Catalysis, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, United States; orcid.org/0000-0003-3440-8306

Data availability

The complete list of calculated structures, their total and adsorption energies and DFT settings can be found under https://www.catalysis-hub.org/publications/HossainInvestigation2022 on Catalysis-hub.org platform.⁶³

Acknowledgments

This research was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division, Catalysis Science Program to the SUNCAT Center for Interface Science and Catalysis. Use of the Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-76SF00515. X.L.Z. would like to thank the National Science Foundation EFRI-DCheM program (Agreement Number: SUB0000425) for their generous support. J. B. would like to acknowledge the Chevron Fellowship in Energy. Part of this work was performed at the Stanford Nano Shared Facilities (SNSF)/Stanford Nanofabrication Facility (SNF), supported by the National Science Foundation under award ECCS-2026822. The authors would like to acknowledge the use of the m2997 computer time allocation at the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

Computational Details. Spin-polarized density functional theory calculations with plane-wave basis set were performed using the Vienna ab initio simulation package (VASP)^53,64,65 and project augmented wave (PAW) pseudopotential.⁶⁶ All the calculations were conducted and analyzed using the atomic simulation environment (ASE).⁶⁷ The Perdew-Burke-Ernzerhof functional was used to describe electronic exchange and correlation.⁶⁸ For all calculations, we applied the DFT+U method and set the energy cutoff to be 500 eV.⁶⁹ The spinel bulk structures of Co₃O₄, Fe₃O₄, Ni₃O₄, Cr₃O_4, and Mn₃O₄ were optimized using 555 k-point mesh sampling,⁷⁰ and their bulk structures were considered to be optimal when the energies and forces drop below 10^-6 eV and 0.01 eV/Å, respectively. We applied initial magnetic moments to achieve targeted spin states on each element by setting the occupation matrix of 3d-electron localization, followed by geometry optimizations.⁷¹

Calculation of bulk spinel oxides. We calculated the bulk spinel structures of Co₃O₄, Fe₃O₄, Ni₃O₄, Cr₃O₄, and Mn₃O₄ using a Hubbard-U corrected DFT method (see Computational Details). The optimized lattice parameters, charge, and magnetic ordering for the employed structures agree well with known experimental bulk values within a 5% difference, tabulated in Table S1. Our DFT results show that only Fe₃O₄ is energetically more favorable in the inverse (I) spinel ordering (B[AB]O₄), while all others prefer the normal (N) spinel ordering (A[B]₂O₄), where A⁺² ions occupy tetrahedral interstices of the oxygen lattice and the B⁺³ ions octahedral interstices in case of normal (N) spinel. The obtained lowest total energy for various bulk spinel oxides is subsequently used to normalize the mixing enthalpies introduced later in the context of HEOs.

The binary combinations from the considered elements behave similarly, as only Fe-containing spinel oxides show a propensity towards inverse spinel, most notably V⁺²Fe⁺³ and Ni⁺²Fe⁺³ (Fig. S2). These findings are also in good quantitative agreement with the known experimental values and crystal field theory predictions (Fig. S3).^50,51 Our calculations of a limited set of ternary spinel oxides of Co₃O₄(N), Fe₃O₄(I), and Ni₃O₄(N), indicate that NN mixtures are always preferred over IN mixtures (Fig. S4). However, generalized bulk DFT models beyond ternary spinel oxides are prohibitively difficult to be constructed and were not pursued. Instead, we devised a simplified HEO impurity model to study these systems.

Calculation of surface models. For pure spinel systems, we cut spinel bulk structures to 22 unit cells of 100-A surfaces studied previously for Co₃O₄,⁵² allowing octahedral sites to be in the surface layer while constraining the bottom half during the optimization. To model HEO systems, we have inserted the HEO impurity (see Results section) into the same Co₃O₄ (100)-A surface. To calculate the OER activity of active sites in HEO systems, we checked the effect of closest neighboring elements by using 55 permutation cells. We used a 15 Å vacuum gap between two slabs for surface calculations to avoid interaction between periodically repeated slabs. A dipole correction was applied to reduce the interactions between the periodically repeated slabs. The surface structures were optimized using a 551 Monkhorst–Pack grid with a cutoff energy of 500 eV. The convergence criteria of the electronic self-consistency loop were set to be 10^-5 eV and 0.02 eV/Å for energy and force.

For both pure and HEO spinel active sites, we evaluated the OER activity by calculating the O* and OH* binding energies. The theoretical overpotentials for each active site of pure spinel and HEO were calculated using the standard OER mechanism, which has been applied to many types of oxides (∗ → OH*, OH* → O*, O* → OOH*, OOH* → O₂(g)). We calculated *OOH adsorption energies for pure spinel and randomly selected 20 HEO surfaces, and those results yielded a scaling relation of OOH* = (0.8318 OH* + 3.1054), which was used for the rest of the HEO calculations (Fig. S1). The Gibbs free energies of each step of OER were calculated via the computational hydrogen electrode method with zero-point energy correction. The vibrational enthalpy and entropy contributions were obtained by the quantum mechanical harmonic approximation at room temperature. For the adsorbate reference energies, we used H₂O (l) and H₂ (g) only as the energy of O₂ in the gas phase is poorly described by DFT calculations.

Synthesis of spinel oxides and HEOs. All chemicals are used as purchased. Chromium(III) chloride hexahydrate (96%, Sigma Aldrich), Manganese(II) chloride tetrahydrate (ReagentPlus®, ≥ 99%, Sigma Aldrich), Iron(II) chloride hexahydrate (Reagent grade, 98%, Sigma Aldrich), Nickel(II) chloride hexahydrate (ReagentPlus®, Sigma Aldrich), and Cobalt(II) chloride (97%, Sigma Aldrich) were used as precursors. Absolute ethanol (99.5+%, Acros Organics) was used as a solvent. Potassium hydroxide (Reagent grade, 90%, Sigma Aldrich) was used as an electrolyte.

We synthesized all the spinel oxides studied here using the reported facile and fast sol-gel flame method.^48,49First, all precursors for metal cations with equimolar concentration (0.1 M) were dissolved in ethanol and mixed through sonication for 30 minutes. Next, the precursor solution was spin-coated on clean fluorine-doped tin oxide glass (FTO/glass, 7-8 ohm/sq, MSE supplies) substrates at 3000 rpm for 20 seconds and then annealed at 150 ˚C on a hot plate. This process was repeated twice to achieve good coverage and desired thickness. Finally, the precursor-coated FTO/glass substrate was annealed in a post-flame region. The flame annealing was conducted using a co-flow premixed flat flame burner (McKenna Burner), operating with premixed CH₄ (fuel) and air (oxidizer) with a fuel/oxygen equivalence ratio of 1.1. The substrate was annealed at 3 cm above the flame for 30 s with a local gas temperature of about 1000 ˚C, measured by a K-type thermocouple (1/16 in. bead size, Omega Engineering, Inc.). The substrate was subsequently removed from the flame to cool down to room temperature naturally. This rapid high-temperature heating and cooling process could facilitate homogeneous multi-elemental mixing.

Materials characterizations. The crystal structure of the synthesized samples was investigated by X-ray diffraction (XRD, PANalytical Empyrean) with a Cu source (Kα, 1.54 Å of the wavelength). In-situ XRD (PANalytical Empyrean HTK 1200N) was used to explore the crystallinity development in the temperature range of 100–1000 C˚ under the ambient condition. The sample morphology was characterized using scanning electron microscopy (SEM, FEI Magellan 400). The surface analysis with an elemental quantification was examined using X-ray photoelectron spectroscopy (XPS, PHI VersaProbe 3) that uses a monochromatized Al Kα radiation (1486 eV). The high-resolution images, selected area electron diffraction (SAED), dark-field image, and energy-dispersive X-ray spectroscopy (EDS) elemental mapping images were collected using a scanning transmission electron microscope (STEM, JEOL JEM ARM 200F). Electron energy loss spectroscopy (EELS) was obtained by STEM (FEI Tecnai G2 F20 X-TWIN) with a Gatan Tridiem spectrometer with an energy resolution of 0.8 eV. The convergence and collection semi-angle of the EELS detector were 15.5 and 21.8 mrad. To investigate the bulk valence states of Fe and Co, X-ray absorption spectroscopy (XAS) was conducted in transmission mode on electrodes sealed under a pouch under argon at beamline 2-2 at SSRL. A Si (220) ϕ = 90° monochromator was used and was detuned to 50–60% of the maximum intensity to eliminate higher-order harmonics. The spectra of Fe reference foils were used to calibrate the photon energy by setting the first crossing of zero of the second derivative of the absorbance spectrum to be 7112 eV. Three ion chambers were used in series to measure I₀, I_sample, and I_ref. Spectrum normalization and alignment were performed using the Athena software package3. XAS analysis and simulation were performed using the Artemis software package.

Electrochemical measurement. All the electrochemical measurements, including linear sweep voltammetry (LSV), cyclic voltammetry (CV), chronopotentiometry (CP), chronoamperometry (CA), and electrochemical impedance spectroscopy (EIS), were conducted using a potentiostat (Model Interface 1010, Gamry) in a standard three-electrode electrochemical cell using 1 M KOH (pH ~14) as the electrolyte. The synthesized spinel oxides (from binary to senary oxide) served as a working electrode with a Pt counter electrode and an Ag/AgCl reference electrode (Sat. KCl). The measured potentials versus Ag/AgCl are converted to the potentials versus reversible hydrogen electrode (RHE) by the equation below:

All LSV curves were measured at a scan rate of 10 mV s^-1, and then the potential was corrected by 95% IR compensation to remove the solution resistance effect. The overpotential (η) was determined by η = E_RHE – 1. 23 (V). The LSV curves were further used to construct the Tafel plots, which plot overpotential (η) as a function of the current density log (j). The EIS measurement was conducted between 20 kHz and 0.05 kHz at 1.54 V vs. RHE for all samples. The stabilities of the samples were evaluated both by CP for 7 days (168 hours) at the initial current density of ~10 mA cm^-2 and by CV for 1000 cycles in the potential window ranging from 0.9 to 1.6 V vs. RHE with a scan rate of 100 mV s^-1. The evolved oxygen was measured by the oxygen fluorescence sensor (Neofox, Ocean optics) and used to calculate the Faradaic efficiency by comparing with the calculated amount from the CA curve at 1.5 V vs. RHE for 2 hours as follows:

where n, , F, I, and t represent the number of electrons (i.e., 4), the mole of oxygen measured, Faradaic constant, measured current, and time, respectively.

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Synergistic Effects of Mixing and Strain in High Entropy Spinel Oxides for Oxygen Evolution Reaction

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